# Problems on Numbers Quiz Set 014

### Question 1

When a two digit number is reversed and added to itself we get 44. The product of the digits of that number is 3. What is the number?

A

13.

B

14.

C

12.

D

15.

Soln.
Ans: a

Let the number be ab. When it is reversed and added to itself we get (10a + b) + (10b + a) = 11 × (a + b). We are given 44 = 11 × (a + b) ⇒ \$a + b = 44 / 11 = 4\$, so the digits are \$a\$ and \$4 - a\$. We are given their product as a × (4 - a) = 3, which is a quadratic expression that can be simplified to \$(a - 1) × (3 - a) = 0\$. So the number could be 13 or 31.

### Question 2

How many odd numbers are there between -1270 and 1358?

A

1314.

B

1315.

C

1313.

D

1316.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1269\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 1357. By the AP formula, \$1357 = -1269 + (n - 1) × 2\$ ⇒ \$n = 1 + {{1357 - (-1269)}/2} = 1314\$.

### Question 3

x should be replaced by which minimum number so that 39x5425441 is completely divisible by 9?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 3 + 9 + x + 5 + 4 + 2 + 5 + 4 + 4 + 1, should be divisible by 9. So we can see that \$x + 37\$ should be divisible by 9. By inspection, x = 8.

### Question 4

The difference between a two digit number and the one obtained by reversing its digits is 54. If one of the digits is 2, 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) = 54, ⇒ a - b = \$54/9\$ = 6, ⇒ the difference between the digits is 6. If one of the digits is 2, the other can be 8.

### Question 5

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. 