Quantitative Aptitude (QA) Test

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Quantitative Aptitude (QA) Test - 33

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Question 1
3 / -1

ABCDE is a regular pentagon of side 6cm. O is the center of the pentagon and perpendicular distance from center O to a side is 4.125cm. Find the area of pentagon ABCDE.

A
30cm²

B
27.5cm²

C
61.875cm²

D
22.5cm²

Solution

The area of a regular polygon

× perimeter × perpendicular distance from the center of the polygon to any side

× 30 × 4.125

= 61.875cm²

Hence, (C).
Question 2
3 / -1

If the students in three batches of CATMock are in ratio 2:3:4 if 30 students get admitted to each of the three batch then the new ratio will be 3:4:5 then the total number of students that enrolled till now is?

A
180

B
240

C
360

D
420

Solution

Let the initial number of students be 2x, 3x & 4x

And the final number of students be 3y, 4y & 5y

Now, 2x + 30 = 3y;.... (1)

3x + 30 = 4y; ......(2)

4x + 30 = 5y ......(3)

Solve for x & y

y = 30 & x = 30

total number of students will be 12y = 12(30) = 360.
Question 3
3 / -1

A and B can do a work in 12 and 18 days respectively. They worked together for 3 days after which C comes from vacation and joined A & B and the remaining work was together completed by A,B & C in next 4 days in how many days will C alone can complete 50% of the same work?

A
36

B
48

C
56

D
72

Solution

Let the total work be 36 units

1 day work of A will 36/12 = 3 units = a

1 day work of B will 36/18 = 2 units = b

In 3 days A & B will total do 3(2 + 3) = 15 units of work

Work left 36 - 15 = 21 units

4(a + b + c) = 21 => c = 0.25

Therefore, C alone can complete 50 % of the same work = 72 days.
Question 4
3 / -1

There are 7 students who appeared for the examination of 100 marks with passing marks of 33. The highest marks scored among them is 85 and the lowest marks scored among them is 35. Which of the following cannot be the value of the average score taken by the 7 students?

A
76

B
77

C
42

D
41

Solution

The highest marks scored is 85 and the lowest marks scored is 35.

CASE 1: Let all the other students score as much time as the highest marks scored by the student

35 + 85 + 85 + 85 + 85 + 85 + 857 = 77.85

CASE 2 : Let all the other students score as much time as the lowest marks scored by the student

35 + 35 + 35 + 35 + 35 + 35 + 857 = 42.14

So, the average score of these 7 students will lie between 42.14 & 77.85.
Question 5
3 / -1

Aman’s weighing machine shows 550gm when the actual weight is 500gm, the cost price of rice is Rs.280/Kg he sells them in a packing of 330gm per packet according to the machine at what rate should be the selling price of each packet so he earns a profit of 50%?

A
84

B
105

C
126

D
130

Solution

For every 500gm weighing machine shows 550gm

Therefore, to show 330gm packet he gives 300gm of rice because of faulty machine

The cost price of 300gm of rice will be = Rs.84

The selling price of each packet of 330gm according to the faulty machine must be 84 × 1.5 = 126.
Question 6
3 / -1

Perimeter of a triangle is equal to 18. How many triangles are possible with such perimeter so that all the sides of the tringle are integers? [Write the closest integer]

A
7

B
8

C
6

D
9

Solution

Since the perimeter is even then the total number of non-congruent triangles must be

The closet integer is 7

Therefore, 7.
Question 7
3 / -1

Determine the dimensions of a single sheet of paper required to completely wrap a cuboid with dimensions 14cm × 2cm × 12cm without tearing the paper?

A
17cm by 11cm

B
13cm by 16cm

C
0.5cm

D
17cm by 13cm

Solution

Total surface area is (14 × 2) + (2 × 12) + (14 × 12) = 220cm²

We need a sheet whose total surface area is greater than 220cm².
Question 8
3 / -1

Karan & Arjun are running along a circular track in opposite direction and they started from different points and they meet at exactly two distinct points along the same track ,If Karan takes 25secs to complete the track then in how many seconds will Arjun complete the track?

A
25sec

B
50sec

C
12sec

D
None of the above

Solution

There are only two meeting points irrespective of their positions

So we can conclude that their speeds are in ratio 1:1

Therefore, time taken by Karan to complete the round will be equal to time taken by Arjun to complete the round therefore, time taken by Arjun will be 25secs.
Question 9
3 / -1

If 16x + 8|y| = 48. How many non-negative integral values of x are possible?

A
1

B
2

C
3

D
4

Solution

8|y| = 48 - 16x

|y| =7 - 2x

Since, |y| will always be positive therefore, 7 - 2x should also be positive

7 - 2x ≥ 0

7 ≥ 2x

3.5 ≥ x

Range of x = (-∞,3.5]

Therefore, non –negative integral values of x will be 0, 1, 2, 3.
Question 10
3 / -1

Log_0.5(n² + 36) > Log_0.5 (15n + 10) then what are the number of values n can hold?

A
8

B
9

C
10

D
11

Solution

when in logab; a < 1 then

n² + 36 < 15n + 10

n² - 15n + 26 < 0

(n - 13) (n - 2) < 0

n belongs to (2, 13)

therefore, number of values n can hold is 10.

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Re-Attempt Weekly Quiz Competition

Quantitative Aptitude (QA) Test - 33

Result

Quantitative Aptitude (QA) Test - 33

Score

-

Rank

-

SHARING IS CARING

Question 1

30cm﻿2

27.5cm﻿2 ﻿

61.875cm﻿2

22.5cm﻿2

Solution

Question 2

180

240

360

420

Solution

Question 3

36

48

56

72

Solution

Question 4

76

77

42

41

Solution

Question 5

84

105

126

130

Solution

Question 6

7

8

6

9

Solution

Question 7

17cm by 11cm

13cm by 16cm

0.5cm

17cm by 13cm

Solution

Question 8

25sec

50sec

12sec

None of the above

Solution

Question 9

1

2

3

4

Solution

Question 10

8

9

10

11

Solution

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30cm²

27.5cm²

61.875cm²

22.5cm²