SSC CPO 2019 PYQ — Question 111

The correct answer is Option 4 i.e. 3738

Let when 3738, 5659, and 9501 are divided by x then the quotient will be A, B, and C respectively and y is the remainder in each case.

So, using remainder theorem:

3738 = Ax + y ……………………. (1)

5659 = Bx + y …………………….. (2)

9501 = Cx + y ……………………… (3)

Subtract equation (2) from equation (3):

⇒ (9501 - 5659) = (C - B) x

⇒ 3842 = (C - B) x ……………… (4)

Subtract equation (1) from equation (2):

5659 - 3738 = (B - A)x

⇒ 1921 = (B - A)x……………..(5)

Now we will evaluate HCF of 3842 & 1921

1921 = 1921 × 1

3842 = 1921 × 2

Hence HCF of 3842 & 1921 = 1921…………………(6)

From (4) , (5) and (6)

x = 1921

So,

3738 = 1921 × 1 + y

⇒ y = 1817

Hence,

Sum of x and y =1921 + 1817 = 3738