General Mental Ability

303 soru

Tüm türler303 Çoktan seçmeli164 Çoklu seçim13 Sayısal38 Eşleştirme35 Sıralama21 Boşluk doldurma10 Kısa cevap22

Six city planners—David, Elena, Felix, Grace, Hassan, and Iris—are sitting around a circular table for a development meeting. Some planners are facing the center of the table while others are facing outward.

Based on the following conditions, determine their exact seating arrangement:
1. David and Grace sit opposite each other, and both are facing the center.
2. Elena sits to the immediate left of David.
3. Iris sits second to the left of Elena.
4. Felix sits to the immediate right of Grace.
5. Elena, Hassan, and Iris all face the same direction.
6. Felix faces the opposite direction to Hassan.

Based on the seating arrangement, who sits to the immediate left of Hassan?

Grace

Iris

Felix

Elena

Cevabı ve açıklamayı göster

Cevap: Grace

Cevap

Grace sits to the immediate left of Hassan.

Based on the clues, Hassan sits between Grace and Iris, facing outward. When facing outward, a person's left side corresponds to the counter-clockwise direction along the circle. The person seated immediately counter-clockwise to Hassan is Grace.

Adım Adım Çözüm

Place David and Grace on a 6-position circular diagram.

David is at position 1 and Grace is at position 4. Both face the center.

Clue 1 states they sit opposite each other and both face the center.

Determine Elena's position and facing direction.

Elena is at position 2 and faces outward.

Clue 2 says Elena is to the immediate left of David. Since David faces the center, his left is clockwise, placing Elena at position 2. Clue 3 states Iris is second to Elena's left. If Elena faced the center, her second left would be position 4 (occupied by Grace). Thus, Elena must face outward.

Determine Iris's position.

Iris sits at position 6.

Since Elena is at position 2 and faces outward, 'left' means moving counter-clockwise. Two positions counter-clockwise from position 2 is position 6.

Place Felix and the remaining person, Hassan.

Felix is at position 3, and Hassan is at position 5.

Clue 4 states Felix is to the immediate right of Grace. Grace faces the center, so her right is counter-clockwise, which is position 3. Hassan must take the only remaining seat at position 5.

Determine the facing directions for Hassan, Iris, and Felix.

Hassan and Iris face outward. Felix faces the center.

Clue 5 states Elena, Hassan, and Iris face the same direction. Since Elena faces outward, Hassan and Iris also face outward. Clue 6 states Felix faces opposite to Hassan, so Felix faces the center.

Find the person to the immediate left of Hassan.

Grace

Hassan is at position 5 facing outward. For an outward-facing person, 'left' is counter-clockwise. The seat counter-clockwise from position 5 is position 4, which is occupied by Grace.

Anahtar Kavram

Mixed-facing circular seating arrangements and relative directional positioning based on orientation.

Soru 82Soru →

Eight colleagues—K, L, M, N, O, P, Q, and R—are sitting around a square table. Four of them sit in the middle of the sides and face the center of the table, while the other four sit at the four corners and face outside (away from the center). They are seated according to the following conditions:

- M sits in the middle of one of the sides.
- K sits third to the left of M.
- Only two people sit between K and R.
- O sits to the immediate right of R.
- P sits second to the left of K.
- N is an immediate neighbor of O.
- Q sits to the immediate right of P.

Based on the given seating arrangement, which of the following statements are correct? (Select all that apply)

Geçerli olan tümünü seçin

L sits to the immediate right of M.

R sits to the immediate left of O.

O sits second to the left of K.

Exactly three people sit between K and L when counted from the right of K.

Cevabı ve açıklamayı göster

Cevap: L sits to the immediate right of M.; Exactly three people sit between K and L when counted from the right of K.

Cevap

The correct statements are that L sits to the immediate right of M, and exactly three people sit between K and L when counted from the right of K.

Based on the seating conditions, M is at a middle position (facing center). K is 3rd to the left (clockwise), placing K at a corner facing outside. R is separated from K by two people, meaning R is at the opposite middle position (facing center). O is to the immediate right of R (counter-clockwise), placing O at a corner facing outside. P is 2nd to the left of K (counter-clockwise), so P is at a corner. N is O's neighbor, leaving only one adjacent spot. Q is immediate right of P (clockwise). L takes the last spot. In this final layout, L is immediately counter-clockwise from M, which is M's right side, making the first statement correct. Counting clockwise from K (K's right side), we pass N, O, and R before reaching L, making the statement about three people between K and L correct.

Adım Adım Çözüm

Determine M and K's positions.

M is at a middle position (facing center). K is 3rd to the left of M. Since M faces the center, left is clockwise, placing K at a corner (facing outside).

M is explicitly given as sitting in the middle. The direction rules (center = left is clockwise) determine K's placement.

Determine R and O's positions.

R must be at the opposite middle position (facing center). O is to the immediate right of R, placing O at the adjacent corner counter-clockwise (facing outside).

Only two people sit between K and R, so R is opposite M. R faces the center, so its right is counter-clockwise.

Place P, N, Q, and L.

P is 2nd to the left of K (counter-clockwise), N is the only available neighbor of O, Q is to the immediate right of P (clockwise), and L takes the final remaining position.

Following the remaining clues step-by-step while strictly adhering to the left/right rules for inward vs. outward facing positions ensures a unique arrangement.

Evaluate the given statements based on the final arrangement.

The statements about L's position relative to M, and the number of people between K and L (counting from K's right) are correct.

By applying the left/right rules to the completed seating layout, we can confirm the validity of each statement.

Anahtar Kavram

Polygonal Seating Arrangement with Mixed Facing Directions

Tahmini Süre:2m 0s

Soru 83Soru →

Five delegates—Alice, Ben, Clara, David, and Emma—are sitting in a single straight row facing North during a conference.

Read the following conditions carefully:
1. David is sitting at the extreme left end of the row.
2. Ben is sitting second to the right of Alice.
3. Clara is an immediate neighbor of Ben, but does not sit next to Alice.

Arrange the delegates in their correct seating order from the extreme left end to the extreme right end of the row.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence from left to right is: David, Alice, Emma, Ben, Clara.

