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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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New post Updated on: 13 Aug 2018, 01:52
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

78% (02:00) correct 22% (02:03) wrong based on 150 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

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Question 8 of The e-GMAT Number Properties Marathon


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Originally posted by EgmatQuantExpert on 28 Feb 2018, 02:14.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:52, 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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New post 28 Feb 2018, 02:52
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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

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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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New post 28 Feb 2018, 03:23
We have to prime factorize N
\(N = 5^4-3^4 = 625-81 = 544 = 17*2^5\)

Evaluating answer options,

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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New post 28 Feb 2018, 11:03

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.
Answer: Option D
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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
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Re: If N = 5^4 - 3^4, then which of the following is not divisible by the &nbs [#permalink] 28 Feb 2018, 11:03
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