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

 It is currently 23 Feb 2019, 01:47

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 11 Feb 2015
Posts: 721
If x and y are positive integers, what is the units digit ....  [#permalink]

### Show Tags

06 Sep 2018, 07:53
1
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:32) correct 36% (02:28) wrong based on 36 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 +1 Kudos if you like this post"

_________________
Manish

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

Math Expert
Joined: 02 Aug 2009
Posts: 7335
Re: If x and y are positive integers, what is the units digit ....  [#permalink]

### Show Tags

06 Sep 2018, 08:03
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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Re: If x and y are positive integers, what is the units digit ....   [#permalink] 06 Sep 2018, 08:03
Display posts from previous: Sort by