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?
Answer : Option D
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 5x6 x 5+ (7C3 x 6C1) + (7C2)
3 x 2 x 12 x 1
= 525 +7 x 6 x 5x 6+7 x 6
3 x 2 x 12 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:
Answer : Option D
Explaination / Solution:

Let the number be x.

Then,1of1of x = 15      x = 15 x 12 = 180.
34

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


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

Required decimal =1=1= .00027
60 x 603600

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

(.000216)1/3=2161/3
106

   =6 x 6 x 61/3
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:
Answer : Option C
Explaination / Solution:

Let the third number be x.

Then, first number = 120% of x =120x=6x
1005

Second number = 150% of x =150x=3x
1002

 Ratio of first two numbers =6x:3x= 12x : 15x = 4 : 5.
52


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?
Answer : Option B
Explaination / Solution:

Part filled by (A + B + C) in 3 minutes = 31+1+1=3 x11=11.
3020106020

Part filled by C in 3 minutes =3.
10

 Required ratio =3x20=6.
101111


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?
Answer : Option C
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 -3xxlitres
8

Quantity of syrup in new mixture =5 -5xlitres
8

3 -3xx=5 -5x
88

 5x + 24 = 40 - 5x

 10x = 16

 x =8.
5

So, part of the mixture replaced =8x1=1.
585


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

A : B = 100 : 90.

A : C = 100 : 72.

B : C =BxA=90x100=90.
AC1007272

When B runs 90 m, C runs 72 m.

When B runs 100 m, C runs72x 100m= 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?
Answer : Option D
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:
Answer : Option A
Explaination / Solution:

T.D.
=B.D. x 100
100 + (R x T)
= Rs.420 x 100
100 +15 x1
3
= Rs.420 x 100
105
= Rs. 400.