General Mental Ability Practice Questions — State PSC Exam — Page 9

Question 161Question →

Given the following coded blood relationship definitions:
- $A \star B$ means ' $A$ is the mother of $B$ '
- $A \sharp B$ means ' $A$ is the brother of $B$ '
- $A \dagger B$ means ' $A$ is the daughter of $B$ '
- $A \Delta B$ means ' $A$ is the father of $B$ '

Based on the expression $K \star L \sharp M \dagger N \Delta P$ , how is $P$ related to $K$ ?

Son

Daughter

Mother

Cannot be determined

Show answer & explanation

Answer: Cannot be determined

Answer

Cannot be determined (the person is either the son or the daughter)

Deconstructing the relation expression shows that

K

(mother) and

N

(father) are married parents of

L

,

M

, and

P

. Because no operator defines whether

P

is male or female,

P

could be either a son or a daughter of

K

. Therefore, the exact relation cannot be determined uniquely.

Step-by-Step Solution

1

Decode the first part of the expression:

K \star L \sharp M

K

is the mother of

L

, and

L

is the brother of

M

. Therefore,

K

is the mother of both

L

and

M

.

Siblings share the same parents.

2

Decode the next part:

M \dagger N

M

is the daughter of

N

. Since

K

is already established as the mother of

M

,

N

must be the father of

M

(and husband of

K

).

A child has one male parent (father) and one female parent (mother).

3

Decode the final part:

N \Delta P

N

is the father of

P

. Since

N

and

K

are the parents of

L

and

M

,

P

is also a child of

K

and

N

.

Children of the same father belong to the same sibling group.

4

Determine the gender of

P

The operator

\Delta

indicates that

N

is the father of

P

, but gives no information regarding

P

's gender.

P

can be male or female.

Gender must be explicitly stated and cannot be assumed.

Key Concept

Gender ambiguity in coded blood relations

Estimated Time:1m 15s

Question 162Question →

A field researcher starting at a base station walks $15\text{ km}$ towards the North. He then turns $135^\circ$ clockwise and walks $8\sqrt{2}\text{ km}$ . Next, he turns $90^\circ$ counter-clockwise and walks $7\sqrt{2}\text{ km}$ . From this location, he turns West and walks $3\text{ km}$ , and finally turns South and walks $9\text{ km}$ to reach an observation post. What is the shortest straight-line distance (in km) between the observation post and the base station?

Show answer & explanation

Answer: 13

Answer

The shortest straight-line distance between the observation post and the base station is

13\text{ km}

.

Resolving each directional segment into horizontal and vertical components gives a net final coordinate of

(12, 5)

relative to the starting origin

(0, 0)

. Applying the Pythagorean theorem

\sqrt{12^2 + 5^2} = \sqrt{169} = 13\text{ km}

yields the exact straight-line distance.

Step-by-Step Solution

1

Represent the trajectory using 2D coordinate vectors starting from origin (0, 0).

Initial position = (0, 0). After moving 15 km North, position = (0, 15).

North movement aligns with the positive y-axis.

2

Decompose the 135-degree clockwise turn vector (South-East displacement).

Displacement is (+8, -8), placing the researcher at (8, 7).

A 135-degree clockwise turn from North faces South-East (45 degrees below positive x-axis).

3

Decompose the 90-degree counter-clockwise turn vector (North-East displacement).

Displacement is (+7, +7), placing the researcher at (15, 14).

A 90-degree counter-clockwise turn from South-East faces North-East (45 degrees above positive x-axis).

4

Apply cardinal direction adjustments for West and South movements.

Moving 3 km West and 9 km South gives final coordinates (12, 5).

West subtracts from x-coordinate, and South subtracts from y-coordinate.

5

Calculate net displacement using Pythagorean theorem.

Distance = sqrt(12^2 + 5^2) = 13 km.

The direct line between (0, 0) and (12, 5) forms a right-angled triangle with sides 12 and 5.

Key Concept

Vector resolution of cardinal and angular displacements using Cartesian coordinates and the Pythagorean theorem

Estimated Time:3m 0s

Question 163Question →

In a certain code language, the word RESOLUTE is written as KHJRQXIH. Based on the exact same transformation logic, how is the word DYNAMICS written in that code language?

YBODPLZV

FBPDOLEV

WBMDNLXV

GDQBPTFJ

Show answer & explanation

Answer: YBODPLZV

Answer

The coded representation for DYNAMICS is YBODPLZV.

The code follows a dual position-dependent rule: odd-numbered positions are converted to their reverse alphabetical letter (

A=1 \leftrightarrow Z=26

) and then shifted forward by 2 positions, whereas even-numbered positions are shifted forward by 3 positions. Applying this systematically to DYNAMICS yields YBODPLZV.

Step-by-Step Solution

1

Analyze the transformation rule in RESOLUTE -> KHJRQXIH by indexing positions 1 to 8

Letters at odd positions (1, 3, 5, 7) undergo reverse alphabetical transformation (

A \leftrightarrow Z

) followed by a forward shift of

+2

. Letters at even positions (2, 4, 6, 8) undergo a standard forward shift of

+3

.

