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If N = 5^4 - 3^4, then which of the following is not divisible by the Updated on: 13 Aug 2018, 02:52
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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Question Stats:

76% (02:04) correct 24% (02:08) wrong based on 584 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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D
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If N = 5^4 - 3^4, then which of the following is not divisible by the 28 Feb 2018, 03:52
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EgmatQuantExpert

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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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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If N = 5^4 - 3^4, then which of the following is not divisible by the 28 Feb 2018, 04:23
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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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If N = 5^4 - 3^4, then which of the following is not divisible by the 28 Feb 2018, 12:03
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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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If N = 5^4 - 3^4, then which of the following is not divisible by the 31 Aug 2020, 11:25
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EgmatQuantExpert

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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Solution:

We see that 5^4 - 3^4 is a difference of squares, so we can factor N:

N = (5^2 + 3^2)(5^2 - 3^2) = (34)(16)

Now, we can further factor N into primes:

N = (2 x 17)(2^4) = 2^5 x 17

We see that the greatest prime factor of N is 17, and all the answer choices are divisible by 17 except choice D, 218.

Answer: D
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If N = 5^4 - 3^4, then which of the following is not divisible by the 31 Aug 2020, 12:15
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Solution:

Find the greatest prime factor of N. We can do the following:
N= (5^4 - 3^4)
N= 625-81 = 544
N=544 --> (2^5)x 17

We can see, greatest prime factor of N is 17
Thus, we need to find, among the choices which is not divisible by 17
All the answer choices are divisible by 17 except D, 218.

Answer: Option D
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If N = 5^4 - 3^4, then which of the following is not divisible by the 31 Aug 2020, 12:16
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EgmatQuantExpert

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

Show more


Solution:

Find the greatest prime factor of N. We can do the following:
N= (5^4 - 3^4)
N= 625-81 = 544
N=544 --> (2^5)x 17

We can see, greatest prime factor of N is 17
Thus, we need to find, among the choices which is not divisible by 17
All the answer choices are divisible by 17 except D, 218.

Answer: Option D
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If N = 5^4 - 3^4, then which of the following is not divisible by the 01 Apr 2021, 12:09
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Hello, could you tell me the shortest way to figure out which of the numbers can't be divided by 17, please?
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