The arrangement must logically begin with David at position 1. Alice must sit at position 2 and Ben at position 4; otherwise, Clara would be forced to sit next to Alice (if Alice were at 3 and Ben at 5). Consequently, Clara takes position 5, leaving position 3 for Emma.

Adım Adım Çözüm

Place David according to the first condition.

David is at position 1. The row configuration from left to right is: David, _, _, _, _.

The condition explicitly states David is at the extreme left end.

Determine the possible positions for Alice and Ben.

Since Ben is second to the right of Alice, the possible position pairs for (Alice, Ben) are (2, 4) or (3, 5).

This maintains exactly one empty seat between Alice and Ben to her right.

Evaluate the (3, 5) position pair using Clara's constraint.

If Alice is at 3 and Ben is at 5, Clara must be at 4 to be an immediate neighbor of Ben. However, this places Clara next to Alice, which violates the third condition.

Testing hypotheses against negative constraints is necessary to eliminate invalid scenarios.

Place Alice, Ben, and Clara in the only valid remaining configuration.

Alice is securely at position 2, and Ben is at position 4. Clara must sit at position 5 to be next to Ben but not next to Alice.

This is the only configuration that satisfies both the 'second to the right' rule and the negative neighbor constraint.

Place Emma in the final remaining seat.

Emma sits at position 3. The final order is David, Alice, Emma, Ben, Clara.

There is only one person left (Emma) and one seat available (position 3).

Anahtar Kavram

Linear Seating Arrangement with negative constraints

Soru 84Soru →

Seven diplomats—Alan, Boris, Chloe, David, Elena, Felix, and Grace—are sitting around a circular table facing the center.

Read the following conditions carefully:
1. Alan sits third to the right of Boris.
2. Chloe sits second to the left of Alan.
3. David sits immediately between Elena and Felix.
4. Elena is not an immediate neighbor of Boris.

Based on the above seating arrangement, who sits second to the right of Grace?

Boris

Felix

Elena

Alan

Cevabı ve açıklamayı göster

Cevap: Elena

Cevap

Elena sits second to the right of Grace.

Following the conditions step-by-step: If we place Boris at position 1, Alan goes to position 4 (third to the right, anti-clockwise). Chloe goes to position 2 (second to the left of Alan, clockwise). The three consecutive seats for Elena, David, and Felix must be 5, 6, and 7, meaning David is at 6. Grace takes the only empty seat at 3. Because Elena cannot be next to Boris (position 1), she must take position 5, leaving Felix at position 7. The complete anti-clockwise order is Boris, Chloe, Grace, Alan, Elena, David, Felix. Grace is at position 3; the second person to her right is at position 5, which is occupied by Elena.

Adım Adım Çözüm

Place Boris and determine Alan's position using the first condition.

Assume Boris is at position 1. Since they face the center, 'right' is anti-clockwise. Alan is third to the right, placing him at position 4.

Fixing a reference point is the standard method for solving circular arrangements.

Place Chloe using the second condition.

Chloe sits second to the left (clockwise) of Alan (position 4). Thus, Chloe is placed at position 2.

Chloe's position is strictly relative to Alan's fixed position.

Identify the seating block for David, Elena, and Felix.

David sits immediately between Elena and Felix, requiring three consecutive empty seats. The currently occupied seats are 1, 2, and 4. The only consecutive empty seats are 5, 6, and 7. Therefore, David must sit exactly in the middle of them, at position 6.

This is the only way to satisfy the requirement of three people sitting together without splitting the group.

Place Grace in the arrangement.

With positions 1, 2, 4, 5, 6, and 7 accounted for, position 3 is the only remaining seat. Grace must sit at position 3.

By the process of elimination, the last remaining person takes the last available seat.

Determine the exact positions of Elena and Felix using the final condition.

Elena and Felix occupy positions 5 and 7 in some order. Boris is at position 1, making positions 2 and 7 his immediate neighbors. Since Elena cannot be an immediate neighbor of Boris, she cannot sit at position 7. Therefore, Elena is at position 5, and Felix is at position 7.

This fully resolves all ambiguities in the arrangement while satisfying the negative constraint.

Answer the specific question asked in the stem.

Grace is at position 3. Facing the center, the second seat to her right (anti-clockwise) is position 5. Elena occupies position 5.

Applying the final relative directional check on the completed diagram.

Anahtar Kavram

Solving complex circular seating arrangements by logically deducing relative positions and applying negative constraints.

Soru 85Soru →

Eight students—P, Q, R, S, T, U, V, and W—are seated in two parallel rows containing four people each, such that there is an equal distance between adjacent persons.

In Row 1, P, Q, R, and S are seated and all of them are facing South.
In Row 2, T, U, V, and W are seated and all of them are facing North.
In the given seating arrangement, each member seated in a row faces another member of the other row.

- Q sits second to the left of S.
- The person facing Q sits to the immediate right of W.
- P sits at one of the extreme ends of the row.
- V faces the person who sits to the immediate right of R.
- T sits at an extreme end of the row, and does not face P.

Based on the given arrangement, which of the following statements are correct? (Select all that apply)

Geçerli olan tümünü seçin

U sits at an extreme end of the row and faces P.

W sits second to the left of U.

R faces the person who sits to the immediate left of T.

P sits to the immediate left of S.

Cevabı ve açıklamayı göster

Cevap: U sits at an extreme end of the row and faces P.; R faces the person who sits to the immediate left of T.

Cevap

The correct statements are that U sits at an extreme end facing P, and R faces the person who sits to the immediate left of T.

Based on the final arrangement, U is at the leftmost extreme end of Row 2 and faces P at the leftmost extreme end of Row 1, making the statement about U correct. T is at the rightmost extreme end of Row 2 facing North, meaning W is to T's immediate left; R sits directly opposite W, making the statement about R correct.

Adım Adım Çözüm

Establish the left and right directions for both rows based on their facing directions.

Row 1 (South): Left is rightward, Right is leftward (from the observer's view). Row 2 (North): Left is leftward, Right is rightward.

Correctly orienting directions is critical before placing individuals in a parallel arrangement.

Place S and Q using the clue: 'Q sits second to the left of S'.

Since S faces South, 'left' means moving to the observer's right. Possibility 1: S is at position 1 (far left), Q is at position 3. Possibility 2: S is at position 2, Q is at position 4.