Deconstructing position-dependent rules is necessary to establish the coding algorithm.

2

Apply the odd-position transformation (Reverse Letter + 2) to DYNAMICS

1st letter D (4) -> Reverse W (23) + 2 = Y; 3rd letter N (14) -> Reverse M (13) + 2 = O; 5th letter M (13) -> Reverse N (14) + 2 = P; 7th letter C (3) -> Reverse X (24) + 2 = Z.

Odd positions follow reverse alphabetical indexing with a shift offset.

3

Apply the even-position transformation (Forward Shift + 3) to DYNAMICS

2nd letter Y (25) + 3 = B; 4th letter A (1) + 3 = D; 6th letter I (9) + 3 = L; 8th letter S (19) + 3 = V.

Even positions advance by 3 alphabetical steps.

4

Combine the resulting transformed letters in sequence

Pos 1 to 8: Y - B - O - D - P - L - Z - V.

Assembling the position results forms the complete final coded word YBODPLZV.

Key Concept

Positional parity coding with reverse alphabetical indexing and incremental shifts

Estimated Time:1m 50s

Question 164Question →

At sunrise, an environmental officer stands facing her own shadow. She then executes the following sequence of movements:
1. She turns $135^\circ$ anti-clockwise and walks $10\sqrt{2}\text{ m}$ .
2. She turns $90^\circ$ to her right and walks $6\sqrt{2}\text{ m}$ .
3. She turns $135^\circ$ to her left and walks $15\text{ m}$ .
4. She turns $135^\circ$ to her left again and walks $7\sqrt{2}\text{ m}$ .

What is her shortest direct distance from the starting point, and in which direction is she positioned relative to her starting point?

15\text{ m}

, North-East

15\text{ m}

, South-East

25\text{ m}

, North-East

21\text{ m}

, North-West

Show answer & explanation

Answer: $15\text{ m}$ , North-East

Answer

15\text{ m}

in the North-East direction

At sunrise, a person facing her shadow faces West. Executing the four angular turns results in successive vectors:

(10, 10)

North-East,

(6, -6)

South-East,

(0, 15)

North, and

(-7, -7)

South-West. Summing these vector components gives a net East-West displacement of

X = 9\text{ m}

East and a net North-South displacement of

Y = 12\text{ m}

North. Using the Pythagorean theorem, the direct distance is

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

in the North-East quadrant.

Step-by-Step Solution

1

Determine initial facing direction

Facing West (

180^\circ

)

At sunrise, the Sun is in the East, so shadows fall toward the West. Facing her own shadow means she initially faces West.

2

Calculate vector displacement for Movement 1

Direction: North-East (

45^\circ

), Vector:

(+10, +10)

From West (

180^\circ

), turning

135^\circ

anti-clockwise gives

180^\circ - 135^\circ = 45^\circ

(North-East). Displacement

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

.

3

Calculate vector displacement for Movement 2

Direction: South-East (

315^\circ

), Vector:

(+6, -6)

From North-East (

45^\circ

), turning

90^\circ

right (clockwise) gives

45^\circ - 90^\circ = -45^\circ = 315^\circ

(South-East). Displacement

= (6\sqrt{2}\cos 315^\circ, 6\sqrt{2}\sin 315^\circ) = (6, -6)

.

4

Calculate vector displacement for Movement 3

Direction: North (

90^\circ

), Vector:

(0, +15)

From South-East (

-45^\circ

), turning

135^\circ

left (anti-clockwise) gives

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

(North). Displacement

= (0, 15)

.

5

Calculate vector displacement for Movement 4

Direction: South-West (

225^\circ

), Vector:

(-7, -7)

From North (

90^\circ

), turning

135^\circ

left (anti-clockwise) gives

90^\circ + 135^\circ = 225^\circ

(South-West). Displacement

= (7\sqrt{2}\cos 225^\circ, 7\sqrt{2}\sin 225^\circ) = (-7, -7)

.

6

Sum total net displacement

(X, Y)

and find direct distance and final cardinal direction

X = 9\text{ m}

East,

Y = 12\text{ m}

North; Distance

= 15\text{ m}

, Direction = North-East

Total East displacement

X = 10 + 6 + 0 - 7 = 9\text{ m}

. Total North displacement

Y = 10 - 6 + 15 - 7 = 12\text{ m}

. Direct distance

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

. Since both

X > 0

and

Y > 0

, the final direction relative to the start is North-East.

Key Concept

Direction and Distance Test - Vector Decomposition & Shadow Orientation

Estimated Time:3m 0s

Question 165Question →

Which of the following terms logically replaces the question mark (?) to complete the given alphanumeric series?

P3C, \quad R7F, \quad ?, \quad V27L, \quad X43O

T15I

S15I

T13I

T15H

Show answer & explanation

Answer: T15I

Answer

T15I

The correct term is obtained by independently evaluating the three sub-series: first letters advance by

+2

(

P, R, T, V, X

), central numbers increment by expanding step differences of

+4, +8, +12, +16

(

3, 7, 15, 27, 43

), and third letters advance by

+3

(

C, F, I, L, O

). Unifying these components produces

T15I

.

