General Mental Ability Alıştırma Soruları — State PSC Exam — Sayfa 15

Soru 281Soru →

An autonomous delivery drone navigation system encodes geographic sector names into numerical strings for secure broadcasting. The sector name "DELTA" is transmitted as 46-44-30-14-52, and the sector name "BRAVO" is transmitted as 50-18-52-10-24. Based on this logic, which numerical string represents the sector name "EAGLE"?

44-52-40-30-44

10-2-14-24-10

22-26-20-15-22

42-50-38-28-42

Cevabı ve açıklamayı göster

Cevap: 44-52-40-30-44

Cevap

The string 44-52-40-30-44 correctly represents the sector name EAGLE.

The correct answer accurately applies the coding logic: it determines the reverse alphabetical position of each letter (found by subtracting the forward position from 27) and multiplies that value by 2. For the word EAGLE: E is 5th, so its reverse is 22 (22 × 2 = 44). A is 1st, reverse is 26 (26 × 2 = 52). G is 7th, reverse is 20 (20 × 2 = 40). L is 12th, reverse is 15 (15 × 2 = 30). Combining these gives 44-52-40-30-44.

Adım Adım Çözüm

1

Analyze the numerical values assigned to the letters in 'DELTA' and 'BRAVO' to find the base transformation.

D corresponds to 46, E to 44, L to 30, T to 14, and A to 52.

Identifying the relationship between the first few letters and their numerical outputs reveals the underlying logic.

2

Determine the mathematical rule applied to the alphabetical positions.

The forward position of D is 4. Its reverse position (27 - 4) is 23. Multiplying 23 by 2 gives 46. This logic holds for all letters.

A consistent pattern must be established that works for every letter in both provided examples.

3

Apply the established logic to the target word 'EAGLE'.

E (5) -> reverse 22 -> 44. A (1) -> reverse 26 -> 52. G (7) -> reverse 20 -> 40. L (12) -> reverse 15 -> 30. E (5) -> reverse 22 -> 44.

Applying the exact rule ensures the correct encryption of the target string.

Anahtar Kavram

Reverse Alphabetical Indexing and Mathematical Transformation

Tahmini Süre:1m 30s

Soru 282Soru →

A geologist leaves her base camp and drives a rover $30\text{ km}$ straight North. From there, she turns $135^{\circ}$ to her right and travels $10\sqrt{2}\text{ km}$ in a straight line. She then turns $45^{\circ}$ to her left and travels $20\text{ km}$ . Finally, she takes a $90^{\circ}$ turn to her right and drives another $20\text{ km}$ . What is her final position relative to the base camp?

30\text{ km}

West

10\text{ km}

West

30\text{ km}

East

30\text{ km}

South

Cevabı ve açıklamayı göster

Cevap: $30\text{ km}$ East

Cevap

30\text{ km}

East

By tracing the movements on a Cartesian plane where North is the positive y-axis and East is the positive x-axis, the sequence unfolds as follows: the initial position is

(0, 30)

after the first drive. A

135^{\circ}

right turn points the rover South-East, and moving

10\sqrt{2}\text{ km}

adds a displacement of

(10, -10)

, resulting in position

(10, 20)

. A

45^{\circ}

left turn points the rover East, adding

(20, 0)

to reach

(30, 20)

. The final

90^{\circ}

right turn points the rover South, adding

(0, -20)

to land precisely at

(30, 0)

. The point

(30, 0)

is exactly

30\text{ km}

East of the starting base camp at

(0, 0)

.

Adım Adım Çözüm

1

Map the first movement from the base camp.

Starting at origin

(0, 0)

, moving

30\text{ km}

North reaches coordinate

(0, 30)

while facing North.

Establishing the initial position and orientation on a Cartesian plane (where North is +y and East is +x) is necessary for calculating subsequent turns.

2

Calculate the second movement after a

135^{\circ}

right turn.

Turning

135^{\circ}

right from North changes the heading to South-East. Traveling

10\sqrt{2}\text{ km}

South-East yields a displacement of

+10

in the x-direction and

-10

in the y-direction. The new position is

(10, 20)

.

A

135^{\circ}

clockwise turn from North equates to a South-East direction. Using trigonometry,

10\sqrt{2} \times \cos(45^{\circ}) = 10

and

10\sqrt{2} \times \sin(45^{\circ}) = 10

for the respective axis displacements.

3

Calculate the third movement after a

45^{\circ}

left turn.

Turning

45^{\circ}

left (counter-clockwise) from South-East aligns the heading to East. Traveling

20\text{ km}

East shifts the position by

+20

on the x-axis, bringing the coordinates to

(30, 20)

.

Adjusting the South-East heading by

45^{\circ}

back towards the counter-clockwise direction points exactly East.

4

Calculate the final movement after a

90^{\circ}

right turn.

Turning

90^{\circ}

right (clockwise) from East changes the heading to South. Traveling

20\text{ km}

South shifts the position by

-20

on the y-axis, resulting in a final coordinate of

(30, 0)

.

A

90^{\circ}

right turn from East is South. Moving

20\text{ km}

South precisely negates the remaining

+20\text{ km}

vertical displacement.

5

Determine the final relative position.