This establishes the relative spacing between two individuals in Row 1.

Incorporate the clues about W and P to test the possibilities.

Using 'P sits at an extreme end': In Possibility 1, P must be at 4. In Possibility 2, P must be at 1. Using 'The person facing Q sits to the immediate right of W': In Possibility 1, Q(3) faces pos 3. W must be at 2. In Possibility 2, Q(4) faces pos 4. W must be at 3.

Combining extreme end constraints with facing constraints helps fill the grid.

Apply the clue regarding V and R: 'V faces the person who sits to the immediate right of R'.

In Possibility 1, the remaining Row 1 person R is at 2. R's right (facing South) is pos 1 (S). V faces S, so V is at 1. In Possibility 2, R is at 3. R's right is pos 2 (S). V faces S, so V is at 2.

This locks in the position of V in Row 2 based on the remaining individuals in Row 1.

Resolve the final positions using the clue: 'T sits at an extreme end... and does not face P'.

In Possibility 1, V=1, W=2. T must be at 4 (extreme end). But P is at 4, meaning T faces P, which violates the condition. Thus, Possibility 1 is invalid. In Possibility 2, V=2, W=3. T must be at 1 or 4. If T is at 1, T faces P (at 1), violating the condition. Therefore, T must be at 4. The remaining person U goes to position 1.

This eliminates the invalid scenario and provides the single correct final arrangement.

Document the finalized seating grid.

Row 1 (South-facing, left-to-right): P, S, R, Q. Row 2 (North-facing, left-to-right): U, V, W, T.

A complete layout is required to evaluate the given statements in the options.

Anahtar Kavram

Applying relative directional reasoning (left/right inversion) in a two-row parallel seating arrangement.

Soru 86Soru →

Seven researchers—Fiona, George, Harry, Iris, Jack, Kelly, and Liam—are sitting around a circular table for a meeting. Four of them face the center, while the remaining three face outward. They are seated according to the following conditions:

1. Harry faces outward. Jack sits second to the left of Harry.
2. Fiona sits exactly between Harry and George.
3. George sits adjacent to Iris and faces the center.
4. Iris sits second to the right of Jack.
5. Kelly is not an immediate neighbor of Harry and faces the same direction as George.
6. The immediate neighbors of Jack face opposite directions (i.e., one faces the center and the other faces outward).
7. Fiona faces the center.

Based on the given information, who sits third to the left of Kelly?

Fiona

George

Liam

Harry

Cevabı ve açıklamayı göster

Cevap: Harry

Cevap

The correct person sitting third to the left of Kelly is Harry.

Based on the conditions, Kelly must sit in seat 5 facing the center, while Harry sits in seat 1 facing outward. Since Kelly is facing the center, her left direction moves clockwise. Moving three positions clockwise from seat 5 (to 6, then 7, then 1) lands exactly on Harry.

Adım Adım Çözüm

Set up a 7-seat circular arrangement (numbered 1 to 7 clockwise) and place Harry and Jack.

Harry is at seat 1 facing outward. Jack is at seat 6.

Since Harry faces outward, his 'left' direction is counter-clockwise. Second to the left of seat 1 (counter-clockwise) is seat 7, then seat 6.

Place Fiona and George based on relative positions.

Fiona is at seat 2 and George is at seat 3.

Fiona must be exactly between Harry (1) and George. This forces them to occupy consecutive seats (1, 2, 3), placing Fiona at 2 and George at 3. George is given as facing the center. Fiona is given as facing the center.

Place Iris and determine Jack's facing direction.

Iris is at seat 4, and Jack faces the center.

George (3) is adjacent to Iris. Since Fiona is already at 2, Iris must be at 4. Iris (4) is second to the right of Jack (6). For seat 4 to be on the right of seat 6 (a counter-clockwise move), Jack must face the center.

Place Kelly and Liam, and deduce the remaining directions.

Kelly is at seat 5 facing the center, and Liam is at seat 7 facing outward. Iris faces outward.

Kelly cannot be next to Harry (1), so Kelly cannot take seat 7. Kelly takes seat 5, leaving seat 7 for Liam. Kelly faces the same direction as George (center). Jack's neighbors are Kelly (5) and Liam (7). Since Kelly faces center, Liam must face outward. We now have 4 facing center (Fiona, George, Jack, Kelly), meaning the rest (Harry, Liam, Iris) must face outward.

Identify the person sitting third to the left of Kelly.

Harry.

Kelly is at seat 5 facing the center. Left of a center-facing person is clockwise. Tracing three spots clockwise from 5: seat 6 (1st), seat 7 (2nd), and seat 1 (3rd), which is occupied by Harry.

Anahtar Kavram

Solving complex circular seating arrangements with mixed facing directions (inward and outward) by tracking relative left-right orientations.

Soru 87Soru →

In a corporate access control mechanism, security codes are generated by applying a specific transformation logic to employee department names. In this system, the word PLANT is coded as SOZQW, and the word TRAIN is coded as WUZRQ. Based on the same logic, how will the word GLOBE be coded in this system?

TOLYV

JOLEV

JOREH

JOKEU

Cevabı ve açıklamayı göster

Cevap: JOLEV

Cevap

The correct answer is JOLEV.

The coding logic treats consonants and vowels differently. Consonants are shifted forward by 3 alphabetical positions (e.g., P becomes S, G becomes J, L becomes O). Vowels are replaced by their reverse alphabetical counterpart, which represents their position from the end of the alphabet (e.g., A becomes Z, O becomes L, E becomes V). Applying this to GLOBE: G (+3) is J, L (+3) is O, O (reverse) is L, B (+3) is E, and E (reverse) is V. This yields JOLEV.

Adım Adım Çözüm

Analyze the first example (PLANT -> SOZQW) to identify the transformation rule.

The consonants P, L, N, T shift forward by 3 alphabetical positions to become S, O, Q, W. The vowel A is replaced by its reverse alphabetical counterpart Z (27 - 1 = 26).

To determine how consonants and vowels are uniquely handled within the coding structure.

Verify the established logic using the second example (TRAIN -> WUZRQ).

The consonants T, R, N shift forward by 3 to W, U, Q. The vowels A and I are replaced by their reverse positions Z and R (27 - 9 = 18).