Step-by-Step Solution

1

Analyze the pattern of the first letter in each term

The first letters follow an increasing positional shift of

+2

:

P(16) \xrightarrow{+2} R(18) \xrightarrow{+2} T(20) \xrightarrow{+2} V(22) \xrightarrow{+2} X(24)

. Thus, the missing first letter is

T

.

Tracking alphabet positional values reveals a constant linear addition of 2 units.

2

Analyze the pattern of the central numerical values

The differences between consecutive numbers form a sequence of multiples of

4

:

7 - 3 = 4

, so the next difference is

4 + 4 = 8

, giving

7 + 8 = 15

. Verifying subsequent terms:

15 + 12 = 27

and

27 + 16 = 43

. Thus, the missing number is

15

.

The number sequence follows an increasing double-difference pattern where each term's increment grows by

+4

.

3

Analyze the pattern of the third letter in each term

The third letters follow an increasing positional shift of

+3

:

C(3) \xrightarrow{+3} F(6) \xrightarrow{+3} I(9) \xrightarrow{+3} L(12) \xrightarrow{+3} O(15)

. Thus, the missing third letter is

I

.

Tracking alphabet positional values reveals a constant shift of 3 steps forward.

4

Combine the results of all three components

Combining the first letter

T

, middle number

15

, and third letter

I

yields the complete term

T15I

.

Each element operates independently according to its own sub-rule.

Key Concept

Alphanumeric Series Completion with Multi-Pattern Positional Shifts

Estimated Time:1m 15s

Question 166Question →

In a family consisting of five members— $A, B, C, D,$ and $E$ — $A$ is the father of $B$ , $C$ is the mother of $D$ , $B$ and $D$ are siblings, and $E$ is the brother of $A$ . Based on the given information, how is $D$ related to $E$ ?

Nephew

Niece

Cousin

Cannot be determined

Show answer & explanation

Answer: Cannot be determined

Answer

The relationship cannot be determined because the gender of

D

is not explicitly specified.

The option stating that the relationship cannot be determined is correct because

D

is the child of

E

's brother

A

. While

E

is definitely the uncle of

D

,

D

can be either a nephew or a niece depending on

D

's gender, which is not provided.

Step-by-Step Solution

1

Analyze parentage and generation of

A

,

B

,

C

, and

D

.

A

is the father of

B

,

C

is the mother of

D

, and

B

and

D

are siblings. Thus,

A

and

C

are married, and

D

is a child of

A

and

C

.

Establishing the parents of

D

determines

D

's position in the family tree relative to

A

.

2

Determine the relationship between

E

and

A

's children.

E

is the brother of

A

. Therefore,

E

is the paternal uncle of both

B

and

D

.

The brother of one's father is one's paternal uncle.

3

Determine the gender of

D

to find

D

's specific relationship to uncle

E

.

No statement defines whether

D

is male or female.

D

could be either a nephew (male) or a niece (female) to

E

.

In blood relations, gender cannot be assumed without explicit confirmation.

Key Concept

Gender Ambiguity in Kinship Puzzles

Estimated Time:1m 15s

Question 167Question →

In a state administration academy, a cohort of $150$ officer trainees completed specialized skill modules in Artificial Intelligence ( $A$ ), Blockchain Technology ( $B$ ), and Cyber Security ( $C$ ). Data from the academy administration indicates:
- $75$ trainees enrolled in Artificial Intelligence ( $A$ )
- $65$ trainees enrolled in Blockchain Technology ( $B$ )
- $60$ trainees enrolled in Cyber Security ( $C$ )
- $30$ trainees enrolled in both Artificial Intelligence and Blockchain Technology
- $25$ trainees enrolled in both Blockchain Technology and Cyber Security
- $20$ trainees enrolled in both Artificial Intelligence and Cyber Security
- $10$ trainees enrolled in all three modules

Based on the provided data, which of the following statements regarding the trainee enrollment are correct?

Select all that apply

The total number of trainees enrolled in exactly one training module is

80

.

The total number of trainees enrolled in exactly two training modules is

75

.

The total number of trainees enrolled in at least two training modules is

55

.

The total number of trainees enrolled in none of the three training modules is

25

.

Show answer & explanation

Answer: The total number of trainees enrolled in exactly one training module is $80$ .; The total number of trainees enrolled in at least two training modules is $55$ .

Answer

The statements asserting that

80

trainees are enrolled in exactly one training module and that

55

trainees are enrolled in at least two training modules are correct.

The correct evaluation shows that exactly one module enrollment totals

35 + 20 + 25 = 80

, and at least two modules enrollment totals

45 + 10 = 55

.

Step-by-Step Solution

1

Identify the region for trainees taking all three modules.

n(A \cap B \cap C) = 10

.

This fundamental triple intersection value must be subtracted from pairwise intersections to isolate dual-module regions.

2

Calculate trainees enrolled in exactly two modules.

Only

A \text{ and } B = 30 - 10 = 20

; Only

B \text{ and } C = 25 - 10 = 15

; Only

A \text{ and } C = 20 - 10 = 10

. Total taking exactly two modules =

20 + 15 + 10 = 45

.

