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

It is currently 21 Sep 2018, 17:10

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x and y are positive integers, what is the units digit ....

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior Manager
Senior Manager
User avatar
P
Joined: 12 Feb 2015
Posts: 431
Premium Member CAT Tests
If x and y are positive integers, what is the units digit ....  [#permalink]

Show Tags

New post 06 Sep 2018, 08:53
1
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:31) correct 43% (02:15) wrong based on 30 sessions

HideShow timer Statistics

If x and y are positive integers, what is the units digit of \(7^{xy+y}\)?

1) \(\frac{x}{16}\)=n, where n is a positive integer.

2) \(\frac{y}{8}\)=m, where m is a positive integer.

_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6797
Re: If x and y are positive integers, what is the units digit ....  [#permalink]

Show Tags

New post 06 Sep 2018, 09:03
CAMANISHPARMAR wrote:
If x and y are positive integers, what is the units digit of \(7^{xy+y}\)?

1) \(\frac{x}{16}\)=n, where n is a positive integer.

2) \(\frac{y}{8}\)=m, where m is a positive integer.



Cyclicity of unit's digit of 7 is 7,9,3,1,7,9,3,1......
\(7^{xy+y}\)=\(7^{(x+1)y}\)

Let us see the statements..

1) \(\frac{x}{16}\)=n, where n is a positive integer.
So x is a multiple of 16
\(7^{(x+1)y}\)=\(7^{(16+1)y}\)
If y is 2, it will be 9..
If y=4, it will be 1..and so on
Insufficient

2) \(\frac{y}{8}\)=m, where m is a positive integer
\(7^{(x+1)y}\)
Y is a multiple of 8, so \(7^{(x+1)y}\)=\(7^{(x+1)8}\)
So power of 7 is a multiple of 8..
Thus irrespective of x ANS will be 1
Sufficient

B
_________________

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

Re: If x and y are positive integers, what is the units digit .... &nbs [#permalink] 06 Sep 2018, 09:03
Display posts from previous: Sort by

If x and y are positive integers, what is the units digit ....

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.