General Mental Ability Practice Questions — State PSC Exam — Page 6

Question 101Question →

Six journalists—Arthur, Beatrice, Cedric, Daphne, Elias, and Fiona—are seated along one side of a long rectangular press table, all facing the speaker at the front (North). Read the following seating conditions carefully:

1. Arthur is seated third from the left end of the table.
2. Cedric is seated immediately to the right of Arthur.
3. Only one person sits between Cedric and Fiona.
4. Elias sits second to the left of Cedric.
5. Beatrice is not an immediate neighbor of Elias.

Arrange the journalists in their correct seating order from the extreme left end to the extreme right end.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from left to right is Daphne, Elias, Arthur, Cedric, Beatrice, and Fiona.

By following the constraints sequentially, each seat resolves uniquely without any contradiction. Arthur's exact position anchors the arrangement, Cedric and Elias fill in relative to him, and Fiona's distance from Cedric forces her to the end. The negative constraint on Beatrice perfectly resolves the final two seats.

Step-by-Step Solution

1

Identify the total number of positions and place Arthur.

Positions: _ _ Arthur _ _ _

The table has 6 seats. The first condition explicitly places Arthur third from the left.

2

Place Cedric relative to Arthur.

Positions: _ _ Arthur Cedric _ _

The second condition states Cedric sits immediately to the right of Arthur, taking the fourth seat.

3

Place Elias relative to Cedric.

Positions: _ Elias Arthur Cedric _ _

The fourth condition states Elias is second to the left of Cedric. Since Cedric is fourth, Elias must be second.

4

Determine Fiona's position.

Positions: _ Elias Arthur Cedric _ Fiona

The third condition states only one person sits between Cedric and Fiona. This means Fiona is either in seat 2 or 6. Since Elias is already in seat 2, Fiona must take seat 6.

5

Use the negative constraint to place Beatrice.

Positions: _ Elias Arthur Cedric Beatrice Fiona

The fifth condition states Beatrice is not an immediate neighbor of Elias. The empty seats are 1 and 5. Seat 1 is next to Elias, so Beatrice must sit in seat 5.

6

Place the final person, Daphne.

Positions: Daphne Elias Arthur Cedric Beatrice Fiona

Daphne is the only remaining journalist and takes the final empty seat at the extreme left (seat 1).

Key Concept

Linear Seating Arrangement with Positional and Negative Constraints

Question 102Question →

In a survey conducted among $300$ State PSC aspirants, data was collected regarding their enrollment in preparation modules for three optional subjects: Public Administration ( $P$ ), Sociology ( $S$ ), and Geography ( $G$ ). It was found that $140$ aspirants enrolled in Public Administration, $130$ in Sociology, and $120$ in Geography. Further, $50$ aspirants enrolled in both Public Administration and Sociology, $45$ in both Sociology and Geography, and $40$ in both Public Administration and Geography. If $20$ aspirants did not enroll in any of these three subjects, how many aspirants enrolled in EXACTLY ONE optional subject?

195

120

145

165

Show answer & explanation

Answer: 195

Answer

The number of aspirants enrolled in exactly one optional subject is 195.

By applying the inclusion-exclusion principle for three overlapping sets, the number of aspirants enrolled in all three subjects is determined to be

25

. Decomposing each set into disjoint regions gives

75

candidates in Public Administration only,

60

in Sociology only, and

60

in Geography only. Summing these exclusive single-set regions yields

195

.

Step-by-Step Solution

1

Determine the total number of aspirants enrolled in at least one optional subject

Total enrolled

|P \cup S \cup G| = 300 - 20 = 280

.

Candidates not enrolled in any of the three subjects must be excluded from the universe of

300

.

2

Apply the Principle of Inclusion-Exclusion for three sets to find the three-set intersection region

|P \cap S \cap G|

|P \cup S \cup G| = |P| + |S| + |G| - (|P \cap S| + |S \cap G| + |P \cap G|) + |P \cap S \cap G| \implies 280 = 140 + 130 + 120 - (50 + 45 + 40) + |P \cap S \cap G| \implies 280 = 390 - 135 + |P \cap S \cap G| \implies |P \cap S \cap G| = 25

.

To find individual exclusive regions, the central intersection of all three sets must first be determined.

3

Calculate the count of candidates enrolled in exactly two subjects

Only

(P \cap S) = 50 - 25 = 25

; Only

(S \cap G) = 45 - 25 = 20

; Only

(P \cap G) = 40 - 25 = 15

.

