General Mental Ability Alıştırma Soruları — State PSC Exam — Sayfa 8

What is the next term that continues the pattern established in the following alphanumeric sequence?

Z2B, X6E, V12H, T20K, \dots

R30N

R28N

R30M

S30N

Cevabı ve açıklamayı göster

Cevap: $R30N$

Cevap

R30N

The sequence consists of three parallel sub-patterns: the first letters decrease by 2 positions (

Z \rightarrow X \rightarrow V \rightarrow T \rightarrow R

), the middle numbers increase by expanding even differences

+4, +6, +8, +10

(

2 \rightarrow 6 \rightarrow 12 \rightarrow 20 \rightarrow 30

), and the trailing letters increase by 3 positions (

B \rightarrow E \rightarrow H \rightarrow K \rightarrow N

). Combining these yields

R30N

.

Adım Adım Çözüm

1

Analyze the pattern of the first letter in each term

Z (26) -> X (24) -> V (22) -> T (20) -> R (18)

Each term's first letter shifts backward by 2 positions in alphabetical order.

2

Analyze the pattern of the middle number in each term

2, 6, 12, 20, 30

The difference between consecutive numbers increases by 2 each step (+4, +6, +8, +10).

3

Analyze the pattern of the last letter in each term

B (2) -> E (5) -> H (8) -> K (11) -> N (14)

Each term's last letter shifts forward by 3 positions in alphabetical order.

4

Combine the derived elements to form the next term

First letter: R, Middle number: 30, Last letter: N => R30N

Synthesizing all three independent rules yields the required term in the sequence.

Anahtar Kavram

Multi-pattern Alphanumeric Series

Tahmini Süre:1m 15s

Soru 142Soru →

In a certain code language, the word 'FLOWER' is written as 'HNQYGT'. How is the word 'GARDEN' written in that code language?

ICTFGP

HBSEFO

JDUGHQ

EYPBCL

Cevabı ve açıklamayı göster

Cevap: ICTFGP

Cevap

The word 'GARDEN' is coded as 'ICTFGP'.

The underlying coding rule shifts each letter forward by 2 positions in alphabetical order (

+2

). Applying this

+2

shift to 'GARDEN' produces

G \rightarrow I

,

A \rightarrow C

,

R \rightarrow T

,

D \rightarrow F

,

E \rightarrow G

, and

N \rightarrow P

, which forms the word 'ICTFGP'.

Adım Adım Çözüm

1

Determine the rule governing the given coded word pair.

Comparing 'FLOWER' to 'HNQYGT':

F+2=H

,

L+2=N

,

O+2=Q

,

W+2=Y

,

E+2=G

, and

R+2=T

. The pattern is a uniform forward shift of

+2

positions in the alphabet.

Identifying the step size and direction of letter shifts.

2

Apply the

+2

forward shift rule to each letter of the word 'GARDEN'.

G+2=I

,

A+2=C

,

R+2=T

,

D+2=F

,

E+2=G

,

N+2=P

.

Transforming the letters of the target word using the established rule.

Anahtar Kavram

Forward Positional Letter Shift Coding

Soru 143Soru →

In a group of $60$ civil service aspirants, $35$ aspirants study History, $25$ study Geography, and $10$ study both History and Geography. How many aspirants study neither History nor Geography?

10

0

20

15

Cevabı ve açıklamayı göster

Cevap: $10$

Cevap

The number of aspirants studying neither History nor Geography is

10

.

By applying the set formula

|H \cup G| = |H| + |G| - |H \cap G|

, we get

|H \cup G| = 35 + 25 - 10 = 50

. The number of aspirants who study neither subject is

60 - 50 = 10

.

Adım Adım Çözüm

1

Calculate the total number of aspirants studying at least one subject using the principle of inclusion-exclusion.

Aspirants studying at least one subject =

35 + 25 - 10 = 50

.

The intersection of

10

is counted in both individual groups and must be subtracted once to avoid double counting.

2

Subtract the number of aspirants studying at least one subject from the total population.

Aspirants studying neither subject =

60 - 50 = 10

.

The total group consists of aspirants studying at least one subject plus those studying neither.

Anahtar Kavram

Principle of Inclusion-Exclusion for two sets:

|A \cup B| = |A| + |B| - |A \cap B|

.

Soru 144Soru →

In a survey of $120$ civil service aspirants, $65$ study Indian History, $55$ study Indian Polity, and $45$ study Geography. Further details reveal that $25$ aspirants study both History and Polity, $20$ study both Polity and Geography, $15$ study both History and Geography, and $8$ study all three subjects. How many aspirants study exactly two subjects?

36

60

52

44

Cevabı ve açıklamayı göster

Cevap: $36$

Cevap

The number of aspirants studying exactly two subjects is 36.

