General Mental Ability

303 questions

All types303 Multiple choice164 Multiple select13 Numeric38 Matching35 Ordering21 Fill in the blank10 Short answer22

What is the next letter in the given alphabetical series: $Z, X, V, T, R, \dots$ ?

P

Q

O

S

Show answer & explanation

Answer: $P$

Answer

The correct next letter in the sequence is

P

Each term in the series moves backward by 2 steps in the standard English alphabet:

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

. Continuing this constant decrease of 2 leads to the 16th letter, which is

P

Step-by-Step Solution

Determine the alphabetical positions of each given letter in the series

Z = 26

X = 24

V = 22

T = 20

R = 18

Converting letters to numerical positions helps reveal the mathematical pattern.

Identify the common difference between consecutive terms

24 - 26 = -2

22 - 24 = -2

20 - 22 = -2

18 - 20 = -2

Each letter is obtained by moving 2 positions backward in the alphabet.

Apply the pattern to find the next position and letter

18 - 2 = 16

, which corresponds to the letter

P

Subtracting 2 positions from the 18th letter (

R

) gives the 16th letter (

P

Key Concept

Reverse Alphabetical Positional Shifts

Question 22Question →

Consider the following multi-pattern alphanumeric sequence:

D4W, G9T, L16P, S35K, D66E, \dots

Which of the following terms logically completes the sequence?

Q137X

Q137L

M137X

Q137Y

Show answer & explanation

Answer: $Q137X$

Answer

The term that logically completes the sequence is

Q137X

The next term in the sequence is obtained by synthesizing three distinct rules: the first letter moves forward by consecutive prime steps (

+13

from

D

yields

Q

), the number multiplies by

2

and adds

5

to yield

137

, and the trailing letter moves

+7

steps in reverse positional values (

E

at reverse index 22 moves to 29, which is reverse index 3 or letter

X

). Combining these gives

Q137X

Step-by-Step Solution

Analyze the first letter progression:

D \rightarrow G \rightarrow L \rightarrow S \rightarrow D \rightarrow ?

Alphabetical positions (1 to 26):

D=4, G=7, L=12, S=19, D=30 \equiv 4\pmod{26}

. The step differences are

+3, +5, +7, +11

, which are prime numbers. The next prime increment is

+13

. Adding

13

D(4)

gives

17

, corresponding to letter

Q

The first letter advances according to consecutive prime increments modulo 26.

Analyze the numerical middle component:

4, 9, 16, 35, 66, ?

9 = 2(4) + 1

16 = 2(9) - 2

35 = 2(16) + 3

66 = 2(35) - 4

. Following

N_k = 2 N_{k-1} + (-1)^{k+1} k

, the next term is

2(66) + 5 = 137

The numerical pattern multiplies the previous number by 2 and alternates adding/subtracting sequential integers.

Analyze the second letter progression using reverse positional values:

W, T, P, K, E, ?

Reverse positions (

Z=1, Y=2, \dots, A=26

W=4, T=7, P=11, K=16, E=22

. Increments in reverse positions are

+3, +4, +5, +6

. The next reverse position increment is

+7

, giving

22 + 7 = 29 \equiv 3\pmod{26}

. Reverse position 3 corresponds to forward letter

X

(

27 - 3 = 24

The second letter steps through increasing increments in reverse alphabetical indexing.

Key Concept

Multi-pattern alphanumeric series involving prime positional shifts, alternating linear recursive relations, and reverse alphabetical indexing.

Estimated Time:2m 30s

Question 23Question →

In a regional agricultural seed bank's categorization system, crop names are converted into numerical codes for database entry. Under this specific protocol, the crop name "WHEAT" is coded as "4-19-5-1-7", and the crop name "BARLEY" is coded as "25-1-9-15-5-2". Following the exact same logical pattern, how will the crop name "MAIZE" be coded?

14-1-9-1-5

14-26-18-1-22

13-1-9-26-5

13-26-18-26-22

Show answer & explanation

Answer: 14-1-9-1-5

Answer

14-1-9-1-5

The correct answer is derived by observing that all consonants are transformed into their reverse alphabetical positions (e.g., M=13 becomes 14, Z=26 becomes 1), while all vowels maintain their standard forward alphabetical positions (e.g., A=1, I=9, E=5). Combining these values in sequence produces 14-1-9-1-5.

Step-by-Step Solution

Determine the standard alphabetical positions of the letters in the first example, 'WHEAT'.

W=23, H=8, E=5, A=1, T=20.

Establishing the base numerical values is the first step in identifying coding transformations.

Compare the base numerical values of 'WHEAT' with its given code: '4-19-5-1-7'.

W(23) becomes 4. H(8) becomes 19. E(5) remains 5. A(1) remains 1. T(20) becomes 7.

This comparison reveals the specific mathematical or logical transformation applied to each letter.