To confirm the dual-rule pattern applies consistently across all provided examples.

Apply the confirmed dual-rule logic to the target word GLOBE.

G (+3) becomes J; L (+3) becomes O; O (reverse, 27 - 15) becomes L; B (+3) becomes E; E (reverse, 27 - 5) becomes V.

To generate the final encoded sequence according to the established transformation parameters.

Anahtar Kavram

Identifying complex dual-rule alphabetic patterns distinguishing between consonants and vowels.

Soru 88Soru →

An archaeological surveyor is mapping an excavation site using a miscalibrated compass. The compass needle that is supposed to point 'North' actually points to the true geographical East.

Starting from the base camp, she faces the direction the compass indicates as 'North' and walks $20\text{ m}$ straight. She then turns $135^\circ$ clockwise and walks $10\sqrt{2}\text{ m}$ in a straight line. Next, she turns $45^\circ$ anti-clockwise and proceeds $10\text{ m}$ forward. Finally, she turns $90^\circ$ clockwise and walks another $10\text{ m}$ to reach the main artifact chamber.

What is the true geographical direction and shortest direct distance of the main artifact chamber relative to the base camp?

20\text{ m}

, South

20\text{ m}

, East

20\text{ m}

, North

10\sqrt{5}\text{ m}

, South-East

Cevabı ve açıklamayı göster

Cevap: $20\text{ m}$ , South

Cevap

The main artifact chamber is

20\text{ m}

directly to the South of the base camp.

By applying each movement as a vector on a coordinate plane, the starting path of

20\text{ m}

East is followed by

10\sqrt{2}\text{ m}

South-West (yielding

-10

East,

-10

North). The surveyor then goes

10\text{ m}

South, and finally

10\text{ m}

West. Summing the horizontal (East/West) components:

+20 - 10 + 0 - 10 = 0

. Summing the vertical (North/South) components:

0 - 10 - 10 + 0 = -20

. The net displacement is exactly

20\text{ m}

South.

Adım Adım Çözüm

Determine the true starting direction based on the faulty compass.

The surveyor walks

20\text{ m}

towards the true East.

The compass's 'North' actually points East. Walking

20\text{ m}

in that direction results in a displacement of

+20\text{ m}

on the East-West axis (Coordinate: 20 East, 0 North).

Calculate the direction and displacement of the second movement.

She turns

135^\circ

clockwise to face South-West, walking

10\sqrt{2}\text{ m}

Facing East, a

135^\circ

clockwise turn lands exactly on South-West. A movement of

10\sqrt{2}\text{ m}

South-West equates to moving

10\text{ m}

West and

10\text{ m}

South (using a

45^\circ

45^\circ

90^\circ

triangle). New coordinate:

(20 - 10)

East,

(0 - 10)

North =

10\text{ m}

East,

10\text{ m}

South.

Calculate the direction and displacement of the third movement.

She turns

45^\circ

anti-clockwise to face South, walking

10\text{ m}

Facing South-West, turning

45^\circ

anti-clockwise (left) brings her to face South. Walking

10\text{ m}

South brings her coordinate to

10\text{ m}

East,

20\text{ m}

South.

Calculate the direction and displacement of the final movement.

She turns

90^\circ

clockwise to face West, walking

10\text{ m}

Facing South, a

90^\circ

clockwise turn points West. Moving

10\text{ m}

West shifts her East-West position by

-10\text{ m}

. Final coordinate:

(10 - 10)

East,

20\text{ m}

South =

0\text{ m}

East,

20\text{ m}

South.

Determine the final distance and direction from the starting point.

The final position is exactly

20\text{ m}

South of the base camp.

The East-West displacements cancel out completely, leaving a pure Southward displacement of

20\text{ m}

Anahtar Kavram

Vector displacement, angular rotation tracing, and relative reference framing.

Tahmini Süre:1m 30s

Soru 89Soru →

Match each word pair in List I with the word pair in List II that exhibits the identical semantic and logical relationship.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Amnesia : Memory pairs with Insomnia : Sleep; Connoisseur : Art pairs with Gourmet : Food; Mendacity : Truth pairs with Cowardice : Courage; Teetotaler : Alcohol pairs with Pacifist : War.

The correct pairings align identical logical relationships across different subjects: medical conditions defined by loss (Amnesia/Insomnia), experts in a domain of taste (Connoisseur/Gourmet), vices defined by the absence of a virtue (Mendacity/Cowardice), and individuals defined by abstention (Teetotaler/Pacifist).

Adım Adım Çözüm

Analyze the semantic relationship of the first item in List I (Amnesia : Memory).

Identified the relationship as 'Condition : Faculty that is lost'.

Finding the exact structural relationship is necessary to find its analogical match.

Scan List II for a pair with the identical 'Condition : Faculty lost' relationship.

Matched with 'Insomnia : Sleep', as insomnia is the loss of sleep.

This establishes the first correct analogical pairing.

Determine the structural relationships for the remaining items in List I and map them to their equivalents in List II.

Connoisseur evaluates Art (matches Gourmet evaluating Food). Mendacity lacks Truth (matches Cowardice lacking Courage). Teetotaler abstains from Alcohol (matches Pacifist abstaining from War).

Solving complex word analogies requires isolating identical logical structures across completely different semantic topics.

Anahtar Kavram

Semantic Word Analogies and Abstract Relationships

Soru 90Soru →

In a single line of applicants waiting for an interview, Oliver is positioned $34^{\text{th}}$ from the front and Maya is positioned $41^{\text{st}}$ from the back. There are exactly $15$ applicants standing between them. If the total number of applicants in the line is the absolute minimum possible to satisfy these conditions, what is the position of the applicant standing exactly halfway between Oliver and Maya, counting from the front of the line?

26^{\text{th}}

27^{\text{th}}

33^{\text{rd}}

42^{\text{nd}}

Cevabı ve açıklamayı göster

Cevap: $26^{\text{th}}$

Cevap

The applicant standing exactly halfway between them is in the

26^{\text{th}}

position from the front.

