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Question 1Analytical Ability - Data Sufficiency

In a data sufficiency problem you are asked: "What is the value of x?" Statement I says x² = 36. Statement II says x is a positive integer. Which conclusion is correct?

  1. Both statements together are not sufficient
  2. Each statement alone is sufficient
  3. Statement I alone is sufficient, but statement II alone is not
  4. Both statements together are sufficient, but neither alone is sufficient Correct answer.

Explanation

Statement I alone yields x = 6 or x = −6, so it does not fix a single value. Statement II alone only restricts x to positive integers, which is far from unique. Combining them forces x = 6, so together they are sufficient while neither alone is.

Question 2Analytical Ability - Data Sufficiency

A question asks for the present age of a father. Statement I: five years ago the father was four times as old as his son. Statement II: the present age of the son is 15 years. Which option is correct?

  1. Statement I alone is sufficient
  2. Both statements together are not sufficient
  3. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  4. Statement II alone is sufficient

Explanation

Statement I relates the two ages but leaves the son's age unknown, so it gives no unique father's age. Statement II gives only the son's age and says nothing about the father. Using both, the father's age five years ago was 4 × (15 − 5) = 40, so he is now 45.

Question 3Analytical Ability - Data Sufficiency

A data sufficiency item asks whether a two-digit number N is divisible by 9. Statement I: the sum of the digits of N is 18. Statement II: N is a multiple of 3. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient
  2. Statement II alone is sufficient, but statement I alone is not
  3. Statement I alone is sufficient, but statement II alone is not Correct answer.
  4. Both statements together are not sufficient

Explanation

A number is divisible by 9 exactly when its digit sum is a multiple of 9, and a digit sum of 18 guarantees divisibility by 9. Being a multiple of 3 does not guarantee divisibility by 9, since 12 is a multiple of 3 but not of 9.

Question 4Analytical Ability - Data Sufficiency

The question asks for the area of a rectangle. Statement I: the perimeter of the rectangle is 30 cm. Statement II: the length exceeds the breadth by 3 cm. Which option is correct?

  1. Statement II alone is sufficient
  2. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  3. Statement I alone is sufficient
  4. Both statements together are not sufficient

Explanation

The perimeter gives only the sum length + breadth = 15, which many pairs satisfy, so statement I alone fails. Statement II gives only a difference between the sides. Together they form two linear equations, giving breadth 6 and length 9, hence a unique area of 54 sq cm.

Question 5Analytical Ability - Data Sufficiency

You must decide whether a quadratic equation has real roots. Statement I: the discriminant of the equation is 25. Statement II: the constant term is negative. Which option is correct?

  1. Statement II alone is sufficient, but statement I alone is not
  2. Both statements together are sufficient, but neither alone is sufficient
  3. Each statement alone is sufficient Correct answer.
  4. Statement I alone is sufficient, but statement II alone is not

Explanation

A quadratic has real roots exactly when its discriminant is non-negative, and a discriminant of 25 is positive, so statement I settles it. With a negative constant term the product of the roots is negative, forcing one positive and one negative real root, so statement II also settles it independently.

Question 6Analytical Ability - Data Sufficiency

The question asks: is the integer n even? Statement I: n² is even. Statement II: 3n is even. Which option is correct?

  1. Each statement alone is sufficient Correct answer.
  2. Statement II alone is sufficient, but statement I alone is not
  3. Both statements together are sufficient, but neither alone is sufficient
  4. Statement I alone is sufficient, but statement II alone is not

Explanation

An integer and its square have the same parity, so n² even forces n even, making statement I sufficient. Likewise 3 is odd, so 3n is even exactly when n is even, making statement II sufficient as well. Hence each statement decides the question on its own.

Question 7Analytical Ability - Data Sufficiency

A question asks for the speed of a train. Statement I: the train covers 240 km in 3 hours. Statement II: the train crosses a 300 m platform in 30 seconds. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient
  2. Each statement alone is sufficient
  3. Statement I alone is sufficient, but statement II alone is not Correct answer.
  4. Statement II alone is sufficient, but statement I alone is not

Explanation

Statement I gives speed directly as 240 ÷ 3 = 80 km/h, so it is sufficient. Statement II involves the train's own length, which is unknown, so the crossing time does not fix the speed. Thus only statement I settles the question.

Question 8Analytical Ability - Data Sufficiency

The question asks for the value of the positive integer k. Statement I: k is a prime number less than 10. Statement II: k divides 21. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  2. Statement I alone is sufficient
  3. Both statements together are not sufficient
  4. Statement II alone is sufficient

Explanation

Statement I allows 2, 3, 5 and 7, so it is not sufficient. Statement II allows 1, 3, 7 and 21, so it is also not sufficient. The common values are 3 and 7, so even together the statements leave two possibilities and the value of k is not determined.

Question 9Analytical Ability - Data Sufficiency

A question asks for the number of students in a class. Statement I: the average marks of the class is 65. Statement II: the total marks of the class is 2600. Which option is correct?

  1. Statement II alone is sufficient
  2. Both statements together are not sufficient
  3. Statement I alone is sufficient
  4. Both statements together are sufficient, but neither alone is sufficient Correct answer.

Explanation

An average alone does not reveal the count, and a total alone does not either. Using both, the number of students is total marks divided by average marks, that is 2600 ÷ 65 = 40, so the two statements together are sufficient.

Question 10Analytical Ability - Data Sufficiency

The question asks for the compound interest on a sum for two years. Statement I: the sum is ₹8000. Statement II: the rate of interest is 10% per annum compounded annually. Which option is correct?

  1. Statement II alone is sufficient
  2. Both statements together are not sufficient
  3. Statement I alone is sufficient
  4. Both statements together are sufficient, but neither alone is sufficient Correct answer.

Explanation

Compound interest depends on the principal, the rate and the time, and the time of two years is already given in the question. Statement I supplies only the principal and statement II only the rate, so neither alone can compute the interest. Together they give ₹8000 × 1.1² − ₹8000 = ₹1680.

Question 11Analytical Ability - Data Sufficiency

A question asks whether triangle ABC is right-angled. Statement I: AB = 5 cm and BC = 12 cm. Statement II: AC = 13 cm. Which option is correct?

  1. Both statements together are not sufficient
  2. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  3. Statement I alone is sufficient
  4. Statement II alone is sufficient

Explanation

Two side lengths alone do not fix the third side or the angles, so statement I is insufficient. One side length alone is plainly insufficient. Taking all three sides, 5² + 12² = 13², so the converse of the Pythagoras theorem confirms a right angle at B.

Question 12Analytical Ability - Data Sufficiency

The question asks for the value of x + y. Statement I: x − y = 4. Statement II: 2x + 2y = 20. Which option is correct?

  1. Each statement alone is sufficient
  2. Both statements together are sufficient, but neither alone is sufficient
  3. Statement I alone is sufficient, but statement II alone is not
  4. Statement II alone is sufficient, but statement I alone is not Correct answer.

Explanation

Statement II can be halved to give x + y = 10 directly, so it answers the question on its own. Statement I gives only the difference of the two variables and cannot determine their sum. Hence only statement II is sufficient.

Question 13Analytical Ability - Data Sufficiency

A question asks for the probability that a card drawn from a standard pack is a king. Statement I: the card drawn is a face card. Statement II: the card drawn is not a queen or a jack. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  2. Both statements together are not sufficient
  3. Statement I alone is sufficient
  4. Statement II alone is sufficient

Explanation

Face cards include kings, queens and jacks, so statement I leaves 12 cards and does not fix the probability. Statement II excludes queens and jacks but still admits aces through tens as well as kings. Together the card must be a face card that is neither queen nor jack, that is a king, so the probability is 4/52 = 1/13.

Question 14Analytical Ability - Data Sufficiency

The question asks for the ratio of two positive numbers a and b. Statement I: a is 25% more than b. Statement II: b is 20% less than a. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient
  2. Each statement alone is sufficient Correct answer.
  3. Statement I alone is sufficient, but statement II alone is not
  4. Statement II alone is sufficient, but statement I alone is not

Explanation

Statement I gives a = 1.25b, so a : b = 5 : 4, which is sufficient. Statement II gives b = 0.8a, so a : b = 1 : 0.8 = 5 : 4, which is also sufficient. The two statements are in fact equivalent, so each determines the ratio alone.

Question 15Analytical Ability - Data Sufficiency

A question asks for the number of diagonals of a convex polygon. Statement I: the polygon has 8 sides. Statement II: the sum of the interior angles of the polygon is 1080°. Which option is correct?

  1. Statement I alone is sufficient, but statement II alone is not
  2. Statement II alone is sufficient, but statement I alone is not
  3. Both statements together are sufficient, but neither alone is sufficient
  4. Each statement alone is sufficient Correct answer.

Explanation

The number of diagonals of an n-sided polygon is n(n − 3)/2, so statement I gives 8 × 5 / 2 = 20 diagonals. The interior-angle sum is (n − 2) × 180°, so 1080° forces n = 8, giving the same answer. Thus each statement alone is sufficient.

Question 16Analytical Ability - Data Sufficiency

The question asks for the value of the two-digit number M. Statement I: the product of the digits of M is 6. Statement II: the sum of the digits of M is 5. Which option is correct?

  1. Statement II alone is sufficient
  2. Statement I alone is sufficient
  3. Both statements together are not sufficient
  4. Both statements together are sufficient, but neither alone is sufficient Correct answer.

Explanation

Digit pairs with product 6 are (1,6), (6,1) and (2,3), (3,2), so statement I alone leaves several numbers. Digit pairs with sum 5 include (1,4), (2,3), (3,2) and (4,1), so statement II alone also fails. Together only the pair (2,3) satisfies both, but 23 and 32 both do, so even together the statements do not determine M.

Question 17Analytical Ability - Data Sufficiency

A question asks whether a positive integer p is divisible by 6. Statement I: p is divisible by 2. Statement II: p is divisible by 3. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  2. Statement I alone is sufficient
  3. Statement II alone is sufficient
  4. Both statements together are not sufficient

Explanation

Divisibility by 6 requires divisibility by both 2 and 3. Statement I alone admits odd multiples of 3 such as 9, which are not divisible by 6, and statement II alone admits 3 itself. When both hold, since 2 and 3 are coprime, p must be divisible by 6.

Question 18Analytical Ability - Data Sufficiency

The question asks for the simple interest earned on a sum in 4 years. Statement I: the principal is ₹5000. Statement II: the rate is 8% per annum. Which option is correct?

  1. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  2. Statement II alone is sufficient
  3. Statement I alone is sufficient
  4. Both statements together are not sufficient

Explanation

Simple interest equals principal × rate × time ÷ 100. The time of 4 years is given in the question, but statement I gives only the principal and statement II only the rate, so neither alone is enough. Using both, the interest is 5000 × 8 × 4 ÷ 100 = ₹1600.

Question 19Analytical Ability - Data Sufficiency

A question asks for the curved surface area of a right circular cylinder. Statement I: the radius of the base is 7 cm. Statement II: the height of the cylinder is 10 cm. Which option is correct?

  1. Statement I alone is sufficient
  2. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  3. Both statements together are not sufficient
  4. Statement II alone is sufficient

Explanation

The curved surface area of a cylinder is 2πrh, which needs both the radius and the height. Statement I supplies only the radius and statement II only the height, so neither alone works. Together they give 2 × 22/7 × 7 × 10 = 440 sq cm.

Question 20Analytical Ability - Data Sufficiency

The question asks for the value of the expression 1/a + 1/b, where a and b are non-zero. Statement I: a + b = 7. Statement II: ab = 12. Which option is correct?

  1. Statement II alone is sufficient
  2. Both statements together are sufficient, but neither alone is sufficient Correct answer.
  3. Statement I alone is sufficient
  4. Both statements together are not sufficient

Explanation

The expression simplifies to (a + b)/ab, so both the sum and the product of a and b are needed. Statement I gives only the sum and statement II only the product, so neither alone determines the value. Together they give 7/12, a single definite value.

Question 21Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Find the next term of the series: 3, 7, 15, 31, 63, ?

  1. 127 Correct answer.
  2. 128
  3. 125
  4. 126

Explanation

Each term is obtained by doubling the previous term and adding 1: 3×2+1=7, 7×2+1=15, and so on. Applying the same rule to 63 gives 63×2+1=127. Equivalently, every term is one less than a power of two.

Question 22Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

In a certain code, MOUSE is written as NPVTF. How is TIGER written in that code?

  1. UJHES
  2. SJHFS
  3. UJHFS Correct answer.
  4. UIHFS

Explanation

Every letter of the word is shifted one place forward in the alphabet: M→N, O→P, U→V, S→T, E→F. Applying the same shift to TIGER gives U, J, H, F, S, that is UJHFS. The shift is uniform, so no letter may be left unchanged.

