If n is a positive integer, which of the following cant be the value

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

chetan2u · Answer

(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

MathRevolution · Answer

=>

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

varun4s · Answer

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.

Answer: C.

EgmatQuantExpert · Answer

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.

Answer: C

QuantMadeEasy · Answer

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.

BrentGMATPrepNow · Answer

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.

Check the answer choices........
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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If n is a positive integer, which of the following cant be the value

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If n is a positive integer, which of the following cant be the value

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards