Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 15 Sep 2014, 21:30

### 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 June
Open Detailed Calendar

# What is the remainder when X^4 + Y^4 is divided by 5 1. When

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Director
Joined: 21 Dec 2009
Posts: 588
Concentration: Entrepreneurship, Finance
Followers: 15

Kudos [?]: 264 [0], given: 20

What is the remainder when X^4 + Y^4 is divided by 5 1. When [#permalink]  20 Jul 2010, 04:02
00:00

Difficulty:

(N/A)

Question Stats:

40% (02:12) correct 60% (01:30) wrong based on 11 sessions
What is the remainder when X^4 + Y^4 is divided by 5

1. When X-Y is divided by 5 remainder is 1
2. When X+Y is divided by 5 remainder is 2

This question has been treated in another thread, but I simply cannot filter
out the posts for reference.

The approach used in one of the post:
Each statement alone is not SUFFICIENT.
Let X - Y = 5A + 1
X + Y = 5B + 2
2X = 5(A+B) + 3
2Y = 5(B-A) + 1
16 (X4 + Y4) = {5(A+B)+3}4 + {5(B-A)+1}4
= (5P+3)4 + (5Q+1)4
= 81 + 1 + 5R
= 82 + 5R
X4 + Y4 = 5 + (5R+2)/16
Since L.H.S is multiple of 16, R.H.S. should also be multiple of 16(since R.H.S cannot be a fraction.).
Lowest value of R for which R.H.S. is an integer is R=6
X4 + Y4 = 82
Remainder of (X4 + Y4)/5 = 2

Hence C

Could anyone assist to especially with the highlighted part. Thanks
_________________

KUDOS me if you feel my contribution has helped you.

Manager
Joined: 03 May 2010
Posts: 89
WE 1: 2 yrs - Oilfield Service
Followers: 11

Kudos [?]: 66 [0], given: 7

Re: Remainder for X^4 + Y^4 divided by 5 [#permalink]  22 Jul 2010, 04:10
The method you posted seems to me to be a bit too contrived and lengthy, though it may work for some people. On the GMAT, it may be better to test cases and visualize possibilities rather than perform too much of algebra that you would be prone to make errors in under a time crunch. The following method may seem pretty contrived too, but in fact it's quite intuitive - you just need to test obvious cases. This approach will work for most DS questions and is something you can rely on for test-day.

x^4 + y^4

1. (x - y) R 5 = 1

i.e. x - y is some number ending in 1 or 6.

There are various values of x and y that could yield such numbers, and would thus yield various different values of x^4 + y^4

INSUFFICIENT

2. (x + y) R 5 = 2

i.e. x + y is some number ending in 2 or 7.

There are various values of x and y that could yield such numbers, and would thus yield various different values of x^4 + y^4

INSUFFICIENT

Both 1 and 2:

x + y is a number ending in 2 or 7 and x - y is a number ending in 1 or 6, i.e. there are 4 combinations we need to test to see if they are possible. i.e. (x+y, x-y) are numbers ending in (2,1) (2,6) (7,1) or (7,6). It shouldn't be too tough to come up with the following examples:

19 + 13 = 32 and 19 - 13 = 6 ... satisfies (2,6)
14 + 13 = 27 and 14 - 13 = 1 ... satisfies (7,1)
19 + 18 = 37 and 19 - 18 = 1 ... satisfies (7,1)

The other 2 cases of (2,1) and (7,6) are evidently contradictory (you won't be able to find two numbers that satisfy it) and are thus not possible. Now let's test our stem for the 3 possible examples:

1. 19^4 is a number ending in 1, and 13^4 is a number ending in 1 => the sum is a number ending in 2... remainder when divided by 5 will also be 2.

2. 14^4 is a number ending in 6, and 13^4 is a number ending in 1 => the sum is a number ending in 7 ... remainder when divided by 5 will be 2.

3. 19^4 is a number ending in 1 and 18^4 is a number ending in 6 => the sum is a number ending in 7 ... remainder when divided by 5 will be 2.

Three solid cases are usually sufficient on the GMAT and this is a safe bet.

SUFFICIENT

Pick C.
Senior Manager
Joined: 20 Jul 2010
Posts: 271
Followers: 2

Kudos [?]: 39 [0], given: 9

Re: Remainder for X^4 + Y^4 divided by 5 [#permalink]  22 Jul 2010, 04:15
Nice explanation!!
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 247
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Followers: 4

Kudos [?]: 47 [0], given: 46

Re: Remainder for X^4 + Y^4 divided by 5 [#permalink]  13 Aug 2011, 11:35
AbhayPrasanna wrote:
The method you posted seems to me to be a bit too contrived and lengthy, though it may work for some people. On the GMAT, it may be better to test cases and visualize possibilities rather than perform too much of algebra that you would be prone to make errors in under a time crunch. The following method may seem pretty contrived too, but in fact it's quite intuitive - you just need to test obvious cases. This approach will work for most DS questions and is something you can rely on for test-day.

x^4 + y^4

1. (x - y) R 5 = 1

i.e. x - y is some number ending in 1 or 6.

There are various values of x and y that could yield such numbers, and would thus yield various different values of x^4 + y^4

INSUFFICIENT

2. (x + y) R 5 = 2

i.e. x + y is some number ending in 2 or 7.

There are various values of x and y that could yield such numbers, and would thus yield various different values of x^4 + y^4

Dear AbhayPrasanna

can you please tell what calues combination we can try

btw when i tries 3 combination remainder was always 2
_________________

WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post.

Re: Remainder for X^4 + Y^4 divided by 5   [#permalink] 13 Aug 2011, 11:35
Similar topics Replies Last post
Similar
Topics:
X^4 is dividable by 32, what is the remainder when X is 4 15 Oct 2012, 15:50
What is the remainder when 9K + 1 is divided by 5? 1 15 Sep 2012, 07:14
25 What is the remainder when 43^86 is divided by 5? 27 21 Jun 2012, 15:59
1 What is the remainder when X^4 + Y^4 divide by 5 A) X-Y 14 04 Jul 2009, 22:08
What is the remainder when 7^n + 2 is divided by 5 (1) when 2 19 Jun 2008, 03:51
Display posts from previous: Sort by

# What is the remainder when X^4 + Y^4 is divided by 5 1. When

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.