Quantitative Aptitude (QA) Test

Result

Quantitative Aptitude (QA) Test - 17

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Weekly Quiz Competition

Question 1
3 / -1

Some milk from a container, having 40 litres of milk, is drawn out and replaced with an equal amount of water. This process is repeated two more times and after that, only 20.48 litres of milk is left in the container. What is the amount of solution (in litres) removed in each iteration?

A
8

B
9

C
10

D
11

Solution
Question 2
3 / -1

Eight years ago, the ratio of ages of Akhil and Akash was 1:5. 12 years from now, the ratio changes to 7 : 15. Find the sum of the antecedent and the consequent of the ratio of their present ages, when the ratio is in its lowest form.

A
4

B
3

C
2

D
1

Solution

Let the present ages of Akhil and Akash be x and y respectively.
Question 3
3 / -1

Ratnesh bought a fridge and a television from big bazaar. He was promised 20% discount on the fridge and 25% discount on the television. However, a con salesman, interchanged the discount offered on both the items and processed the bill. If the mark price of the television is 4 times that of the fridge, then what is the ratio of the amount actually paid by Ratnesh to that he would have paid if he was not cheated?

A
8/7

B
79/76

C
41/39

D
21/19

Solution

Let Rs. 'x' be the mark price of the fridge. Then, the mark price of the television = Rs. 4x. Ratnesh was promised 20% discount on the fridge and 25% discount on the television. But the salesman interchanged the discounts on both the items. Therefore, Ramesh would have received 25% discount on the fridge whereas he would have received 20% discount on the television.

The actual amount which Ratnesh paid = 0.75 ∗ x + 0.80 ∗ 4x = 3.95x

The amount that he would have paid if he was not cheated = 0.80*x + 0.75*4x = 3.80x
Hence, the ratio of the amount actually paid by Ratnesh to that he would have paid if he was not cheated

Therefore, option B is the correct answer.
Question 4
3 / -1

Arun, Barun, Chandan and Diksha have books in the ratio respectively. What is the the minimum number of books they must be having altogether?

(Enter ‘0’ as the answer if the answer cannot be determined.)

A
886

B
887

C
888

D
881

Solution
Question 5
3 / -1

Given that [(x-y)^(1/4)] = 2 and [(3x−2y) ^1/2] = 5. What is the minimum possible integral value of y? [x] is equal to greatest integer less than or equal to x.

A
- 217

B
- 218

C
- 219

D
- 216

Solution
Question 6
3 / -1

How many points in the region enclosed by x > 0, y < 0 and 7x - 9y < 63 have integral coordinates?

A
41

B
36

C
24

D
39

Solution

The region enclosed by the lines is a triangle in the third quadrant formed by the points (0,-7), (0,0) and (9,0). The number of coordinates in the region with x coordinate are as follows

x=0 ⇒ 8 points,

x=1, 7points,

x=2, 6points,

x=3, 5points,

x=4, 4points,

x=5, 4points and so on.

Total no. of points =41
Question 7
3 / -1

A circle with radius 6 cm is inscribed inside an equilateral triangle ABC. Three smaller circle are drawn touching the incircle and the sides of ABC as shown in the figure. Another triangle is formed by joining centres P,Q and R of these smaller circles. What is the perimeter of triangle PQR?

A
24√3

B
36√3

C
8√3

D
12√3

Solution

Consider radius of each smaller circle be r and that of the larger circle be R = 6 cm.

Construct PD such that PD is perpendicular to AB.

In right triangle ADP, AP = DP/cos(APD) = DP/ cos(60) = 2DP = 2r

In right triangle OFA, OF/cos(AOF) = AO ⇒ R/(1/2) = AP+OP ⇒ 2R=2r+r+R ⇒ R = 3r

In right triangle OEP, EP=OPcos(EPO) = (R + r)((√3)/2 = (4R/3)((√3) = 2R/(√3)

PQ=2EP = 4R/√3)

Perimeter = 12R/(√3) = 24√3 cm (R = 6cm)
Question 8
3 / -1

In a circle, two chords AB and CD intersect at a point E as shown in the figure. If AB = 6 cm and CD = 10 cm and ∠ OED = 30°, then find out the radius of the given circle.

A
√34cm

B
√31cm

C
√33cm

D
4√2cm

Solution
Question 9
3 / -1

How many scalene triangles with integral sides can be formed with a perimeter of 45 cm?

A
37

B
38

C
39

D
40

Solution
Question 10
3 / -1

AB and AC are tangents to the circle with centre O. If the radius of the circle is 5 and length of the tangent is 5√3, what is the area of the shaded region?

A

B

C

D

Solution