Identify the underlying logical rule governing the transformations.

Consonants (W, H, T) are assigned their reverse alphabetical positions (calculated as 27 - forward position). Vowels (E, A) retain their standard forward alphabetical positions.

Defining the conditional rule is required before it can be reliably applied to other words.

Verify the identified rule using the second example, 'BARLEY'.

Forward positions: B=2, A=1, R=18, L=12, E=5, Y=25. Applying the rule: B(consonant) -> 25, A(vowel) -> 1, R(consonant) -> 9, L(consonant) -> 15, E(vowel) -> 5, Y(consonant) -> 2. Code is 25-1-9-15-5-2, which perfectly matches the given code.

Testing the hypothesis against a second dataset confirms the logic is universally applied within the system.

Apply the verified rule to the target word 'MAIZE'.

M(13, consonant) -> 27-13 = 14. A(1, vowel) -> 1. I(9, vowel) -> 9. Z(26, consonant) -> 27-26 = 1. E(5, vowel) -> 5.

Translating the target string using the established algorithm yields the final answer.

Key Concept

Mixed Alphanumeric Substitution using Vowel/Consonant Conditional Logic and Reverse Indexing

Question 24Question →

Select the letter-cluster that is related to the third letter-cluster in the same way that the second letter-cluster is related to the first letter-cluster.

TASK : XYWI :: POND : ?

TMRB

TSRH

LQJF

RKPZ

Show answer & explanation

Answer: TMRB

Answer

The correct letter-cluster is TMRB.

The relationship between the first and second letter-clusters follows an alternating alphabetical shift pattern. The first and third letters are shifted forward by 4 positions (+4), while the second and fourth letters are shifted backward by 2 positions (-2), with standard circular alphabetical wrap-around. Applying this identical +4, -2, +4, -2 sequence to the letters P, O, N, and D yields T, M, R, and B respectively.

Step-by-Step Solution

Analyze the positional shifts between the first pair of letter-clusters: TASK and XYWI.

T(20) to X(24) is +4. A(1 or 27) to Y(25) is -2. S(19) to W(23) is +4. K(11) to I(9) is -2.

Establishing the underlying logical rule requires checking the step interval for every individual letter to ensure the full pattern is identified.

Determine the unified rule governing the analogy.

The alternating shift sequence is +4, -2, +4, -2.

This confirms that the transformation is not a uniform shift, but an alternating forward and backward arithmetic progression.

Apply the identical +4, -2, +4, -2 pattern to the target letter-cluster: POND.

P(16) + 4 = T(20). O(15) - 2 = M(13). N(14) + 4 = R(18). D(4) - 2 = B(2).

To maintain the analogical relationship, the exact sequence of operations must be applied to the new group.

Key Concept

Alphabetical Positional Alternating Shifts

Question 25Question →

A tourist is exploring a historical monument. He starts from the main gate and walks $30\text{ m}$ towards the West. He then turns $135^{\circ}$ to his left and walks $20\sqrt{2}\text{ m}$ . Next, he turns $45^{\circ}$ to his right and walks $10\text{ m}$ . Finally, he turns $90^{\circ}$ to his left and walks $50\text{ m}$ . What is his shortest distance and direction from the main gate?

50\text{ m}

, South-East

50\text{ m}

, North-East

50\text{ m}

, North-West

70\text{ m}

, South-East

Show answer & explanation

Answer: $50\text{ m}$ , South-East

Answer

The shortest distance is

50\text{ m}

and the direction is South-East.

By tracking the movements sequentially on a 2D coordinate plane from an origin of (0, 0), the tourist's positions are (-30, 0), (-10, -20), (-10, -30), and finally (40, -30). The straight-line distance from the origin to (40, -30) is the hypotenuse of a right triangle with legs of 40 and 30, which equals 50. The coordinate (40, -30) lies in the lower-right quadrant, indicating a South-East direction.

Step-by-Step Solution

Map the starting point as the origin (0, 0) and execute the first movement.

Walking

30\text{ m}

West places the tourist at (-30, 0) facing West.

Establishing a Cartesian coordinate system allows for precise tracking of movements.

Calculate the second movement: turn

135^{\circ}

left and walk

20\sqrt{2}\text{ m}

135^{\circ}

left turn from West changes the facing direction to South-East. Moving

20\sqrt{2}\text{ m}

South-East adds

+20

to the X-axis and

-20

to the Y-axis. New position: (-30 + 20, 0 - 20) = (-10, -20).

A left turn is counter-clockwise. West minus

135^{\circ}

equals South-East. Breaking this diagonal vector into components yields equivalent

+20\text{ m}

East and

-20\text{ m}

South.

Calculate the third movement: turn

45^{\circ}

right and walk

10\text{ m}

45^{\circ}

right (clockwise) turn from South-East points South. Walking

10\text{ m}

South subtracts 10 from the Y-axis. New position: (-10, -20 - 10) = (-10, -30).

