Research Aptitude Test

Result

Research Aptitude Test - 24

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Weekly Quiz Competition

Question 1
2 / -0.5

Direction: A cuboid is divided into 192 identical cubelets This is done by making minimum no. ot cuts possible. All cuts are parallel to some of the face. But before doing so. The cube is painted with green color on one set of opposite faces. Blue on other set of opposite faces and red on their pair of annosit faces.

What is the number of cubelets possible which are painted with none of the color?

A
A. 16

B
B. 24

C
C. 36

D
D. 48

Solution

Number of unpainted cubelets will be (4 -2) x (6 - 2) x (8 - 2) = 2 x 4 x 6 = 48

Hence option (d)
Question 2
2 / -0.5

How many cuboids of dimensions 4 x 5 x 6 are required to form a cube of least size if cuboids have to the placed adjacent, above or below each other?

A
A. 1600

B
B. 1800

C
C. 1200

D
D. None of these

Solution

Least possible dimension of cube is ICM of (4, 5,6) = 60

The number of cuboids required
Question 3
2 / -0.5

A cube has been cut into cuboids of size 2 x 3 x 4. What is least possible integer length of the edge of cube and how many such cuboids are obtained from this cube?

A
A. 96

B
B. 72

C
C. 60

D
D. 84

Solution

The least possible dimension of cube LCM of 2,3,4 = 12

No, of cuboids that can be obtained
Question 4
2 / -0.5

Direction: Three adjacent faces of one cube is painted in pink, one adjacent pair of faces is painted in black and the remaining faces are painted in violet. The cube is the cut into 216 identical cubelets.

How many of the cubelets have exactly one painted surface of exactly one color?

A
84

B
108

C
96

D
102

Solution

In this question only the cubelets from middle of faces of cube will be considered = 6 x (6 - 2) ² = 96 cubelets.
Question 5
2 / -0.5

Direction: Three adjacent faces of one cube is painted in pink, one adjacent pair of faces is painted in black and the remaining faces are painted in violet. The cube is the cut into 216 identical cubelets.

How many cubelets do not have pink color on them?

A
120

B
140

C
150

D
125

Solution

The number of cubelets with no pink color = 216 - (36 from one pink surface + 30 from second + 25 from third)

= 125 cubelets
Question 6
2 / -0.5

Direction: Three adjacent faces of one cube is painted in pink, one adjacent pair of faces is painted in black and the remaining faces are painted in violet. The cube is the cut into 216 identical cubelets.

How many cubelets have black or violet color on them but not pink color on them?

A
60

B
59

C
61

D
64

Solution

Here cubelets without any face colored has to be removed from previous question number. The number of cubelets with black or violet but not pink

= 125 - (6 - 2)³ = 61
Question 7
2 / -0.5

Vinod walks 20 m towards the North. He then turns left and walks 40 m. He again turns left and walks 20 m. Further, he moves 20 m after turning to the right. How far is he from his original position?

A
A. 20m

B
B. 30m

C
C. 50 m

D
D. 60 m

Solution

The movements of Vinod are as shown in Fig,

Clearly; Vinod’s distance from his initial position

P ⇒ PX = (PS + SX)

= (OR + SX)

= (40 + 20) m = 60 m.
Question 8
2 / -0.5

From his house Sanjay went 15 kms to the North, Then he turned West and covered 10 kms. Then, he turned South and covered 5 kms. Finally, turning to East, he covered 10 kms. In which direction is he from his house?

A
A. East

B
B. West

C
C. North

D
D. South

Solution

The movements of Sanjay are as shown in Fig.

(A to B, B to C, C to D and D to E)

Clearly, his final position is E which is to the North of his house at A..
Question 9
2 / -0.5

Direction: The figure given below consists of three interesting circles which represent sets of students who play Tennis, Badminton and Volleyball Each region in the figure is represented by a small letter.

On the basis of the above figure, answer the questions given below.

Which letter represents the set of persons who play all the three games?

A
A. b

B
B. c

C
C. f

D
D. g

Solution

The required regions is the one common to all the three circles i.e. c.
Question 10
2 / -0.5

Direction: The figure given below consists of three interesting circles which represent sets of students who play Tennis, Badminton and Volleyball Each region in the figure is represented by a small letter.

On the basis of the above figure, answer the questions given below.
Which letter represents the set of persons who play Tennis and Volleyball but not Badminton?

A
A. g

B
B. e

C
C. c

D
D. b

Solution

The required region is the one which is common to circle s P and R but is not a part of circle Q. i.e. b.