The final coordinate is

(30, 0)

while the base camp is at

(0, 0)

. This represents a displacement of

30\text{ km}

directly East.

Comparing the final position coordinates directly to the origin determines the exact distance and direction.

Anahtar Kavram

Vector displacement combining angular turns and cardinal directions

Soru 283Soru →

At exactly $4:28$ PM, what is the exact acute angle (in degrees) between the hour hand and the minute hand of a standard analog clock?

Cevabı ve açıklamayı göster

Cevap: 34

Cevap

34

The angle is determined by finding the exact position of both hands relative to the 12 o'clock mark. The minute hand is at 168 degrees (28 minutes multiplied by 6 degrees). The hour hand is at 134 degrees, which includes its base position at 4 o'clock (120 degrees) plus the drift from the 28 minutes that have passed (14 degrees). The absolute difference between these two positions is exactly 34 degrees.

Adım Adım Çözüm

1

Calculate the angle of the minute hand from the 12 o'clock position.

28 \times 6^\circ = 168^\circ

The minute hand moves at a rate of 6 degrees per minute.

2

Calculate the base angle of the hour hand exactly at 4 o'clock.

4 \times 30^\circ = 120^\circ

Each hour marking on the clock represents 30 degrees from the top.

3

Calculate the drift of the hour hand caused by the 28 elapsed minutes.

28 \times 0.5^\circ = 14^\circ

The hour hand continuously moves at a rate of 0.5 degrees per minute.

4

Determine the true position of the hour hand.

120^\circ + 14^\circ = 134^\circ

Adding the drift to the base position gives the exact current location of the hour hand.

5

Calculate the acute angle between the two hands.

|168^\circ - 134^\circ| = 34^\circ

The angle between the hands is the absolute difference between their positions from the 12 o'clock mark.

Anahtar Kavram

Calculating the precise angle between clock hands by accounting for hour-hand drift

Soru 284Soru →

Consider the standard sequence of events in criminal justice. In what chronological order do the following events naturally occur?

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The events occur in the following chronological sequence: Crime, Police, Arrest, Trial, Judgment, Punishment.

The logical flow begins when an offense is committed (Crime). This immediately triggers the involvement of law enforcement (Police), who then take the suspect into custody (Arrest). The suspect is brought before a court for hearings (Trial). After examining the case, the court issues a verdict (Judgment), which results in a penalty (Punishment) if the suspect is found guilty.

Adım Adım Çözüm

1

Identify the initial triggering event.

'Crime' is placed first.

The entire legal framework is initiated by the commission of an offense, making it the undeniable starting point.

2

Determine the immediate response and subsequent action.

'Police' followed by 'Arrest'.

Law enforcement must respond to the incident before they have the authority or opportunity to formally apprehend a suspect.

3

Arrange the judicial proceedings.

'Trial' followed by 'Judgment', and finally 'Punishment'.

The suspect must face court proceedings first. These proceedings conclude with a verdict, which then dictates the final consequence.

Anahtar Kavram

Logical Sequence and Chronological Classification

Tahmini Süre:1m 0s

Soru 285Soru →

A deep sea research submarine logs environmental phenomena in an encrypted transmission system. In this protocol, the phenomenon "TRENCH" is recorded as "VTDPEJ", and "CORAL" is recorded as "ENTZN". Based on this cryptographic pattern, what will be the recorded code for the word "TIDES"?

Cevabı ve açıklamayı göster

Cevap: VHFDU; vhfdu

Cevap

VHFDU

The established coding pattern shifts consonants forward by 2 positions in the English alphabet and shifts vowels backward by 1 position. Applying this rule to 'TIDES', the consonants (T, D, S) become (V, F, U) and the vowels (I, E) become (H, D). Combining these letters in sequence yields 'VHFDU'.

Adım Adım Çözüm

1

Analyze the letter shifts in the first example 'TRENCH' -> 'VTDPEJ'.

T(+2)=V, R(+2)=T, E(-1)=D, N(+2)=P, C(+2)=E, H(+2)=J. Consonants move forward by 2 positions, while the vowel 'E' moves backward by 1 position.

Identifying the initial transformation rule for different letter types.

2

Verify the identified pattern with the second example 'CORAL' -> 'ENTZN'.

C(+2)=E, O(-1)=N, R(+2)=T, A(-1)=Z, L(+2)=N. The pattern is confirmed: Consonants +2, Vowels -1.

Confirming the hypothesis to ensure the rule is universally applied in this cryptographic protocol.

3

Classify the letters of the target word 'TIDES' into vowels and consonants.

Consonants: T, D, S. Vowels: I, E.

Preparing to apply the appropriate shift rule to each letter.

4

Apply the verified shift rules (+2 for consonants, -1 for vowels) to 'TIDES'.

T(+2)=V, I(-1)=H, D(+2)=F, E(-1)=D, S(+2)=U. The final code is VHFDU.

Executing the final translation to obtain the required answer.

Anahtar Kavram

Coding and decoding using bifurcated shift rules for vowels and consonants

Soru 286Soru →

A wildlife biologist tracking a radio-collared leopard starts at a research outpost and drives $10\text{ km}$ straight East. She then turns $45^{\circ}$ to her left and drives $10\sqrt{2}\text{ km}$ along a dirt trail. Next, she turns $90^{\circ}$ to her right and travels $4\sqrt{2}\text{ km}$ through the brush. Finally, she turns $135^{\circ}$ to her left and drives $1\text{ km}$ straight North to locate the leopard. What is the shortest straight-line distance, in kilometers, between the research outpost and the leopard's final location?