Right turns add clockwise rotation, shifting the direction from diagonal to a cardinal line.

Calculate the final movement: turn

90^{\circ}

left and walk

50\text{ m}

90^{\circ}

left (counter-clockwise) turn from South points East. Walking

50\text{ m}

East adds 50 to the X-axis. Final position: (-10 + 50, -30) = (40, -30).

Standard orthogonal rotation maps the final displacement vector.

Calculate the direct distance and direction from the origin (0,0) to the final point (40, -30).

Distance =

\sqrt{40^2 + (-30)^2} = \sqrt{1600 + 900} = 50\text{ m}

. Since X is positive (East) and Y is negative (South), the direction is South-East.

The Pythagorean theorem determines the shortest straight-line Euclidean distance, and the quadrant dictates the cardinal direction.

Key Concept

Vector displacement combining angular turns, Cartesian mapping, and the Pythagorean theorem.

Question 26Question →

Six historic ships��Bounty, Cutty Sark, Discovery, Endeavour, Mayflower, and Victoria—are anchored in a single straight row facing North (towards the harbor). Their left-to-right positions are determined by the following conditions:

1. The Discovery is anchored at the extreme left end of the row.
2. The Victoria is anchored exactly midway between the Mayflower and the Endeavour.
3. The Bounty anchors immediately to the right of the Mayflower.
4. The Cutty Sark anchors immediately to the left of the Endeavour.
5. The Cutty Sark and the Victoria are anchored next to each other.

Arrange the ships in the correct order from the extreme left (1st position) to the extreme right (6th position).

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from left to right is: Discovery, Mayflower, Bounty, Victoria, Cutty Sark, Endeavour.

The correct sequence is established by recognizing how the adjacency rules merge into larger blocks. By deducing that the Cutty Sark and Endeavour form a 'C-E' pair, and Victoria must sit next to Cutty Sark to form 'V-C-E', we establish the exact distance between Victoria and Endeavour (2 positions). Because Victoria must be midway between Mayflower and Endeavour, the Mayflower must also be exactly 2 positions away on the opposite side. This forces the 'Mayflower-Bounty' pair to sit immediately left of Victoria, yielding a unified 5-ship block 'M-B-V-C-E' that perfectly slots in next to the Discovery.

Step-by-Step Solution

Establish the given anchor.

Position 1 is Discovery (D). The sequence is currently D, _, _, _, _, _.

Condition 1 explicitly states Discovery is at the extreme left end.

Combine adjacency conditions to form fixed spatial blocks.

We identify a two-ship block (M - B) and a three-ship block (V - C - E).

Condition 4 requires Cutty Sark (C) to be immediately left of Endeavour (E), forming 'C - E'. Condition 5 requires Victoria (V) to be next to C. Since placing V to the right of C would break the 'C - E' block, V must be immediately to the left of C, forming 'V - C - E'. Condition 3 requires Bounty (B) to be immediately right of Mayflower (M), forming 'M - B'.

Apply the midway condition to combine the blocks into a single sequence.

The combined sequence becomes M - B - V - C - E.

Condition 2 states V is exactly midway between M and E. In our 'V - C - E' block, E is exactly two positions to the right of V. Therefore, M must be exactly two positions to the left of V. Placing the 'M - B' block immediately before V perfectly satisfies this midway requirement.

Finalize the arrangement by placing the unified block.

The final arrangement is D, M, B, V, C, E.

We have a solid 5-ship sequence (M - B - V - C - E). With Discovery anchored at position 1, the only way to fit the remaining 5 ships is consecutively in positions 2 through 6.

Key Concept

Linear seating arrangement combining relative positional blocks and distance/midpoint constraints.

Estimated Time:2m 30s

Question 27Question →

In a cryptographic system used for secure communications, the word 'CROWN' is coded as 'ETNYP'. Based on this same coding logic, match the following words on the left with their correct coded forms on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

PAINT matches with RZHPV, SHARK matches with UJZTM, MOUSE matches with ONTUD, and BRICK matches with DTHEM.

Each word perfectly aligns with its encrypted code when applying the specific rule derived from the stem: shifting consonants forward by 2 letters in the alphabet, and shifting vowels backward by 1 letter.

Step-by-Step Solution

Analyze the example 'CROWN' to identify the shift pattern for each letter.

C becomes E (+2), R becomes T (+2), O becomes N (-1), W becomes Y (+2), and N becomes P (+2).

Identifying how the example word is transformed is the first step in decoding the underlying encryption logic.

Generalize the coding rule based on the distinct letter types.

Consonants (C, R, W, N) are shifted forward by 2 positions (+2). The vowel (O) is shifted backward by 1 position (-1).

A consistent rule must be established that applies differently to vowels and consonants in order to decode other words.

