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

It is currently 13 Dec 2019, 04:13

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x is a positive integer, what is the units digit of 567^24*x^y

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

Hide Tags

Find Similar Topics 
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8309
If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post Updated on: 22 Sep 2016, 23:56
5
3
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

52% (01:59) correct 48% (02:06) wrong based on 157 sessions

HideShow timer Statistics

If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


Self made

_________________

Originally posted by chetan2u on 22 Sep 2016, 23:16.
Last edited by Bunuel on 22 Sep 2016, 23:56, edited 1 time in total.
RENAMED THE TOPIC.
Manager
Manager
avatar
S
Joined: 24 Oct 2013
Posts: 127
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post Updated on: 23 Sep 2016, 00:26
1
I go with B

Statement 1: -3<x<2 so x is 1
statement 2 : y=0, what ever the value of x, if y = 0 , the value of the term will be 1 so only term to consider to determine the value of entire expression is 7^(24)

Hence D

Originally posted by deepthit on 22 Sep 2016, 23:20.
Last edited by deepthit on 23 Sep 2016, 00:26, edited 1 time in total.
Intern
Intern
avatar
Joined: 23 Sep 2016
Posts: 1
If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 23 Sep 2016, 00:21
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0



statement1: x^2+x-6<0 so -3<x<2. given x is positive integer. so the value of x will be 1
the value of y is independent. SUFFICIENT

statement2: y=0. so what ever is the positive value of x, anything power 0 will be 1.
SUFFICIENT


SO D

#NEELAGIRI
Intern
Intern
avatar
Joined: 23 Jun 2016
Posts: 41
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 23 Sep 2016, 11:07
Statement 1: X^2 - X < 6 for it to be true. Since x is a positive integer the only value for x is 1. Sufficient since the value or sign of y doesn't matter
Statement 2: states than x^y is 1 so sufficient.

Ans D
Current Student
User avatar
B
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 227
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Reviews Badge
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 23 Sep 2016, 22:50
chetan2u wrote:
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


Self made


My take is D.

Before approaching, 567^24 follows a unit digit cycle of 3 : 567^1 = 7, 567^2 = 9, 567^3 = 3, and rem(24/3) = 0. That means the question gets reduced to 3*(x)^y.

Statement 1: X is a positive integer x=1 alone satisfies the equation and y can take any value less than 5

3(1)^y...since irrespective of value of y , the result is going to be 3 ---Sufficient

Statement 2:

Y=0....we know that 3(x)^0 = 3 as anything to the power of zero is 1 ---Sufficient
_________________
Aiming for a 3 digit number with 7 as hundredths Digit
Manager
Manager
User avatar
Joined: 14 May 2014
Posts: 52
Location: India
GMAT 1: 680 Q49 V31
GPA: 3.44
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 24 Sep 2016, 11:23
chetan2u wrote:
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


Self made


Guys is not 0 a positive integer?
Answer may be 0 or 1. why are you all not including the value x=0??
Ans is not D
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3564
Reviews Badge
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 24 Sep 2016, 11:34
RatneshS wrote:
chetan2u wrote:
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


Self made


Guys is not 0 a positive integer?
Answer may be 0 or 1. why are you all not including the value x=0??
Ans is not D


0 is a non negative non positive integer. So, x cannot be 0.
_________________
My LinkedIn abhimahna.
My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog
GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.
Current Student
User avatar
B
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 227
Location: India
Concentration: Strategy, Operations
GMAT 1: 690 Q48 V36
GPA: 4
WE: Consulting (Manufacturing)
Reviews Badge
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 24 Sep 2016, 11:40
RatneshS wrote:
chetan2u wrote:
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


Self made


Guys is not 0 a positive integer?
Answer may be 0 or 1. why are you all not including the value x=0??
Ans is not D


Hi
0 is considered as a neutral number. That's the reason it separates positive and negative in a graph.

So positive integer starts from 1

Hope this helps

Posted from my mobile device
_________________
Aiming for a 3 digit number with 7 as hundredths Digit
Intern
Intern
avatar
B
Joined: 09 Sep 2016
Posts: 4
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 24 Sep 2016, 23:52
The answer would be D.

As the statement for 1 is enough to get the unique ans.

The unit digit of 567^24 comes for 4 cycles of the unit digit 7 and which will result as 1.
x lies between -3 and 2 and its mentioned that the x is positive number hence we can take x as 1 . And 1^y will result as 1

And the statement 2 also satisfies the ans .as the y=0.

Hence option D
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2550
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 24 Nov 2016, 04:52
One of the Best Questions on Units digit concept.
Here we need the units digit of n=> (567)^24 * x^y
Applying the concept of unit digit ->
Units digit of (567)^24 is always 1
So we need the unit digit of x^y to be able to tell the unit digit of n.


Statement 1
Here x=> (-3,2) is the range of x
x>0 so x must be 1
and y is a integer <5

Basically y can be anything
as (one)^any integer = one
hence the unit digit of n will be 1*1 => 1

Statement 2
y=0
So in this case x can be any integer >0
Because x^0 will be 1
hence the unit digit of n will be 1*1 => 1


Hence D
_________________
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 963
Location: United States
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 07 Nov 2019, 12:24
chetan2u wrote:
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


x = positive integer

\(units.digit:567^{24}*x^y=units(7^{24}*x^y)\)
\(cycles(7)=[7,9,3,1]=4…units:7^{24}=24/4=integer=4th.cycle=[1]\)
\(find:units(1*x^y)=units(x^y)\)

(1) \(x^2+x-6<0\) and y is an integer less than 5. sufic.

\(x^2+x-6<0…(x+3)(x-2)<0…(less.than=inside.rng)…-3<x=positive.integer<2…x=1\)
\(units(x^y)=(1^y)=1\)

(2) y=0 sufic.

\(units(x^y)=(x^0)=1\)

Ans. (D)
Intern
Intern
avatar
B
Joined: 06 Jan 2019
Posts: 6
CAT Tests
Re: If x is a positive integer, what is the units digit of 567^24*x^y  [#permalink]

Show Tags

New post 29 Nov 2019, 02:33
Balajikarthick1990 wrote:
chetan2u wrote:
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?

(1) \(x^2+x-6<0\) and y is an integer less than 5.
(2) y=0


Self made


My take is D.

Before approaching, 567^24 follows a unit digit cycle of 3 : 567^1 = 7, 567^2 = 9, 567^3 = 3, and rem(24/3) = 0. That means the question gets reduced to 3*(x)^y.

Statement 1: X is a positive integer x=1 alone satisfies the equation and y can take any value less than 5

3(1)^y...since irrespective of value of y , the result is going to be 3 ---Sufficient

Statement 2:

Y=0....we know that 3(x)^0 = 3 as anything to the power of zero is 1 ---Sufficient


Hi, just to correct the cyclicity piece. The unit digit cyclicity for 7 is 4 ( 7,9,3,1) and not 3. In this case it worked as 24 is divisible by both 3 and 4 but just something to keep in mind.

Thanks
GMAT Club Bot
Re: If x is a positive integer, what is the units digit of 567^24*x^y   [#permalink] 29 Nov 2019, 02:33
Display posts from previous: Sort by

If x is a positive integer, what is the units digit of 567^24*x^y

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





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