Cevabı ve açıklamayı göster

Cevap: 25

Cevap

25

The correct answer is found by tracking the Cartesian coordinates after each vector movement. By breaking diagonal distances into their horizontal and vertical components, the final position is located exactly at

(24, 7)

. Using the distance formula

\sqrt{24^2 + 7^2}

, the shortest direct distance from the origin is

25\text{ km}

.

Adım Adım Çözüm

1

Establish a coordinate system with the starting point at

(0,0)

and translate the first movement of

10\text{ km}

East.

Current position is

(10, 0)

.

East corresponds to the positive x-axis direction.

2

Determine the new heading after turning

45^{\circ}

left from East, and calculate the displacement for

10\sqrt{2}\text{ km}

.

New heading is North-East. Displacement is

(10, 10)

, making the current position

(20, 10)

.

A

45^{\circ}

left turn from East (

0^{\circ}

) results in

45^{\circ}

(NE). The vector components are

d \times \cos(45^{\circ})

and

d \times \sin(45^{\circ})

.

3

Determine the new heading after turning

90^{\circ}

right from North-East, and calculate the displacement for

4\sqrt{2}\text{ km}

.

New heading is South-East. Displacement is

(4, -4)

, making the current position

(24, 6)

.

A

90^{\circ}

right turn from NE (

45^{\circ}

) results in SE (

-45^{\circ}

). The vector components are

d \times \cos(-45^{\circ})

and

d \times \sin(-45^{\circ})

.

4

Determine the new heading after a

135^{\circ}

left turn from South-East, and calculate the displacement for

1\text{ km}

.

New heading is North. Displacement is

(0, 1)

, making the final position

(24, 7)

.

A

135^{\circ}

left turn (positive rotation) from SE (

-45^{\circ}

) yields

-45^{\circ} + 135^{\circ} = 90^{\circ}

(North).

5

Apply the Pythagorean theorem to find the straight-line distance from the origin

(0,0)

to the final coordinates

(24, 7)

.

The shortest distance is

25\text{ km}

.

The straight-line distance between two points on a Cartesian plane is given by

\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

.

Anahtar Kavram

Vector displacement, angular turns mapping to cardinal/ordinal directions, and the Pythagorean theorem.

Soru 287Soru →

Eight colleagues—P, Q, R, S, T, U, V, and W—are seated around a circular table. Exactly four of them are facing the center, while the other four are facing outward (away from the center).

1. P sits third to the left of U, and both are facing the center.
2. T sits second to the left of P.
3. V and Q are immediate neighbors of each other, but neither is an immediate neighbor of P.
4. Q is not an immediate neighbor of U.
5. W sits second to the right of Q.
6. R sits second to the left of V.
7. The immediate neighbors of T face opposite directions (one faces the center, the other faces outward).

Based on the seating arrangement, which of the following statements is definitely TRUE?

W sits to the immediate left of T, and both face outward.

S sits second to the right of U, and they face opposite directions.

Q sits to the immediate left of V, and both face the center.

T sits to the immediate left of Q, and they face opposite directions.

Cevabı ve açıklamayı göster

Cevap: W sits to the immediate left of T, and both face outward.

Cevap

The statement claiming that W sits to the immediate left of T, and both face outward, is definitely true.

Based on the completed arrangement, T is seated at position 6 and W is at position 5. Both face outward. For an outward-facing person, their left is in the counter-clockwise direction. Moving one position counter-clockwise from T (6) brings us to W (5). Therefore, W sits to the immediate left of T, and both face outward.

Adım Adım Çözüm

1

Set up a circular layout with 8 numbered positions (1 to 8) moving clockwise.

Assume U is at position 1, facing the center.

Establishing a fixed anchor point simplifies relative positioning.

2

Place P and T using clues 1 and 2.

P is at position 4 (facing center) because left of U (center-facing) is clockwise. T is at position 6 because left of P (center-facing) is clockwise.

Direct directional application from the fixed anchor U.

3

Determine positions for V and Q using clues 3 and 4.

Neighbors of P (positions 3 and 5) cannot hold V and Q. The only adjacent open seats are 7 and 8. Since Q cannot be next to U (position 1), V must be at 8 and Q must be at 7.

Process of elimination based on adjacency constraints.

4

Determine W's position and Q's direction using clue 5.

W is 2nd to the right of Q(7). If Q faced outward, right would be clockwise (positions 8, 1), but U is at 1. Thus, Q faces the center, making right counter-clockwise (positions 6, 5). W is placed at position 5.

Deducing direction by testing which orientation allows a valid placement.

5

Determine R's position and V's direction using clue 6.

R is 2nd to the left of V(8). If V faced outward, left would be counter-clockwise (positions 7, 6), but T is at 6. Thus, V faces the center, making left clockwise (positions 1, 2). R is placed at position 2.

Similar to Step 4, V's direction is deduced by the availability of the target seat.

6

Place S and deduce the remaining directions.

