# Problems on Numbers Quiz Set 014

### Question 1

x should be replaced by which minimum number so that 828517x265 is completely divisible by 9?

A

1.

B

2.

C

4.

D

3.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 8 + 2 + 8 + 5 + 1 + 7 + x + 2 + 6 + 5, should be divisible by 9. So we can see that \$x + 44\$ should be divisible by 9. By inspection, x = 1.

### Question 2

The sum of two numbers is 39. Their difference is 21. They are in the ratio?

A

\$3{1/3}\$.

B

\$6{1/2}\$.

C

\$2{1/3}\$.

D

\$3{4/5}\$.

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 = 39\$ ⇒ \$b(k + 1) = 39\$. Similarly, from the difference we can obtain \$b(k - 1) = 21\$. Dividing we get \${k + 1}/{k - 1} = 39/21\$. By componendo and dividendo, \$k = {39 + 21}/{39 - 21}\$ = \${10/3}\$, which is same as: \$3{1/3}\$.

### Question 3

15 times the middle of three consecutive even numbers is 150 more than 11 times the smallest of the three numbers. What is the middle number?

A

32.

B

33.

C

31.

D

34.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 15 × 2n = 150 + 11 × (2n - 2).
⇒ 15 × 2n = 150 + 11 × 2n - 11 × 2.
⇒ 2n × (15 - 11) = 150 - 11 × 2, so 2n = \${150 - 11 × 2}/{15 - 11} = 32\$

### Question 4

The sum of three consecutive integer numbers is -96. The smallest of the three is?

A

-33.

B

-32.

C

-30.

D

-31.

Soln.
Ans: a

Let the numbers be n - 1, n and n + 1. The sum is 3n. We are given 3n = -96, ⇒ n = \$-96/3\$, i.e., n = -32. So the smallest is -33.

### Question 5

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}\$.