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20 Nov 2022, 07:53
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Let q be a prime number less than 100. When q is divided by 5, the remainder is 2. When q is divided by 7, the remainder is 6, what is the remainder when q is divided by 8?
A. 1
B. 3
C. 5
D. 6
E. 7
A. 1
B. 3
C. 5
D. 6
E. 7
20 Nov 2022, 12:48
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Bunuel
q can be represented as -
q = 5x + 2; x is the quotient when q is divided by 5
q = 7y + 6; y is the quotient when q is divided by 7
Combined, we can represent q as
q = LCM(5,7) z + First common term in the series
q = 35z + 27
Possible values of q = 27, 62, 97.
We can eliminate 62 & 27 as q is prime.
97 when divided by 8, remainder = 1
Option A