S takes the last remaining seat, position 3. From clue 7, T's neighbors (Q at 7 and W at 5) face opposite directions. Since Q faces the center, W must face outward. We now have exactly four people facing the center: U, P, Q, and V. Therefore, the remaining four (R, S, T, and W) must face outward.

Completing the arrangement and satisfying the global condition of 4 center-facing and 4 outward-facing individuals.

Anahtar Kavram

Advanced Seating Arrangement with Mixed Facing Directions

Tahmini Süre:2m 30s

Soru 288Soru →

Analyze the logical relationship between the pairs of words in List I. Match each pair with the corresponding pair in List II that exhibits the identical underlying logical relationship.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Odometer : Distance matches Barometer : Pressure; Mycology : Fungi matches Numismatics : Coins; Blueprint : Architect matches Script : Playwright; Penicillin : Infection matches Antidote : Poison.

The correct matches are based on identifying identical relational logic: Instrument-to-Measurement, Study-to-Subject, Creation-to-Creator, and Remedy-to-Condition.

Adım Adım Çözüm

1

Determine the relationship in 'Odometer : Distance'.

An odometer is an instrument used to measure distance.

Identifying the 'Instrument : Measurement' pattern allows us to find its match in List II, which is 'Barometer : Pressure'.

2

Determine the relationship in 'Mycology : Fungi'.

Mycology is the scientific study of fungi.

Identifying the 'Field of Study : Subject' pattern allows us to find its match in List II, which is 'Numismatics : Coins'.

3

Determine the relationship in 'Blueprint : Architect'.

A blueprint is a detailed plan created by an architect.

Identifying the 'Document/Plan : Creator' pattern allows us to find its match in List II, which is 'Script : Playwright'.

4

Determine the relationship in 'Penicillin : Infection'.

Penicillin is a medication used to cure an infection.

Identifying the 'Treatment : Condition' pattern allows us to find its match in List II, which is 'Antidote : Poison'.

Anahtar Kavram

Identifying identical semantic and logical relationships between word pairs (Analogies).

Soru 289Soru →

Arrange the following words in a logical sequence as they would appear in an English dictionary:

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct dictionary order is: Objection, Objective, Obligation, Oblivion, Obscure.

By strictly applying alphabetical ordering rules, we group the words by their initial letters and then differentiate within groups. 'Objection' precedes 'Objective' because 'o' comes before 'v'. 'Obligation' precedes 'Oblivion' because 'g' comes before 'v'. 'Obscure' is last because 's' comes after 'j' and 'l'.

Adım Adım Çözüm

1

Compare the first three letters of all words.

All words start with 'Ob'. The third letters are 'j' (Objection, Objective), 'l' (Obligation, Oblivion), and 's' (Obscure).

Dictionary order strictly follows alphabetical order from left to right.

2

Sort the groups based on the third letter.

The 'j' group comes first, followed by the 'l' group, and finally the 's' group (Obscure).

In the alphabet, 'j' precedes 'l', which precedes 's'.

3

Order the words within the 'j' group (Objection, Objective).

'Objection' comes before 'Objective'.

The first seven letters (O-b-j-e-c-t-i) are identical. The eighth letter 'o' in Objection comes before the 'v' in Objective.

4

Order the words within the 'l' group (Obligation, Oblivion).

'Obligation' comes before 'Oblivion'.

The first three letters (O-b-l) are identical, and the fourth letter is 'i' for both. The fifth letter 'g' in Obligation comes before the 'v' in Oblivion.

5

Combine the sorted groups into the final sequence.

Objection, Objective, Obligation, Oblivion, Obscure.

This maintains the strict alphabetical sorting established in the previous steps.

Anahtar Kavram

Dictionary Arrangement and Alphabetical Order

Soru 290Soru →

Four marine exploration vessels (Alpha, Beta, Gamma, and Delta) are deployed for oceanographic surveying. Each vessel begins facing a specific cardinal direction and executes a sequence of angular maneuvers as described below:

- Vessel Alpha: Starts facing North, rotates $135^{\circ}$ clockwise, moves forward, and then rotates $45^{\circ}$ anti-clockwise.
- Vessel Beta: Starts facing East, rotates $90^{\circ}$ clockwise, moves forward, and then rotates $135^{\circ}$ clockwise.
- Vessel Gamma: Starts facing South, rotates $45^{\circ}$ anti-clockwise, moves forward, rotates $180^{\circ}$ clockwise, and finally rotates $90^{\circ}$ anti-clockwise.
- Vessel Delta: Starts facing West, rotates $135^{\circ}$ anti-clockwise, moves forward, rotates $90^{\circ}$ clockwise, and finally rotates $45^{\circ}$ anti-clockwise.

Match each vessel with its final facing direction.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

Vessel Alpha matches with East; Vessel Beta matches with North-West; Vessel Gamma matches with South-West; Vessel Delta matches with South.

Each vessel's final direction is calculated by applying its sequence of clockwise and anti-clockwise rotations mathematically or visually, starting from its initial cardinal direction.

Adım Adım Çözüm

1

Calculate the final direction for Vessel Alpha by summing its angular turns from North.

North (0°) + 135° CW - 45° ACW = 90° (East).

