# Problems on Numbers Quiz Set 005

### Question 1

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 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

The sum of three consecutive even integer numbers is -2862. The middle among the three is?

A

-954.

B

-953.

C

-951.

D

-952.

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 = -2862, ⇒ middle = \$-2862/3\$, i.e., middle = -954.

### Question 4

If \$9/17\$ of a number is 90, what is the number?

A

170.

B

171.

C

169.

D

172.

Soln.
Ans: a

Let the number be N. Then \${9/17}\$ x N = 90. ⇒ N = 90 x \${17/9}\$ = 170

### Question 5

What is x in \$3{113/x}\$ × \$3{1/13}\$ = \$11{5/7}\$?

A

140.

B

141.

C

139.

D

142.

Soln.
Ans: a

We can see that \$3{113/x}\$ = \${82/7}\$ × \${13/40}\$. ⇒ \${3x + 113}/x\$ = \${533/140}\$ ⇒ x = 140. 