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# If n is an integer between 10 and 100, is the tens digit of n even?

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If n is an integer between 10 and 100, is the tens digit of n even?  [#permalink]

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23 Aug 2015, 09:23
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85% (hard)

Question Stats:

55% (02:24) correct 45% (02:32) wrong based on 154 sessions

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If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

(2) The only prime factor of n is 3.

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Re: If n is an integer between 10 and 100, is the tens digit of n even?  [#permalink]

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23 Aug 2015, 10:26
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If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

(2) The only prime factor of n is 3.

If n is an integer between 10 and 100, is the tens digit of n even?

(1) The remainder when n is divided by 4 is equal to the remainder when n is divided by 5.

First of all, since the remainder is less than the divisor then the remainder must be 0, 1, 2, or 3.

n = 4q + r;
n = 5p + r;

4q + r = 5p + r;
4q = 5p --> q/p = 5/4 --> q must be a multiple of 5 and p must be a multiple of 4.

Thus, n = 4q + r = 4(5k) + r = 20k + r = (a multiple of 20) + r --> n could be 20, 21, 22, 23, 40, 41, 42, 43, 60, 61, 62, 63, 80, 81, 82, or 83. In any case the tens digit of n is even. Sufficient.

(2) The only prime factor of n is 3 --> n = 3^m. Since n is between 10 and 100, then it can be 3^3 = 27 or 3^4 = 81. In any case the tens digit of n is even. Sufficient.

Hope it's clear.
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Re: If n is an integer between 10 and 100, is the tens digit of n even?  [#permalink]

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08 Mar 2017, 04:55
ST 1: LCM is 20. hence the number can be 20, 21, 22, 23,40, 41,42,43, 60,61, 62, 63, 80, 81, 82, 83. All the cases, the tens digit is even. ANSWER

St 2: the possibilities are 03,09,27,81. All the cases, the tens digit is even.

Option D
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Re: If n is an integer between 10 and 100, is the tens digit of n even?  [#permalink]

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20 Aug 2019, 04:05
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Re: If n is an integer between 10 and 100, is the tens digit of n even?   [#permalink] 20 Aug 2019, 04:05
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# If n is an integer between 10 and 100, is the tens digit of n even?

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