Question 23Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Pointing to a photograph, Ravi says, "She is the daughter of my grandfather's only son." How is the woman in the photograph related to Ravi?

  1. Cousin
  2. Aunt
  3. Niece
  4. Sister Correct answer.

Explanation

Ravi's grandfather's only son must be Ravi's own father, since Ravi's father is the sole male child of that grandfather. The daughter of Ravi's father is therefore Ravi's sister. No other relationship is consistent with the word 'only son'.

Question 24Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Six friends A, B, C, D, E and F sit in a row facing north. A sits at the extreme left end. F sits immediately to the right of A. C sits at the extreme right end. If B sits exactly between A and C, which friend sits immediately to the left of C?

  1. B
  2. F
  3. D
  4. E Correct answer.

Explanation

Positions 1 to 6 from left: A is 1, F is 2, C is 6. B is exactly midway between A (position 1) and C (position 6), which is not an integer, so the only consistent reading is that B occupies the middle seat of the six, position 3 or 4, and E and D fill the rest. The seat immediately left of C, position 5, is then E, since B is placed at position 3 and D at position 4.

Question 25Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Statements: All pens are books. Some books are red. Conclusions: I. Some pens are red. II. Some books are pens. Which conclusion follows?

  1. Only II follows Correct answer.
  2. Both I and II follow
  3. Only I follows
  4. Neither I nor II follows

Explanation

From 'All pens are books' the converse partial statement 'Some books are pens' is valid, so conclusion II follows. The red books may be entirely outside the pen group, so conclusion I does not necessarily follow. This is the standard trap of combining an All statement with a Some statement that shares only the middle term.

Question 26Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A clock shows 3:30. What is the angle between the hour hand and the minute hand?

  1. 60 degrees
  2. 90 degrees
  3. 75 degrees Correct answer.
  4. 105 degrees

Explanation

At 3:30 the minute hand points at 6, covering 180 degrees from 12. The hour hand is halfway between 3 and 4, at 3.5 hours, that is 3.5 × 30 = 105 degrees. The difference is 180 − 105 = 75 degrees.

Question 27Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A solid cube is painted on all faces and then cut into 64 equal smaller cubes. How many of the small cubes have exactly two faces painted?

  1. 24 Correct answer.
  2. 32
  3. 8
  4. 16

Explanation

A 4×4×4 cut gives 64 small cubes. Cubes with exactly two painted faces lie along the edges but exclude the corners, so each edge contributes 4 − 2 = 2 such cubes. With 12 edges, the count is 12 × 2 = 24.

Question 28Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

If 15 August 2023 was a Tuesday, what day of the week was 15 August 2024?

  1. Wednesday
  2. Thursday Correct answer.
  3. Saturday
  4. Friday

Explanation

From 15 August 2023 to 15 August 2024 the span includes 29 February 2024, so it covers 366 days. Since 366 = 52 × 7 + 2, the day advances by two: Tuesday plus two days is Thursday.

Question 29Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Find the missing term: 2, 6, 12, 20, 30, ?

  1. 44
  2. 42 Correct answer.
  3. 40
  4. 36

Explanation

The differences are 4, 6, 8, 10, so the next difference is 12 and 30 + 12 = 42. Equivalently each term is n(n+1) for n = 1, 2, 3, …, and for n = 6 this gives 6 × 7 = 42.

Question 30Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

In a code language, if 'rose is red' is written as 'pa ka ta' and 'red is bright' is written as 'ta ka ma', what is the code for 'rose'?

  1. ta
  2. ka
  3. ma
  4. pa Correct answer.

Explanation

The words common to both sentences are 'is' and 'red', and the common codes are ka and ta, so those two codes stand for 'is' and 'red' in some order. The word 'rose' appears only in the first sentence, so its code must be the remaining code there, pa.

Question 31Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Five people P, Q, R, S and T sit around a circular table facing the centre. P sits second to the right of Q. R sits immediately to the left of Q. If S sits second to the left of P, who sits immediately to the right of P?

  1. Q
  2. T Correct answer.
  3. R
  4. S

Explanation

Fix Q at a seat. R is immediately to Q's left, P is second to Q's right, so the seats already used are Q, R and P. S is second to the left of P, occupying the remaining seat next to R on P's far side, leaving T in the only open seat, which is immediately to the right of P. Hence T is the answer.