Clockwise (CW) turns add to the angle and anti-clockwise (ACW) turns subtract, assuming North is 0° and measuring clockwise.

2

Calculate the final direction for Vessel Beta by summing its angular turns from East.

East (90°) + 90° CW + 135° CW = 315° (North-West).

Tracking successive CW rotations from 90° gives the final orientation on the 360° compass.

3

Calculate the final direction for Vessel Gamma by summing its angular turns from South.

South (180°) - 45° ACW + 180° CW - 90° ACW = 225° (South-West).

Alternating CW and ACW turns are added and subtracted respectively.

4

Calculate the final direction for Vessel Delta by summing its angular turns from West.

West (270°) - 135° ACW + 90° CW - 45° ACW = 180° (South).

Tracking all ACW and CW maneuvers determines the exact final coordinate.

Anahtar Kavram

Direction and Distance Test

Soru 291Soru →

At exactly 10:10 AM, the hour hand of a standard analog clock is mechanically locked in its precise current position. The minute hand is then manually rotated forward (clockwise) by exactly $210^{\circ}$ . Calculate the new angle (in degrees) formed between the hour and minute hands after this adjustment. Provide the smaller of the two possible angles.

Cevabı ve açıklamayı göster

Cevap: 35

Cevap

The smaller angle between the hands after the adjustment is 35 degrees.

The correct calculation properly tracks the absolute angular positions from the 12 o'clock reference, correctly adding the

5^{\circ}

proportional movement of the hour hand before finding the difference against the shifted minute hand.

Adım Adım Çözüm

1

Find the initial position of the minute hand at 10:10 AM relative to the 12 o'clock mark.

The minute hand is at the 10-minute mark. Since each minute is

6^{\circ}

, its position is

10 \times 6^{\circ} = 60^{\circ}

.

Establishing the starting angle of the minute hand is required before applying the rotation.

2

Find the exact initial position of the hour hand at 10:10 AM.

The 10 o'clock mark is at

10 \times 30^{\circ} = 300^{\circ}

. In 10 minutes, the hour hand drifts

10 \times 0.5^{\circ} = 5^{\circ}

. The exact position is

300^{\circ} + 5^{\circ} = 305^{\circ}

.

The hour hand continuously moves. It does not stay exactly on the 10 while the minute hand moves.

3

Calculate the new position of the minute hand after the manual rotation.

The new minute hand position is

60^{\circ} + 210^{\circ} = 270^{\circ}

.

The problem states the minute hand is pushed forward by exactly

210^{\circ}

.

4

Calculate the angle between the locked hour hand and the new minute hand position.

The difference is

305^{\circ} - 270^{\circ} = 35^{\circ}

.

Subtracting the smaller angular position from the larger one gives the acute interior angle between the hands.

Anahtar Kavram

Clock hand angular positioning, rotational displacement, and proportional hour-hand drift.

Soru 292Soru →

Trees are planted in a single straight line along a newly constructed highway. An Oak tree is the $42^{\text{nd}}$ tree from the northern end of the line, and a Maple tree is the $58^{\text{th}}$ tree from the southern end. If there are exactly $18$ trees planted between the Oak tree and the Maple tree, what is the minimum possible total number of trees in this line?

Cevabı ve açıklamayı göster

Cevap: 80

Cevap

80

To find the minimum possible number of trees, we must assume an overlapping scenario where the Maple tree is situated north of the Oak tree. In this arrangement, adding their positions from opposite ends (

42 + 58

) double-counts the

18

trees between them, as well as the Oak and Maple trees themselves. Therefore, the minimum total is

42 + 58 - (18 + 2) = 80

.

Adım Adım Çözüm

1

Identify the given positional values and the condition.

Oak tree = 42nd from North, Maple tree = 58th from South, trees between = 18.

These are the core variables needed to determine the total number of items in the line.

2

Determine the spatial arrangement required for a 'minimum' total.

The two trees must overlap. The Maple tree (counted from the South) must be located further North than the Oak tree (counted from the North).

If the positions do not overlap, we get the maximum possible number of trees. Overlapping them minimizes the total line length.

3

Apply the overlapping rank formula.

Total = (Position from one end) + (Position from other end) - (Number in between) - 2.

Adding the two ranks double-counts the items between them AND double-counts the two specific boundary items (the Oak and Maple trees) themselves.

4

Substitute the values and calculate the result.

Total = 42 + 58 - 18 - 2 = 100 - 20 = 80.

Computing the arithmetic expression gives the minimum number of trees.

Anahtar Kavram

Calculating minimum capacity in overlapping queues

Soru 293Soru →

Evaluate the mathematical logic governing the number pairs in Group X. Match each pair with its analog in Group Y that follows the exact same logical transformation.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Cevabı ve açıklamayı göster

Cevap

The correct pairings align identical underlying mathematical transformations:

5:124

matches

7:342

(cubes minus one),

9:90

matches

11:132

(squares plus the number),

27:81

matches

34:49

(square of digit sum), and

14:43

matches

19:58

(multiplied by three plus one).

Each pair from Group X must be matched with a pair from Group Y that demonstrates the identical algebraic or numeric transformation rule. Solving these requires looking past simple differences and testing for squares, cubes, consecutive products, and digit manipulations.

