# Problems on Numbers Quiz Set 006

### Question 1

The sum of two numbers is 53. Their difference is 15. They are in the ratio?

A

\$1{15/19}\$.

B

\$2{17/18}\$.

C

\${5/7}\$.

D

\$4{1/3}\$.

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 = 53\$ ⇒ \$b(k + 1) = 53\$. Similarly, from the difference we can obtain \$b(k - 1) = 15\$. Dividing we get \${k + 1}/{k - 1} = 53/15\$. By componendo and dividendo, \$k = {53 + 15}/{53 - 15}\$ = \${34/19}\$, which is same as: \$1{15/19}\$.

### Question 2

The sum of three consecutive odd integer numbers is -2211. The middle among the three is?

A

-737.

B

-736.

C

-734.

D

-735.

Soln.
Ans: a

Let the numbers be 2n - 3, 2n - 1 and 2n + 1. The sum is 3(2n - 1) = 3 x middle. We are given 3 x middle = -2211, ⇒ middle = \$-2211/3\$, i.e., middle = -737.

### Question 3

How many odd numbers are there between -1714 and 2242?

A

1978.

B

1979.

C

1977.

D

1980.

Soln.
Ans: a

Odd numbers are in an AP. First term \$a = -1713\$, common difference \$d = 2\$, the last term \$t_n\$ is given as 2241. By the AP formula, \$2241 = -1713 + (n - 1) × 2\$ ⇒ \$n = 1 + {{2241 - (-1713)}/2} = 1978\$.

### Question 4

If  \$x/7 = y/19 = z/24\$, then \${x + y + z}/x\$ = ?

A

\$7{1/7}\$.

B

\$9{1/2}\$.

C

\$4{7/9}\$.

D

\$7{8/9}\$.

Soln.
Ans: a

Let \$x/7 = y/19 = z/24\$ = k. Then \${x + y + z}/x\$ is same as \${7k + 19k + 24k}/{7k}\$ which equals \$7{1/7}\$.

\${50/7}\$ is same as \$7{1/7}\$.

### Question 5

If \$6/17\$ of a number is 24, what is the number?

A

68.

B

69.

C

67.

D

70.

Soln.
Ans: a

Let the number be N. Then \${6/17}\$ x N = 24. ⇒ N = 24 x \${17/6}\$ = 68 