To find the minimum possible number of people in the line, the positions of Oliver and Maya must overlap (Maya is closer to the front than Oliver). Since Oliver is

34^{\text{th}}

from the front and there are

15

people between them, Maya's position from the front is

34 - 15 - 1 = 18^{\text{th}}

. The person exactly in the middle of the

15

people between them is the

8^{\text{th}}

person after Maya. Therefore, their position from the front is

18 + 8 = 26^{\text{th}}

Adım Adım Çözüm

Identify the arrangement type required for the minimum total number of applicants.

An overlapping arrangement must be used, meaning Maya is standing ahead of Oliver in the line.

If Oliver is ahead of Maya, the total number of applicants maximizes. For the minimum capacity, they must cross over so their positional counts overlap.

Calculate Maya's exact position from the front of the line.

Maya is

18^{\text{th}}

from the front.

Oliver is

34^{\text{th}}

. Since Maya is ahead of him with

15

people in between, Maya's position is

34 - 15 \text{ (people between)} - 1 \text{ (Oliver)} = 18^{\text{th}}

from the front.

Determine the relative position of the middle applicant between Oliver and Maya.

The middle applicant is exactly

8

positions after Maya.

There are

15

applicants between them. The exact middle of a

15

-person gap is the

8^{\text{th}}

person (

7

people on one side, the middle person, and

7

people on the other side).

Calculate the middle applicant's absolute position from the front.

18 + 8 = 26^{\text{th}}

position from the front.

Adding the relative

8

-position offset to Maya's starting position of

18^{\text{th}}

from the front yields the final answer.

Anahtar Kavram

Overlapping Minimum Capacity in Linear Ranking

Tahmini Süre:2m 0s

Soru 91Soru →

A mechanical clock is synchronized to the correct standard time at exactly 00:00 (midnight) on February 15th of a leap year. This particular clock is known to gain exactly $4$ minutes every $24$ hours of true time.

What is the acute angle (in degrees) between the hour and minute hands of this faulty clock at exactly 12:00 noon (true time) on March 2nd of the same leap year?

Cevabı ve açıklamayı göster

Cevap: 3

Cevap

The acute angle between the hands is 3 degrees.

By determining the exact time elapsed across the leap year boundary (

16.5

days), the total time gained by the clock is

16.5 \times 4 = 66

minutes. Adding this to the true time of 12:00 yields a faulty clock time of 13:06 (or 1:06). At 1:06, the minute hand is at

36^\circ

(

6 \times 6^\circ

) and the hour hand has moved past the 1 o'clock mark (

30^\circ

) by an additional

3^\circ

(

(6/60) \times 30^\circ

). The difference between

36^\circ

and

33^\circ

3^\circ

Adım Adım Çözüm

Calculate the total true time elapsed in days.

The total elapsed time is 16.5 days.

From February 15th 00:00 to March 1st 00:00 in a leap year (29 days in February) is exactly 15 days. From March 1st to March 2nd 00:00 is 1 day. From 00:00 to 12:00 noon is 0.5 days. Total: 15 + 1 + 0.5 = 16.5 days.

Calculate the total time gained by the faulty clock.

The clock gains a total of 66 minutes.

The clock gains 4 minutes per 24 hours (1 day). For 16.5 days, the total gain is 16.5 * 4 = 66 minutes.

Determine the time shown on the faulty clock.

The faulty clock shows 13:06 (or 1:06 PM).

The true time is 12:00 noon. Adding the gained 66 minutes (1 hour and 6 minutes) gives 13:06.

Calculate the precise position of the minute and hour hands at 1:06.

Minute hand is at 36 degrees; Hour hand is at 33 degrees.

The minute hand moves 6 degrees per minute: 6 * 6 = 36 degrees from the 12 o'clock position. The hour hand moves 30 degrees per hour plus 0.5 degrees per minute: (1 * 30) + (6 * 0.5) = 30 + 3 = 33 degrees.

Find the acute angle between the two hands.

The acute angle is 3 degrees.

The difference between the two positions is |36 - 33| = 3 degrees.

Anahtar Kavram

Calculating elapsed time across leap year month boundaries combined with continuous clock drift and geometric clock angle formulas.

Tahmini Süre:2m 30s

Soru 92Soru →

A city hall maintains an antique mechanical tower clock that has a constant drift, falling behind standard time by exactly $2.5$ minutes every $24$ hours. The maintenance crew calibrates the clock to the precise standard time on January 14, $1900$ , at exactly 12:00 PM (Noon). Calculate the total amount of time, in minutes, that the clock will have drifted behind standard time by exactly 12:00 PM (Noon) on March 15, $1900$ .

Cevabı ve açıklamayı göster

Cevap: 150

Cevap

The clock will have accumulated a total drift of 150 minutes.

The correct answer is derived by accurately counting the exact number of days between January 14, 1900, and March 15, 1900. Since 1900 is not a leap year (it is a century year not divisible by 400), February has exactly 28 days. Adding the 17 days in January, 28 days in February, and 15 days in March gives a total of 60 days. Multiplying the 60 days by the daily drift rate of 2.5 minutes yields exactly 150 minutes.

Adım Adım Çözüm

Calculate the days elapsed in January.

31 - 14 = 17

days.

To find the time accumulated during the first month.

Determine the number of days in February

1900

February has

28

days.

The year

1900

is a century year not divisible by

400

, making it a standard non-leap year.

Sum the total days from January 14 to March 15.

17 + 28 + 15 = 60

days.

To find the total

24

-hour periods over which the drift occurred.

Calculate the total drift in minutes.

60 \times 2.5 = 150

minutes.

The clock loses exactly

2.5

minutes for every full

24

-hour period elapsed.

Anahtar Kavram

Century Leap Year Rule and Time Accumulation

Tahmini Süre:1m 30s

Soru 93Soru →

A botanist leaves her base camp to collect soil samples in a dense forest. She first walks $35\text{ m}$ straight East. She then turns $135^{\circ}$ to her left and walks $20\sqrt{2}\text{ m}$ . Finally, she turns $135^{\circ}$ to her left again and walks $12\text{ m}$ . What is the shortest straight-line distance, in meters, between her current position and the base camp?

Cevabı ve açıklamayı göster

Cevap: 17

Cevap

The shortest straight-line distance between the botanist's current position and the base camp is 17 meters.

