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

 It is currently 09 Dec 2018, 22:30

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.

# What is the value of x if x is the remainder obtained when

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 24 Nov 2010
Posts: 178
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
What is the value of x if x is the remainder obtained when  [#permalink]

### Show Tags

Updated on: 25 Mar 2011, 22:36
3
00:00

Difficulty:

(N/A)

Question Stats:

65% (01:37) correct 35% (01:32) wrong based on 59 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

Originally posted by dreambeliever on 25 Mar 2011, 19:19.
Last edited by dreambeliever on 25 Mar 2011, 22:36, edited 1 time in total.
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 800
Location: India
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Re: Divided by 5  [#permalink]

### Show Tags

25 Mar 2011, 20:16
2(8p+2)+z
=16p+(z+4)

given:

16p + (z+4) = 5k + x

where k is a whole number

Statement 1:
Given: z = 6

If p = 1

16 + 10 = 26

26/5 leaves remainder 1

If p = 2
32 + 10 = 42
42/5 leaves remainder 2

Thus, insufficient!

Statement 2:
Z is even. So let z = 6
We already know that for z = 6, the statement is insufficient!
Therefore, statement 2 is also not sufficient.

Statement 1 & 2:
z = 6 obeys both the constraints imposed by Statement 1 & 2
But z = 6 does not yield a unique value of x

Therefore, insufficient!

ANS - 'E'
_________________

"Wherever you go, go with all your heart" - Confucius

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Manager
Joined: 24 Nov 2010
Posts: 178
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Re: Divided by 5  [#permalink]

### Show Tags

25 Mar 2011, 22:35
dreambeliever 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

Sorry corrected question stem.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1820
Re: Divided by 5  [#permalink]

### Show Tags

25 Mar 2011, 23:24
1
dreambeliever 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

$$2^{8p+2}$$

The unit digit of the above expression will always be 4.

Here's how;
$$2^n$$ has a cyclicity of 4. And the unit digits appear as 2,4,8,6 with every increment in n.

When "8p+2" is divided by 4, it always render a remainder of 2.
8p is divisible by 4 leaving the remainder as 0.
When 2 is divided by 4, it will leave a remainder of 2.

Whenever; in expression $$2^n$$, n divides by 4 and leaves a remainder of 2, the unit digit of the expression will be 4.

1. Z=6

4+6=0

The expression $$2^{8p+2} + Z$$ will always be divisible by 5 as the unit digit will always be 0. x=0;

Sufficient.

2. Z=even;

Z=2; The expression's units digit will be 6 and x=1;
Z=6; The expression's units digit will be 0 and x=0;

Not Sufficient.

Ans: "A"
_________________
Retired Moderator
Joined: 16 Nov 2010
Posts: 1426
Location: United States (IN)
Concentration: Strategy, Technology
Re: Divided by 5  [#permalink]

### Show Tags

26 Mar 2011, 06:36
(2)^(8p+2) + Z

= (4)^(4p+1) + Z

4 raised to odd power ends with 4

So (4 +Z)/5 = x, x = ?

1) Z = 6, then x = 0

2) Insufficient as (4+2)/5 = Rem 1

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 20 Mar 2011
Posts: 4
Re: Divided by 5  [#permalink]

### Show Tags

01 Apr 2011, 10:02
1. Z=6
8(p+2) = 2(4p+1)
hence 2 ^(8p+2) become 4^(4P+1)
any odd power to 4 gives 4 as the last digit
2 ^(8p+2) +Z = 4^(4P+1) +6 = <no with last digit as 0>
is divisible by 5. therefore remainder = 0

A or D

2. Z=even
<no with last digit as 4> +even will give different no.s for each value of Z
hence no fixed remainder

Therefore ans= A
Intern
Joined: 06 Sep 2010
Posts: 30
Re: Divided by 5  [#permalink]

### Show Tags

01 Apr 2011, 19:49
The answer should be A. Whatz the OA ?

obidan wrote:
1. Z=6
8(p+2) = 2(4p+1)
hence 2 ^(8p+2) become 4^(4P+1)
any odd power to 4 gives 4 as the last digit
2 ^(8p+2) +Z = 4^(4P+1) +6 = <no with last digit as 0>
is divisible by 5. therefore remainder = 0

A or D

2. Z=even
<no with last digit as 4> +even will give different no.s for each value of Z
hence no fixed remainder

Therefore ans= A
Director
Status: My Thread Master Bschool Threads-->Krannert(Purdue),WP Carey(Arizona),Foster(Uwashngton)
Joined: 27 Jun 2011
Posts: 821
Re: Divided by 5  [#permalink]

### Show Tags

17 Oct 2011, 13:20
Before the correction i thought its E..But yes IMO A
Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Re: What is the value of x if x is the remainder obtained when  [#permalink]

### Show Tags

23 Mar 2017, 04:48
Option A

Remainder of $$\frac{[2^{8p+2} + Z]}{5}$$

*To find remainder of any number when divided by 5, all we need to find is the remainder when unit's digit of that number is divided by 5*

$$2^{X}$$ has a cyclicity of 4, hence $$2^{8p+2}$$ will have the same unit's digit as $$2^{2}$$.

So unit's digit of $$2^{8p+2} = 4$$.

I: Z = 6
Now unit's digit of $$[2^{8p+2} + Z] = 4 + 6 = 10$$. Hence, remainder of $$\frac{[2^{8p+2} + Z]}{5}$$ = 0.
Sufficient.

II: Z = even. For every even number, unit's digit of $$[2^{8p+2} + Z]$$ will be different. Insufficient.
_________________

Press Kudos if you liked the post!

Rules for posting - PLEASE READ BEFORE YOU POST

Re: What is the value of x if x is the remainder obtained when &nbs [#permalink] 23 Mar 2017, 04:48
Display posts from previous: Sort by

# What is the value of x if x is the remainder obtained when

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

 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®.