Apply the derived rule to the target words on the left.

Applying the rule yields: PAINT -> RZHPV, SHARK -> UJZTM, MOUSE -> ONTUD, BRICK -> DTHEM.

Encoding each word accurately allows us to find its correct corresponding match on the right side.

Key Concept

Coding based on letter categorization (vowels vs. consonants) with distinct positional shifts.

Question 28Question →

A university establishes a new scholarship fund on September 15, 2195, which happens to be a Friday. The founding document states that a major administrative review of the fund will occur exactly $12$ years later on September 15, 2207. What day of the week will this review take place?

Show answer & explanation

Answer: Friday; friday; FRIDAY

Answer

Friday

The

12

-year period from 2195 to 2207 contains only

2

leap years (2196 and 2204). The year 2200 is a century year not divisible by

400

, meaning it is a common year with

365

days. The total shift in days of the week is equal to the number of years (

12

) plus the number of extra leap days (

2

), resulting in a total shift of

14

days. Since

14

is a perfect multiple of

7

, there are

0

odd days. The day of the week shifts by exactly

0

days, meaning the review will also take place on a Friday.

Step-by-Step Solution

Identify the total number of years in the given interval.

From 2195 to 2207 is exactly

12

years.

This sets the baseline shift, as every standard year shifts the calendar by at least

1

day.

Determine the number of leap years in this 12-year interval.

The years divisible by

4

in this range are 2196, 2200, and 2204. However, century years are only leap years if divisible by

400

. Since 2200 is not divisible by

400

, it is not a leap year. Thus, there are only

2

leap years: 2196 and 2204.

Each leap year adds an additional

1

day to the shift because it has

366

days instead of

365

Calculate the total number of odd days (total shift in days of the week).

Each normal year contributes

1

odd day, and each leap year contributes

2

odd days. For

12

years with

2

leap years, the easiest calculation is:

12

(one for each year)

+ 2

(extra day for each leap year)

= 14

days.

This gives the absolute number of days the weekday will advance.

Determine the final day of the week.

A shift of

14

days is exactly

2

full weeks (

14

divided by

7

leaves a remainder of

0

). Therefore, the day of the week remains the same. Friday

+ 0

days

=

Friday.

Days of the week repeat every

7

days, so we use modulo

7

arithmetic.

Key Concept

Calculating day of the week shifts across century boundaries, accounting for the rule that non-400 century years are not leap years.

Question 29Question →

If the letter-group SOUL transforms into the code VLFO according to a specific alphanumeric rule, which of the following letter-groups represents the word DIRT under the identical rule?

GRUW

GLUW

WRIG

WLIG

Show answer & explanation

Answer: GRUW

Answer

GRUW

The underlying logical rule distinguishes between consonants and vowels. Consonants are shifted forward by 3 positions in the English alphabet (e.g., S becomes V, L becomes O). Vowels are replaced by their opposite/mirror letter from the reverse alphabetical order (e.g., O becomes L, U becomes F). Applying this rule to DIRT: The consonants D, R, and T shift forward by 3 to become G, U, and W. The vowel I is replaced by its reverse alphabetical counterpart, R. Therefore, the resulting letter-group is GRUW.

Step-by-Step Solution

Analyze the transformation from the reference word SOUL to its corresponding code VLFO to deduce the underlying rule.

By examining the alphabetical positions, consonants (S, L) shift forward by 3 positions to become (V, O). Vowels (O, U) are replaced by their opposite/mirror letters from the reverse alphabet (L, F).

Establishing the precise logical coding pattern is necessary to solve the analogy.

Categorize the letters in the target word DIRT into consonants and vowels.

Consonants: D, R, T. Vowel: I.

The established rule relies on treating consonants and vowels differently.

Apply the respective rules to the categorized letters of DIRT.

D (+3) yields G. I (reverse mirror) yields R. R (+3) yields U. T (+3) yields W. Combining these results in the string GRUW.

Applying the exact established rule provides the final encoded letter-cluster.

Key Concept

Letter Pattern Analogies and Positional Coding

Question 30Question →

Consider the following pair of character sequences that share a specific structural relationship:

PLANT : MQBOI

Applying the exact same underlying logic, which sequence correctly completes the analogous pair below?

YIELD : ?

BRVOW

AKGNF

DTXQY

ZPTMU

Show answer & explanation

Answer: DTXQY

Answer

The correct sequence is DTXQY.

The established relationship relies on a two-step transformation: first, finding the alphabetical opposite (mirror) of each letter, and second, shifting that new letter forward by 2 positions in the alphabet. Applying this logic to YIELD first gives its alphabetical mirror BRVOW. Shifting each letter in BRVOW forward by 2 positions produces DTXQY.

Step-by-Step Solution

Analyze the transformation from the first word (PLANT) to the second word (MQBOI) by examining the primary letter relationship.