Adım Adım Çözüm

1

Analyze the first pair in Group X (

5 : 124

) to determine its underlying logic.

The number

124

is exactly

1

less than

125

(

5^3

), revealing the rule

n : n^3 - 1

. Locating the same rule in Group Y yields

7 : 342

since

7^3 - 1 = 342

.

Identifying the structural pattern involving powers allows for accurate cross-referencing with the target group.

2

Examine the second pair (

9 : 90

).

The number

90

is the product of

9

and

10

, indicating the rule

n : n(n+1)

. In Group Y,

11 : 132

perfectly matches this logic because

11 \times 12 = 132

.

Testing consecutive multipliers is a standard method for identifying patterns in numeric classification.

3

Evaluate the third pair (

27 : 81

).

While

81

is a direct multiple (

27 \times 3

), no pair in Group Y shares this specific multiplier. Alternatively, summing the digits of

27

gives

2+7=9

, and

9^2=81

. Applying this rule to Group Y isolates

34 : 49

, since

(3+4)^2 = 7^2 = 49

.

When standard arithmetic operations fail to yield a matching pair, analyzing digit-level operations is required.

4

Determine the rule for the final pair (

14 : 43

).

The number

43

is obtained via the operation

14 \times 3 + 1

. The corresponding pair in Group Y is

19 : 58

, since

19 \times 3 + 1 = 57 + 1 = 58

.

Establishing a standard linear transformation finalizes the correct matching process.

Anahtar Kavram

Identifying multi-step mathematical operations, power series, and digit-based transformations to classify and match logical sequences.

Soru 294Soru →

In a fully automated logistics center, a single row of delivery robots is lined up facing the loading bay. Robot $M$ is positioned $27^{\text{th}}$ from the left end of the row, while Robot $P$ is positioned $31^{\text{st}}$ from the right end. If Robot $M$ and Robot $P$ interchange their positions, Robot $P$ becomes $48^{\text{th}}$ from the right end. Based on this rearrangement, what is the new position of Robot $M$ from the left end?

43^{\text{rd}}

44^{\text{th}}

74^{\text{th}}

31^{\text{st}}

Cevabı ve açıklamayı göster

Cevap: $44^{\text{th}}$

Cevap

The new position of Robot M from the left end is the

44^{\text{th}}

position.

The correct answer accurately synthesizes the overlapping ranks. By analyzing Robot P's new position (which is Robot M's old position), we find the total number of robots is

27 + 48 - 1 = 74

. Robot M moves to Robot P's old position, which is

31^{\text{st}}

from the right. Its position from the left is then calculated as

74 - 31 + 1 = 44

.

Adım Adım Çözüm

1

Identify the coordinates of the interchange spot.

Robot

P

moves to Robot

M

's original spot. This spot is known to be

27^{\text{th}}

from the left end. After the swap, we are told Robot

P

is now

48^{\text{th}}

from the right end.

Establishing both the left and right ranks for a single spot allows us to calculate the total number of entities in the sequence.

2

Calculate the total number of delivery robots (

N

).

N = (\text{Rank from Left}) + (\text{Rank from Right}) - 1

. Therefore,

N = 27 + 48 - 1 = 74

robots.

Adding the left and right ranks counts the robot sitting in that spot twice, so we must subtract 1 to get the accurate total count.

3

Identify Robot

M

's new physical location.

Robot

M

moves to Robot

P

's original spot, which is stated as being

31^{\text{st}}

from the right end.

To find Robot

M

's rank from the left, we first need to isolate its exact rank from the right side.

4

Calculate Robot

M

's new rank from the left end.

\text{Rank from Left} = N - (\text{Rank from Right}) + 1

. Therefore, Rank =

74 - 31 + 1 = 44

.

Subtracting the right rank from the total gives the number of robots to the left of Robot

M

. Adding 1 includes Robot

M

in the final positional count.

Anahtar Kavram

Positional Interchange and Total Sequence Capacity

Soru 295Soru →

In a linear arrangement of food stalls at a weekend night market, the "Spice Hub" stall is positioned $18^{\text{th}}$ from the left end, and the "Grill Master" stall is positioned $25^{\text{th}}$ from the right end. If the two stalls interchange their exact positions, the "Spice Hub" stall becomes $31^{\text{st}}$ from the left end. Based on this new arrangement, what is the total number of food stalls in the row?

56

55

48

42

Cevabı ve açıklamayı göster

Cevap: $55$

Cevap

The total number of food stalls is

55

.

By interchanging positions, "Spice Hub" moves to the spot originally held by "Grill Master". We know this specific spot is

25^{\text{th}}

from the right end. The problem states that "Spice Hub" is now

31^{\text{st}}

from the left end. Since we have both the left rank (

31

) and the right rank (

25

) for the exact same physical position, we can find the total by adding them and subtracting

1

to correct for double-counting the stall itself:

31 + 25 - 1 = 55

.

Adım Adım Çözüm

1

Identify a single physical position where both the left and right ranks are known.

After the interchange, the new position of "Spice Hub" is the original position of "Grill Master".

To calculate the total number of items in a row, we need the exact distance from both ends for the exact same point.

2

Determine the specific left and right ranks for this identified position.

The position is

25^{\text{th}}

from the right (original "Grill Master" rank) and

31^{\text{st}}

from the left (new "Spice Hub" rank).

