Quantitative Aptitude (QA) Test

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Quantitative Aptitude (QA) Test - 23

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Weekly Quiz Competition

Question 1
3 / -1

Akhsay travels on a straight route joining P and Q in a way such that after each of the 20^th, 40^th and 60^th minute from his starting point P, he increases his speed by 10 kmph and after each of the 70^th, 80^th, 90^th, 100^th and the 110^th minute from the start, he decreases his speed by 10 kmph. If Akshay began his journey at a speed of 50 kmph and took exactly 2 hours to reach Q, the distance from P to Q (in km) is _______.

A
115

B
120

C
130

D
100

Solution
Question 2
3 / -1

If the sum of the roots of the quadratic equations mx² + (2m - 1)x + 4 and (3m + 1)x² - 6x + (2m - 3) are equal, then find the sum of values of m.

A
5/6

B
1/6

C
-5/6

D
Cannot be determined

Solution

The sum of the roots of a quadratic equation ax² + bx + c is - b / a

⇒ -(2m - 1)/m = 6/(3m + 1)

⇒ 6m² - m -1 = -6m

⇒ 6m² + 5m -1 = 0

⇒ m = 1/6 or -1

Thus, the sum of the values of m: 1/6 -1 = -5/6
Question 3
3 / -1

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. find the volume of the solid so formed.

A
76.8π

B
32π

C
6π

D
301.7 cm³

Solution

When a right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm, then solid formed is a cone whose height, h = 8 cm.

The radius of the cone, r = 6 cm.

Slant height of the cone, l = 10 cm.

Hence, the volume and surface area of the cone are 301.7 cm³.
Question 4
3 / -1

The largest integer n, such that n + 10 divides n³ + 100, is

A
890

B
900

C
800

D
700

Solution

As, we know that :

n³ + 1000 = (n + 10) (n² - 10n + 100)

So,

n³ + 100 = (n + 10) (n² - 10n + 100) - 900

Therefore, 900 must be divided by (n + 10)

Since largest divisor of 900 is 900, So n + 10 is divisible by 900 i.e. largest value of n is 890.
Question 5
3 / -1

How many subsets of S = (1, 2, 3 , . . . , 400) have the product of their elements an even number?

A
2⁴⁰⁰ - 2²⁰⁰

B
2²⁰⁰- 2¹⁵⁰

C
100

D
225

Solution

For a given set containing N elements, the number of non-zero subsets = 2^N - 1

Number of non-zero subsets in S = 2⁴⁰⁰ - 1

The product of the elements of a subset will be odd when all the elements of the subset are odd.

The odd elements in S are S_odd = (1, 3, 5 , ..., 399)

Number of non-zero subsets in S_odd = 2²⁰⁰-1

Number of subsets where product of its elements is even = (2⁴⁰⁰ - 1) -(2²⁰⁰-1) = 2⁴⁰⁰ - 2²⁰⁰

Hence, option 1.
Question 6
3 / -1

Find the maximum area of the isosceles trapezium (in units²) whose unequal sides are 4 units and 6 units. Given that it is inscribed in a circle whose radius is 2√3

A
5(2√2 - √3)

B
5(2√2 + √3)

C
10(2√2 - √3)

D
10(2√2 + √3)

Solution

The maximum area of trapezium will be obtained when the two sides are on the opposite sides of the diameter.

The height of the trapezium = OE + OF

OE = √OC² - √EC² = √3

OF = √OB² - √FB² = 2√2

∴ the area of the trapezium = (1 / 2) x (2√2 + √3) x (6 + 4) = 5(2√2 + √3)

Hence, option 2.
Question 7
3 / -1

The average speed of Mumbai metro train which travels from Ghatkopar to Versova is 30 km/hr and the distance between the two stations is 32 km. Which function represents the distance 'd(t)' remaining in a trip from Ghatkopar to Versova after a certain time 't' from the start?

A
d(t) = 30t - 32

B
d(t) = 32 - 30t

C
d(t) = 32t / 30

D
d(t) = 30 / 32t

Solution

We know that,

Distance remaining = Total distance - Distance travelled

⇒ d(t) = 32 - 30t
Question 8
3 / -1

Find the value of M in the figure given below,

A
6.5

B
7.5

C
8.5

D
1.5

Solution

⇒ 3M + 9 + M + 5 + 140= 180

⇒ 4M = 26

⇒ M = 6.5°
Question 9
3 / -1

6 equally spaced girls are standing along the circumference of a circle of radius 10 m and facing the center. What is the shortest distance between any two girls facing each other?

A
20

B
40

C
50

D
100

Solution

If we draw a figure according to the information provided in the question then we can note that:

In the question it is good that each girl is facing the center of the circle.

Radius of circle =10m, Diameter of circle =20m

We need to find the shortest distance between any two girls faces each other.

We can see from the image that oppositely standing girls will only face each other so the shortest distance between any two girls facing each other will be equal to the diameter of the circle ie 20 m.
Question 10
3 / -1

A shopkeeper gives a discount of 10% on the marked price and sells it for Rs. 540 to earn a profit of Rs. 90. Find the profit percentage if the product is marked Rs. 200 above its cost price for the same absolute value of discount.

A
30%

B
31.11%

C
40%

D
Cannot be determined

Solution

Case 1:

Let the marked price be m.

The selling price = 0.9m

⇒ 0.9m = 540

⇒ m = 600

Cost price = 540 -90 = Rs. 450

Case 2:

Discount = Rs. 60, Marked price = Rs. 650

Selling price = 650 - 60 = Rs. 590

Profit = 590 - 450 = Rs. 140

Profit percentage = (140/450) x 100 = 31.11%

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Quantitative Aptitude (QA) Test - 23

Result

Quantitative Aptitude (QA) Test - 23

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SHARING IS CARING

Question 1

115

120

130

100

Solution

Question 2

5/6

1/6

-5/6

Cannot be determined

Solution

Question 3

76.8π

32π

6π

301.7 cm3

Solution

Question 4

890

900

800

700

Solution

Question 5

2400 - 2200

2200- 2150

100

225

Solution

Question 6

5(2√2 - √3)

5(2√2 + √3)

10(2√2 - √3)

10(2√2 + √3)

Solution

Question 7

d(t) = 30t - 32

d(t) = 32 - 30t

d(t) = 32t / 30

d(t) = 30 / 32t

Solution

Question 8

6.5

7.5

8.5

1.5

Solution

Question 9

20

40

50

100

Solution

Question 10

30%

31.11%

40%

Cannot be determined

Solution

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301.7 cm³

2⁴⁰⁰ - 2²⁰⁰

2²⁰⁰- 2¹⁵⁰