# Problems on Numbers Quiz Set 017

### Question 1

If \$3/17\$ of a number is 9, what is the number?

A

51.

B

52.

C

50.

D

53.

Soln.
Ans: a

Let the number be N. Then \${3/17}\$ x N = 9. ⇒ N = 9 x \${17/3}\$ = 51

### Question 2

A number is multiplied by 3, then 11 is added to it. The result remains the same if 11 is multiplied to the number and then 101 subtracted. What is the number?

A

14.

B

15.

C

13.

D

16.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$3n + 11 = 11n - 101\$. Rearranging we have \$101 + 11 = 11n - 3n\$, ⇒ \$n = {101 + 11}/{11 - 3}\$. So n = 14.

### Question 3

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 4

The difference between a two digit number and the one obtained by reversing its digits is 81. If one of the digits is 6, what is the other?

A

Cannot exist.

B

4.

C

5.

D

0.

Soln.
Ans: a

Let the numbers be a and b. ab = 10a + b, and ba = 10b + a. The difference is 10a + b - (10b + a) = 9(a - b). It is given that 9(a - b) = 81, ⇒ a - b = \$81/9\$ = 9, ⇒ the difference between the digits is 9. If one of the digits is 6, the other cannot be determined.

### Question 5

What is 0.75757575...?

A

\$25/33\$.

B

\$26/33\$.

C

\$25/34\$.

D

\$25/35\$.

Soln.
Ans: a

0.75757575... is same as \$0.\ov 75\$. Let y = \$0.\ov 75\$. Multiply by 100, 100y = 75 + \$0.\ov 75\$ which is same as 75 + y. So 99y = 75, ⇒ y = \$75/99\$. So answer = \${25/33}\$.