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

 It is currently 17 Aug 2018, 06:04

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

What is the value of x if x is the remainder obtained when 2^(8p + 2)

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47967
What is the value of x if x is the remainder obtained when 2^(8p + 2)  [#permalink]

Show Tags

18 Jul 2018, 23:32
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:53) correct 49% (02:19) wrong based on 45 sessions

HideShow timer Statistics

What is the value of x if x is the remainder obtained when $$2^{8p+2} + Z$$ is divided by 5 and p is a positive integer?

(1) Z = 6
(2) Z is even

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6540
Re: What is the value of x if x is the remainder obtained when 2^(8p + 2)  [#permalink]

Show Tags

19 Jul 2018, 00:16
What is the value of x if x is the remainder obtained when $$2^{8p+2} + Z$$ is divided by 5 and p is a positive integer?
Due to cyclicity the units digit of $$2^{8p+2}$$ will be SAME as $$2^2$$
So the units digit will be 2^2+z=4+z
since we are looking for divisiblity by 5, which requires 5, or 0 as units digit to divide a number, we can get the remainder by knowing units digit of the term
hence we require only z

(1) Z = 6
z =6, so units digit = 4+6=10
remainder is 0
suff

(2) Z is even
nothing much
insuff

A
_________________

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

Manager
Joined: 17 Jan 2017
Posts: 137
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Re: What is the value of x if x is the remainder obtained when 2^(8p + 2)  [#permalink]

Show Tags

19 Jul 2018, 00:29
1
Bunuel wrote:
What is the value of x if x is the remainder obtained when $$2^{8p+2} + Z$$ is divided by 5 and p is a positive integer?

(1) Z = 6
(2) Z is even

2^{8p+2} + Z
Given:
P>0
Substitute p in the equation. For all the values of p we get cyclicity of 2 as 4m+2, which will give us a unit digit of 4

Statement 1:
Z=6
unit digit of 2^{8p+2} is 4+6 gives 10 which is divisible by 5. Hence remainder 0
Sufficient

Statement 2:
Z is even
We get a different remainder for different values of Z. Hence insufficient
_________________

Correct me If I'm wrong !! looking for valuable inputs

KUDOS please, if you like the post or if it helps !!

Re: What is the value of x if x is the remainder obtained when 2^(8p + 2) &nbs [#permalink] 19 Jul 2018, 00:29
Display posts from previous: Sort by

Events & Promotions

 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®.