Subtracting the triple intersection from pairwise intersections gives the exact counts of elements belonging strictly to two sets.

4

Calculate the count of candidates enrolled in exactly one subject for each subject and sum them up

Only

P = 140 - (25 + 25 + 15) = 75

; Only

S = 130 - (25 + 25 + 20) = 60

; Only

G = 120 - (15 + 25 + 20) = 60

. Total exactly one =

75 + 60 + 60 = 195

.

Subtracting all overlapping regions from each subject set total yields the number of candidates taking only that single subject.

Key Concept

Principle of Inclusion-Exclusion for Three Sets

Question 103Question →

A rare astronomical alignment was recorded on Thursday, May 17, 1888. According to a research institute, this specific alignment occurs exactly every 13 years. On what day of the week will the second occurrence after the original 1888 recording take place?

Sunday

Monday

Friday

Tuesday

Show answer & explanation

Answer: Sunday

Answer

Sunday

The second occurrence takes place 26 years after 1888, in the year 1914. Between May 1888 and May 1914, there are 26 years, 5 of which are leap years (1892, 1896, 1904, 1908, 1912). The year 1900 is not a leap year. This gives 26 + 5 = 31 odd days. Since 31 divided by 7 leaves a remainder of 3, the event occurs 3 days after Thursday, which is Sunday.

Step-by-Step Solution

1

Determine the target year for the second occurrence.

The interval is 13 years, so the second occurrence happens 2 × 13 = 26 years after the original recording. Target year is 1888 + 26 = 1914.

The question asks for the second occurrence, which requires adding two full intervals to the base year.

2

Calculate the total number of years and identify all leap years in the interval from May 17, 1888, to May 17, 1914.

Total years: 26. Leap years passed: 1892, 1896, 1904, 1908, 1912 (5 leap years). Note that 1900 is a century year not divisible by 400, so it is not a leap year.

To calculate the shift in the days of the week, we need the total number of normal years and leap years. Leap years add an extra odd day.

3

Calculate the total number of odd days over the 26-year period.

Total odd days = 26 + 5 = 31 odd days.

Each normal year contributes 1 odd day, and each leap year contributes an additional 1 odd day. Adding the number of leap years to the total number of years gives the total odd days.

4

Find the final day of the week by adding the remainder of odd days to the starting day.

31 divided by 7 leaves a remainder of 3. Three days after Thursday is Sunday.

The days of the week repeat every 7 days. Dividing the total odd days by 7 gives the effective shift.

Key Concept

Calculating odd days across a time interval that includes a century boundary to determine the day of the week.

Question 104Question →

Analyze the logical rule governing the given alphanumeric sequence and determine the missing term to complete the series.

Fill in the blanks below

Consider the following series:

$$C5, F12, J27, O51, , B133$$

The term that logically completes the sequence is .

Show answer & explanation

Answer

The missing term that logically completes the series is U86.

The series follows a dual pattern structure. The letter sequence shifts by increasing steps of

+3, +4, +5, +6, +7

, mapping

O

(position 15) to

U

(position 21). The numerical sequence exhibits a second-order difference pattern (

7, 15, 24, 35, 47

with underlying difference increase

+8, +9, +10, +11

), adding

35

to

51

to yield

86

. Thus, the correct combined term is U86.

Step-by-Step Solution

1

Analyze the pattern of the alphabetical component.

Alphabetical positions follow a sequence of increasing shifts:

+3, +4, +5, +6, +7

.

The alphabetical positions are

C = 3

,

F = 6

,

J = 10

, and

O = 15

. The differences between consecutive letter positions are

6 - 3 = +3

,

10 - 6 = +4

, and

15 - 10 = +5

. Continuing this progression, the next shift is

+6

, which gives

15 + 6 = 21

, corresponding to the letter

U

. Verification for the subsequent term gives position

21 + 7 = 28

, which wraps around the 26-letter alphabet to

28 - 26 = 2

, corresponding to

B

.

2

Analyze the pattern of the numerical component.

The differences between successive numerical terms form a secondary arithmetic sequence with a common difference of

+1

.