The physical location of the stall hasn't changed relative to the ends, only the stall occupying it has changed.

3

Apply the total rank formula:

\text{Total} = \text{Left Rank} + \text{Right Rank} - 1

.

\text{Total} = 31 + 25 - 1 = 55

.

We must subtract

1

because adding the left and right ranks counts the stall at that specific position twice.

Anahtar Kavram

Positional Ranking and Interchange

Soru 296Soru →

A multinational corporation signed a $100$ -year lease for its global headquarters on Monday, May 18, 2026. The lease agreement explicitly states that it will expire on exactly the same date $100$ years later, on May 18, 2126. On what day of the week will this lease expire?

Saturday

Sunday

Wednesday

Friday

Cevabı ve açıklamayı göster

Cevap: Saturday

Cevap

Saturday

The interval between May 18, 2026, and May 18, 2126 is exactly

100

years. Normally, a

100

-year span contains

25

leap years, but because the year

2100

is a century year not divisible by

400

, it is not a leap year. This leaves exactly

24

leap years in the period. The total number of odd days is the sum of ordinary years and leap year extras:

100 + 24 = 124

odd days. When dividing

124

by

7

, the remainder is

5

. Advancing

5

days from Monday results in Saturday.

Adım Adım Çözüm

1

Calculate the total number of years in the given timeframe.

The period from May 18, 2026 to May 18, 2126 is exactly

100

years.

This establishes the base number of odd days, as every ordinary year contributes exactly

1

odd day.

2

Determine the number of leap years within this 100-year interval.

There are

24

leap years.

Normally, a

100

-year span contains

25

leap years (

100 \div 4 = 25

). However, the span crosses the year

2100

. Because

2100

is a century year but is not divisible by

400

, it is not a leap year. Therefore, we subtract

1

from

25

to get

24

leap years.

3

Calculate the total number of odd days accumulated over the 100 years.

The total is

124

odd days.

Each of the

100

years contributes

1

base odd day (

100

days), and each of the

24

leap years contributes an additional odd day (

24

days).

100 + 24 = 124

.

4

Find the final day of the week by evaluating the total odd days modulo 7.

The remainder is

5

, which shifts the day from Monday to Saturday.

124 \div 7 = 17

weeks with a remainder of

5

days. Counting

5

days forward from Monday gives Saturday.

Anahtar Kavram

Calculating odd days over a multi-year period while correctly applying the century non-leap year rule.

Soru 297Soru →

In a single-file queue of passengers waiting to board a ferry, Oliver is standing $14^{\text{th}}$ from the front and Maya is standing $29^{\text{th}}$ from the back. If Oliver and Maya completely interchange their positions, Maya becomes $37^{\text{th}}$ from the back. How many passengers are standing in the queue?

50

51

42

65

Cevabı ve açıklamayı göster

Cevap: 50

Cevap

There are 50 passengers in the queue.

Upon interchanging positions, Maya occupies Oliver's original spot. This specific spot in the queue is

14^{\text{th}}

from the front (established by Oliver) and

37^{\text{th}}

from the back (established by Maya's new rank). Adding these two directional ranks and subtracting

1

(to correct for double-counting the person in that exact spot) yields exactly

50

passengers.

Adım Adım Çözüm

1

Analyze the positional interchange.

Maya moves to Oliver's original position.

When two people swap places, the physical position in the queue remains constant while the occupants change.

2

Determine the dual rank of the shared position.

The position is

14^{\text{th}}

from the front (Oliver's old rank) and

37^{\text{th}}

from the back (Maya's new rank).

To find the total number of people, we need the exact rank of a single specific spot from both ends of the queue.

3

Apply the total queue length formula.

Total

= (\text{Position from front}) + (\text{Position from back}) - 1

Adding the two ranks counts the person at that specific spot twice, so

1

must be subtracted to get the accurate total.

4

Calculate the final total.

14 + 37 - 1 = 50

Direct mathematical substitution provides the total count.

Anahtar Kavram

Positional Interchange and Dual Rank Calculation

Alternatif Yöntem

Find the total positional shift: Maya moved from

29^{\text{th}}

from the back to

37^{\text{th}}

from the back, an

8

-position leap forward. Since she took Oliver's spot (

14^{\text{th}}

from the front), Oliver was

8

positions ahead of her original spot. Her original spot from the front was

14 + 8 = 22^{\text{nd}}

. Therefore, the total is her original front rank (

22

) plus her original back rank (

29

) minus

1

, which equals

50

.

Tahmini Süre:1m 15s

Soru 298Soru →

An international exhibition is inaugurated on January 26th of a leap year, which falls on a Thursday. The closing ceremony is scheduled for October 15th of the same year. On what day of the week will the closing ceremony take place?

Cevabı ve açıklamayı göster

Cevap: Monday; monday

Cevap

Monday

The total number of days elapsed from January 26th to October 15th in a leap year is exactly

263

days. Dividing

263

by

7

gives

37

full weeks and a remainder of

4

odd days. Counting

4

days forward from Thursday results in Monday.

Adım Adım Çözüm

1

Calculate the remaining days in January and note the full days in the intervening months.