The correct answer is

36

. To find the number of people in 'exactly two' sets in a 3-circle Venn diagram, we subtract the center region (all three sets) from each of the two-set overlapping regions:

(25 - 8) + (20 - 8) + (15 - 8) = 17 + 12 + 7 = 36

.

Adım Adım Çözüm

1

Identify the given region values from the problem statement

Total aspirants =

120

,

n(H) = 65

,

n(P) = 55

,

n(G) = 45

,

n(H \cap P) = 25

,

n(P \cap G) = 20

,

n(H \cap G) = 15

, and

n(H \cap P \cap G) = 8

.

Establishing set parameters enables standard Venn diagram region calculations.

2

Calculate aspirants studying only History and Polity

n(H \cap P \text{ only}) = n(H \cap P) - n(H \cap P \cap G) = 25 - 8 = 17

.

Sub-regions representing exactly two subjects must exclude elements in all three sets.

3

Calculate aspirants studying only Polity and Geography

n(P \cap G \text{ only}) = n(P \cap G) - n(H \cap P \cap G) = 20 - 8 = 12

.

Isolate the dual-subject overlap specific to Polity and Geography.

4

Calculate aspirants studying only History and Geography

n(H \cap G \text{ only}) = n(H \cap G) - n(H \cap P \cap G) = 15 - 8 = 7

.

Isolate the dual-subject overlap specific to History and Geography.

5

Sum the three exclusive dual-subject regions

17 + 12 + 7 = 36

.

The total number of aspirants studying exactly two subjects is the sum of the three mutually exclusive regions.

Anahtar Kavram

Inclusion-Exclusion Principle and Logical Venn Diagram Region Identification

Soru 145Soru →

During a network security test, an encryption algorithm alters text strings based on character classification. When the algorithm processes the input string PLANET, it generates the cipher NJDLHR. Applying the exact same logical transformation, which of the following is the cipher for the input ORBIT?

RUELW

MPZGR

RPZLR

MUEGW

Cevabı ve açıklamayı göster

Cevap: RPZLR

Cevap

The cipher for ORBIT is RPZLR.

The encryption algorithm applies a specific positional shift based on whether a letter is a vowel or a consonant. Consonants are shifted backward by 2 steps in the alphabet, while vowels are shifted forward by 3 steps. Applying this to ORBIT: O(+3)=R, R(-2)=P, B(-2)=Z, I(+3)=L, and T(-2)=R, yielding the cipher RPZLR.

Adım Adım Çözüm

1

Analyze the alphabetical position shift between the input PLANET and the cipher NJDLHR.

P(16) → N(14) is -2; L(12) → J(10) is -2; A(1) → D(4) is +3; N(14) → L(12) is -2; E(5) → H(8) is +3; T(20) → R(18) is -2.

Determining the individual letter transformations reveals the underlying logic of the encryption algorithm.

2

Identify the pattern distinguishing the different shift values.

All consonants (P, L, N, T) are shifted backward by 2 positions (-2). All vowels (A, E) are shifted forward by 3 positions (+3).

Coding sequences often depend on character classification such as vowels versus consonants.

3

Apply the established consonant rule (-2) and vowel rule (+3) to the target string ORBIT.

O (vowel) + 3 = R; R (consonant) - 2 = P; B (consonant) - 2 = Z; I (vowel) + 3 = L; T (consonant) - 2 = R.

Applying the exact algorithm guarantees the correct cipher generation.

4

Combine the transformed characters to form the final cipher.

The final string is RPZLR.

This completes the encryption process.

Anahtar Kavram

Coding and Decoding based on Vowel and Consonant conditions

Tahmini Süre:1m 30s

Soru 146Soru →

During a corporate seminar, 60 employees are seated in a single straight row facing the stage. If David is seated in the $38^{\text{th}}$ position when counting from the left end of the row, what is his position when counting from the right end?

22^{\text{nd}}

23^{\text{rd}}

24^{\text{th}}

38^{\text{th}}

Cevabı ve açıklamayı göster

Cevap: $23^{\text{rd}}$

Cevap

23^{\text{rd}}

To find a person's position from one end when the total and the position from the other end are known, use the formula: Position = Total - Known Position + 1. Here, 60 - 38 + 1 equals 23.

Adım Adım Çözüm

1

Identify the total number of employees and David's position from the left.

Total = 60, Left position = 38.

These are the known variables needed for the ranking formula.

2

Apply the single-person dual rank formula to find the position from the right.

Right position = Total - Left position + 1.

Subtracting the left position removes everyone up to and including David. Adding 1 back includes David in the count from the right.

3

Calculate the final value.

60 - 38 + 1 = 22 + 1 = 23.

Basic arithmetic completion yields the correct rank.

