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

 It is currently 14 Nov 2018, 08:23

### 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
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

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

Author Message
TAGS:

### Hide Tags

Director
Joined: 11 Feb 2015
Posts: 562
If x and y are positive integers, what is the units digit ....  [#permalink]

### Show Tags

06 Sep 2018, 07:53
1
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:32) correct 40% (02:10) wrong based on 35 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: 7029
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

GMAT online Tutor

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