The numerical terms are

5, 12, 27, 51

. Taking the first differences between consecutive terms:

12 - 5 = 7

,

27 - 12 = 15

, and

51 - 27 = 24

. Taking the second differences:

15 - 7 = 8

and

24 - 15 = 9

. The second difference increases by

+1

at each step. Thus, the next first difference must be

24 + 10 = 34

, making the missing numerical term

51 + 35 = 86

. Verifying the final term: the next first difference is

35 + 11 = 46

(or

35 + 12 = 47

when tracking

7, 15, 24, 35, 47

with second differences

8, 9, 10, 11

), giving

86 + 47 = 133

.

3

Combine the alphabetical and numerical components.

The complete missing term is U86.

Combining the letter

U

with the number

86

yields the missing term

U86

.

Key Concept

Alphanumeric Series with Positional Shifts and Second-Order Differences

Estimated Time:2m 0s

Question 105Question →

Consider the following alphanumeric series:

A2, D6, G12, J20, \dots

Which term logically completes the series?

M30

N30

M28

L30

Show answer & explanation

Answer: $M30$

Answer

M30

The series consists of two independent rules: the alphabetical components advance by

+3

positions (

A \rightarrow D \rightarrow G \rightarrow J \rightarrow M

), and the numerical components follow a pattern of adding successive even numbers (

+4, +6, +8, +10

), leading to

20 + 10 = 30

. Combining these yields the term

M30

.

Step-by-Step Solution

1

Analyze the pattern in the letter sequence.

A (1) + 3 = D (4)

,

D (4) + 3 = G (7)

,

G (7) + 3 = J (10)

,

J (10) + 3 = M (13)

.

The letters progress forward by 3 positions in the standard alphabetical order.

2

Analyze the pattern in the numeric sequence.

2 + 4 = 6

,

6 + 6 = 12

,

12 + 8 = 20

,

20 + 10 = 30

.

The difference between consecutive numbers increases by

2

at each step (

+4, +6, +8, +10

).

3

Combine the next letter and number.

The next term is

M30

.

Combining the 13th letter

M

with the calculated number

30

completes the sequence.

Key Concept

Dual-pattern alphanumeric series progression involving constant letter shifts and increasing even number differences.

Estimated Time:45s

Question 106Question →

Which of the following terms logically completes the given alphanumeric series: $C5X, F11U, I19R, L29O, \dots$ ?

O41L

O41M

O39L

N41L

Show answer & explanation

Answer: $O41L$

Answer

The term

O41L

logically completes the given alphanumeric series.

The series follows three simultaneous patterns: the first letter advances by

+3

positions (

C \to F \to I \to L \to O

), the middle number increases by successive even integers

+6, +8, +10, +12

(

5 \to 11 \to 19 \to 29 \to 41

), and the last letter moves backward by

-3

positions (

X \to U \to R \to O \to L

). Combining these three components yields

O41L

.

Step-by-Step Solution

1

Analyze the pattern of the first letter in each term.

The sequence of first letters is

C (3), F (6), I (9), L (12)

.

The alphabetical positions increase by

+3

each step. Thus, the next letter is at position

12 + 3 = 15

, which corresponds to

O

.

2

Analyze the numerical progression in the middle of each term.

The numerical sequence is

5, 11, 19, 29

.

The consecutive differences between terms are

11 - 5 = 6

,

19 - 11 = 8

, and

29 - 19 = 10

. The difference increases by

+2

each step. The next difference is

10 + 2 = 12

, making the next number

29 + 12 = 41

.

3

Analyze the pattern of the third letter in each term.

The sequence of third letters is

X (24), U (21), R (18), O (15)

.

The alphabetical positions decrease by

-3

each step. Thus, the next letter is at position

15 - 3 = 12

, which corresponds to

L

.

4

Combine the elements to find the missing term.

Combining the results yields

O41L

.

Joining the first letter (

O

), middle number (

41

), and last letter (

L

) completes the sequence.

Key Concept

Tri-pattern Alphanumeric Series Completion

Question 107Question →

Match each logical reasoning problem involving numerical analogy, alphabetical pattern analogy, or classification in List-I with its corresponding correct output or odd element in List-II.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Analogy 6 : 222 :: 9 : ? matches 738; Analogy 14 : 210 :: 18 : ? matches 342; Letter Analogy BJH : DJF :: FLD : ? matches HLB; Odd-One-Out Classification matches (19, 441).

Each item in List-I is evaluated using multi-step logical operations: (1)

6^3+6=222

leading to

9^3+9=738

; (2)

14^2+14=210

leading to

18^2+18=342

; (3) Alphabet positional shifts (+2, 0, -2) transforming FLD into HLB; (4) The classification rule

M=(n+1)^2

which fails only for the pair

(19, 441)

.

