31000+ Important MCQs for CDS

Explanation: Suppose the numbers are P and Q
So, according to the question -
P + Q = 12
P * Q = 35
Sum of reciprocals of P and Q is = 1/P + 1/Q
= Q + P/PQ
= 12/35

Explanation: Suppose the number is a.

So, according to the question -

a + 1/a = 2

(a^2 + 1)/a = 2

a^2 + 1 = 2a

Or, a^2 + 1 -2a = 0

We can say that (a - 1)2 = 0

So, a =1

Hence the required number is 1, whose sum and reciprocal are equal to 2.

Explanation: Given ration 7 : 9
So, let the numbers be 7a and 9a. According to the question -
7a * 9a = 1575
63a² = 1575
a² = 1575/63
Or a² = 25
And a =5
So, the two numbers will be -
7a = 7 * 5 = 35
And 9a = 9 * 5 = 45
Hence, the greater number is 45 between the given numbers.

Explanation: Let the numbers be 'a' and 'b'. According to the question -
(a + b) = 3(a - b)
(a + b) = 3a - 3b
2a = 4b
a = 2b
So, a/b = 2 : 1

Explanation: According to the identity,

a^2 - b^2 = (a + b) (a - b)

It is given that (a^2 - b^2)/(a + b) = 25

So, it can be written as (a + b) (a - b)/(a + b) = 25

Hence, (a - b) = 25

Explanation: Pick up the unit digit of each number and multiply them;

0^2 in (1570)^2 = 0

1^2 in (1571)^2 = 1

2^2 in (1572)^2 = 4

3^2 in (1573)^2 = 9

On adding the unit digits, we will get,

0 1 4 9 = 14 (unit digit = 4)

So, on adding (1570)^2 (1571)^2 (1572)^2 (1573)^2, the unit digit will be 4.