# Basic Numeracy - Online Test

Q1. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Explaination / Solution:

We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).

Required number of ways= (7C3 x 6C2) + (7C4 x 6C1) + (7C5)
 = 7 x 6 x 5 x 6 x 5 + (7C3 x 6C1) + (7C2) 3 x 2 x 1 2 x 1
 = 525 + 7 x 6 x 5 x 6 + 7 x 6 3 x 2 x 1 2 x 1
= (525 + 210 + 21)
= 756.

Q2. If one-third of one-fourth of a number is 15, then three-tenth of that number is:
Explaination / Solution:

Let the number be x.

 Then, 1 of 1 of x = 15      x = 15 x 12 = 180. 3 4

 So, required number = 3 x 180 = 54. 10

Q3. What decimal of an hour is a second ?
Explaination / Solution:

 Required decimal = 1 = 1 = .00027 60 x 60 3600

Q4. The cube root of .000216 is:
Explaination / Solution:

 (.000216)1/3 = 216 1/3 106

 = 6 x 6 x 6 1/3 102 x 102 x 102

 = 6 102

 = 6 100

= 0.06

Q5. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Explaination / Solution:

Let the third number be x.

 Then, first number = 120% of x = 120x = 6x 100 5

 Second number = 150% of x = 150x = 3x 100 2

 Ratio of first two numbers = 6x : 3x = 12x : 15x = 4 : 5. 5 2

Q6. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
Explaination / Solution:

 Part filled by (A + B + C) in 3 minutes = 3 1 + 1 + 1 = 3 x 11 = 11 . 30 20 10 60 20

 Part filled by C in 3 minutes = 3 . 10

 Required ratio = 3 x 20 = 6 . 10 11 11

Q7. A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Explaination / Solution:

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

 Quantity of water in new mixture = 3 - 3x + x litres 8

 Quantity of syrup in new mixture = 5 - 5x litres 8

 3 - 3x + x = 5 - 5x 8 8

5x + 24 = 40 - 5x

10x = 16

 x = 8 . 5

 So, part of the mixture replaced = 8 x 1 = 1 . 5 8 5

Q8. In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
Explaination / Solution:

A : B = 100 : 90.

A : C = 100 : 72.

 B : C = B x A = 90 x 100 = 90 . A C 100 72 72

When B runs 90 m, C runs 72 m.

 When B runs 100 m, C runs 72 x 100 m = 80 m. 90

B can give C 20 m.

Q9. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
Explaination / Solution:

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

 P(E) = n(E) = 9 . n(S) 20

Q10. The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Explaination / Solution:

T.D.
 = B.D. x 100 100 + (R x T)
= Rs.420 x 100
 100 + 15 x 1 3
 = Rs. 420 x 100 105
= Rs. 400.