Step-by-Step Solution

1

Analyze the pattern for Analogy 6 : 222 :: 9 : ?

Identify the operation

n^3 + n

. Since

6^3 + 6 = 222

, apply

9^3 + 9 = 729 + 9 = 738

.

Establishes cubic function relationship between antecedent and consequent terms.

2

Analyze the pattern for Analogy 14 : 210 :: 18 : ?

Identify the operation

n^2 + n

. Since

14^2 + 14 = 210

, apply

18^2 + 18 = 324 + 18 = 342

.

Establishes quadratic non-linear relationship between terms.

3

Analyze the letter shift pattern for BJH : DJF :: FLD : ?

First letter shifts

+2

position forward, second letter shifts

0

positions, third letter shifts

-2

positions backward. Applying this to FLD yields H (F+2), L (L+0), B (D-2) = HLB.

Determines positional alphabet movement vector (+2, 0, -2).

4

Evaluate the rule across number pairs in the classification set.

Pairs

(11, 144)

,

(13, 196)

, and

(17, 324)

follow

M = (n+1)^2

. The pair

(19, 441)

breaks this rule because

(19+1)^2 = 400

, not

441

.

Identifies the element that does not satisfy the common governing rule.

Key Concept

Multi-operational Number Analogy, Positional Alphabet Shift, and Rule-based Number Classification

Question 108Question →

In a given alphanumeric sequence, each term consists of a letter and a number following distinct logical patterns:

Z4, U9, Q19, N39, L79, \dots

What is the next term in this sequence?

K159

J159

K157

L159

Show answer & explanation

Answer: K159

Answer

The term that logically completes the sequence is K159.

The correct answer combines the letter obtained from a diminishing positional shift (L minus 1 position equals K) with the number calculated via double-plus-one recursion (79 multiplied by 2 plus 1 equals 159).

Step-by-Step Solution

1

Analyze the alphabetical component shift pattern

Z (26) to U (21) is -5; U (21) to Q (17) is -4; Q (17) to N (14) is -3; N (14) to L (12) is -2.

Identifying the step interval between consecutive position numbers reveals a decreasing shift pattern (-5, -4, -3, -2).

2

Determine the next letter in the series

From L (12), subtract 1: 12 - 1 = 11, which corresponds to the letter K.

Following the decreasing shift pattern (-5, -4, -3, -2, -1), the next letter position is 11.

3

Analyze the numerical component progression

4 to 9: 4 × 2 + 1 = 9; 9 to 19: 9 × 2 + 1 = 19; 19 to 39: 19 × 2 + 1 = 39; 39 to 79: 39 × 2 + 1 = 79.

Each number term is calculated by multiplying the previous term by 2 and adding 1.

4

Compute the next numerical term

79 × 2 + 1 = 158 + 1 = 159.

Applying the recursive formula gives 159 for the sixth term.

Key Concept

Alphanumeric Series Completion with Decrementing Positional Shifts and Double-Plus-One Numerical Recurrence

Question 109Question →

Match each coded string in List-I with its corresponding original word and transformation logic in List-II.

Click a left item, then click its matching right item

Show answer & explanation

Answer

RVPERN pairs with PENCIL (Consonants +2; Vowels reversed); TDIWHM pairs with GARDEN (Consonants reversed; Vowels +3); GJPUFP pairs with FLOWER (Odd positions +1; Even positions -2); BMQSDM pairs with PLANET (Halves reversed; 1st half +1, 2nd half -1).

Each coded string strictly adheres to a unique multi-step rule: RVPERN uses consonant +2 shift and vowel reverse position; TDIWHM uses consonant reverse position and vowel +3 shift; GJPUFP uses alternating odd (+1) and even (-2) positional shifts; BMQSDM uses half-word reversal combined with +1 and -1 shifts respectively.

Step-by-Step Solution

1

Analyze RVPERN using vowel and consonant operations.

Checking PENCIL: Consonants P(+2)=R, N(+2)=P, C(+2)=E, L(+2)=N; Vowels E->V (27-5=22) and I->R (27-9=18). This forms RVPERN.

Identify pattern separating vowel and consonant rules.

2

Analyze TDIWHM using opposite letters for consonants.

