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23 Nov 2011, 09:14
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Two numbers when divided by a divisor leave reminders of 248 and 372 respectively. The reminder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
A. 276
B. 552
C. 414
D. 1104
E. 2202
A. 276
B. 552
C. 414
D. 1104
E. 2202
23 Nov 2011, 09:57
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Fun question.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division.
y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68
552 = a*(M-N-K)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.
Therefore, a = 552. B.
Say the two numbers are x and y, and divisor is a.
x divided by a leaves a remainder of 248. This means that x = a*N + 248, where N is the integer result of the division.
y divided by a leaves a remainder of 372. This means that x = a*K + 372, where K is the integer result of the division.
x+y divided by a leaves a remainder of 68. This means that x = a*M + 68, where M is the integer result of the division.
From definitions above:
x+y = (a*N + 248) + (a*K + 372) = a*(N+K) + 620.
a*(N+K) + 620 = a*M + 68
552 = a*(M-N-K)
We know that M, N, and K are integers and that a must be at least 373 (to leave a 372 remainder). The only possible value for (M-N-K) is 1.
Therefore, a = 552. B.
06 Oct 2012, 06:32
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A rule to solve all similar problems ---
If two numbers, say a & b, are divided by the same divisor (d) leaving remainders r1 & r2.
Then the remainder (R), when Sum (a+b) / d = (r1+r2) - d.
Note - If R becomes negative, then R = (r1+r2) only.
Hence Solution to the above problem -
d = 68, r1 = 248, r2 = 372
so Remainder R when Sum (a+b) / 68 = (248+372) - 68 = 620 - 68 = 552
Note - Difference (a-b) is exactly divisible by the same divisor (d).
Hope it helps.
If two numbers, say a & b, are divided by the same divisor (d) leaving remainders r1 & r2.
Then the remainder (R), when Sum (a+b) / d = (r1+r2) - d.
Note - If R becomes negative, then R = (r1+r2) only.
Hence Solution to the above problem -
d = 68, r1 = 248, r2 = 372
so Remainder R when Sum (a+b) / 68 = (248+372) - 68 = 620 - 68 = 552
Note - Difference (a-b) is exactly divisible by the same divisor (d).
Hope it helps.