By breaking each movement into its horizontal and vertical components on a Cartesian plane, the final position is found to be 15 meters East and 8 meters North of the origin. The shortest direct distance is the hypotenuse of the triangle formed by these coordinates: √(15² + 8²) = 17.

Adım Adım Çözüm

Plot the first movement on a coordinate plane.

Position 1 is at

(35, 0)

Setting the starting base camp at the origin

(0, 0)

, moving East means traveling along the positive x-axis.

Calculate the vector and position for the second movement.

Position 2 is at

(15, 20)

Facing East (0°), a left turn of 135° results in facing North-West. Moving

20\sqrt{2}\text{ m}

diagonally at a 45° angle to the axes translates to

\Delta x = -20\text{ m}

(West) and

\Delta y = +20\text{ m}

(North). New coordinate:

(35 - 20, 0 + 20)

Calculate the vector and position for the third movement.

Position 3 is at

(15, 8)

Facing North-West, another left turn of 135° places her facing directly South. Walking

12\text{ m}

South subtracts 12 from the y-coordinate. New coordinate:

(15, 20 - 12)

Calculate the shortest straight-line distance to the origin.

The final distance is

17\text{ m}

The straight-line distance from

(0, 0)

(15, 8)

forms a right-angled triangle. Using Pythagoras:

d = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17

Anahtar Kavram

Calculating continuous displacement using angular turns, vector breakdown, and the Pythagorean theorem.

Tahmini Süre:1m 30s

Soru 94Soru →

A solid wooden block has dimensions $12 \text{ cm} \times 15 \text{ cm} \times 18 \text{ cm}$ . Three of its mutually adjacent faces (which meet at a single corner) are painted Red, and the remaining three faces are painted Blue. The block is then cut into smaller, identical cubes of size $1 \text{ cm} \times 1 \text{ cm} \times 1 \text{ cm}$ . How many of these smaller cubes have AT LEAST one Red face AND at least one Blue face?

Cevabı ve açıklamayı göster

Cevap: 84

Cevap

The unit cubes with both colors lie exactly on the 6 boundary edges separating the Red and Blue faces. By summing the lengths of these 6 edges (

12+12+15+15+18+18 = 90

) and subtracting the 6 overlapping corner cubes to correct for double-counting, we arrive at exactly 84 cubes.

Adım Adım Çözüm

Identify the configuration of the painted faces on the block.

The 3 Red faces share one corner, and the 3 Blue faces share the diagonally opposite corner.

To accurately locate where the Red and Blue paints meet on the surface.

Determine which unit cubes satisfy the condition of having both Red and Blue faces.

Only the cubes lying exactly on the boundary edges between a Red face and a Blue face will have both colors.

Cubes fully within a Red face have no Blue paint, internal cubes have no paint, and purely corner cubes not on the boundary have only one color.

Count the number of boundary edges.

There are exactly 6 boundary edges forming a continuous zig-zag hexagonal ring around the block.

Each of the 3 Red faces shares an edge with exactly 2 Blue faces.

Determine the lengths of these 6 boundary edges.

The ring wraps around all three dimensions symmetrically, covering two edges of 12 cm, two of 15 cm, and two of 18 cm.

A cuboid has 4 edges of each dimension; the boundary ring traverses exactly half of them.

Calculate the total number of unit cubes on these edges using the inclusion-exclusion principle.

2 \times (12 + 15 + 18) - 6 = 90 - 6 = 84

cubes.

Summing the edge lengths gives 90 cubes, but the 6 corners connecting these edges in the ring are counted twice, so we must subtract 6 to prevent double-counting.

Anahtar Kavram

Spatial reasoning and painted cube boundary edge calculation.

Soru 95Soru →

Arrange the following geometric figures in a logical classification sequence based on the sum of their interior angles, in ascending order (from the smallest sum to the largest sum).

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct logical sequence from smallest to largest sum of interior angles is: Triangle, Pentagon, Hexagon, Heptagon, and Octagon.

The sum of the interior angles of a polygon increases as the number of its sides increases, defined by the formula

S = (n-2) \times 180^\circ

. Therefore, ordering the shapes by their interior angle sums is mathematically identical to sorting them by their side count. The correct progression is Triangle (3 sides), Pentagon (5 sides), Hexagon (6 sides), Heptagon (7 sides), and Octagon (8 sides).

Adım Adım Çözüm

Identify the relationship between a polygon and the sum of its interior angles.

The formula for the sum of interior angles is

S = (n-2) \times 180^\circ

, where

n

is the number of sides.

Establishing the mathematical rule is required to find the underlying numerical logic for the sequence.

Determine the number of sides (

n

) for each geometric figure.

Triangle (

n=3

), Pentagon (

n=5

), Hexagon (

n=6

), Heptagon (

n=7

), Octagon (

n=8

The number of sides directly dictates the magnitude of the interior angle sum.

Arrange the figures based on the side count in ascending order.

Since a larger number of sides always results in a larger sum of interior angles, ordering by

n

gives: Triangle (3) < Pentagon (5) < Hexagon (6) < Heptagon (7) < Octagon (8).

This establishes the correct classification sequence from smallest to largest without needing to manually calculate every angle sum.

Anahtar Kavram

Classification based on numerical and geometric properties

Soru 96Soru →

A city planner is inspecting a newly constructed botanical garden. She starts at the Main Gate and walks $80\text{ m}$ straight North. She then turns $90^{\circ}$ to her right and walks $30\text{ m}$ . Following this, she turns $45^{\circ}$ to her left and walks $20\sqrt{2}\text{ m}$ . Finally, she turns $45^{\circ}$ to her left again and walks $20\text{ m}$ to reach the Central Greenhouse. What is the shortest distance between the Main Gate and the Central Greenhouse, and in which direction is the Greenhouse located with respect to the Main Gate?

130\text{ m}

, North-East

130\text{ m}

, North-West

130\text{ m}

, South-West

170\text{ m}

, North-East

Cevabı ve açıklamayı göster

Cevap: $130\text{ m}$ , North-East

Cevap

The shortest distance is

130\text{ m}

and the direction is North-East.

By plotting each movement sequentially on a Cartesian coordinate system, the final position resolves to

50\text{ m}

East and

120\text{ m}

North of the starting point. Using the Pythagorean theorem, the shortest straight-line distance is calculated as

\sqrt{50^2 + 120^2} = 130\text{ m}

. Since the final coordinates are located in the upper-right quadrant relative to the starting point, the final direction is North-East.