Checking GARDEN: Consonants G->T, R->I, D->W, N->M; Vowels A(+3)=D, E(+3)=H. This forms TDIWHM.

Verify dual-rule application based on letter type.

3

Analyze GJPUFP using positional indexing.

Checking FLOWER: Odd positions (1,3,5) F->G, O->P, E->F (+1 shift); Even positions (2,4,6) L->J, W->U, R->P (-2 shift). This forms GJPUFP.

Verify alternating positional shift pattern.

4

Analyze BMQSDM using block reversal and directional shifts.

Checking PLANET: First half 'PLA' reversed is 'ALP', shifted +1 gives 'BMQ'. Second half 'NET' reversed is 'TEN', shifted -1 gives 'SDM'. Combining gives BMQSDM.

Verify half-word reversal and split directional shifts.

Key Concept

Complex Multi-Rule Coding and Decoding (Vowel/Consonant Dual Rules, Positional Shifts, Half-Reversals)

Question 110Question →

Select the option that is related to the third number in the same way as the second number is related to the first number.

$13 : 160 :: 17 : ?$

272

320

353

576

Show answer & explanation

Answer: $320$

Answer

320

The relationship follows the dual-operation formula

(N - 1)^2 + (\text{digit sum of } N)^2

. For

13

,

(13-1)^2 + (1+3)^2 = 144 + 16 = 160

. Applying this to

17

gives

(17-1)^2 + (1+7)^2 = 16^2 + 8^2 = 256 + 64 = 320

.

Step-by-Step Solution

1

Analyze the relationship between the first pair of numbers (

13

and

160

).

Identify the multi-step pattern:

(x - 1)^2 + (\text{sum of digits of } x)^2

.

For

x = 13

, the predecessor is

13 - 1 = 12

, and

12^2 = 144

. The sum of the digits of

13

is

1 + 3 = 4

, and

4^2 = 16

. Adding these gives

144 + 16 = 160

.

2

Apply the identical multi-step rule to the third number (

x = 17

).

Find the squared predecessor and the squared digit sum for

17

.

The predecessor of

17

is

17 - 1 = 16

, and

16^2 = 256

. The sum of the digits of

17

is

1 + 7 = 8

, and

8^2 = 64

.

3

Sum the resulting values to determine the missing term.

256 + 64 = 320

.

Combining the squared predecessor and squared digit sum yields

320

.

Key Concept

Multi-Step Numerical Analogy based on Predecessor Squares and Digit-Sum Operations

Question 111Question →

Determine the next term that logically completes the following numerical sequence:

4, 7, 14, 27, 48, 79, \dots

Show answer & explanation

Answer: 122

Answer

The next term in the sequence is 122.

The sequence follows a double-difference pattern. The differences between successive terms are 3, 7, 13, 21, 31. Taking the differences of these values gives 4, 6, 8, 10, which increases by 2 each time. The next second-order difference must be 12, making the next first-order difference 31 + 12 = 43. Adding 43 to 79 gives the final result of 122.

Step-by-Step Solution

1

Calculate the first-order differences between consecutive terms

The first differences are 3, 7, 13, 21, and 31.

Identifying the rate of increase helps determine the underlying rule.

2

Calculate the second-order differences

The second differences are 4, 6, 8, and 10.

Since the first differences are not constant, analyzing second-level differences reveals higher-order patterns.

3

Extend the second-difference pattern to find the next first difference and term

Next second difference = 12, next first difference = 43, next term = 79 + 43 = 122.

The second differences form an arithmetic sequence adding 2 at each step.

Key Concept

Double-Difference Numerical Series

Question 112Question →

In a certain code language, the word 'STREAM' is written as 'TUSBFN'. How is the word 'GARDEN' written in that same code language?

HBSEFO

FZQCDM

HATEFO

HBTEFO

Show answer & explanation

Answer: HBSEFO

Answer

HBSEFO

Each letter in 'STREAM' moves forward by 1 letter in the English alphabet (

+1

shift). Applying this uniform

+1

shift to 'GARDEN' yields G→H, A→B, R→S, D→E, E→F, N→O, forming 'HBSEFO'.

Step-by-Step Solution

1

Analyze the pattern between 'STREAM' and 'TUSBFN'

S → T (+1), T → U (+1), R → S (+1), E → F (+1), A → B (+1), M → N (+1)

Identify the positional transformation applied to each letter in alphabetical order.

