# Problems on Numbers Quiz Set 018

### Question 1

How many prime factors does 67500 have?

A

9.

B

10.

C

8.

D

11.

Soln.
Ans: a

We can see that \$67500 = 2^2 × 3^3 × 5^4\$. The number of prime factors is sum of the powers = 9.

### Question 2

What is x in \$1{19/x}\$ × \$1{7/8}\$ = \$2{9/23}\$?

A

69.

B

70.

C

68.

D

71.

Soln.
Ans: a

We can see that \$1{19/x}\$ = \${55/23}\$ × \${8/15}\$. ⇒ \${1x + 19}/x\$ = \${88/69}\$ ⇒ x = 69.

### Question 3

If 1 of a number is 10, what is \${3/8}\$ of that number?

A

\$3{3/4}\$.

B

\$6{1/3}\$.

C

\$1{5/6}\$.

D

\$4{1/2}\$.

Soln.
Ans: a

Let the number be N. Then it is given that 1 x N = 10. ⇒ N = 10 X 1. ⇒ \${3/8}\$ x N = \${3/8}\$ x 10 X 1 = \${15/4}\$.

\${15/4}\$ is same as \$3{3/4}\$.

### Question 4

How many prime factors does 810810000 have?

A

15.

B

16.

C

14.

D

17.

Soln.
Ans: a

We can see that \$810810000 = 2^4 × 3^4 × 5^4 × 7^1 × 11^1 × 13^1\$. The number of prime factors is sum of the powers = 15.

### Question 5

If \$6/17\$ of a number is 78, what is the number?

A

221.

B

222.

C

220.

D

223.

Soln.
Ans: a

Let the number be N. Then \${6/17}\$ x N = 78. ⇒ N = 78 x \${17/6}\$ = 221