Adım Adım Çözüm

Map the initial movement from the starting point.

The planner walks

80\text{ m}

North to the coordinate

(0, 80)

Establishing the Main Gate at the origin

(0,0)

and translating the first movement along the y-axis.

Calculate the second movement after a

90^{\circ}

right turn.

The planner now faces East and walks

30\text{ m}

. The new position is

(30, 80)

A right turn from North corresponds to the East direction (+x axis).

Calculate the third movement after a

45^{\circ}

left turn.

The planner now faces North-East. Walking

20\sqrt{2}\text{ m}

adds

20\text{ m}

to the East and

20\text{ m}

to the North. The new position is

(30 + 20, 80 + 20) = (50, 100)

Resolving the diagonal distance into horizontal (

\Delta x = 20\sqrt{2} \cos 45^{\circ}

) and vertical (

\Delta y = 20\sqrt{2} \sin 45^{\circ}

) components.

Calculate the final movement after another

45^{\circ}

left turn.

The planner now faces straight North and walks

20\text{ m}

. The final position is

(50, 100 + 20) = (50, 120)

45^{\circ}

left turn from North-East points exactly North again.

Calculate the shortest distance and final direction from the origin.

Distance =

\sqrt{50^2 + 120^2} = \sqrt{2500 + 14400} = \sqrt{16900} = 130\text{ m}

. Since the final coordinate

(50, 120)

is positive on both axes, the direction is North-East.

Applying the Pythagorean theorem to find the Euclidean distance from the starting point.

Anahtar Kavram

Vector displacement and directional rotation tracking on a 2D Cartesian plane.

Soru 97Soru →

A large solid cube of dimensions $5 \times 5 \times 5$ is painted using three colors: Red, Blue, and Green. The painting is applied such that the Top and Bottom faces are Red, the Front and Right faces are Blue, and the Back and Left faces are Green. The large cube is then cut into 125 smaller, identical cubes of dimensions $1 \times 1 \times 1$ . Match the categories of the smaller cubes described in List I with their exact counts in List II.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct matches are: Cubes with three different colors to 4; Cubes with two faces of the same color to 6; Cubes with one face Blue to 18; Cubes with no painted faces to 27.

The exact structural breakdown of the 5x5x5 cube under this specific adjacent-face coloring scheme yields exactly 4 three-color corners, 6 two-color edges (from 2 identical color intersections), 18 one-color blue face centers, and a 27-cube unpainted core.

Adım Adım Çözüm

Analyze the corner cubes (exactly 3 faces painted) to match the first category.

There are 8 corners. Top-Front-Left is Red-Blue-Green (3 colors). Top-Front-Right is Red-Blue-Blue (2 colors). Analyzing all 8 corners yields exactly 4 corners that touch three different colors.

Because Front/Right are both Blue and Back/Left are both Green, corners sharing these adjacent identical faces will not have three different colors.

Analyze the edge cubes (exactly 2 faces painted) to match the second category.

There are 12 edges, each containing (5-2) = 3 cubes with exactly two painted faces. The condition requires both faces to be the same color. This only happens on the Front-Right edge (Blue-Blue) and Back-Left edge (Green-Green). Thus, 2 edges × 3 cubes = 6 cubes.

Edges represent the intersection of two faces. Only adjacent faces painted with the same color produce these specific cubes.

Analyze the face center cubes (exactly 1 face painted) to match the third category.

Each of the 6 faces has a central grid of (5-2)² = 9 cubes that have exactly one face painted. Since exactly 2 faces are painted Blue (Front and Right), there are 2 × 9 = 18 such cubes.

This singles out the purely Blue surface area minus edges and corners.

Calculate the completely unpainted inner core cubes to match the fourth category.

The unpainted inner volume is a smaller cube of dimensions (5-2) × (5-2) × (5-2) = 3³ = 27 cubes.

Removing the outer layer (1 cube thick) from all 6 sides leaves the unpainted core.

Anahtar Kavram

Advanced visualization of 3D spatial properties, edge intersections, and non-standard coloring rules on a subdivided cube.

Soru 98Soru →

Eight executives—K, L, M, N, P, Q, R, and S—are seated in two parallel rows of four members each for a strategic meeting.

Members in Row 1 (P, Q, R, and S) are facing South.
Members in Row 2 (K, L, M, and N) are facing North.
Each executive in Row 1 sits exactly opposite to and faces one executive in Row 2.

The seating arrangement follows these conditions:
1. P sits second to the right of Q.
2. The executive facing Q sits to the immediate right of K.
3. M sits at one of the extreme ends of the row and does not face Q.
4. R sits to the immediate right of P.
5. N is an immediate neighbor of M.

Based on the above arrangement, which of the following statements is true?

S faces the executive who sits to the immediate left of L.

R faces the executive who sits to the immediate right of N.

Q sits second to the right of P.

L sits adjacent to the executive who faces P.

Cevabı ve açıklamayı göster

Cevap: S faces the executive who sits to the immediate left of L.

Cevap

The statement 'S faces the executive who sits to the immediate left of L' is true.

Based on the deductions, Row 1 (South) from left to right is R, P, S, Q. Row 2 (North) from left to right is M, N, K, L. The executive sitting to the immediate left of L (who faces North) is K. The executive facing K is S. Therefore, the statement accurately describes the arrangement.

Adım Adım Çözüm

Determine the layout of Row 1 (South-facing) using conditions 1 and 4.

Row 1 left-to-right (viewer's perspective) is R, P, S, Q.

Since Row 1 faces South, their 'right' is the viewer's left. P sits second to the right of Q means Q is at position 4 and P is at position 2. R sits to the immediate right of P places R at position 1. The remaining seat (position 3) belongs to S.

Locate K in Row 2 (North-facing) using condition 2.

K sits at position 3 (viewer's perspective).

Q is at position 4, so the executive facing Q is also at position 4. This person sits to the immediate right of K. Since Row 2 faces North, K must be at position 3 for position 4 to be its immediate right.

Place M and N in Row 2 using conditions 3 and 5.

