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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42 GPA: 3.82
If n is a positive integer, which of the following can’t be the value  [#permalink]

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Difficulty:   15% (low)

Question Stats: 81% (01:41) correct 19% (01:58) wrong based on 114 sessions

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[Math Revolution GMAT math practice question]

If $$n$$ is a positive integer, which of the following can’t be the value of $$(n+1)^4-n^4$$?

A. 2465
B. 4641
C. 6096
D. 7825
E. 9855

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Math Expert V
Joined: 02 Aug 2009
Posts: 8302
Re: If n is a positive integer, which of the following can’t be the value  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$n$$ is a positive integer, which of the following can’t be the value of $$(n+1)^4-n^4$$?

A. 2465
B. 4641
C. 6096
D. 7825
E. 9855

$$(n+1)^4-n^4$$ is the difference of some power of consecutive numbers, so it will always be ODD..
O-E=O
E-O=0

C
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If n is a positive integer, which of the following can’t be the value  [#permalink]

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=>

If$$n + 1$$ is an even number, then$$n$$ is an odd number and $$(n+1)^4-n^4$$must be an odd number.
If $$n + 1$$ is an odd number, then $$n$$ is an even number and $$(n+1)^4-n^4$$must be an odd number.
All answer choices except for C) are odd numbers.

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Senior Manager  P
Joined: 07 Jul 2012
Posts: 365
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: If n is a positive integer, which of the following can’t be the value  [#permalink]

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Difference between Odd & Even or Even & Odd is always odd. So the answer must be odd. C is the only even number in the given answer choices.

e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
Re: If n is a positive integer, which of the following can’t be the value  [#permalink]

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Solution

Given:
• n is a positive integer.

To find:
• The option which cannot be the value of $$(n+1)^4−n^4$$

Approach and Working:
• Now, $$(n+1)^4−n^4$$ is subtraction between two consecutive numbers, one of which always be odd and another will always be even.
o And, O-E or E-O is always Odd.
o Hence. 6096 cannot be the value of $$(n+1)^4−n^4$$.

Hence, the correct answer is option C.

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Manager  G
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Re: If n is a positive integer, which of the following can’t be the value  [#permalink]

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First statement, says that n is a positive integer ie n> 0. Now, they are asking the value of (n+1)^4−n^4. Lets say n is even, so (n+1)^4 – n^4 = Odd – Even = Odd. And if we take n as odd, the expression (n+1)^4−n^4 becomes Even – Odd = Odd. So in both the cases the answer is odd and if we analyse the question it says which of the following cant be the value, hence even cant be the value. So the answer option is C.
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4134
Re: If n is a positive integer, which of the following can’t be the value  [#permalink]

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Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$n$$ is a positive integer, which of the following can’t be the value of $$(n+1)^4-n^4$$?

A. 2465
B. 4641
C. 6096
D. 7825
E. 9855

KEY CONCEPTS:
#1) If n is an integer, then n and n+1 are consecutive integers
#2) If n and n+1 are consecutive integers, then one value is ODD and the other value is EVEN
#3) ODD^4 = (ODD)(ODD)(ODD)(ODD) = ODD
#4) EVEN^4 = (EVEN)(EVEN)(EVEN)(EVEN) = EVEN
#5) ODD - ODD = EVEN
#6) ODD - EVEN = ODD
#7) EVEN - ODD = ODD
#8) EVEN - EVEN = EVEN

From #2, there are two possible cases to consider:
case 1: n is EVEN and n+1 is ODD
case 2: n is ODD and n+1 is EVEN

case 1: n is EVEN and n+1 is ODD
In this case, (n+1)^4 - n^4 = ODD^4 - EVEN^4
= ODD - EVEN (from #3 and #4)
= ODD (from #6)

case 2: n is ODD and n+1 is EVEN
In this case, (n+1)^4 - n^4 = EVEN^4 - ODD^4
= EVEN - ODD (from #3 and #4)
= ODD (from #7)

In both cases, (n+1)^4 - n^4 = some ODD integer.

All of the answer choices are ODD, except for answer choice C

Since (n+1)^4 - n^4 can't be EVEN, the correct answer is C

Cheers,
Brent
_________________ Re: If n is a positive integer, which of the following can’t be the value   [#permalink] 24 Aug 2018, 06:50
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