Anahtar Kavram

Single-person dual rank calculation in a linear arrangement.

Soru 147Soru →

To categorize inventory, a warehouse management system generates unique reference tags for items based on their names by applying a consistent alphabetical transformation. For example, the item named PUBLIC is assigned the reference tag LGZPSY.

Applying this exact same tagging algorithm, what reference tag will be generated for the item named SECTOR?

IWYHMJ

HVXGLI

TFDUPS

GUWFKH

Cevabı ve açıklamayı göster

Cevap: IWYHMJ

Cevap

The correct reference tag generated for the item SECTOR is IWYHMJ.

The correct algorithm applies a two-step transformation to each letter. First, it finds the reverse alphabetical counterpart (Opposite: A becomes Z, B becomes Y, etc.). Second, it shifts that opposite letter forward by 1 position (+1). Applying this exact logic to SECTOR yields IWYHMJ.

Adım Adım Çözüm

1

Examine the relationship between the first letter of 'PUBLIC' (P) and its corresponding tag letter (L).

P is the 16th letter of the alphabet. Its reverse alphabetical counterpart is K (the 11th letter, since 27 - 16 = 11). Shifting K forward by 1 position (+1) results in L.

To establish the underlying, multi-step mathematical pattern applied by the algorithm.

2

Verify this 'Opposite + 1' pattern with the remaining letters of 'PUBLIC'.

U(21) → F(6) → G; B(2) → Y(25) → Z; L(12) → O(15) → P; I(9) → R(18) → S; C(3) → X(24) → Y. The pattern perfectly matches the provided tag 'LGZPSY'.

To confirm the rule is consistent across the entire word before applying it to the target.

3

Apply the confirmed algorithm to the target word 'SECTOR'.

S → Opposite is H → +1 is I
E → Opposite is V → +1 is W
C → Opposite is X → +1 is Y
T → Opposite is G → +1 is H
O → Opposite is L → +1 is M
R → Opposite is I → +1 is J
The final string is IWYHMJ.

To generate the final reference tag as requested by the question stem.

Anahtar Kavram

Identifying compound character transformations (reverse indexing paired with standard interval shifting) in alphanumeric strings.

Soru 148Soru →

A scientist was born on February 29, 2096, which happens to be a Wednesday. Because of the specific rules governing the Gregorian calendar, they only celebrate their birthday on the exact date of February 29. On what day of the week will they celebrate their first actual birthday?

Friday

Monday

Thursday

Saturday

Cevabı ve açıklamayı göster

Cevap: Friday

Cevap

Friday

The next leap year after 2096 is 2104, making an 8-year gap because 2100 is an ordinary year. This 8-year interval consists of 7 ordinary years and 1 leap year. Calculating the odd days yields (7 × 1) + (1 × 2) = 9 odd days. Dividing 9 by 7 gives a remainder of 2. Adding 2 days to Wednesday results in Friday.

Adım Adım Çözüm

1

Determine the year of the first actual birthday.

February 29, 2104.

The year 2100 is a century year not divisible by 400, making it a common year. The next leap year containing February 29 after 2096 is 2104.

2

Calculate the total number of years and identify leap years in the interval.

8 years total, consisting of 7 ordinary years and 1 leap year (2104).

The period from February 29, 2096, to February 29, 2104, spans exactly 8 years. Only 2104 contributes a February 29th at the end of its respective annual cycle within this specific gap.

3

Calculate the total number of odd days.

9 odd days.

The 7 ordinary years contribute 1 odd day each (7), and the 1 leap year contributes 2 odd days. Total = 7 + 2 = 9.

4

Determine the final day of the week.

Friday.

9 days divided by 7 leaves a remainder of 2 odd days. Adding 2 days to the starting day of Wednesday results in Friday.

Anahtar Kavram

Leap year identification across century boundaries and odd day calculation.

Soru 149Soru →

If January 15, 1894 fell on a Monday, what day of the week was January 15, 1904?

Cevabı ve açıklamayı göster

Cevap: Friday; friday; FRIDAY

Cevap

Friday

The period from January 15, 1894 to January 15, 1904 covers exactly 10 years. Within this period, we must count how many times February 29th is crossed. The year 1896 contributes one extra day. The year 1900 is a century year not divisible by 400, so it is a common year and contributes no extra days. The year 1904 is a leap year, but because the end date is January 15, we do not cross its February 29th, so it also contributes no extra days to this interval. The total number of odd days is 10 (for the 10 years) + 1 (for 1896) = 11. Dividing 11 by 7 leaves a remainder of 4. Four days after Monday is Friday.

Adım Adım Çözüm

1

Determine the total number of years between the two dates.

The interval from January 15, 1894 to January 15, 1904 is exactly 10 years.

This provides the base number of odd days, as each standard 365-day year shifts the day of the week by 1.

