GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Nov 2018, 01:00

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis

Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Oct 2016
Posts: 81
Concentration: Technology, General Management
WE: Information Technology (Computer Software)
If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis  [#permalink]

### Show Tags

21 Oct 2016, 09:13
3
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:06) correct 33% (01:56) wrong based on 87 sessions

### HideShow timer Statistics

If x is positive integer, is x^4 - 1 divisible by 5?

(1) x-1 is divisible by 5.

(2) When x^2 + 1 is divided by 5, the remainder is 2.

_________________

KINDLY KUDOS IF YOU LIKE THE POST

Manager
Status: Trying...
Joined: 15 Aug 2016
Posts: 104
Location: India
GMAT 1: 660 Q51 V27
GMAT 2: 690 Q48 V37
GPA: 4
WE: Consulting (Internet and New Media)
Re: If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis  [#permalink]

### Show Tags

21 Oct 2016, 09:45
idontknowwhy94 wrote:
If x is positive integer, is $$x^{4}$$-1 divisible by 5?

1) x-1 is divisible by 5.

2) When $$x^{2}$$+1 is divided by 5, the
remainder is 2.

Statement 1: This holds true for 6,11,16,.. all of which have powers ending with 1 or 6. so $$x^{4}$$-1 has to be divisible by 5
Statement 2: When $$x^{2}$$+1 is divided by 5, the remainder is 2. This indicates that the number can never be divisible by 5.

Hence, D must be the answer. A question like this, where the 2 statements give 2 contradictory answers is highly unlikely to come.
VP
Joined: 05 Mar 2015
Posts: 1000
Re: If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis  [#permalink]

### Show Tags

21 Oct 2016, 10:11
1
mankodim wrote:
idontknowwhy94 wrote:
If x is positive integer, is $$x^{4}$$-1 divisible by 5?

1) x-1 is divisible by 5.

2) When $$x^{2}$$+1 is divided by 5, the
remainder is 2.

Statement 1: This holds true for 6,11,16,.. all of which have powers ending with 1 or 6. so $$x^{4}$$-1 has to be divisible by 5
Statement 2: When $$x^{2}$$+1 is divided by 5, the remainder is 2. This indicates that the number can never be divisible by 5.

Hence, D must be the answer. A question like this, where the 2 statements give 2 contradictory answers is highly unlikely to come.

Hi mankodim

rephrasing Question x^4-1=(x^2-1)(x^2+1)----->(x-1)(x+1)(x^2+1) is divisible by 5??

1) x-1 is divisible means (x-1)(x+1)(x^2+1) is div by 5----->Yes.....suff
2)X^2+1 is div by 5 means x=4, 6,9,11,14,16.....(series having two consecutive even then two consecutive odd pairs)
if we take x=4 then (x+1) is div. by 5.....suff..
if x=6 then x-1 is div by 5 .....suff.

both cases weare getting number divisible by 5
Ans D
Manager
Joined: 28 Jun 2016
Posts: 207
Concentration: Operations, Entrepreneurship
Re: If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis  [#permalink]

### Show Tags

21 Oct 2016, 11:06
1
idontknowwhy94 wrote:
If x is positive integer, is $$x^{4}$$-1 divisible by 5?

1) x-1 is divisible by 5.

2) When $$x^{2}$$+1 is divided by 5, the
remainder is 2.

x^4 -1 = 5z??

(x^2+1)(x+1)(x-1)=5z??

Statement 1:

Sufficient

Statement 2:

x^2 +1 = 5y+2

On simplifying

x^2 - 1 = 5y

We know that

x^4 -1 = (x^2 +1)(x^2 - 1) = (5y+2)*5y

Therefore it is definitely divisible by 5.

D

Sent from my iPhone using GMAT Club Forum mobile app
Manager
Joined: 01 Nov 2016
Posts: 66
Concentration: Technology, Operations
Re: If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis  [#permalink]

### Show Tags

21 Mar 2017, 12:35
Great explanation acegmat123. It took me a while to understand what you wrote, but I got it.

The question: Is $$(x^4 - 1)$$ divisible by 5?
In other words, is this true: $$(x^4 - 1)/5 = quotient + 0/5$$
The first thing to do is to factor $$x^4 - 1$$ which is equal to: $$(x^2+1)(x+1)(x-1)$$

Statement 1:
$$(x-1)$$ is divisible by 5
Well if (x-1) is divisible by 5, then the entire statement is divisible by 5, because (x-1) is part of $$x^4 - 1$$. This makes statement 1 sufficient.

Statement 2:
When $$x^2 +1$$ is divided by 5, the remainder is 2. Or in other words:
$$(x^2 +1)/5 = quotient + 2/5$$
Simplify to:
$$(x^2 +1) = (5*quotient) + 2$$
$$(x^2 - 1) = (5*quotient) + 0$$

This proves that $$(x^2 - 1)$$ is divisible by 5, and $$(x^2 - 1)$$ is part of $$(x^2+1)(x+1)(x-1)$$, so then $$x^4 - 1$$ is divisible by 5. Statement 2 is sufficient. Both statements are sufficient by themselves, so the answer is D.
Re: If x is positive integer, is x^4 - 1 divisible by 5? (1) x-1 is divis &nbs [#permalink] 21 Mar 2017, 12:35
Display posts from previous: Sort by