Mental Ability, Analytical and Logical Reasoning (UPSC) Part-I

Total Questions: 50

41. An equilateral triangular plate is to be cut into a number of identical small equilateral triangular plates. Which of the following can be possible value of n? [2005]

(a) 196
(b) 216
(c) 256
(d) 296

Correct Answer: (c) 256

Solution:An equilateral triangle whenever divided into equal parts, gives rise to 4 equilateral triangles. Hence, it is always in powers of 4, whenever it is equally divided further. Thus 4⁴256

42. P, Q, R, S and T reside in a five-storeyed (Ground + 4) building, and each of them resides on a separate floor. Further: [2005]

1. T does not reside on the topmost floor.

2. Q does not reside on the ground floor.

3. S resides on one storey above that of P and one storey below that of R. To know as the which one of the five persons resides on the ground floor which of the above statements are sufficient/ insufficient?

(a) 1 and 3 are sufficient
(b) 2 and 3 are sufficient
(c) 1, 2 and 3 are sufficient
(d) 1, 2 and 3 are insufficient

Correct Answer: (d) 1, 2 and 3 are insufficient

Solution:On the basis of the given statements there can be 3 arrangements:

As either of T or P can reside on the ground floor, so to exactly find who resides on the ground floor, given statements are insufficient.

43. A box contains five sets of balls while there are 3 balls in each set. Each set of balls has one color which is different from every other set, what is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed? [2006]

(a) 6
(b) 7
(c) 8
(d) 9

Correct Answer: (a) 6

Solution:

Now, any further removal of balls from any set will ensure that removed ball is of the same colour as one of the already removed balls, thus constituting a pair of the removed balls of the same colour.

Hence, minimum no. of removed balls = 6

44. In an office, the number of persons who take tea is twice the number of persons who take only coffee. The number of persons who take coffee is twice the number of persons who take only tea. [2006]

Consider the following statement:

1. The sum of the number of persons who take either tea or coffee or both is four times the number of persons who take both coffee and tea.

2. The sum of the number of persons who take only coffee and those who take only tea is twice the number of persons who take both tea and coffee.

Which of the statement(s) given above is/are correct?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Correct Answer: (b) 2 only

Solution:Let the no. of only tea takers be x, number of only coffee takers be y and number of both tea and coffee takers be z.

Now, x + z = 2y ....(i)

y + z = 2x .....(ii)

Solving (i) and (ii), we get,

x = y = z ∴ x + y + z = z + z + z = 3z

Thus, statement 1 is not correct.

Also, x + y = z + z = 2z

Thus, statement 2 is correct.

45. Each of the six faces of a cube is numbered by one of the digits from 1 to 6. This cube is shown in its four different positions in the figure I, II, III, and IV. [2006]

Consider the following statements.

1. Figures II and III are sufficient to known as to which face is opposite to the face numbered 6.

2. figures II and III are sufficient to known as to which face is opposite to the face numbered 4.

3. Figures I and IV are sufficient to known as to which face is opposite to the face numbered 3.

Which of the statements given above are correct?

(a) 1 and 3 only
(b) 1 and 2 only
(c) 2 and 3 only
(d) 1, 2 and 3

Correct Answer: (d) 1, 2 and 3

Solution:Statement 1 is correct as it clearly shows that 1, 2, 5 and 6 are on the sides of 4 and 1 is opposite. Statement 2 is correct on the same lines. 3 is opposite 4. 3 is correct as I & IV clearly tells that 4 is opposite 3. All the three statements regarding the figure given in the question are correct. Hence, the answer is (d).

46. A watch showed a time of fourteen minutes past nine (9 hrs and 14 minutes). The positions of the hour-hand and the minute hand of the watch are exactly interchanged. The new time shown by the watch is closest to which one of the following? [2006]

(a) Twelve minutes to three
(b) Thirteen minutes to three
(c) Fourteen minutes to three
(d) Fifteen minutes to three

Correct Answer: (c) Fourteen minutes to three

Solution:Angle rotated by hour hand at time 9 : 14
9 × 30° + 14 × 30°/60 = 270 + 7 = 277°
when hour and minute hand interchange their position, then time when minutes hand rotated by

277° = 277°/6° = 46.16 mins ≈ 46 mins

So, new time will be 14 min. to go to there.
According to question
After Interchange hour and mine hand.

The new time shown by the watch is closet to fourteen minutes to three.

47. Solve it. [2006]

What is the value of X in figure III ?

(a) 4
(b) 16
(c) 25
(d) 36

Correct Answer: (d) 36

Solution:In every figure the sum of square route of all corner digits comes in middle box. Here, underoot of 9 =3
Underoot of 64 = 8, underoot of 1 = 1

Now, 3+8+1 = 12

18-12 = 6 ∴ x = (6)2 = 36

48. Six faces of a cube are numbered from 1 to 6, each face carrying one different number. Further, [2007]

1. The face 2 is opposite to the face 6.

2. The face 1 is opposite to the face 5.

3. The face 3 is between the face 1 and the face 5

4. The face 4 is adjacent to the face 2.

Which one of the following is correct?

(a) The face 2 is adjacent to the face 3
(b) The face 6 is between the face 2 and the face 4
(c) The face 1 is between the face 5 and the face 6
(d) None of the above

Correct Answer: (a) The face 2 is adjacent to the face 3

Solution:As it is clear from the figure that face 2 is adjacent to face 3.

49. How many different triangles are there in the figure shown below? [2008]

(a) 28
(b) 24
(c) 20
(d) 16

Correct Answer: (a) 28

Solution:Total number of triangles in the three square boxes = 24. Number of triangles formed in two adjacent square boxes = 4.
Hence, total number triangles = 24 + 4 = 28

50. Six persons A, B, C, D, E and F are standing in a row. Cand D are standing close to each other alongside E. B is standing beside A only. A is fourth from F. Who are standing on the extremes?

(a) A and F
(b) B and D
(c) B and F
(d) None of the above

Correct Answer: (c) B and F

Solution:C, D, E are together.

Also, A and B are together.

Possible arrangements,

BACDE or CDE AB

Now, since A is fourth from F,

F must lie on the extreme end.

Thus, B and F are on the extreme positions.

BACDEF or FCDEAB

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