The opposite (mirror) letters for P, L, A, N, T are K, O, Z, M, G respectively.

A common structural pattern in alphabet analogies is reverse indexing, where A=Z, B=Y, C=X, etc.

Determine the secondary transformation required to get from the intermediate mirror letters to the final code.

Shifting K, O, Z, M, G forward by 2 positions (+2) results in M, Q, B, O, I.

This establishes the complete two-step rule: find the alphabetical opposite, then shift forward by 2.

Apply the first step of the established rule to the target word (YIELD).

The opposite letters for Y, I, E, L, D are B, R, V, O, W.

Consistency in applying the exact same logical framework to the analogous pair.

Apply the second step of the rule to the intermediate result.

Shifting B, R, V, O, W forward by 2 positions yields D, T, X, Q, Y.

Completing the logic gives the final analogous character group.

Key Concept

Dual-Step Alphabet Analogy (Reverse Indexing and Positional Shifting)

Question 31Question →

In a regional sports academy, a group of $70$ trainees were surveyed about their participation in two sports: Cricket and Football. $45$ trainees play Cricket, $30$ trainees play Football, and $10$ trainees play neither sport. How many trainees play both Cricket and Football?

15

5

25

10

Show answer & explanation

Answer: $15$

Answer

15 trainees play both Cricket and Football.

The total number of trainees participating in at least one sport is found by subtracting the

10

non-participants from the total

70

, giving

60

. Summing the individual sport counts gives

45 + 30 = 75

. The overlap represents those counted twice, which is

75 - 60 = 15

Step-by-Step Solution

Calculate the total number of trainees who play at least one sport.

Trainees playing at least one sport =

70 - 10 = 60

Subtract trainees playing neither sport from the total group size.

Apply the Principle of Inclusion-Exclusion for two sets.

N(\text{Cricket} \cup \text{Football}) = N(\text{Cricket}) + N(\text{Football}) - N(\text{Cricket} \cap \text{Football})

The sum of individual sets double-counts the intersection.

Substitute the known values into the equation and solve for the intersection.

60 = 45 + 30 - N(\text{Cricket} \cap \text{Football}) \implies N(\text{Cricket} \cap \text{Football}) = 75 - 60 = 15

Algebraic simplification yields the number of trainees playing both sports.

Key Concept

Two-Set Inclusion-Exclusion Principle

Question 32Question →

In a state policy research institute, a survey of $200$ research analysts was conducted regarding their domain specializations in three sectors: Health ( $H$ ), Education ( $E$ ), and Agriculture ( $A$ ). The data revealed that $90$ analysts specialize in Health, $85$ in Education, and $80$ in Agriculture. Furthermore, $35$ analysts specialize in both Health and Education, $30$ in both Education and Agriculture, $25$ in both Health and Agriculture, and $10$ analysts specialize in all three sectors. How many research analysts specialize in corporate policy research analysts who specialize in exactly two of these sectors?

60

70

80

90

Show answer & explanation

Answer: $60$

Answer

The number of research analysts who specialize in exactly two sectors is

60

To find the number of analysts specializing in exactly two sectors, we must determine the exclusive intersection of each pair of sectors. The given intersections represent analysts in at least two sectors.
- Analysts specializing in ONLY Health and Education =

35 - 10 = 25

- Analysts specializing in ONLY Education and Agriculture =

30 - 10 = 20

- Analysts specializing in ONLY Health and Agriculture =

25 - 10 = 15

Summing these exclusive regions gives

25 + 20 + 15 = 60

Step-by-Step Solution

Identify given set values and intersections

n(H \cap E) = 35

n(E \cap A) = 30

n(H \cap A) = 25

, and

n(H \cap E \cap A) = 10

Each pairwise intersection given includes both analysts specializing in exactly two sectors and analysts specializing in all three sectors.

Calculate the number of analysts specializing ONLY in each specific pair of two sectors

Only Health & Education =

35 - 10 = 25

; Only Education & Agriculture =

30 - 10 = 20

; Only Health & Agriculture =

25 - 10 = 15

Subtracting

n(H \cap E \cap A)

isolates the analysts specializing in exactly two sectors for each pair.

Sum the three isolated regions of exactly two specializations

Total =

25 + 20 + 15 = 60

Adding these three mutually exclusive regions yields the overall count of analysts specializing in exactly two sectors.

Key Concept

Logical Venn Diagrams - Intersection Exclusion Principle

Alternative Method

Using the general formula:

\text{Exactly two sets} = n(H \cap E) + n(E \cap A) + n(H \cap A) - 3 \times n(H \cap E \cap A) = 35 + 30 + 25 - 3(10) = 90 - 30 = 60

Estimated Time:1m 30s

Question 33Question →

In a consolidated merit list of 90 applicants for a university fellowship, Marcus is ranked $25^{\text{th}}$ from the top, while Elena is ranked $44^{\text{th}}$ from the bottom. If David is positioned exactly in the middle of Marcus and Elena in this merit list, what is David's rank from the bottom?