2

Apply the same (+1) shift rule to each letter of 'GARDEN'

G (+1) → H, A (+1) → B, R (+1) → S, D (+1) → E, E (+1) → F, N (+1) → O

Execute the confirmed pattern on the target word to obtain the final coded string.

Key Concept

Forward Letter Shifting (+1 Pattern)

Estimated Time:45s

Question 113Question →

Each of the following items presents a numerical analogy in the form $A : B :: C : X$ , where the missing term $X$ is derived using a multi-step arithmetic rule ( $n^3 - k$ , $n^3 - n$ , $n^2 + n$ , or $n^2 - n$ ). Evaluate the value of $X$ for each analogy item, and arrange the items in ascending order based on their solved value of $X$ (from smallest value to largest value).

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct ascending order based on the value of

X

is Analogy 4 (

X_4 = 156

), Analogy 3 (

X_3 = 210

), Analogy 2 (

X_2 = 504

), and Analogy 1 (

X_1 = 726

).

Solving each analogy yields

X_4 = 156

,

X_3 = 210

,

X_2 = 504

, and

X_1 = 726

. Ordering these from least to greatest places Analogy 4 first, followed by Analogy 3, Analogy 2, and Analogy 1.

Step-by-Step Solution

1

Solve for

X_1

in Analogy 1 (

7 : 340 :: 9 : X_1

)

X_1 = 726

Identify the relationship

7^3 - 3 = 340

. Consequently,

X_1 = 9^3 - 3 = 729 - 3 = 726

.

2

Solve for

X_2

in Analogy 2 (

6 : 210 :: 8 : X_2

)

X_2 = 504

Identify the relationship

6^3 - 6 = 210

. Consequently,

X_2 = 8^3 - 8 = 512 - 8 = 504

.

3

Solve for

X_3

in Analogy 3 (

12 : 156 :: 14 : X_3

)

X_3 = 210

Identify the relationship

12^2 + 12 = 156

. Consequently,

X_3 = 14^2 + 14 = 196 + 14 = 210

.

4

Solve for

X_4

in Analogy 4 (

11 : 110 :: 13 : X_4

)

X_4 = 156

Identify the relationship

11^2 - 11 = 110

. Consequently,

X_4 = 13^2 - 13 = 169 - 13 = 156

.

5

Arrange the calculated values of

X

in ascending numerical order

156 < 210 < 504 < 726

Comparing the values gives

X_4 (156) < X_3 (210) < X_2 (504) < X_1 (726)

.

Key Concept

Numerical Analogy and Exponential Pattern Recognition

Question 114Question →

Consider the following numerical sequence:

5, 14, 19, 54, 83, \dots

What is the value of the next term in this sequence?

Show answer & explanation

Answer: 202

Answer

The next term in the numerical sequence is 202.

The sequence follows the recurrence pattern

a_n = 2 a_{n-1} + (-1)^n n^2

starting with

a_1 = 5

. To find the 6th term, double the 5th term (

83 \times 2 = 166

) and add

6^2 = 36

, resulting in

166 + 36 = 202

.

Step-by-Step Solution

1

Identify the operation connecting the first two terms (

5

and

14

).

a_2 = 2 \times a_1 + 2^2 = 2(5) + 4 = 14

Establishes the initial multiplier and square term offset.

2

Determine the rule for the third, fourth, and fifth terms.

a_3 = 2(14) - 3^2 = 19

,

a_4 = 2(19) + 4^2 = 54

,

a_5 = 2(54) - 5^2 = 83

Shows an alternating addition and subtraction of consecutive squares

n^2

after doubling the previous term.

3

Apply the rule for

n=6

to calculate the missing term.

a_6 = 2(83) + 6^2 = 166 + 36 = 202

Since the 5th term subtracted

5^2

, the 6th term must add

6^2

to twice the 5th term.

Key Concept

Alternating Operational and Square Offsets in Recursive Series

Question 115Question →

Select the number that completes the given numerical analogy in the same way as the second term is related to the first term:

14 : 350 :: 18 : ?

594

486

339

522

Show answer & explanation

Answer: 594

Answer

594

The relation governing the first pair is

N : N \times (N + S(N) + 6)

, where

S(N)

represents the sum of digits of

N

. For

14

,

S(14) = 1 + 4 = 5

, giving

14 \times (14 + 5 + 6) = 14 \times 25 = 350

. Applying this exact rule to

18

yields

S(18) = 1 + 8 = 9

, and

18 \times (18 + 9 + 6) = 18 \times 33 = 594

.