Subtracting the triple intersection isolates individuals taking exclusively two subjects.

3

Calculate trainees enrolled in exactly one module.

Only

A = 75 - (20 + 10 + 10) = 35

; Only

B = 65 - (20 + 15 + 10) = 20

; Only

C = 60 - (10 + 15 + 10) = 25

. Total taking exactly one module =

35 + 20 + 25 = 80

.

Subtracting dual and triple overlaps from total single set numbers yields single-module counts.

4

Determine total trainees taking at least one module and trainees taking none.

Total taking at least one module

= 80 \text{ (single)} + 45 \text{ (double)} + 10 \text{ (triple)} = 135

. Trainees taking none

= 150 - 135 = 15

.

Applying set summation gives total enrolled trainees, from which the non-enrolled count is derived.

Key Concept

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

Estimated Time:2m 0s

Question 168Question →

Based on the family relationships described below, match each person in List I with their correct relationship to $A$ in List II:

- $A$ and $D$ are a married couple, where $A$ is male.
- $B$ and $C$ are the children of $A$ and $D$ , where $B$ is male and $C$ is female.
- $E$ is the son of $C$ .
- $F$ is the daughter of $B$ .

Click a left item, then click its matching right item

Show answer & explanation

Answer

B corresponds to Son of A; D corresponds to Wife of A; E corresponds to Grandson of A; and F corresponds to Granddaughter of A.

Each member is mapped according to explicit generation depth and gender: D is the female spouse (Wife of A), B is the male child (Son of A), E is the child of daughter C (Grandson of A), and F is the female child of son B (Granddaughter of A).

Step-by-Step Solution

1

Determine the relationship between A and D

Since A and D are married and A is male, D is female and is the Wife of A.

Marriage establishes a spouse relationship between A and D.

2

Determine the relationship of B to A

B is a male child of A and D, so B is the Son of A.

Direct male offspring of a parent is a son.

3

Determine the relationship of E to A

C is the female child (daughter) of A, and E is the male child (son) of C. Thus, E is the Grandson of A.

A child's child represents the grand-generation, specifically maternal grandson here.

4

Determine the relationship of F to A

B is the son of A, and F is the female child (daughter) of B. Thus, F is the Granddaughter of A.

A son's daughter is a paternal granddaughter.

Key Concept

Multi-generational Family Tree Relationship Deduction

Question 169Question →

In a family of seven members spanning three generations— $P, Q, R, S, T, U,$ and $V$ —there are two married couples. $P$ is the mother-in-law of $T$ . $R$ is the unmarried paternal uncle of $V$ . $Q$ is the father of $R$ . $U$ is the sister of $V$ , and $S$ is the husband of $T$ . Based on this information, how is $V$ related to $P$ ?

Grandson

Granddaughter

Cannot be determined

Son

Show answer & explanation

Answer: Cannot be determined

Answer

Cannot be determined

Tracing the generations reveals that

P

is the mother of

S

, and

S

is the father of

V

. This establishes

V

as the grandchild of

P

. However, because the text only states '

U

is the sister of

V

', we know

U

's gender (female), but

V

's gender remains unknown. Hence, whether

V

is a grandson or granddaughter cannot be definitively determined.

Step-by-Step Solution

1

Analyze the relationship between

S, T,

and

P

.

S

is the husband of

T

, making

T

female and

S

male. Since

P

is the mother-in-law of

T

,

P

is the mother of

S

.

Mother-in-law of a wife is her husband's mother.

2

Determine the lineage of

R, Q,

and

V

.

R

is the unmarried paternal uncle of

V

. Paternal uncle means father's brother. Therefore,

R

is the brother of

V

's father (

S

).

Q

is the father of

R

(and thus also the father of

S

, making

P

and

Q

the grandparent couple).

Paternal uncle shares the same father and mother as the child's father.

3

Identify the parentage and generation of

U

and

V

.

S

and

T

are the parents of

U

and

V

.

U

is the sister of

V

, placing

V

in the third generation as the child of

S

(and grandchild of

P

and

Q

).

Children of

S

are the grandchildren of

S

's mother,

P

.

4

Evaluate the gender of

V

to answer the question.

U

is female (sister of

V

), but no information defines whether

V

is male or female.

V

can be either a grandson or a granddaughter to

P

.

Gender cannot be assumed without explicit relationship statements.

Key Concept

Gender Ambiguity in Blood Relations

Question 170Question →

In a certain coding system, vowels are replaced by their reverse alphabetical position letters ( $A \leftrightarrow Z$ , $E \leftrightarrow V$ , $I \leftrightarrow R$ , $O \leftrightarrow L$ , $U \leftrightarrow F$ ). Consonants appearing at odd-numbered position indices (1st, 3rd, 5th, etc.) are shifted forward by $3$ positions in the alphabet ( $+3$ ), while consonants appearing at even-numbered position indices (2nd, 4th, 6th, etc.) are shifted backward by $2$ positions ( $-2$ ).

For example, under this system, the word BASKET is coded as EZVIVR.