54^{\text{th}}

45^{\text{th}}

55^{\text{th}}

36^{\text{th}}

Show answer & explanation

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

Answer

David's rank from the bottom is the

55^{\text{th}}

position.

To find David's position, we first standardise the reference points. Elena's

44^{\text{th}}

position from the bottom corresponds to the

47^{\text{th}}

position from the top (calculated as

90 - 44 + 1

). The exact midpoint between the

25^{\text{th}}

and

47^{\text{th}}

ranks is the

36^{\text{th}}

rank from the top (calculated as the average:

(25 + 47) / 2 = 36

). Finally, converting David's

36^{\text{th}}

top rank to a bottom rank yields

90 - 36 + 1 = 55^{\text{th}}

Step-by-Step Solution

Convert Elena's bottom rank to a top rank to establish a common directional reference.

Elena's rank from the top is

90 - 44 + 1 = 47^{\text{th}}

To calculate the number of people strictly between Marcus and Elena, both ranks must be measured from the same end (the top).

Calculate the number of applicants positioned strictly between Marcus and Elena.

There are

47 - 25 - 1 = 21

applicants between them.

Subtracting the top ranks and deducting 1 excludes both Marcus and Elena from the middle count.

Determine David's exact relative position starting from Marcus.

David is the

11^{\text{th}}

person after Marcus.

The exact midpoint of 21 people is

(21 + 1) / 2 = 11

positions away from the starting person.

Calculate David's overall absolute rank from the top.

David's top rank is

25 + 11 = 36^{\text{th}}

Adding David's relative interval to Marcus's top rank yields David's absolute top rank.

Convert David's top rank back to a bottom rank to answer the final question.

David's rank from the bottom is

90 - 36 + 1 = 55^{\text{th}}

Applying the standard linear ranking formula:

\text{Total} = \text{Top Rank} + \text{Bottom Rank} - 1

Key Concept

Positional overlap calculation and dual-rank directional conversion

Question 34Question →

A historian finds a perfectly preserved wall calendar for the year 1892. In which of the following subsequent years could this exact same calendar be used for the entire year without any discrepancies?

1897

1898

1904

1920

Show answer & explanation

Answer: 1904

Answer

The exact same calendar as 1892 can be reused in the year 1904.

For a calendar to completely match a leap year like 1892, the target year must start on the same day of the week and also be a leap year. While leap years typically repeat every 28 years, the inclusion of the non-leap century year 1900 disrupts this cycle. Counting the odd days from 1892 forward yields exactly 14 odd days by the end of 1903. This means 1904 starts on the same weekday, and because 1904 is a leap year itself, it shares the exact same calendar.

Step-by-Step Solution

Determine the properties required for the calendar to match.

The target year must begin on the same day of the week and must also be a leap year, just like 1892.

A leap year has 366 days. If the target year is not a leap year, the days will not match after February 28th.

Calculate the cumulative odd days year by year starting from 1892.

1892 (2 odd days), 1893 (1), 1894 (1), 1895 (1), 1896 (2), 1897 (1), 1898 (1), 1899 (1). The sum so far is 10 odd days.

Every standard year adds 1 odd day, while a leap year adds 2 odd days. We must find a point where the sum is a multiple of 7.

Evaluate the century year 1900 and continue the odd days calculation.

1900 is a standard year (1 odd day). Continuing: 1900 (1), 1901 (1), 1902 (1), 1903 (1). The total sum of odd days from 1892 to 1903 is exactly 14.

Century years are only leap years if divisible by 400. Since 1900 is not divisible by 400, it is a standard year, which breaks the usual 28-year repetition cycle.

Verify the candidate year 1904.

Because the odd days up to 1903 sum to 14 (a multiple of 7), 1904 starts on the same day. Since 1904 is divisible by 4 and not a century year, it is a leap year.

Satisfying both requirements (same starting day and leap year status) means the entire calendar for 1904 is identical to 1892.

Key Concept

Calendar Repetition Across Non-Leap Century Years

Question 35Question →

Based on the specific letter transformation rule demonstrated in the first pair, which letter cluster correctly completes the second pair?

PLUM : NJXK :: BEAR : ?

ZHDP

ZCYP

EHDU

ECYU

Show answer & explanation

Answer: ZHDP

Answer

The correct letter cluster is ZHDP.

The underlying logic applies different shift rules based on whether a letter is a consonant or a vowel. In the first word, the consonants (P, L, M) are shifted backward by 2 positions in the English alphabet, while the vowel (U) is shifted forward by 3 positions. Applying this exact rule to the target word, the consonants (B, R) shift backward by 2 (resulting in Z, P) and the vowels (E, A) shift forward by 3 (resulting in H, D). This produces the final cluster 'ZHDP'.