January:

5

days (

31 - 26

). February:

29

days (since it is a leap year). March:

31

, April:

30

, May:

31

, June:

30

, July:

31

, August:

31

, September:

30

.

To find the total number of days elapsed between January 26th and October 15th, we must sum the relevant days in each month.

2

Add the days of the final month (October) to the sum of the previous months.

5 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 15 = 263

days.

This calculation yields the exact number of days that pass from the inauguration to the closing ceremony.

3

Divide the total number of elapsed days by

7

to find the remainder (odd days).

263 \div 7 = 37

with a remainder of

4

days.

Since the days of the week repeat every

7

days, only the remainder affects the final day of the week.

4

Count

4

days forward from the starting day (Thursday).

Thursday

+ 1 =

Friday,

+ 2 =

Saturday,

+ 3 =

Sunday,

+ 4 =

Monday.

Adding the odd days to the initial day correctly determines the final day of the week.

Anahtar Kavram

Calculating elapsed days across multiple months and using the concept of odd days (modulo 7 arithmetic) to determine the exact day of the week.

Soru 299Soru →

During a graduation ceremony, graduates are standing in a single file line facing the stage. Liam is standing $18^{\text{th}}$ from the front, while Sophia is standing $31^{\text{st}}$ from the rear. After exchanging their places, Liam becomes $42^{\text{nd}}$ from the front. What is Sophia's new position from the rear?

54^{\text{th}}

72^{\text{nd}}

55^{\text{th}}

7^{\text{th}}

Cevabı ve açıklamayı göster

Cevap: $55^{\text{th}}$

Cevap

Sophia's new position from the rear is

55^{\text{th}}

.

When Liam and Sophia exchange places, Liam moves from the

18^{\text{th}}

position to the

42^{\text{nd}}

position from the front, representing a shift of

24

places backward (

42 - 18 = 24

). Since Sophia takes Liam's old spot, she shifts

24

places forward (towards the rear end of the line). Therefore, her new position from the rear is her old position plus the shift:

31 + 24 = 55

. Alternatively, finding the total number of people (

42 + 31 - 1 = 72

) and applying the formula for rank from the opposite end (

72 - 18 + 1 = 55

) yields the exact same correct result.

Adım Adım Çözüm

1

Determine the total number of graduates in the line.

Total =

42

(Liam's new position from front) +

31

(Sophia's initial position from rear) -

1

=

72

.

After swapping, Liam occupies Sophia's original position. The sum of positions from both ends minus one gives the total count.

2

Identify Sophia's new position from the front.

Sophia is now at Liam's original position, which is

18^{\text{th}}

from the front.

Because they exchanged places, Sophia takes over Liam's initial spot.

3

Calculate Sophia's new position from the rear.

New position =

72

(Total) -

18

(Position from front) +

1

=

55^{\text{th}}

.

The position from the rear is calculated by taking the total number of people, subtracting the position from the front, and adding one.

Anahtar Kavram

Position Interchange and Total Queue Calculation

Soru 300Soru →

A solid wooden cube is painted Black on two adjacent faces, while the remaining four faces are painted White. The large cube is then cut into $64$ identical smaller cubes. What is the total number of smaller cubes that have at least one Black face?

Cevabı ve açıklamayı göster

Cevap: 28

Cevap

28

The large cube is divided into

64

smaller cubes, which means it forms a

4 \times 4 \times 4

grid. A single face of this large cube contains

4 \times 4 = 16

smaller cubes. Since two adjacent faces are painted Black, we count the cubes on both faces. The first face has

16

Black cubes. The second face also has

16

Black cubes, but it shares one edge with the first face. This shared edge consists of

4

smaller cubes. If we simply add

16 + 16 = 32

, we double-count the

4

cubes on the shared edge. Subtracting the overlap gives

32 - 4 = 28

unique smaller cubes that have at least one Black face.

Adım Adım Çözüm

1

Find the edge length of the large cube in terms of smaller cubes.

n = 4

The total number of smaller cubes is

64

, and the total volume of a cube is

n^3

. Therefore,

n = \sqrt[3]{64} = 4

.

2

Count the smaller cubes on the first Black face.

16

cubes

Each face of an

n \times n \times n

cube contains

n^2

smaller cubes. Here,

4^2 = 16

cubes.

3

Count the smaller cubes on the second Black face and identify the overlap.

The second face adds

16

cubes, but the two faces share an edge of

4

cubes.

Since the two Black faces are adjacent, they intersect along one edge. The cubes on this edge are counted as part of both faces.

4

Calculate the total unique cubes with at least one Black face.

28

cubes

Using the inclusion-exclusion principle:

16

(first face) +

16

(second face) -

4

(shared edge) =

28

.

Anahtar Kavram

Calculation of painted smaller cubes from a larger cut cube, specifically handling adjacent face intersections.

General Mental Ability

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

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Sık Yapılan Hatalar

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Sık Yapılan Hatalar

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Sık Yapılan Hatalar

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Sık Yapılan Hatalar

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Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

Cevap

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Anahtar Kavram

Sık Yapılan Hatalar

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Anahtar Kavram

Sık Yapılan Hatalar

Cevap

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Anahtar Kavram

Sık Yapılan Hatalar

Alternatif Yöntem

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Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Cevap

Adım Adım Çözüm