2

Identify the leap years that contribute an extra day (February 29) strictly within this interval.

The only leap year whose February 29th is crossed is 1896.

The year 1896 is a regular leap year. The year 1900 is a century year not divisible by 400, so it is NOT a leap year. The year 1904 is a leap year, but the target date is January 15, meaning its February 29th has not yet occurred.

3

Calculate the total number of odd days.

10 (base years) + 1 (extra day for crossing February 29, 1896) = 11 odd days.

We add one extra day for each leap year February actually experienced in the given time window.

4

Determine the remainder when dividing the total odd days by 7.

11 divided by 7 leaves a remainder of 4.

The days of the week repeat in a standard 7-day cycle, so we use modulo 7 arithmetic.

5

Add the remainder to the starting day of the week.

Monday + 4 days = Friday.

Counting forward four days from Monday gives Tuesday, Wednesday, Thursday, and finally Friday.

Anahtar Kavram

Calculating odd days across a century boundary and evaluating leap year inclusion based on the month.

Alternatif Yöntem

You can count the shift year by year: 1894 to 1895 (+1), '95 to '96 (+1), '96 to '97 (+2, crosses Feb '96), '97 to '98 (+1), '98 to '99 (+1), '99 to 1900 (+1), 1900 to '01 (+1), '01 to '02 (+1), '02 to '03 (+1), '03 to 1904 (+1, stops in Jan). The total is 11, giving a net shift of 4 days.

Tahmini Süre:1m 0s

Soru 150Soru →

A newly constructed high-speed railway network begins its first commercial operation on Sunday, January 15, 2096. The operating company schedules a comprehensive decade-review on the exact same date 10 years later, January 15, 2106. On what day of the week will this decade-review take place?

Thursday

Friday

Saturday

Wednesday

Cevabı ve açıklamayı göster

Cevap: Friday

Cevap

Friday

The interval from January 15, 2096, to January 15, 2106, covers exactly 10 years. During this time, we cross February 29th in the years 2096 and 2104, making them leap years. Crucially, the year 2100 is a century year. Century years are only leap years if they are divisible by 400. Since 2100 is not divisible by 400, it is a normal year. This means we have 8 normal years and 2 leap years in this 10-year span. Calculating the odd days: (8 × 1) + (2 × 2) = 12 odd days. Dividing 12 by 7 gives a remainder of 5. Counting 5 days forward from Sunday lands exactly on Friday.

Adım Adım Çözüm

1

Determine the total number of years in the given time frame.

The period from January 15, 2096, to January 15, 2106, is exactly 10 years.

This establishes the baseline period for calculating odd days.

2

Identify the leap years that fall within this 10-year period.

The leap years are 2096 (since February 29th is crossed) and 2104. The year 2100 is a century year not divisible by 400, so it is a normal year.

Century years must be divisible by 400 to be leap years, which is a critical rule for crossing the year 2100 boundary.

3

Calculate the total number of normal years and leap years.

Out of 10 years, there are 2 leap years and 8 normal years.

Leap years have 2 odd days and normal years have 1 odd day.

4

Calculate the total number of odd days for the 10-year period.

(8 normal years × 1 odd day) + (2 leap years × 2 odd days) = 8 + 4 = 12 odd days.

This translates the years into a continuous shift in the days of the week.

5

Find the net shift in the day of the week by finding the remainder when dividing by 7.

12 divided by 7 leaves a remainder of 5 odd days.

The days of the week repeat every 7 days.

6

Add the odd days to the starting day of the week.

Sunday + 5 days = Friday.

This determines the exact final day of the week for the scheduled event.

Anahtar Kavram

Calculation of odd days across century boundaries

Soru 151Soru →

At a busy immigration checkpoint, a single line of passengers is waiting to be processed. Fatima is standing $22^{\text{nd}}$ from the front of the line, while Diego is $32^{\text{nd}}$ from the back.

Due to a lane reassignment, Fatima and Diego completely swap their positions in the line. After the swap, Fatima becomes $40^{\text{th}}$ from the front.

A third passenger, Haruki, is standing exactly halfway between Diego's new position and Fatima's new position.

If $5$ passengers at the very back of the line give up and leave, what is Haruki's new position counting from the back of the line?

35^{\text{th}}

36^{\text{th}}

37^{\text{th}}

41^{\text{st}}

Cevabı ve açıklamayı göster

Cevap: $35^{\text{th}}$

Cevap

The correct answer is the

36^{\text{th}}

position.

By determining the initial total number of passengers (

40 + 32 - 1 = 71

) and identifying Haruki's position from the front (the midpoint of

22

and

40

, which is

31

), we can find Haruki's final position from the back after

5

people leave. The new total is

66

, making Haruki's position from the back

66 - 31 + 1 = 36

.