What is the coded representation for the word HARVEST?

Show answer & explanation

Answer: KZUTVQW; kzutvqw

Answer

KZUTVQW

Transforming each letter of HARVEST according to its position and type yields: Position 1 (H, odd-index consonant)

\rightarrow

H

+ 3 = \mathbf{K}

; Position 2 (A, vowel)

\rightarrow

reverse of A

= \mathbf{Z}

; Position 3 (R, odd-index consonant)

\rightarrow

R

+ 3 = \mathbf{U}

; Position 4 (V, even-index consonant)

\rightarrow

V

- 2 = \mathbf{T}

; Position 5 (E, vowel)

\rightarrow

reverse of E

= \mathbf{V}

; Position 6 (S, even-index consonant)

\rightarrow

S

- 2 = \mathbf{Q}

; Position 7 (T, odd-index consonant)

\rightarrow

T

+ 3 = \mathbf{W}

. Concatenating these transformed letters produces KZUTVQW.

Step-by-Step Solution

1

Analyze the position index (1 to 7), letter type (vowel or consonant), and index parity (odd or even) for each letter in HARVEST.

H (1st, odd consonant), A (2nd, vowel), R (3rd, odd consonant), V (4th, even consonant), E (5th, vowel), S (6th, even consonant), T (7th, odd consonant).

Establishing individual letter rules based on position and character type is required before transformation.

2

Apply

+3

shift to odd-positioned consonants (H, R, T).

H (8) + 3 = 11 (K); R (18) + 3 = 21 (U); T (20) + 3 = 23 (W).

Consonants at positions 1, 3, and 7 move forward by 3 letters in the alphabet.

3

Apply reverse alphabetical indexing to vowels (A, E).

A (1st letter) becomes Z (26th letter); E (5th letter) becomes V (22nd letter).

Vowels map to their opposite position pairs (

27 - \text{position}

).$

4

Apply

-2

shift to even-positioned consonants (V, S).

V (22) - 2 = 20 (T); S (19) - 2 = 17 (Q).

Consonants at positions 4 and 6 move backward by 2 letters in the alphabet.

5

Combine the transformed letters sequentially from positions 1 through 7.

K + Z + U + T + V + Q + W = KZUTVQW.

Assembling the converted characters in original sequence yields the final coded string.

Key Concept

Positional Parity Shift and Vowel Reverse Alphabetical Encoding

Estimated Time:2m 0s

Question 171Question →

Based on the family relationships described below, match each person in List I with their correct relationship to $F$ in List II:

Narrative:
In a family of seven members— $A, B, C, D, E, F,$ and $G$ —spanning three generations, there are exactly two married couples.
- $A$ is the paternal grandfather of $G$ , and $B$ is the spouse of $A$ .
- $D$ is an unmarried female and the only sister of $C$ .
- $E$ is the sister-in-law of $D$ and the mother of $F$ .
- $C$ is the father of two children, $F$ (a male) and $G$ .

Match the members in List I with their corresponding relationships in List II:

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are:

B

matches with Paternal grandmother,

D

matches with Paternal aunt,

E

matches with Mother, and

G

matches with Sister.

By analyzing the three-generation structure: Generation 1 consists of the couple

A

(male, paternal grandfather) and

B

(female, paternal grandmother). Generation 2 consists of

C

(father), his wife

E

(mother), and

C

's unmarried sister

D

(paternal aunt). Generation 3 consists of

F

(male) and

G

(female, sister). Thus,

B

is the paternal grandmother,

D

is the paternal aunt,

E

is the mother, and

G

is the sister.

Step-by-Step Solution

1

Determine the first-generation members and married couple.

A

is the paternal grandfather of

G

(and

F

).

B

is married to

A

. Thus, Generation 1 consists of

A

(male) and

B

(female), who are the paternal grandparents of

F

and

G

.

A

is explicitly named as paternal grandfather, establishing

A

and

B

as the top generation.

2

Analyze Generation 2 members and sibling relationships.

C

is the father of

F

and

G

, so

C

is a son of

A

and

B

.

D

is the only sister of

C

, making

D

an unmarried female in Generation 2.

Since

C

is the father, his sister

D

is the father's sister, which means

D

is the paternal aunt of

F

.

3

Identify the remaining Generation 2 member and married couple.

E

is the sister-in-law of

D

and mother of

F

. Since

C

is

F

's father,

C

and

E

form the second married couple.

E

is married to

C

, making

E

the mother of

F

and

G

.

4

Establish Generation 3 relationships.

F

is a male child of

C

and

E

.

G

is the second child of

C

and

E

, making

G

the sister of

F

.

C

has two children (

F

and

G

). Since

F

is male and

G

is the other child,

G

is the female sibling (sister) of

F

.

Key Concept

Deducing multi-generational family structures and identifying kinship relations based on explicit gender and lineage constraints.

Question 172Question →

Consider the following alphanumeric sequence:

C3Z, E7Y, H16V, M35Q, T74J, \dots

What is the next term in this sequence?

E153A

E153B

F153A

E154A

Show answer & explanation

Answer: $E153A$

Answer

The next term in the sequence is

E153A

.