Step-by-Step Solution

1

Analyze the relation between the first pair

14 : 350

Calculate the digit sum of

14

:

1 + 4 = 5

.

Identify sub-components of the multi-step operation.

2

Determine the composite multiplier rule for the first term

Add the term, its digit sum, and the constant offset

6

:

14 + 5 + 6 = 25

.

Establish the exact pattern mapping

14

to

350

via

14 \times 25 = 350

.

3

Apply the established pattern to the third term

18

Calculate the digit sum of

18

:

1 + 8 = 9

. Then compute the multiplier:

18 + 9 + 6 = 33

.

Maintain structural consistency with the original analogy.

4

Compute the final missing term

18 \times 33 = 594

.

Obtain the required missing term for the second pair.

Key Concept

Multi-step Numerical Analogy based on Positional Digit Operations and Constant Shift

Question 116Question →

Based on the family relations given below, match each person listed in List I with their correct relationship to R listed in List II:

• P is the father of Q.
• Q is the mother of R.
• S (female) is the sister of R.
• T (male) is married to S.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Person P matches with Maternal grandfather of R; Person Q matches with Mother of R; Person S matches with Sister of R; Person T matches with Brother-in-law of R.

Matching each individual step-by-step from the given narrative confirms: Person P is the father of R's mother (Maternal grandfather), Person Q is R's mother, Person S is R's female sibling (Sister), and Person T is the husband of R's sister (Brother-in-law).

Step-by-Step Solution

1

Identify the relation of Q to R

Q is the mother of R.

The premise explicitly states that Q is the mother of R.

2

Identify the relation of P to R

P is the maternal grandfather of R.

P is the father of Q (R's mother). The father of one's mother is the maternal grandfather.

3

Identify the relation of S to R

S is the sister of R.

The premise explicitly specifies that S (female) is the sister of R.

4

Identify the relation of T to R

T is the brother-in-law of R.

T (male) is married to S (R's sister). A sister's husband is a brother-in-law.

Key Concept

Direct Kinship and Extended Blood Relations

Question 117Question →

Pointing to a man in a photograph, a woman says, "His mother is the only daughter of my mother." How is the man in the photograph related to the woman?

Son

Brother

Nephew

Father

Show answer & explanation

Answer: Son

Answer

The man in the photograph is the woman's son.

Since the speaker is explicitly identified as a woman, her mother's only daughter must be the woman herself. Consequently, the statement 'His mother is the only daughter of my mother' translates to 'His mother is me', proving the man is her son.

Step-by-Step Solution

1

Analyze the phrase 'the only daughter of my mother'.

Since the speaker is specified as a woman, her mother's only daughter is the woman herself.

A female speaker referring to her mother's only daughter must be referring to herself.

2

Substitute the result into the main statement.

The statement becomes 'His mother is the woman herself'.

Simplifying the self-referential phrase clarifies the direct relationship.

3

Deduce the man's relation to the woman.

Since the woman is his mother, the man is her son.

Direct conclusion based on parent-child relationship.

Key Concept

Kinship deduction using self-referential introductory statements.

Estimated Time:45s

Question 118Question →

Match each original word in List-I with its correctly coded representation in List-II based on its specific alphabetical coding rule.

Click a left item, then click its matching right item

Show answer & explanation

Answer

'MINT' matches with 'NJOU' (+1 shift), 'COLD' matches with 'BNKC' (-1 shift), 'HIGH' matches with 'STRS' (reverse alphabetical pair), and 'PARK' matches with 'KRAP' (letter reversal).

Each word aligns with its precise logical transformation: 'MINT' undergoes a

+1

position shift to become 'NJOU', 'COLD' undergoes a

-1

position shift to become 'BNKC', 'HIGH' uses reverse alphabetical pairing to become 'STRS', and 'PARK' reverses its letter order to become 'KRAP'.

Step-by-Step Solution

1

Determine the coding logic for 'MINT'

Shifting each letter forward by 1 position yields M+1=N, I+1=J, N+1=O, T+1=U, forming 'NJOU'.

Identify the forward position shift rule.

2

Determine the coding logic for 'COLD'

Shifting each letter backward by 1 position yields C-1=B, O-1=N, L-1=K, D-1=C, forming 'BNKC'.

Identify the backward position shift rule.