Adım Adım Çözüm

1

Calculate the initial total number of passengers in the line.

Total =

40 + 32 - 1 = 71

passengers.

After the swap, Fatima moves to Diego's old position. Since her new rank is

40^{\text{th}}

from the front and Diego's old rank was

32^{\text{nd}}

from the back, this single position's front and back ranks sum to the total plus one.

2

Determine Diego's new position from the front.

Diego is now

22^{\text{nd}}

from the front.

Because Fatima and Diego completely swapped places, Diego assumes Fatima's original position.

3

Find Haruki's position from the front of the line.

Haruki's position =

\frac{22 + 40}{2} = 31^{\text{st}}

from the front.

Haruki is exactly halfway between Diego's new position (

22^{\text{nd}}

) and Fatima's new position (

40^{\text{th}}

).

4

Calculate the new total number of passengers and Haruki's position from the back.

New total =

71 - 5 = 66

. Haruki's back rank =

66 - 31 + 1 = 36

.

Since

5

people left from the very back, Haruki's front rank (

31^{\text{st}}

) remains unchanged, but the overall line length shrinks to

66

. The standard formula for finding a back rank is (Total - Front Rank + 1).

Anahtar Kavram

Position Interchange and Midpoint Ranking

Tahmini Süre:2m 30s

Soru 152Soru →

To correctly calculate dates across decades, one must accurately identify which years contain $366$ days. According to the rules of the Gregorian calendar, which of the following groups of years contains ONLY leap years?

1988, 1996, 2100

1896, 1904, 2000

1900, 1992, 2004

2008, 2012, 2018

Cevabı ve açıklamayı göster

Cevap: $1896, 1904, 2000$

Cevap

The group containing

1896, 1904

, and

2000

The correct answer contains years that all perfectly satisfy leap year conditions. Both

1896

and

1904

are non-century years that divide evenly by

4

. The year

2000

is a century year that divides evenly by

400

. Therefore, all three are leap years.

Adım Adım Çözüm

1

Recall the rules for determining a leap year.

A standard year is a leap year if it is divisible by

4

. However, century years (ending in

00

) are only leap years if they are exactly divisible by

400

.

To evaluate each individual year listed in the options.

2

Evaluate the group containing

1896, 1904

, and

2000

.

1896

and

1904

are divisible by

4

. The year

2000

is a century year and is divisible by

400

.

This confirms all years in this specific group satisfy the leap year rules.

3

Evaluate the remaining groups to find their non-leap years.

The year

2100

is not divisible by

400

, the year

1900

is not divisible by

400

, and the year

2018

is not divisible by

4

.

To eliminate the incorrect choices based on the presence of standard years.

Anahtar Kavram

Century Leap Year Logic

Tahmini Süre:45s

Soru 153Soru →

Six students—Leo, Maya, Noah, Olivia, Paul, and Quinn—are sitting in a single straight row facing North for a presentation. Based on the following conditions, answer the question below:

1. Paul is sitting at the extreme right end of the row.
2. Noah is sitting immediately to the left of Paul.
3. Maya is sitting immediately to the left of Noah.
4. Leo is sitting at the extreme left end of the row.
5. Quinn is sitting immediately to the left of Olivia.

Who is sitting immediately to the left of Maya?

Noah

Leo

Olivia

Quinn

Cevabı ve açıklamayı göster

Cevap: Olivia

Cevap

Olivia

Based on the step-by-step seating arrangement from left to right, the final order is: Leo, Quinn, Olivia, Maya, Noah, Paul. Since Maya is sitting in the fourth position, the person sitting immediately to her left is in the third position, which is occupied by Olivia.

Adım Adım Çözüm

1

Determine the positions of Paul, Noah, and Maya based on the first three clues.

Paul is at position 6 (extreme right), Noah is at position 5 (immediate left of Paul), and Maya is at position 4 (immediate left of Noah).

The row has 6 positions. Starting from the extreme right establishes a clear anchor point for placing adjacent people.

2

Place Leo based on the fourth clue.

Leo is at position 1.

The clue explicitly states Leo is at the extreme left end.

3

Place Quinn and Olivia based on the fifth clue in the remaining empty positions.

Quinn is at position 2 and Olivia is at position 3.

Positions 2 and 3 are the only consecutive empty spots left. Since Quinn is immediately to the left of Olivia, Quinn takes the left-most spot of the two (position 2).

4

Identify the person sitting immediately to the left of Maya.

Olivia is the correct person.

Maya is at position 4. The position immediately to the left is position 3, which is occupied by Olivia.