The term

E153A

is derived by combining three distinct concurrent rules: adding consecutive prime numbers (+2, +3, +5, +7, +11) to the first letter's position, applying the operations

\times 2 + 1, \times 2 + 2, \dots

to the numeric value, and subtracting consecutive odd numbers (-1, -3, -5, -7, -9) from the last letter's position.

Step-by-Step Solution

1

Analyze the pattern of the first letter in each term

The positional values of the first letters are

C=3, E=5, H=8, M=13, T=20

. The differences between consecutive terms are

+2, +3, +5, +7

. These differences are prime numbers. The next prime number to add is

+11

.

T(20) + 11 = 31

. Subtracting 26 for alphabetical wraparound gives

31 - 26 = 5

, which corresponds to the letter

E

.

To establish the rule governing the first component of each term.

2

Analyze the numerical pattern in the middle of each term

The numerical sequence is

3, 7, 16, 35, 74

. The recurrence relation is

\text{Term}_{k+1} = \text{Term}_k \times 2 + k

. Specifically:

3 \times 2 + 1 = 7

,

7 \times 2 + 2 = 16

,

16 \times 2 + 3 = 35

,

35 \times 2 + 4 = 74

. The next term is

74 \times 2 + 5 = 148 + 5 = 153

.

To identify the algebraic multiplier and incremental addition rule of the numeric component.

3

Analyze the pattern of the second letter in each term

The positional values of the second letters are

Z=26, Y=25, V=22, Q=17, J=10

. The differences between consecutive terms are

-1, -3, -5, -7

. These subtractions follow consecutive odd numbers. The next odd number to subtract is

-9

.

J(10) - 9 = 1

, which corresponds to the letter

A

.

To determine the positional shift pattern for the final letter element.

4

Combine the results from all three components

Combining the first letter (

E

), the middle number (

153

), and the second letter (

A

) yields

E153A

.

To form the complete missing term of the alphanumeric sequence.

Key Concept

Alphanumeric Series Completion with Interdependent Prime, Odd, and Linear Operations

Question 173Question →

Consider the following numerical series: $4, 7, 12, 19, 28, \dots$ . What is the next number in this series?

Show answer & explanation

Answer: 39

Answer

The next number in the series is

39

.

The difference between consecutive terms increases by 2 each time (

+3, +5, +7, +9

). The next difference to add is

+11

, yielding

28 + 11 = 39

.

Step-by-Step Solution

1

Calculate the difference between each pair of consecutive terms.

The differences are

3, 5, 7, 9

.

Identifying the first-order difference sequence reveals the pattern of progression.

2

Find the next value in the difference sequence.

The next odd number after

9

is

11

.

The pattern of differences consists of consecutive prime/odd increments (specifically, odd numbers

+2

each step).

3

Add the calculated difference to the final given term of the series.

28 + 11 = 39

Applying the pattern to find the subsequent term.

Key Concept

Number series completion using a sequence of increasing odd differences.

Question 174Question →

Consider the following alphanumeric series:
$Z1A, X2C, V6E, T24G, R120I, \dots$

What is the next term in this series?

P720K

Q720K

P720J

P144K

Show answer & explanation

Answer: P720K

Answer

The correct next term is P720K.

The term P720K correctly combines all three independent patterns: the first letter decreases by 2 positional steps in the alphabet (Z -> X -> V -> T -> R -> P), the central numerical term multiplies by increasing integers (

1 \times 2

,

2 \times 3

,

6 \times 4

,

24 \times 5

,

120 \times 6 = 720

), and the last letter increases by 2 positional steps (A -> C -> E -> G -> I -> K).

Step-by-Step Solution

1

Analyze the first letter sequence

Alphabetical positions:

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

. The pattern is a step shift of

-2

. The next letter position is

18 - 2 = 16

, which corresponds to

P

.

Determine the rule governing the initial letter of each term.

2

Analyze the middle numerical sequence

The sequence is

1, 2, 6, 24, 120

. The multipliers increase sequentially:

1 \times 2 = 2

,

2 \times 3 = 6

,

6 \times 4 = 24

,

24 \times 5 = 120

. The next multiplier is

6

, so

120 \times 6 = 720

.

Identify the multiplication progression for the numerical components.

3

Analyze the final letter sequence

Alphabetical positions:

A (1), C (3), E (5), G (7), I (9)

. The pattern is a step shift of

+2

. The next letter position is

9 + 2 = 11

, which corresponds to

K

.

Determine the rule governing the trailing letter of each term.

4

Combine the components

Combining the first letter (

P

), middle number (

720

), and last letter (

K

) yields

P720K

.

Assemble the complete final term of the series.

Key Concept

Multi-component alphanumeric series pattern recognition combining arithmetic step shifts and factorial multiplication.

Estimated Time:1m 0s

Question 175Question →

Which of the following letter pairs logically completes the given sequence?

ZA, YC, XF, WJ, \dots

VO

VN

UO

VP

Show answer & explanation

Answer: $VO$

Answer

VO

The sequence consists of two independent letter patterns. The first letter decreases monotonically by 1 position (Z -> Y -> X -> W -> V). The second letter follows an increasing difference series (+2, +3, +4, +5), advancing J (10th position) to O (15th position). Combining these yields VO.