Step-by-Step Solution

Analyze the transformation from 'PLUM' to 'NJXK' by checking the positional shifts in the alphabet.

P(16) → N(14) is -2; L(12) → J(10) is -2; U(21) → X(24) is +3; M(13) → K(11) is -2.

Establishing the individual letter shifts is necessary to identify the governing logical pattern.

Determine the rule that explains the different shifts (-2, -2, +3, -2).

The letters P, L, and M are consonants and they shift backward by 2. The letter U is a vowel and shifts forward by 3. The rule is: Consonants -2, Vowels +3.

Since the shift is not uniform or simply alternating, categorizing letters into vowels and consonants reveals the true logic.

Apply the identified rule to the target word 'BEAR'.

B (Consonant) - 2 = Z; E (Vowel) + 3 = H; A (Vowel) + 3 = D; R (Consonant) - 2 = P.

Applying the exact same vowel/consonant transformation rule yields the correct analogous pair.

Combine the transformed letters to form the final cluster.

Z, H, D, P combined form the cluster ZHDP.

This completes the analogy PLUM : NJXK :: BEAR : ZHDP.

Key Concept

Alphabet Pattern Analogy (Consonant and Vowel rules)

Question 36Question →

A commemorative time capsule was sealed by a city council on Tuesday, August 15, 1876. The municipal charter mandates that it must be opened exactly 50 years later, on August 15, 1926. Based on the standard Gregorian calendar, on what day of the week will the capsule be opened?

Sunday

Monday

Tuesday

Wednesday

Show answer & explanation

Answer: Sunday

Answer

The capsule will be opened on Sunday.

The correct answer accurately calculates the shift by accounting for 50 base years and exactly 11 leap days. It properly excludes 1900 as a leap year (due to the century rule) and correctly skips the 1876 leap day because the interval starts in August. Adding the resulting 61 odd days to Tuesday (61 mod 7 = 5) shifts the day forward by 5 days to Sunday.

Step-by-Step Solution

Determine the total number of base years in the interval.

1926 - 1876 = 50 years.

Each normal year adds exactly 1 odd day to the calendar shift.

Count the number of leap days crossed between August 15, 1876, and August 15, 1926.

There are 11 leap days (1880, 1884, 1888, 1892, 1896, 1904, 1908, 1912, 1916, 1920, 1924).

We must add 1 extra odd day for every February 29th crossed. The year 1876 is skipped because the start date is in August. The year 1900 is skipped because century years not divisible by 400 are not leap years.

Calculate the total number of odd days.

50 (from base years) + 11 (from leap days) = 61 total odd days.

Combining the normal yearly shift with the extra leap day shifts provides the total day shift.

Find the remainder when dividing the total odd days by 7 and apply it to the starting day.

61 divided by 7 leaves a remainder of 5. Tuesday + 5 days = Sunday.

The days of the week repeat in cycles of 7. Adding the remainder to the starting day gives the final day of the week.

Key Concept

Calculating odd days across century boundaries using the Gregorian calendar leap year rules.

Question 37Question →

A network administrator is establishing a 5-step automated security protocol. The five steps—Backup Creation, Database Sync, Malware Scan, System Initialization, and User Authentication—must be arranged in a specific sequence based on the following constraints:

1. The Database Sync must occur exactly two steps after User Authentication.
2. The Malware Scan must occur sometime after System Initialization, but before Backup Creation.
3. The Database Sync cannot be the final step, and User Authentication cannot be the first step.

Arrange the five security steps in the correct chronological order from first to last.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence is: System Initialization, User Authentication, Malware Scan, Database Sync, and Backup Creation.

The rules restrict the User Authentication and Database Sync pair strictly to steps 2 and 4. The remaining three steps (System Initialization, Malware Scan, Backup Creation) must maintain a strict relative order to satisfy the second rule, naturally falling into the remaining slots 1, 3, and 5.

Step-by-Step Solution

Determine the fixed positions for User Authentication and Database Sync based on constraints 1 and 3.

User Authentication must be step 2 and Database Sync must be step 4.

They have a fixed gap of one step between them. They cannot be steps 1 and 3 (User Authentication cannot be first), nor steps 3 and 5 (Database Sync cannot be last). Therefore, they must occupy steps 2 and 4.

Assign the remaining three steps (System Initialization, Malware Scan, and Backup Creation) to the empty slots.

System Initialization is step 1, Malware Scan is step 3, and Backup Creation is step 5.

Constraint 2 requires them to be in the strict relative order: System Initialization -> Malware Scan -> Backup Creation. The only remaining empty slots are 1, 3, and 5, so they must sequentially fill these slots.

