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24 Feb 2020, 20:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
66% (01:36) correct
34%
(01:37)
wrong
based on 370
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24 Feb 2020, 23:29
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GMATinsight
BINOMIAL THEOREM !! is the savior in such questions..
\(37^{37}=(35+2)^{37}\) divided by 7 will give \(2^{37}\).......
\(2^{37}=(2^3)^{12}*2=8^{12}*2=(7+1)^{12}*2\)..
\((7+1)^{12}*2\) when divided by 7 will leave \(1^{12}*2=2\)
B
25 Feb 2020, 03:01
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When a question on remainders involves powers, always try to find such a power of the dividend which gives a remainder of 1 when divided by the divisor.
\(37^1\) when divided by 7 leaves a remainder of 2.
\(37^2\) = \(37^1\) * \(37^1\); when divided by 7, remainder = 2 * 2 = 4.
Remember, Remainder (A*B) = Remainder (A) * Remainder (B).
\(37^3\) = \(37^2\) * \(37^1\); when divided by 7, remainder = 4 * 2 = 8 which means the final remainder will be 1.
If you obtain a remainder greater than the divisor, you need it do divide it again till you get a remainder smaller than the divisor because, remainder< divisor. ALWAYS!
This means, \(37^3\) leaves a remainder of 1 when divided by 7. So, we can now try to write \(37^{37}\) in terms of \(37^3\) as much as we can.
\(37^{37}\) = \((37^3) ^ {12}\) * \(37^1\); when divided by 7, the remainder = \((1)^{12}\) * 2. This means the final remainder will be 2.
The correct answer option is B.
Hope that helps!
\(37^1\) when divided by 7 leaves a remainder of 2.
\(37^2\) = \(37^1\) * \(37^1\); when divided by 7, remainder = 2 * 2 = 4.
Remember, Remainder (A*B) = Remainder (A) * Remainder (B).
\(37^3\) = \(37^2\) * \(37^1\); when divided by 7, remainder = 4 * 2 = 8 which means the final remainder will be 1.
If you obtain a remainder greater than the divisor, you need it do divide it again till you get a remainder smaller than the divisor because, remainder< divisor. ALWAYS!
This means, \(37^3\) leaves a remainder of 1 when divided by 7. So, we can now try to write \(37^{37}\) in terms of \(37^3\) as much as we can.
\(37^{37}\) = \((37^3) ^ {12}\) * \(37^1\); when divided by 7, the remainder = \((1)^{12}\) * 2. This means the final remainder will be 2.
The correct answer option is B.
Hope that helps!