Anahtar Kavram

Linear Seating Arrangement

Soru 154Soru →

A state planning commission reviewed $350$ rural development grants to evaluate their allocation across three critical sectors: Healthcare ( $H$ ), Education ( $E$ ), and Infrastructure ( $I$ ). The review revealed the following data:

- $160$ grants were allocated to Healthcare.
- $150$ grants were allocated to Education.
- $140$ grants were allocated to Infrastructure.
- $50$ grants were allocated to both Healthcare and Education.
- $45$ grants were allocated to both Education and Infrastructure.
- $40$ grants were allocated to both Healthcare and Infrastructure.
- $15$ grants were allocated to all three sectors.

Based on the information above, which of the following statements are correct?

Geçerli olan tümünü seçin

Exactly

20

grants were not allocated to any of these three sectors.

Exactly

135

grants were allocated to exactly two sectors.

Exactly

70

grants were allocated only to Education.

Exactly

50

grants were allocated to only Healthcare and Education.

Cevabı ve açıklamayı göster

Cevap: Exactly $20$ grants were not allocated to any of these three sectors.; Exactly $70$ grants were allocated only to Education.

Cevap

The correct statements are that exactly 20 grants were not allocated to any of these three sectors, and exactly 70 grants were allocated only to Education.

The correct statements accurately identify the number of unallocated grants and the grants allocated exclusively to Education. The total number of allocated grants is found using the formula

|H \cup E \cup I| = 160 + 150 + 140 - 50 - 45 - 40 + 15 = 330

. Therefore,

350 - 330 = 20

grants are unallocated. Additionally, grants for ONLY Education equals the total for Education minus all its intersections:

150 - (35 + 30 + 15) = 70

.

Adım Adım Çözüm

1

Identify the values for the intersections of exactly two sets by subtracting the 'all three' value (

15

) from the given two-set intersections.

Healthcare & Education only =

50 - 15 = 35

. Education & Infrastructure only =

45 - 15 = 30

. Healthcare & Infrastructure only =

40 - 15 = 25

.

The given intersections (e.g., Healthcare and Education) include the grants that belong to all three sectors. These must be separated to find exclusive regions.

2

Calculate the number of grants allocated to exactly two sectors.

Total for exactly two =

35 + 30 + 25 = 90

.

Adding the distinct 'only two' regions provides the total for grants overlapping in exactly two sectors.

3

Calculate the number of grants allocated exclusively to each single sector.

Only Healthcare =

160 - (35 + 25 + 15) = 85

. Only Education =

150 - (35 + 30 + 15) = 70

. Only Infrastructure =

140 - (25 + 30 + 15) = 70

.

Subtracting all overlapping parts of a set from its total yields the exclusive 'only one category' count.

4

Determine the total number of grants allocated to at least one sector and those allocated to none.

Total allocated =

85 + 70 + 70 + 35 + 30 + 25 + 15 = 330

. Unallocated (None) =

350 - 330 = 20

.

Summing all distinct regions of the Venn diagram gives the union of the sets. Subtracting this from the universal set gives the complement (None).

5

Evaluate each given statement based on the calculated regions.

Statement 1 (20 unallocated) is true. Statement 2 (135 exactly two) is false (actual is 90). Statement 3 (70 only Education) is true. Statement 4 (50 only H and E) is false (actual is 35).

Matching calculated values against the options reveals the correct selections.

Anahtar Kavram

Solving 3-set logical Venn diagrams using the inclusion-exclusion principle and identifying specific overlapping regions.

Soru 155Soru →

In a municipal office survey of $100$ administrative officers, $50$ officers speak English, $40$ officers speak Hindi, and $20$ officers speak both English and Hindi. Based on this information, which of the following statements are correct?

Geçerli olan tümünü seçin

The number of officers who speak only English is

30

.

The number of officers who speak neither English nor Hindi is

30

.

The number of officers who speak only Hindi is

40

.

The total number of officers who speak at least one of the two languages is

90

.

Cevabı ve açıklamayı göster

Cevap: The number of officers who speak only English is $30$ .; The number of officers who speak neither English nor Hindi is $30$ .

Cevap

The correct statements are that the number of officers who speak only English is

30

, and the number of officers who speak neither English nor Hindi is

30

.

The number of officers speaking only English is obtained by subtracting the shared region (

20

) from the total English speakers (

50

), giving

30

. The officers speaking at least one language equals

30 \text{ (only English)} + 20 \text{ (both)} + 20 \text{ (only Hindi)} = 70

. Subtracting

70

from the total

100

officers gives

30

officers who speak neither language.

Adım Adım Çözüm

1

Calculate the number of officers who speak only English.

\text{Only English} = 50 - 20 = 30

Subtract the intersection (both languages) from the total English speakers.

2

Calculate the number of officers who speak only Hindi.

\text{Only Hindi} = 40 - 20 = 20

Subtract the intersection (both languages) from the total Hindi speakers.

3

Calculate the total number of officers speaking at least one language (the union of sets).

\text{At least one language} = 30 + 20 + 20 = 70

Sum the exclusive counts and the shared intersection count.

4

Calculate the number of officers speaking neither language.

\text{Neither language} = 100 - 70 = 30

Subtract the number of officers speaking at least one language from the total group size.

Anahtar Kavram

Inclusion-Exclusion Principle for Two Sets

Tahmini Süre:1m 0s

Soru 156Soru →

Consider the following complex alphanumeric sequence:

C3F, E8I, H18L, L38O, Q78R, \dots

Which of the following terms logically completes the series?

W158U

V158U

W156U

W158V

Cevabı ve açıklamayı göster

Cevap: $W158U$

Cevap

W158U

The term is obtained by breaking the alphanumeric code into three parallel streams: (1) First letter follows increasing step intervals (+2, +3, +4, +5, +6), bringing Q (17) to W (23). (2) Numerical component uses the rule

2x + 2

, converting 78 to 158. (3) Second letter has a constant increment of +3, moving R (18) to U (21). Combining these gives the complete term

W158U

.

Adım Adım Çözüm

1

Analyze the pattern of the first letter in each term

Positions in alphabet: C (3), E (5), H (8), L (12), Q (17). The positional increments are +2, +3, +4, +5. Following this pattern, the next increment must be +6. Adding 6 to Q (17) yields 23, which corresponds to the letter W.

The first element follows an increasing arithmetic step pattern.

2

Analyze the numerical progression in the terms

Sequence of numbers: 3, 8, 18, 38, 78. The recurrence relation is

N_k = 2 \times N_{k-1} + 2

. Calculating the next value:

2 \times 78 + 2 = 156 + 2 = 158

.

Each number is formed by doubling the previous term and adding 2.

3

Analyze the pattern of the second letter in each term

Positions in alphabet: F (6), I (9), L (12), O (15), R (18). The positional increment is constant at +3. Adding 3 to R (18) yields 21, which corresponds to the letter U.

The third element follows a constant positional step pattern.

4

Synthesize the components to form the final term

Combining the calculated first letter (W), numerical middle value (158), and second letter (U) yields

W158U

.

All three independent term rules must be combined.

Anahtar Kavram

Multi-Pattern Alphanumeric Series Completion

Tahmini Süre:2m 0s

Soru 157Soru →

Consider the following alphanumeric sequence:

B2D, E6H, J14N, Q30V, \dots

Which of the following terms correctly completes the given series?

Z62F

Y62F

Z62E

A60F

Cevabı ve açıklamayı göster

Cevap: Z62F

Cevap

The term that correctly completes the given alphanumeric series is Z62F.

The correct term is obtained by breaking down the alphanumeric pattern into three separate sub-series. The first letter advances by odd increments (+3, +5, +7, +9) from B to Z. The middle number doubles and adds 2 at each step (

2 \times 30 + 2 = 62

). The third letter advances by even increments (+4, +6, +8, +10) from D to F (with alphabet wrap-around). Combining these yields Z62F.

Adım Adım Çözüm

1

Analyze the pattern of the first letter in each term.

The alphabetical positions of the first letters are B (2), E (5), J (10), Q (17). The differences between consecutive terms are

+3

,

+5

, and

+7

. The next difference must be

+9

. Adding

+9

to Q (17) yields

17 + 9 = 26

, which corresponds to the letter Z.

The first letter follows an increasing sequence of consecutive odd integer positional shifts.

2

Analyze the numerical pattern in the middle of each term.

The numbers are 2, 6, 14, 30. The progression rule is

n_{k+1} = 2 \times n_k + 2

. Applying this to the last known number:

2 \times 30 + 2 = 62

.

Each number is generated by doubling the previous number and adding 2.

3

Analyze the pattern of the third letter in each term.

The alphabetical positions of the third letters are D (4), H (8), N (14), V (22). The positional shifts are

+4

,

+6

,

+8

. The next shift must be

+10

. Adding

+10

to V (22) gives

22 + 10 = 32

. Modulo 26 alphabet cycle gives

32 - 26 = 6

, which corresponds to the letter F.

The third letter follows an increasing sequence of consecutive even integer positional shifts with alphabetical wrap-around.

4

Combine the derived components into the final term.

Combining the first letter (Z), the number (62), and the third letter (F) gives Z62F.

The complete term must satisfy all three sub-patterns simultaneously.

