# Numbers Questions

Q:

476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:

 A) 6 and 2 B) 8 and 2 C) 6 and 5 D) 8 and 5

Explanation:

Let the number  be 476ab0

476ab0 is divisible by 3

=> 4 + 7 + 6 + a + b + 0 is divisible by 3

=> 17 + a + b is divisible by 3 ------------------------(i)

476ab0 is divisible by 11

[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11

=> [3 + (b - a)] is 0 or divisible by 11  --------------(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.

if a=6 and b=2,

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a=8 and b=2,

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer

if a=6 and b=5,

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a=8 and b=5,

17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1

[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2

Since these values satisfies both equation 1 and equation 2, this is the answer

3 3578
Q:

If the product 4864*9 P 2 is divisible by 12, the value of p:

 A) 1 B) 2 C) 3 D) 4

Explanation:

clearly 4864 is divisible by 4
So 9 P 2 must be divisible by 3.So(9+P+2) must be divisible by 3.
so P=1.

6 3209
Q:

If 60% of $\inline \frac{3}{5}$ of a number is 36, then the number is

 A) 86 B) 94 C) 100 D) 115

Explanation:

Let the number be x.Then

60% of ${\color{Black}&space;\frac{3}{5}}$of x=36.

${\color{Black}&space;\Rightarrow&space;}$${\color{Black}&space;\frac{60}{100}\times&space;\frac{3}{5}\times&space;x=36}$

${\color{Black}&space;\Rightarrow&space;x=100}$

Required number is 100.

11 3010
Q:

A piece of ribbon 4 yards long is used to make bows requiring 15 inches of ribbon for each. What is the maximum number of bows that can be made?

 A) 8 B) 9 C) 10 D) 11

Explanation:

The maximum number of bows will be 4 yards (= 4 x 36 inches) divided by 15 inches.

This gives 9.6. But as a fraction of a bow is no use, we can only make 9 bows.

9 2818
Q:

The sum of the two numbers is 12 and their product is 35.What is the sum of the reciprocals of these numbers?

 A) 12/35 B) 1/35 C) 35/8 D) 7/32

$\inline \fn_cm \frac{a+b}{ab}=\frac{12}{35}$
$\inline \fn_cm \frac{1}{b}+\frac{1}{a}=\frac{12}{35}$