Quantitative and Numerical Ability Test

Result

Quantitative and Numerical Ability Test - 1

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Weekly Quiz Competition

Question 1
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AP is tangent at point P to the circle with centre O and diameter BC. If AP = 20 and AB = 10, what is the length of AO?

A
25

B
29

C
35

D
30

E
37

Solution

Suppose OP = r. Then, OA = 10 + r.

In triangle APO, (10 + r)² = 400 + r². Solving this equation gives r = 15. So, AO = 10 + 15 = 25.
Question 2
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Ashim is creating a mathematical quiz for his students. He is thinking of a geometric progression in which the third term is 16 and the sixth term is twice the square of the second term. What is the eleventh term in this geometric progression?

A
1,024

B
2,048

C
4,096

D
6,144

Solution
Question 3
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In the following question, two equations numbered land Il are given. You have to solve both the equations and give answer if

A

B

C

D

E

Solution
Question 4
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A
19

B
26

C
22

D
28

E
13

Solution
Question 5
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There are two bags A and B. Bag A contains 6 red balls and 10 green balls and Bag B contains 4 red balls and 6 green balls. One bag is selected at random. From the selected bag one ball is drawn at random. What is the probability that the ball drawn is red?

A
27/80

B
31/80

C
39/80

D
29/80

E
33/80

Solution
Question 6
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An iron cube of size 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet be in the ratio 1 : 5, then the sides are

A
20 cm, 100 cm

B
10 cm, 50 cm

C
40 cm, 200 cm

D
50 cm, 100 cm

E
None of these

Solution
Question 7
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X₁, X₂, X₃, X₄, X₅, X₆, X₇are 7 natural numbers. The median and mode of the given set of observations are 14 and 12 respectively. The mean of the given observation is 19. X₄is the median. No two scores above the median are similar

What can be the minimum value of X₇?

A
1

B
2

C
3

D
4

E
5

Solution

As nothing can be said about numbers, so mimimum value of X₇ can be 1.
Question 8
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What is the equation of a circle centre (2, 3) and radius equal to 11?

A
x² + y² - 2x + 6y - 108 = 0

B
x² + y² + 4x + 6y +108 = 0

C
x² + y²-4x + 6y + 108 = 0

D
x² + y² - 4x - 6y + 108 = 0

E
x² + y² - 4x - 6y - 108 = 0

Solution

The equation of a circle centre (2, 3) and radius 11 is (x – 2)² + (y – 3)²= 121 ⇒ x² + y²- 4x - 6y - 108 = 0
Question 9
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In Peepal Tree School, the ratio of the number of students in Junior KG to Senior KG is 7 : 5. The ratio of (the number of) Junior KG Boys to Junior KG girls is 3 : 2. The ratio of number of Senior KG boys to Senior KG girls is 4 : 3. What is the ratio of Junior KG boys to Senior KG girls?

A
2 : 1

B
12 : 49

C
49 : 25

D
7 : 61

E
None of these

Solution

Let us start by finding a common multiple for (7)(5)(3)(4). It is 420.

Let this be the total number of students.

Now Jr. KG to Sr. KG is 7x + 5x = 420

Hence x = 12

So Jr/Sr = 245/175

JB to JG: 3y +2y = 245

y = 49

So JM/JF = 147/98

SB to SG: 4z + 3z = 175

z = 25

So SB/SG = 100/75

Hence, JB/SG 147/75 = 49/25

Hence, the correct answer is option C.
Question 10
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A alone can complete a work in 20 days, B alone can complete the same work in 30 days and C alone can complete the same work in 60 days. They work together for some time, then A and B left the work. If C completes the remaining work in 6 days, then A and B work for?

A
1 day

B
3 days

C
6 days

D
9 days

E
11 days

Solution