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

 It is currently 18 Oct 2018, 04:36

### 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

# If x is a positive integer, does the remainder, when (7^x + 1) is divi

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49993
If x is a positive integer, does the remainder, when (7^x + 1) is divi  [#permalink]

### Show Tags

01 Oct 2018, 04:55
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:39) correct 34% (02:14) wrong based on 38 sessions

### HideShow timer Statistics

If x is a positive integer, does the remainder, when $$(7^x + 1)$$ is divided by 100, have 0 as the units’ digit?

(1) x = 4n + 2, where n is a positive integer.
(2) x > 5

_________________
CEO
Joined: 08 Jul 2010
Posts: 2540
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If x is a positive integer, does the remainder, when (7^x + 1) is divi  [#permalink]

### Show Tags

01 Oct 2018, 05:11
Bunuel wrote:
If x is a positive integer, does the remainder, when $$(7^x + 1)$$ is divided by 100, have 0 as the units’ digit?

(1) x = 4n + 2, where n is a positive integer.
(2) x > 5

CONCEPT: Remainder when any number is divided by hundred are the last two digits of the number e.g. 137 divided by 100 leaves 37 remainder and likewise 923 divided by 100 leaves 23 remainder etc

i.e. we only need to know if the unit digit of $$(7^x + 1)$$ is Zero or NOT

i.e. we need to know if $$7^x$$ has unit digit 9 or not which is possible when $$x = 4a+2$$ because cyclicity of 7 is 4 and $$7^2$$ and $$7^6$$ and $$7^10$$ etc have unit digit 9

Statement 1: x = 4n + 2, where n is a positive integer.
i.e. $$7^x$$ will always have unit digit 9 hence
SUFFICIENT

$$Statement 2: x > 5$$
x may be 6 or 7 etc. hence unit digit of $$7^x$$ may or may not be 9 hence
NOT SUFFICIENT

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Re: If x is a positive integer, does the remainder, when (7^x + 1) is divi &nbs [#permalink] 01 Oct 2018, 05:11
Display posts from previous: Sort by