M is at position 1 and N is at position 2.

M is at an extreme end (position 1 or 4) but does not face Q (who is at 4). Therefore, M is at position 1. N is M's immediate neighbor, placing N at position 2.

Complete Row 2 and evaluate the options.

Row 2 left-to-right is M, N, K, L. Evaluating the correct option: L is at 4, immediate left is K (at 3), and S (at 3) faces K.

L is the only remaining executive for position 4. Checking the valid spatial relationships against the options proves only one statement is factually accurate.

Anahtar Kavram

Linear Seating Arrangement in Dual Parallel Rows

Tahmini Süre:2m 0s

Soru 99Soru →

A biomedical research facility tags its genetic samples using a specialized alphabetical encryption logic to maintain anonymity. In this system, the word PLASMA is coded as LPAIOA and the word SERUM is coded as IWJGO. Based on this specific coding logic, how will the word VIRUS be coded?

FSJGI

WJSVT

ERIFH

DQHEG

Cevabı ve açıklamayı göster

Cevap: FSJGI

Cevap

The correct sequence is FSJGI.

The established coding rule dictates that each letter is first replaced by its reverse alphabetical counterpart (e.g., A becomes Z, B becomes Y), and then shifted forward by one letter (+1). Applying this to VIRUS: V becomes E (+1 = F), I becomes R (+1 = S), R becomes I (+1 = J), U becomes F (+1 = G), and S becomes H (+1 = I), yielding FSJGI.

Adım Adım Çözüm

Analyze the transformation applied to the word PLASMA to produce LPAIOA.

P(16) reverses to K(11), K+1 = L. L(12) reverses to O(15), O+1 = P. A(1) reverses to Z(26), Z+1 = A. S(19) reverses to H(8), H+1 = I. M(13) reverses to N(14), N+1 = O. A(1) reverses to Z(26), Z+1 = A.

To decode the underlying multi-step logic by testing position values and reverse alphabet mappings.

Verify the identified rule (Reverse Letter + 1) using the second example, SERUM.

S reverses to H, H+1 = I. E reverses to V, V+1 = W. R reverses to I, I+1 = J. U reverses to F, F+1 = G. M reverses to N, N+1 = O. The result IWJGO matches the given code.

To confirm the encryption rule is consistent and completely understood before applying it to the target word.

Apply the verified two-step rule to the target word VIRUS.

V reverses to E, E+1 = F. I reverses to R, R+1 = S. R reverses to I, I+1 = J. U reverses to F, F+1 = G. S reverses to H, H+1 = I.

To determine the final encrypted tag for the target sample.

Anahtar Kavram

Multi-step letter coding involving reverse alphabetical indexing and positional shifts.

Soru 100Soru →

Eight officials (Auditor, Clerk, Governor, Judge, Mayor, Senator, Sheriff, and Treasurer) are seated around a square table. Four of them sit at the corners facing the center of the table, while the other four sit in the middle of each side facing outward away from the center.

- The Sheriff sits at one of the corners.
- The Governor sits third to the right of the Sheriff.
- The Mayor sits second to the right of the Governor.
- The Senator and the Judge are immediate neighbors, but neither is an immediate neighbor of the Governor or the Sheriff.
- The Treasurer sits third to the right of the Judge.
- The Clerk is not an immediate neighbor of the Governor.

Based on the given seating arrangement, which of the following statements are correct?

Geçerli olan tümünü seçin

The Clerk and the Governor sit exactly opposite each other.

The Auditor sits second to the left of the Treasurer.

Exactly three people sit between the Judge and the Mayor.

The Senator sits to the immediate left of the Clerk.

Cevabı ve açıklamayı göster

Cevap: The Clerk and the Governor sit exactly opposite each other.; Exactly three people sit between the Judge and the Mayor.

Cevap

The statements indicating that the Clerk and Governor sit opposite each other, and that exactly three people sit between the Judge and the Mayor, are correct.

Based on the systematic deduction of all constraints, the table is arranged as follows (clockwise from top-left): Sheriff, Clerk, Senator, Judge, Auditor, Governor, Treasurer, and Mayor. In this specific configuration, the Clerk and Governor occupy directly opposite middle seats, and the Judge and Mayor occupy opposite middle seats, meaning there are exactly three people between them on either side.

Adım Adım Çözüm

Establish the directional rules for the inward and outward facing seats.

For the 4 corners facing inward, 'right' moves counter-clockwise and 'left' moves clockwise. For the 4 middle positions facing outward, 'right' moves clockwise and 'left' moves counter-clockwise.

Correctly identifying left and right based on facing direction is mandatory before placing any individuals.

Place the Sheriff, Governor, and Mayor to create a foundational layout.

Place the Sheriff at a corner (e.g., top-left, inward). Third to the right (counter-clockwise) places the Governor at the bottom-middle position (outward). Second to the right of the Governor (clockwise) places the Mayor at the left-middle position (outward).

These three linked conditions provide fixed anchor points on the table.

Determine the available positions for the Senator and the Judge.

They must sit in adjacent seats but cannot sit next to the Governor or the Sheriff. Eliminating the seats adjacent to the Governor and Sheriff leaves only the top-right corner and the right-middle position as the single valid pair of adjacent seats.

Negative constraints drastically reduce the possible locations for grouped individuals.

Differentiate the specific seats for the Senator and the Judge using the Treasurer's condition.

The Treasurer is third to the right of the Judge. If the Judge were at the top-right corner (inward), third to the right would be the left-middle seat, which is already occupied by the Mayor. Thus, the Judge must be at the right-middle seat (outward). Third to the right (clockwise) places the Treasurer at the bottom-left corner. The Senator takes the top-right corner.

Testing the directional constraint ensures no two people are assigned to the same seat.

Place the remaining officials, the Clerk and the Auditor.

The remaining empty seats are the top-middle and bottom-right corner. The Clerk cannot be a neighbor of the Governor, so the Clerk takes the top-middle seat. The Auditor fills the final seat at the bottom-right corner.

Applying the final negative constraint finalizes the complete seating arrangement.

Anahtar Kavram

Solving complex seating arrangements with mixed facing directions by systematically tracking relative left/right movements.

ÖncekiSayfa 5 / 16Sonraki

General Mental Ability

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