# Problems on Numbers Quiz Set 017

### Question 1

A number is multiplied by 8, then 18 is added to it. The result remains the same if 11 is multiplied to the number and then 45 subtracted. What is the number?

A

21.

B

22.

C

20.

D

23.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$8n + 18 = 11n - 45\$. Rearranging we have \$45 + 18 = 11n - 8n\$, ⇒ \$n = {45 + 18}/{11 - 8}\$. So n = 21.

### Question 2

The difference between a two digit number and the one obtained by reversing its digits is 72. If one of the digits is 0, what is the other?

A

8.

B

9.

C

10.

D

11.

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) = 72, ⇒ a - b = \$72/9\$ = 8, ⇒ the difference between the digits is 8. If one of the digits is 0, the other can be 8.

### Question 3

If \$5{3/4}\$ of a number is 3, what is \${3/14}\$ of that number?

A

\${18/161}\$.

B

\$1{19/160}\$.

C

\$2{14/163}\$.

D

\$3{12/163}\$.

Soln.
Ans: a

Let the number be N. Then it is given that \$5{3/4}\$ x N = 3. ⇒ N = 3 X \${4/23}\$. ⇒ \${3/14}\$ x N = \${3/14}\$ x 3 X \${4/23}\$ = \${18/161}\$.

\${23/4}\$ is same as \$5{3/4}\$.

### 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

The sum of three consecutive even integer numbers is -1752. The middle among the three is?

A

-584.

B

-583.

C

-581.

D

-582.

Soln.
Ans: a

Let the numbers be 2n - 2, 2n and 2n + 2. The sum is 6n = 3 x 2n = 3 x middle. We are given 3 x middle = -1752, ⇒ middle = \$-1752/3\$, i.e., middle = -584. 