Step-by-Step Solution

1

Analyze the pattern of the first letter in each pair

Z (26), Y (25), X (24), W (23). The letters move backward by 1 step continuously. The next letter is V (22).

Determines the first letter of the missing term.

2

Analyze the pattern of the second letter in each pair

A (1) to C (3) is +2; C (3) to F (6) is +3; F (6) to J (10) is +4. The increment increases by 1 at each term. Adding 5 to J (10) gives 15, which corresponds to the letter O.

Determines the second letter of the missing term.

3

Combine both components to form the final term

Combining V and O gives VO.

Completes the sequence.

Key Concept

Dual-Pattern Alphabet Series with Positional Shifts

Question 176Question →

Consider the following multi-pattern alphanumeric series:

B3Y, E5W, I13T, N49P, T241K, \dots

Which of the following alphanumeric terms correctly completes the given sequence?

A1441E

Z1446F

A1440Q

B1441E

Show answer & explanation

Answer: A1441E

Answer

A1441E

The correct term is determined by combining three distinct concurrent rules: the first letter shifts forward by incrementally larger intervals (+3, +4, +5, +6, +7) wrapping from T to A; the middle number follows the operational recurrence relation (Previous × n) - (n - 1) yielding (241 × 6) - 5 = 1441; and the third letter shifts backward by expanding steps (-2, -3, -4, -5, -6) moving from K to E.

Step-by-Step Solution

1

Analyze the pattern of the first letters in the terms: B, E, I, N, T

Positions in alphabet: B(2) → (+3) → E(5) → (+4) → I(9) → (+5) → N(14) → (+6) → T(20). The next shift must be +7. T(20) + 7 = 27, which wraps around to A(1).

The forward positional shift increases by +1 at each successive step.

2

Analyze the pattern of the middle numerical sequence: 3, 5, 13, 49, 241

Step 1 to 2 (n=2): (3 × 2) - 1 = 5. Step 2 to 3 (n=3): (5 × 3) - 2 = 13. Step 3 to 4 (n=4): (13 × 4) - 3 = 49. Step 4 to 5 (n=5): (49 × 5) - 4 = 241. Step 5 to 6 (n=6): (241 × 6) - 5 = 1446 - 5 = 1441.

The operational formula for the nth transition is Term_n = (Term_{n-1} × n) - (n - 1).

3

Analyze the pattern of the third letters in the terms: Y, W, T, P, K

Positions in alphabet: Y(25) → (-2) → W(23) → (-3) → T(20) → (-4) → P(16) → (-5) → K(11). The next shift must be -6. K(11) - 6 = 5, which corresponds to E.

The backward positional shift magnitude increases by 1 step sequentially.

4

Combine the results of the three independent sub-patterns

First letter: A, Middle number: 1441, Last letter: E. Combined term: A1441E.

Formulating the final composite term completing the series.

Key Concept

Multi-layered Alphanumeric Series Completion

Question 177Question →

Which of the following alphanumeric terms logically completes the given series: $B7Z, E14W, J23T, Q34Q, \dots$ ?

Z47N

Y47N

Z45N

Z47M

Show answer & explanation

Answer: $Z47N$

Answer

Z47N

Each character position follows a distinct rule: the first letters (

B, E, J, Q

) advance by

+3, +5, +7, +9

to reach

Z

; the middle numbers (

7, 14, 23, 34

) advance by

+7, +9, +11, +13

to reach

47

; and the last letters (

Z, W, T, Q

) step backward by

3

positions each time to reach

N

. Combining these produces the correct completed term

Z47N

.

Step-by-Step Solution

1

Analyze the first letter in each term

The positional values of the first letters are

B=2, E=5, J=10, Q=17

. The differences between consecutive letters are

+3, +5, +7

. Following this pattern, the next increment is

+9

, so

17 + 9 = 26

, which corresponds to

Z

.

The difference between consecutive first-letter positions increases by

+2

at each step.

2

Analyze the middle number in each term

The numbers are

7, 14, 23, 34

. The differences are

14 - 7 = 7

,

23 - 14 = 9

, and

34 - 23 = 11

. The next difference must be

+13

, so

34 + 13 = 47

.

The numerical pattern follows an increasing sequence of odd numbers starting from

7

.

3

Analyze the last letter in each term

The positional values of the last letters are

Z=26, W=23, T=20, Q=17

. The pattern is a constant decrease of

3

positions (

26 \rightarrow 23 \rightarrow 20 \rightarrow 17

). The next position is

17 - 3 = 14

, which corresponds to

N

.

A uniform reverse shift of

3

units is applied to the final letter of each term.

4

Combine all three components

Merging the first letter (

Z

), middle number (

47

), and last letter (

N

) yields the term

Z47N

.

All three sub-patterns operate independently to define the next term in the series.

Key Concept

Multi-Pattern Alphanumeric Series Completion

Question 178Question →

Consider the following alphanumeric series:

B4, E9, I19, N39, T79, \dots

Which of the following terms logically completes the series?