Question 32Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Statements: No cat is a dog. All dogs are animals. Conclusions: I. No cat is an animal. II. Some animals are not cats. Which conclusion follows?

  1. Only II follows Correct answer.
  2. Both I and II follow
  3. Neither I nor II follows
  4. Only I follows

Explanation

Dogs are animals and no cat is a dog, so those animal dogs are outside the cat set, which makes 'Some animals are not cats' valid. Conclusion I is too strong, because a cat could still be an animal of another kind. Hence only II follows.

Question 33Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

What was the day of the week on 26 January 1950?

  1. Thursday Correct answer.
  2. Tuesday
  3. Friday
  4. Wednesday

Explanation

Counting odd days from 1 January 1900, a Thursday, to 26 January 1950: the years 1900 to 1949 contribute 49 years with 12 leap years, giving 49 + 12 = 61 odd days, which is 5. The 25 days from 1 January to 26 January give 4 odd days. Total odd days = 5 + 4 = 9, that is 2, and Thursday plus 2 is Thursday again after a full week plus two days, landing on Thursday.

Question 34Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A cube of side 5 cm is painted green on all faces and cut into 125 unit cubes. How many unit cubes have no face painted?

  1. 54
  2. 8
  3. 36
  4. 27 Correct answer.

Explanation

The unpainted cubes form an inner cube of side 5 − 2 = 3, since one layer is removed from every face. Its count is 3 × 3 × 3 = 27. This is the standard interior-cube formula (n − 2)³ for an n × n × n cut.

Question 35Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

In a family, A is the father of B. B is the sister of C. C is the son of D. D is the mother of E. How is A related to E?

  1. Brother
  2. Uncle
  3. Grandfather
  4. Father Correct answer.

Explanation

A and D are the parents of B and C, since A is B's father and D is C's mother. E is the child of D, so E is a sibling of B and C and therefore also a child of A. Thus A is E's father.

Question 36Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Complete the series: AZ, BY, CX, DW, ?

  1. EU
  2. EV Correct answer.
  3. FV
  4. DV

Explanation

The first letters advance A, B, C, D, so the next is E. The second letters move backward Z, Y, X, W, so the next is V. Combining them gives EV, and the two letters always sit at opposite ends of the alphabet.

Question 37Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Seven students sit in a row facing north. M is fourth from the left. N is third from the right. If M and N are neighbours, how many students sit between M and the right end?

  1. 4
  2. 2
  3. 3 Correct answer.
  4. 5

Explanation

With seven seats, M is at position 4 from the left, which is also position 4 from the right. N is third from the right, at position 5. They are neighbours, consistent with the data. From M at position 4 to the right end at position 7 there are positions 5, 6, 7, so three students sit to M's right.

Question 38Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A clock gains 5 minutes every hour of real time. If it is set right at 8:00 a.m., what time will it show when the real time is 4:00 p.m. on the same day?

  1. 4:35 p.m.
  2. 4:45 p.m.
  3. 4:30 p.m.
  4. 4:40 p.m. Correct answer.

Explanation

In 8 real hours the faulty clock gains 8 × 5 = 40 minutes. So when the true time is 4:00 p.m., the clock shows 4:00 p.m. plus 40 minutes, that is 4:40 p.m. The gain accumulates at a constant rate of 5 minutes per real hour.

Question 39Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

If in a certain year 1 March falls on a Sunday, which date in the same month falls on a Tuesday?

  1. 24 March
  2. 17 March
  3. 10 March
  4. 3 March Correct answer.

Explanation

1 March is Sunday, so 2 March is Monday and 3 March is Tuesday. Every date that is 3 plus a multiple of 7 also falls on Tuesday, but among the given choices only 3 March satisfies this within the same week.

Question 40Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

In a certain code, if 'water' is coded as 'liquid', 'liquid' is coded as 'solid', 'solid' is coded as 'gas' and 'gas' is coded as 'plasma', then what is the code for 'solid'?

  1. liquid
  2. plasma
  3. water
  4. gas Correct answer.

Explanation

This is a direct substitution code, so the code for a word is simply the word listed against it. Against 'solid' the code given is 'gas'. No chaining of substitutions is involved.

Question 41Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Statements: All roses are flowers. All flowers are plants. Some plants are trees. Conclusions: I. All roses are plants. II. Some trees are roses. Which conclusion follows?

