# Problems on Numbers Quiz Set 012

### Question 1

What is 0.19191919...?

A

\$19/99\$.

B

\$20/99\$.

C

\$19/100\$.

D

\$19/101\$.

Soln.
Ans: a

0.19191919... is same as \$0.\ov 19\$. Let y = \$0.\ov 19\$. Multiply by 100, 100y = 19 + \$0.\ov 19\$ which is same as 19 + y. So 99y = 19, ⇒ y = \$19/99\$. So answer = \${19/99}\$.

### Question 2

How many prime factors does 4095000 have?

A

11.

B

12.

C

10.

D

13.

Soln.
Ans: a

We can see that \$4095000 = 2^3 × 3^2 × 5^4 × 7^1 × 13^1\$. The number of prime factors is sum of the powers = 11.

### Question 3

x should be replaced by which minimum number so that 36318x5944 is completely divisible by 9?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 3 + 6 + 3 + 1 + 8 + x + 5 + 9 + 4 + 4, should be divisible by 9. So we can see that \$x + 43\$ should be divisible by 9. By inspection, x = 2.

### Question 4

If  \$x/6 = y/12 = z/28\$, then \${x + y + z}/x\$ = ?

A

\$7{2/3}\$.

B

13.

C

\$6{2/3}\$.

D

\$6{2/5}\$.

Soln.
Ans: a

Let \$x/6 = y/12 = z/28\$ = k. Then \${x + y + z}/x\$ is same as \${6k + 12k + 28k}/{6k}\$ which equals \$7{2/3}\$.

\${23/3}\$ is same as \$7{2/3}\$.

### Question 5

If \${13/20}\$ of a number is 23, what is \$1{10/13}\$ of that number?

A

\$62{102/169}\$.

B

\$63{55/56}\$.

C

\$60{151/171}\$.

D

\$64{143/171}\$.

Soln.
Ans: a

Let the number be N. Then it is given that \${13/20}\$ x N = 23. ⇒ N = 23 X \${20/13}\$. ⇒ \${23/13}\$ x N = \${23/13}\$ x 23 X \${20/13}\$ = \${10580/169}\$.

\${23/13}\$ is same as \$1{10/13}\$. \${10580/169}\$ is same as \$62{102/169}\$.