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# If n is a positive integer, which of the following can’t be the value

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6620
GMAT 1: 760 Q51 V42
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If n is a positive integer, which of the following can’t be the value  [#permalink]

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14 Aug 2018, 16:48
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:16) correct 21% (01:50) wrong based on 82 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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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7101 Re: If n is a positive integer, which of the following can’t be the value [#permalink] ### Show Tags 14 Aug 2018, 17:14 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 _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6620 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] ### Show Tags 16 Aug 2018, 07:54 => 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. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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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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16 Aug 2018, 22:36
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.

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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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17 Aug 2018, 00:55

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

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21 Aug 2018, 22:09
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.
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Joined: 11 Sep 2015
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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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24 Aug 2018, 05:50
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
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Re: If n is a positive integer, which of the following can’t be the value &nbs [#permalink] 24 Aug 2018, 05:50
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