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If N = 5^4 - 3^4, then which of the following is not divisible by the

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If N = 5^4 - 3^4, then which of the following is not divisible by the  [#permalink]

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Updated on: 13 Aug 2018, 02:52
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Difficulty:

35% (medium)

Question Stats:

71% (02:04) correct 29% (02:04) wrong based on 170 sessions

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e-GMAT Question:

If $$N=5^4-3^4$$, then which of the following is not divisible by the greatest prime factor of $$N$$.

A) 51
B) 119
C) 187
D) 218
E) 340

This is

Question 8 of The e-GMAT Number Properties Marathon

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Originally posted by EgmatQuantExpert on 28 Feb 2018, 03:14.
Last edited by EgmatQuantExpert on 13 Aug 2018, 02:52, edited 3 times in total.
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Re: If N = 5^4 - 3^4, then which of the following is not divisible by the  [#permalink]

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28 Feb 2018, 03:52
1
EgmatQuantExpert wrote:

Question:

If $$N=5^4-3^4$$, then which of the following is not divisible by the greatest prime factor of $$N$$.
A) 51
B) 119
C) 187
D) 218
E) 340

5^4 = 625
3^4 = 81
625-81 = 544

544 = 17 x 2^5 ( prime factorisation)

largest prime = 17

we know multiples of 17 are 51,119, 187, 340

218/17 = 12.xx

(D) imo
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Re: If N = 5^4 - 3^4, then which of the following is not divisible by the  [#permalink]

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28 Feb 2018, 04:23
1
We have to prime factorize N
$$N = 5^4-3^4 = 625-81 = 544 = 17*2^5$$

A) 51 = 3*17
B) 119 = 7*17
C) 187 = 11*17

D) 218 = 2*109
E) 340 = 2*2*5*17

Therefore, Only Option D(218) is not divisble by the greatest prime factor of $$N$$
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Re: If N = 5^4 - 3^4, then which of the following is not divisible by the  [#permalink]

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28 Feb 2018, 12:03

Solution:

We need to find the greatest prime factor of $$N$$. To calculate the greatest prime factor, we need to write $$5^4-3^4$$ in prime factorization form.
$$N= 5^4-3^4$$
$$N= (5^2 – 3^2)* (5^2 + 3^2)$$
$$N= (5 – 3)* (5 + 3)* (5^2 + 3^2)$$
$$N= 2* 8* 34$$
$$N= 2* (2*2*2)*(2*17)$$
$$N= 2^5 *17$$
We can see, greatest prime factor of $$N$$ is $$17$$.
Thus, we need to see, among the given option which is not divisible by $$17$$.
We can easily find that $$218$$ is not divisible by $$17$$. Hence, $$218$$ is the answer.
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Re: If N = 5^4 - 3^4, then which of the following is not divisible by the  [#permalink]

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07 Apr 2019, 10:53
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Re: If N = 5^4 - 3^4, then which of the following is not divisible by the   [#permalink] 07 Apr 2019, 10:53
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