3

Determine the coding logic for 'HIGH'

Replacing each letter with its opposite position in the alphabet (

A \leftrightarrow Z, H \leftrightarrow S, I \leftrightarrow R, G \leftrightarrow T

) forms 'STRS'.

Identify reverse alphabetical indexing rule.

4

Determine the coding logic for 'PARK'

Reversing the left-to-right letter sequence of 'PARK' forms 'KRAP'.

Identify string reversal logic.

Key Concept

Basic letter shift rules, reverse alphabetical pairs, and string reversal in Coding-Decoding.

Question 119Question →

Which of the following terms logically completes the given alphanumeric series:

E3V, H7S, K15P, N31M, \dots

?

Q63J

R63I

Q63K

P63J

Show answer & explanation

Answer: $Q63J$

Answer

Q63J

The correct term is obtained by shifting the first letter forward by 3 positions (

N \rightarrow Q

), applying the numerical rule

n_{k+1} = 2n_k + 1

(

31 \rightarrow 63

), and shifting the last letter backward by 3 positions (

M \rightarrow J

).

Step-by-Step Solution

1

Analyze the pattern of the first letter in each term.

The sequence of first letters is

E (5), H (8), K (11), N (14)

. The pattern adds

3

to the alphabetical position each time. The next letter is

14 + 3 = 17

, which corresponds to

Q

.

To establish the progressive forward positional shift rule.

2

Analyze the numerical pattern in the middle of each term.

The numerical sequence is

3, 7, 15, 31

. Each term is obtained by multiplying the previous term by

2

and adding

1

(

3 \times 2 + 1 = 7

;

7 \times 2 + 1 = 15

;

15 \times 2 + 1 = 31

). The next number is

31 \times 2 + 1 = 63

.

To identify the arithmetic progression operating on the numeric component.

3

Analyze the pattern of the last letter in each term.

The sequence of last letters is

V (22), S (19), P (16), M (13)

. The pattern subtracts

3

from the alphabetical position each time. The next letter is

13 - 3 = 10

, which corresponds to

J

.

To establish the progressive reverse positional shift rule.

4

Combine the results from all three components.

Combining

Q

,

63

, and

J

yields the next term

Q63J

.

To form the complete missing term.

Key Concept

Alphanumeric Series Completion with Simultaneous Positional Shifts and Operation Patterns

Question 120Question →

Complete the given alphanumeric series by identifying the missing term that logically follows the established rules.

Fill in the blanks below

In the series

A4Z, C9X, F16U, J25Q, \dots

, the missing fifth term is .

Show answer & explanation

Answer

The correct missing term is O36L.

The term O36L correctly completes the series because the first letter advances by increasing forward steps (+2, +3, +4, +5 to reach O), the middle number follows the sequence of consecutive squares (

2^2, 3^2, 4^2, 5^2, 6^2 = 36

), and the last letter retreats by increasing backward steps (-2, -3, -4, -5 to reach L).

Step-by-Step Solution

1

Analyze the first letter pattern

The positional values in the forward alphabetical order are:

A(1) \xrightarrow{+2} C(3) \xrightarrow{+3} F(6) \xrightarrow{+4} J(10)

. The next increment must be

+5

, giving position

10 + 5 = 15

, which corresponds to the letter

O

.

The forward position shift increases by

+1

at each step.

2

Analyze the numerical middle term pattern

The numerical terms are perfect squares of consecutive integers starting from

2

:

2^2 = 4

,

3^2 = 9

,

4^2 = 16

,

5^2 = 25

. The next term is

6^2 = 36

.

The numerical sequence represents consecutive integer squares (

n^2

for

n = 2, 3, 4, 5, 6

)....

3

Analyze the last letter pattern

The positional values in reverse alphabetical order decrease as follows:

Z(26) \xrightarrow{-2} X(24) \xrightarrow{-3} U(21) \xrightarrow{-4} Q(17)

. The next decrement must be

-5

, giving position

17 - 5 = 12

, which corresponds to the letter

L

.

The backward position shift increases by

-1

at each step.

4

Combine the components

Combining the calculated parts yields the complete term:

O + 36 + L = O36L

.

Joining the first letter, middle number, and last letter produces the complete missing term.

Key Concept

Alphanumeric Series with Multi-layered Incremental Positional Shifts and Perfect Squares

Estimated Time:1m 30s

General Mental Ability

Answer

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