Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 13:39

### 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)

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56244
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:

54% (01:59) correct 46% (02:23) wrong based on 60 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: 7764
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
_________________
Senior Manager
Joined: 17 Jan 2017
Posts: 300
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
_________________
Only those who risk going too far, can possibly find out how far one can go
Re: What is the value of x if x is the remainder obtained when 2^(8p + 2)   [#permalink] 19 Jul 2018, 00:29
Display posts from previous: Sort by

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

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

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