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05 Jan 2022, 06:30
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B
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Difficulty:
85%
(hard)
Question Stats:
41% (02:09) correct
59%
(02:34)
wrong
based on 86
sessions
History
Date
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Not Attempted Yet
If p and q are positive integers, what is the remainder when \(27^{12p} + 3^{6q}\) is divided by 5?
(1) p is an odd prime number
(2) q is divisible by 10
(1) p is an odd prime number
(2) q is divisible by 10
08 Jan 2022, 08:42
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Bunuel
Note that \(27^{12} = (XY9)^6 = (ABCD1)^4\) will always have a unit digit of 1. So we only need to know the unit digit of \(3^{6q}\).
Also \(3^{6q} = 9^{3q}\) which can only have a unit digit of 9 or 1. This depends on whether q is even/odd, so we only need to know the parity of q for sufficiency.
Statement 1 Alone:
We don't care about the value of p, so this is insufficient.
Statement 2 Alone:
This tells us q is even, so this is sufficient.
Answer: B
17 Jan 2022, 15:34
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JerryAtDreamScore
Hi Jerry,
How you got \(27^{12} = (XY9)^6\) ? My rational to get 1 as UD was that \(27^{12} = (7)^{12} = (7)^4 = 1\)
Thanks!