Anahtar Kavram

Alphanumeric Series Completion with Multi-Pattern Positional Shifts and Arithmetic Operations

Tahmini Süre:2m 0s

Soru 158Soru →

In a municipal department of $120$ officers, a survey was conducted regarding three operational responsibilities: Urban Planning ( $U$ ), Environmental Compliance ( $E$ ), and Public Works ( $P$ ). The survey revealed the following data:
- $65$ officers handle Urban Planning ( $U$ ).
- $50$ officers handle Environmental Compliance ( $E$ ).
- $55$ officers handle Public Works ( $P$ ).
- $5$ officers handle none of these three responsibilities.
- $45$ officers handle at least two of these responsibilities.
- $10$ officers handle all three responsibilities.
- $20$ officers handle both Urban Planning and Environmental Compliance.
- $18$ officers handle both Environmental Compliance and Public Works.

How many officers handle ONLY Urban Planning?

18

28

35

38

Cevabı ve açıklamayı göster

Cevap: 28

Cevap

The number of officers handling ONLY Urban Planning is 28.

Subtracting all overlapping regions connected to Urban Planning (

10

for Urban Planning & Environmental only,

17

for Urban Planning & Public Works only, and

10

for all three) from the total Urban Planning count (

65

) leaves

65 - 37 = 28

officers handling Urban Planning exclusively.

Adım Adım Çözüm

1

Determine the total number of officers handling at least one responsibility.

Total in at least one set =

120 - 5 = 115

.

5 officers handle none of the three tasks.

2

Identify the regions of overlapping sets using given intersection values.

Let the 3-set intersection be

g = 10

. The region for ONLY Urban Planning and Environmental Compliance is

d = 20 - 10 = 10

. The region for ONLY Environmental Compliance and Public Works is

e = 18 - 10 = 8

.

The total count for two sets includes those who also handle all three.

3

Calculate the region for ONLY Urban Planning and Public Works (

f

).

Since officers handling at least two responsibilities equals

d + e + f + g = 45

, we have

10 + 8 + f + 10 = 45 \implies f = 17

.

The sum of all two-set-only regions and the three-set region equals 45.

4

Compute the number of officers handling ONLY Urban Planning (

a

).

a = n(U) - (d + f + g) = 65 - (10 + 17 + 10) = 65 - 37 = 28

.

Subtracting all shared regions from the total Urban Planning count leaves the officers dedicated solely to Urban Planning.

Anahtar Kavram

3-Set Venn Diagram Region Decomposition using Inclusion-Exclusion Principle

Tahmini Süre:2m 30s

Soru 159Soru →

Consider the following alphabetical sequence:

C, F, I, L, \dots

Which letter completes the given series?

O

N

P

M

Cevabı ve açıklamayı göster

Cevap: O

Cevap

The letter that completes the series is O.

Each letter advances by 3 positions in forward alphabetical order: C (3) → F (6) → I (9) → L (12). Adding 3 positions to 12 gives 15, which corresponds to the letter O.

Adım Adım Çözüm

1

Determine the numerical positions of each letter in the standard alphabet.

C = 3, F = 6, I = 9, L = 12.

Translating letters to positional values simplifies pattern identification.

2

Identify the pattern of position shifts between consecutive terms.

6 - 3 = 3; 9 - 6 = 3; 12 - 9 = 3. Each term increases by +3 positions.

Finding the consistent rule enables calculating the next term.

3

Apply the rule (+3 positions) to the last given letter L (12).

12 + 3 = 15, which corresponds to the letter O.

Adding the common difference yields the next alphabetical term.

Anahtar Kavram

Alphabetical Positional Series with Constant Step Shift

Soru 160Soru →

A delivery cyclist starts from a warehouse and rides $12\text{ km}$ towards the South. He then turns left and rides $9\text{ km}$ . What is the shortest direct distance, in kilometers, between his current location and the warehouse?

Cevabı ve açıklamayı göster

Cevap: 15

Cevap

The shortest direct distance between the current location and the warehouse is

15\text{ km}

.

The straight-line displacement forms the hypotenuse of a right triangle with perpendicular sides of length

12\text{ km}

and

9\text{ km}

. Applying the Pythagorean theorem yields

\sqrt{12^2 + 9^2} = \sqrt{225} = 15\text{ km}

.

Adım Adım Çözüm

1

Determine the cardinal directions of each movement segment

First displacement is

12\text{ km}

South. Turning left while facing South directs the cyclist towards East, so the second displacement is

9\text{ km}

East.

A 90-degree left turn from South points towards East.

2

Set up the right-angled displacement triangle

The two perpendicular legs of the right triangle are

12\text{ km}

(South) and

9\text{ km}

(East).

South and East form a perpendicular angle (

90^\circ

).

3

Calculate the straight-line distance using the Pythagorean theorem

Distance

= \sqrt{12^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15\text{ km}

.

The direct distance corresponds to the hypotenuse:

c = \sqrt{a^2 + b^2}

.

Anahtar Kavram

Shortest direct distance calculation using the Pythagorean theorem

Tahmini Süre:45s

General Mental Ability

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