# Problems on Numbers Quiz Set 015

### Question 1

What is x in \$1{19/x}\$ × \$5{12/17}\$ = \$5{11/14}\$?

A

1358.

B

1359.

C

1357.

D

1360.

Soln.
Ans: a

We can see that \$1{19/x}\$ = \${81/14}\$ × \${17/97}\$. ⇒ \${1x + 19}/x\$ = \${1377/1358}\$ ⇒ x = 1358.

### Question 2

14 times the middle of three consecutive even numbers is 160 more than 11 times the smallest of the three numbers. What is the middle number?

A

46.

B

47.

C

45.

D

48.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 14 × 2n = 160 + 11 × (2n - 2).
⇒ 14 × 2n = 160 + 11 × 2n - 11 × 2.
⇒ 2n × (14 - 11) = 160 - 11 × 2, so 2n = \${160 - 11 × 2}/{14 - 11} = 46\$

### Question 3

If  \$x/2 = y/19 = z/28\$, then \${x + y + z}/x\$ = ?

A

\$24{1/2}\$.

B

\$25{1/2}\$.

C

\$23{1/2}\$.

D

\$13{3/4}\$.

Soln.
Ans: a

Let \$x/2 = y/19 = z/28\$ = k. Then \${x + y + z}/x\$ is same as \${2k + 19k + 28k}/{2k}\$ which equals \$24{1/2}\$.

\${49/2}\$ is same as \$24{1/2}\$.

### Question 4

A number is multiplied by 6, then 21 is added to it. The result remains the same if 13 is multiplied to the number and then 84 subtracted. What is the number?

A

15.

B

16.

C

14.

D

17.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$6n + 21 = 13n - 84\$. Rearranging we have \$84 + 21 = 13n - 6n\$, ⇒ \$n = {84 + 21}/{13 - 6}\$. So n = 15.

### Question 5

5 times the middle of three consecutive even numbers is 46 more than 2 times the smallest of the three numbers. What is the middle number?

A

14.

B

15.

C

13.

D

16.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 5 × 2n = 46 + 2 × (2n - 2).
⇒ 5 × 2n = 46 + 2 × 2n - 2 × 2.
⇒ 2n × (5 - 2) = 46 - 2 × 2, so 2n = \${46 - 2 × 2}/{5 - 2} = 14\$