451 and 607 are divided by a three-digit integer and the remainder is

Question

451 and 607 are divided by a three-digit integer and the remainder is same in both cases. What is the value of the three-digit integer?

(A) 145
(B) 156
(C) 183
(D) 203
(E) 223

yashikaaggarwal · Answer

Let, Quotient 1 = Q1, Quotient 2 = Q2, Remainder = R, and divisor = X
Therefore, 
451 = Q1*X + R ----------(1)
607 = Q2*X + R ------------(2)

Equating both,
451 - Q1*X = 607 - Q2*X
Q2*X - Q1*X = 156
X(Q2-Q1) = 156

from this, we can say,
X is a multiple of the factors of 156
and Only the B option satisfy all.

Answer is B

NandishSS · Answer

451= nX+R -- (1)
607= nY+R -- (2)

(2) - (1) Gives

156 = n(Y-X)

Hence B

MathRevolution · Answer

451 = pN + R => R = 451 - pN

607 = qN + R => R = 607 - qN

=> 451 - pN = 607 - qN

=> N(q - p) = 607 - 451 = 156

=> N must be multiple of 156 and hence Answer B.

Answer B

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