  1. Neither I nor II follows
  2. Only I follows Correct answer.
  3. Only II follows
  4. Both I and II follow

Explanation

Chaining the two All statements gives 'All roses are plants', so conclusion I is valid. The trees mentioned are only some plants, and nothing guarantees that those trees overlap with roses, so conclusion II is not forced.

Question 42Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Five boxes are stacked one above another. Box P is above box Q. Box R is below box Q. Box S is above box P. Box T is between P and Q. Which box is at the bottom if R is directly below Q?

  1. P
  2. R Correct answer.
  3. Q
  4. T

Explanation

Ordering from top: S is above P, T is between P and Q, and R is directly below Q, so the stack reads S, P, T, Q, R. The bottom position is therefore held by R. Every constraint is satisfied by this single arrangement.

Question 43Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A cube is painted on all faces and cut into 216 equal smaller cubes. How many small cubes have exactly one face painted?

  1. 24
  2. 48
  3. 64
  4. 96 Correct answer.

Explanation

A 6×6×6 cut gives 216 cubes. On each face the painted cubes that are not on an edge form a (6 − 2) × (6 − 2) = 16 square. Six faces give 6 × 16 = 96 cubes with exactly one painted face.

Question 44Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

In a row of children facing north, Arun is 11th from the left and Bala is 15th from the right. If they interchange positions, Arun becomes 19th from the left. How many children are in the row?

  1. 29
  2. 35
  3. 31
  4. 33 Correct answer.

Explanation

After the interchange Arun occupies Bala's original place, which is 19th from the left. That same seat is 15th from the right, so the total is 19 + 15 − 1 = 33. The formula adds the two ranks and subtracts one for the shared child.

Question 45Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Three statements are given: All engineers are graduates. Some graduates are managers. No manager is a doctor. Which of the following must be true?

  1. Some graduates are not doctors Correct answer.
  2. All engineers are managers
  3. No graduate is a doctor
  4. Some engineers are doctors

Explanation

The managers who are graduates are excluded from doctors by the third statement, so at least some graduates are not doctors. The other options either overgeneralise or contradict the given statements. Hence only the first option is forced.

Question 46Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A series is given: 3, 7, 15, 31, 63, ? Which number continues the pattern?

  1. 125
  2. 126
  3. 129
  4. 127 Correct answer.

Explanation

Each term equals twice the previous term plus one: 3×2+1=7, 7×2+1=15, and so on. Applying the rule to 63 gives 63×2+1=127. The gaps 4, 8, 16, 32 also double each time, confirming the same result.

Question 47Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

In a certain code, MOUSE is written as NPVTF. Using the same code, how is TIGER written?

  1. SJHFS
  2. UJHFR
  3. UJHFS Correct answer.
  4. UIHFS

Explanation

Each letter of the word is replaced by the letter immediately after it in the alphabet: M→N, O→P, U→V, S→T, E→F. Applying the same shift to TIGER gives T→U, I→J, G→H, E→F, R→S, that is UJHFS.

Question 48Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Pointing to a photograph, Ravi said, 'She is the daughter of my grandfather's only son.' Ravi's father has no brothers. How is the girl in the photograph related to Ravi?

  1. Aunt
  2. Sister Correct answer.
  3. Cousin
  4. Niece

Explanation

The grandfather's only son must be Ravi's own father, since the father has no brothers. The daughter of Ravi's father is therefore Ravi's sister.

Question 49Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

A clock shows 7:00. What is the smaller angle between the hour hand and the minute hand?

  1. 120 degrees
  2. 210 degrees
  3. 150 degrees Correct answer.
  4. 180 degrees

Explanation

At 7:00 the minute hand points at 12 and the hour hand points at 7. Each hour mark is 30 degrees apart, so the separation is 5×30=150 degrees. This is already the smaller angle because it is below 180 degrees.

Question 50Analytical Ability - Problem Solving (series, coding-decoding, blood relations, seating, syllogisms, clocks and calendars, cubes, puzzles)

Find the missing term: 5, 11, 23, 47, 95, ?

  1. 189
  2. 190
  3. 193
  4. 191 Correct answer.

Explanation

Each term is obtained by doubling the previous term and adding one: 5×2+1=11, 11×2+1=23, and so on. Applying the rule to 95 gives 95×2+1=191. The differences 6, 12, 24, 48, 96 also double each time, which confirms the answer.