# Problems on Numbers Quiz Set 006

### Question 1

The sum of two numbers is 24. Their product is 143. One of the two numbers is?

A

13.

B

14.

C

12.

D

15.

Soln.
Ans: a

Let the numbers be \$a\$ and \$24 - a\$. We are given their product as a × (24 - a) = 143, which is a quadratic expression that can be simplified to \$(a - 13) × (11 - a) = 0\$. So the numbers could be 13 and 11.

### Question 2

x should be replaced by which minimum number so that 9961x95681 is completely divisible by 9?

A

0.

B

1.

C

3.

D

2.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 9 + 9 + 6 + 1 + x + 9 + 5 + 6 + 8 + 1, should be divisible by 9. So we can see that \$x + 54\$ should be divisible by 9. By inspection, x = 0.

### Question 3

A number is multiplied by 2, then 24 is added to it. The result remains the same if 14 is multiplied to the number and then 240 subtracted. What is the number?

A

22.

B

23.

C

21.

D

24.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$2n + 24 = 14n - 240\$. Rearranging we have \$240 + 24 = 14n - 2n\$, ⇒ \$n = {240 + 24}/{14 - 2}\$. So n = 22.

### Question 4

A number is multiplied by 3, then 13 is added to it. The result remains the same if 13 is multiplied to the number and then 67 subtracted. What is the number?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$3n + 13 = 13n - 67\$. Rearranging we have \$67 + 13 = 13n - 3n\$, ⇒ \$n = {67 + 13}/{13 - 3}\$. So n = 8.

### Question 5

If \${23/34}\$ of a number is 17, what is \${19/21}\$ of that number?

A

\$22{356/483}\$.

B

\$23{379/482}\$.

C

\$21{314/485}\$.

D

\$25{306/485}\$.

Soln.
Ans: a

Let the number be N. Then it is given that \${23/34}\$ x N = 17. ⇒ N = 17 X \${34/23}\$. ⇒ \${19/21}\$ x N = \${19/21}\$ x 17 X \${34/23}\$ = \${10982/483}\$.

\${10982/483}\$ is same as \$22{356/483}\$.