A159

Z159

A158

Z158

Show answer & explanation

Answer: $A159$

Answer

The term that logically completes the series is

A159

.

The letter sequence advances by increasing positional shifts (+3, +4, +5, +6, +7), bringing T (20) to 27, which wraps around to A. The number sequence follows

n_{k} = 2n_{k-1} + 1

, transforming 79 into 159. Combining these yields

A159

.

Step-by-Step Solution

1

Analyze the pattern governing the letter component of the series.

Positions in the English alphabet: B is 2, E is 5, I is 9, N is 14, T is 20.
Differences between consecutive letter positions:

5 - 2 = +3

9 - 5 = +4

14 - 9 = +5

20 - 14 = +6

Following this progression, the next shift must be

+7

.
Adding 7 to the position of T (20) gives

20 + 7 = 27

. Wrapping around the 26-letter alphabet (

27 - 26 = 1

), the 1st letter is A.

The letter pattern increases the positional shift increment by 1 at each step.

2

Analyze the pattern governing the numerical component of the series.

The numerical terms are 4, 9, 19, 39, 79.
Evaluating the relation between consecutive terms:

4 \times 2 + 1 = 9

9 \times 2 + 1 = 19

19 \times 2 + 1 = 39

39 \times 2 + 1 = 79

Applying the same rule to 79:

79 \times 2 + 1 = 159

.

Each number is generated by doubling the preceding number and adding 1.

3

Combine the letter and numerical results.

The next term in the series is

A159

.

Joining the identified letter A with the calculated number 159 yields the complete next term.

Key Concept

Alphanumeric Series Completion via Increasing Positional Shift and Recurrence Progression

Question 179Question →

Which of the following alphanumeric terms logically completes the given sequence?

A2P, D9M, I28J, P65G, \dots

Y126D

Z126D

Y124D

Y126E

Show answer & explanation

Answer: $Y126D$

Answer

Y126D

The correct term combines three distinct structural rules: the first letter follows perfect square positions (

1^2, 2^2, 3^2, 4^2, 5^2 \rightarrow Y

), the numerical value follows

n^3 + 1

(

5^3 + 1 = 126

), and the last letter decreases by 3 positions (

G - 3 = D

), giving

Y126D

.

Step-by-Step Solution

1

Analyze the pattern of the first letter in each term

The alphabetical positions are

A=1

,

D=4

,

I=9

, and

P=16

. These numbers are perfect squares (

1^2, 2^2, 3^2, 4^2

). The 5th position is

5^2 = 25

, which corresponds to the letter

Y

.

Establishing the sequence rule for the first component.

2

Analyze the pattern of the middle number in each term

The numeric values are

2, 9, 28, 65

. Expressing them in terms of term position

n

:

1^3 + 1 = 2

,

2^3 + 1 = 9

,

3^3 + 1 = 28

,

4^3 + 1 = 65

. For

n=5

, the value is

5^3 + 1 = 125 + 1 = 126

.

Establishing the algebraic relation governing the middle numeric component.

3

Analyze the pattern of the third letter in each term

The alphabetical positions are

P=16

,

M=13

,

J=10

, and

G=7

. The pattern decreases by 3 each step (

-3

). The next position is

7 - 3 = 4

, which corresponds to the letter

D

.

Establishing the reverse linear shift rule for the third component.

4

Combine the three derived components

Combining the first letter (

Y

), middle number (

126

), and final letter (

D

) yields

Y126D

.

Constructing the final term of the series.

Key Concept

Multi-Pattern Alphanumeric Series

Estimated Time:2m 0s

Question 180Question →

Consider the numerical sequence: $5, 11, 24, 51, 106, 217, \dots$ . What is the value of the next term in this sequence?

Show answer & explanation

Answer: 440

Answer

The next term in the sequence is 440.

The sequence follows the recurrence pattern where each term is twice the previous term plus an increasing integer offset:

5 \times 2 + 1 = 11

,

11 \times 2 + 2 = 24

,

24 \times 2 + 3 = 51

,

51 \times 2 + 4 = 106

,

106 \times 2 + 5 = 217

. Following this pattern, the next term is

217 \times 2 + 6 = 440

.

Step-by-Step Solution

1

Examine the relationship between successive terms.

The differences between successive terms are

6, 13, 27, 55, 111

, and the second-level differences are

7, 14, 28, 56

(doubling each step). Alternatively, each term is multiplied by 2 and increased by an incrementing integer.

Analyzing both direct operations and higher-order differences establishes the recurrence rule

a_{n+1} = 2a_n + n

.

2

Determine the required operation for the next step in the sequence.

Multiply the 6th term (217) by 2 and add 6.

The additive component increases by 1 at each term (

+1, +2, +3, +4, +5 \rightarrow +6

).

3

Calculate the value of the next term.

217 \times 2 + 6 = 440

.

217 \times 2 = 434

, and adding 6 yields 440.

Key Concept

Recurrent series with multiplicative factor and sequential linear increment

Estimated Time:1m 30s

General Mental Ability

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