Key Concept

Relative Positional Arrangement and Constraint Satisfaction

Estimated Time:1m 30s

Question 38Question →

Determine the correct chronological progression of the following entities, from their foundational biological origin to the finalized consumer product:

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct logical and chronological sequence is: Cotton Seed, Plant, Yarn, Fabric, Garment.

The sequence accurately traces the continuous lifecycle of textile production, moving logically from agriculture to manufacturing. It begins with the biological origin (Cotton Seed), which grows into a living organism (Plant). The plant produces raw cotton fibers that are extracted and spun into threads (Yarn). These threads are then woven together on a loom to create sheets of cloth (Fabric). Finally, the cloth is cut and tailored to create a finished piece of clothing (Garment).

Step-by-Step Solution

Identify the absolute origin point of the lifecycle.

Cotton Seed is the starting point.

Before any agricultural growth or industrial manufacturing can begin, the seed must be planted.

Determine the natural biological outcome of the seed.

The seed grows into a Plant.

Biological maturation must occur to produce the raw agricultural resource (cotton bolls).

Identify the first industrial transformation step.

The harvested cotton is spun into Yarn.

Raw cotton fibers cannot be woven directly; they must first be processed and spun into continuous threads.

Determine the next manufacturing stage.

The Yarn is woven into Fabric.

Individual threads are interlaced on a loom to create a solid, continuous sheet of textile material.

Identify the final consumer end-product.

The Fabric is sewn into a Garment.

The woven material is finally measured, cut, and stitched to create wearable clothing.

Key Concept

Logical Sequencing and Process Classification

Question 39Question →

A global climate summit was inaugurated on Tuesday, March 15, 2016. Based on the standard Gregorian calendar, on what day of the week will the same date fall in the year 2027?

Show answer & explanation

Answer: Monday; monday; MONDAY

Answer

Monday

To find the day of the week, we track the odd days. Between 2016 and 2027, there are 11 years, providing a baseline of 11 odd days. The interval strictly crosses two leap days (in 2020 and 2024), adding 2 more odd days. Crucially, the 2016 leap day is not counted because the interval starts in March, after February 29th. The total is

13 \text{ odd days}

, and since

13 \pmod{7} = 6

, shifting 6 days forward from Tuesday gives Monday.

Step-by-Step Solution

Calculate the total number of years between the two dates.

2027 - 2016 = 11 \text{ years}

Each standard year shifts the calendar forward by

1 \text{ odd day}

because

365 \pmod{7} = 1

Identify the leap days (February 29th) that actually fall within this specific date range.

Only

2

leap days are crossed: February 29, 2020, and February 29, 2024.

Although 2016 is a leap year, its February 29th occurred before the start date of March 15, 2016, so it does not add an extra day to this interval.

Calculate the total number of odd days accumulated over the interval.

11 \text{ base days} + 2 \text{ leap days} = 13 \text{ total odd days}

Combining the normal year shifts and the extra days from leap years gives the total day shift.

Determine the final day of the week by taking the total odd days modulo 7.

13 \pmod{7} = 6 \text{ odd days}

. Tuesday

+ 6 \text{ days} = \text{Monday}

The days of the week operate on a 7-day repeating cycle.

Key Concept

The inclusion of a leap year's extra day in a calculation strictly depends on whether February 29th falls within the exact given date interval, not just whether the year itself is a leap year.

Alternative Method

Instead of grouping odd days at the end, you can calculate the day year-by-year: 2016 to 2017 (+1, Wednesday), 2017 to 2018 (+1, Thursday), 2018 to 2019 (+1, Friday), 2019 to 2020 (+2 due to Feb 2020, Sunday), and so on, arriving at Monday for 2027.

Estimated Time:1m 0s

Question 40Question →

In a single row of books on a library shelf, an Encyclopedia is $28^{\text{th}}$ from the left end and a Dictionary is $35^{\text{th}}$ from the right end. If there are exactly 12 books placed strictly between them, what is the minimum possible total number of books in this row?

Show answer & explanation

Answer: 49

Answer

The minimum possible total number of books is 49.

The minimum total is found using the overlapping queue formula:

L + R - M - 2

. Substituting the given values yields

28 + 35 - 12 - 2 = 49

Step-by-Step Solution

Identify the queue configuration for the minimum capacity.

The minimum possible number of books occurs in an overlapping scenario.

In an overlapping scenario, the item counted from the right (Dictionary) is placed to the left of the item counted from the left (Encyclopedia), yielding the smallest overall total length.

Apply the minimum capacity formula.

\text{Total} = L + R - M - 2

We add the rank from the left (

L

) and the rank from the right (

R

), then subtract the number of items strictly between them (

M

) and the 2 reference items to correct for double-counting.

Substitute the given values and calculate the final count.

\text{Total} = 28 + 35 - 12 - 2 = 49

This yields the exact minimum count of books on the shelf.

Key Concept

Overlapping Minimum Capacity in Ordering and Ranking

Estimated Time:1m 0s

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