# Problems on Numbers Quiz Set 009

### Question 1

When a two digit number is reversed and added to itself we get 110. The product of the digits of that number is 21. What is the number?

A

73.

B

74.

C

72.

D

75.

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 110 = 11 × (a + b) ⇒ \$a + b = 110 / 11 = 10\$, so the digits are \$a\$ and \$10 - a\$. We are given their product as a × (10 - a) = 21, which is a quadratic expression that can be simplified to \$(a - 7) × (3 - a) = 0\$. So the number could be 73 or 37.

### Question 2

The sum of two numbers is 25. Their difference is 19. They are in the ratio?

A

\$7{1/3}\$.

B

\$12{1/2}\$.

C

\$6{1/3}\$.

D

\$6{1/5}\$.

Soln.
Ans: a

Let the numbers be a and b, and let their ratio be k such that \$a/b = k\$. We are given \$a + b = 25\$ ⇒ \$b(k + 1) = 25\$. Similarly, from the difference we can obtain \$b(k - 1) = 19\$. Dividing we get \${k + 1}/{k - 1} = 25/19\$. By componendo and dividendo, \$k = {25 + 19}/{25 - 19}\$ = \${22/3}\$, which is same as: \$7{1/3}\$.

### Question 3

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}\$.

### Question 4

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 5

The sum of three consecutive integer numbers is -1113. The smallest of the three is?

A

-372.

B

-371.

C

-369.

D

-370.

Soln.
Ans: a

Let the numbers be n - 1, n and n + 1. The sum is 3n. We are given 3n = -1113, ⇒ n = \$-1113/3\$, i.e., n = -371. So the smallest is -372. 