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

It is currently 24 Mar 2019, 12:30

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

What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y

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

Hide Tags

 
Senior Manager
Senior Manager
User avatar
G
Joined: 18 Jun 2016
Posts: 262
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
GMAT ToolKit User Reviews Badge
What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post Updated on: 23 Apr 2017, 11:35
2
8
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (02:06) correct 35% (02:18) wrong based on 123 sessions

HideShow timer Statistics

What is the last non-zero digit of this expression if x and y are positive integers?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)


(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)



Spoiler: :: Edit - 4-23-17
Edited to fix a loophole as mentioned by chetan2u. Sorry about it because I did not anticipate the additional possibilities.

_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html


Originally posted by umg on 23 Apr 2017, 08:14.
Last edited by umg on 23 Apr 2017, 11:35, edited 2 times in total.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7440
What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 09:01
5
4
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)

(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)



Hi..

Q should have mentioned that x and and y are positive integers

We are looking for last non zero digit...
It will depend on the last non-zero digit of each term
Example...
\(260*3*40\) would depend on \(6*3*4...\)
\(260^4*27^6*800^{567}\) would depend on \(6^4*7^6*8^{567}\)
Let's see the statements..

(1) \(x = 10, y = 18\)
X and y are given, so we will be able to find exact value of equation.
Sufficient

(2) \(y^2 - 36y + 324= 0\)
This equation comes down to \((y-18)^2=0\) or y=18..
But what about x? This is the tricky part.

We are looking for LAST non-zero digit of each term.
Rest all terms are known except x as y is 18
Here the term is 860^x and it will be same as 6^x.
Since the last non-zero digit is 6 here and 6 to any power will have last digit as 6 only, the value of x will not affect the last non-zero digit of entire term..
6^1=6.....
6^2=36.... Last digit 6
6^3=216.... Last digit again 6
Sufficient

D
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

General Discussion
Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 40
Location: India
Concentration: Operations, Leadership
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 08:24
imo A

You will need to know the value of both x and y.

how is it OA=d?

what if x is 1/2 and 2? won't we get different answers?
Intern
Intern
avatar
B
Joined: 09 Mar 2017
Posts: 35
Concentration: Accounting
GMAT 1: 730 Q48 V41
GPA: 3.64
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 08:56
This is tricky. If we're just looking at the last digits, \(860^x\) should give us a last digit of 0 for all x except x=0, since anything to the zeroth power equals 1. So for all x except x=0. the last digit of the whole expression should be zero. I don't see how the second option (\(y^2−36y+324=0\)) tells us that x isn't zero. But then I guess the last non-zero digit would be the tens digit, so clearly I'm still missing something...
Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 40
Location: India
Concentration: Operations, Leadership
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 09:57
chetan2u wrote:
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)

(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)



Hi..

Q should have mentioned that x and and y are positive integers

We are looking for last non zero digit...
It will depend on the last non-zero digit of each term
Example...
260*3*40 would depend on 6*3*4...
260^4*27^6*800^567 would depend on 6^4*7^6*8^567
Let's see the statements..

(1) \(x = 10, y = 18\)
X and y are given, so we will be able to find exact value of equation.
Sufficient

(2) \(y^2 - 36y + 324= 0\)
This equation comes down to (y-18)^2=0 or y=18..
But what about x? This is the tricky part.

We are looking for LAST non-zero digit of each term.
Rest all terms are known except x as y is 18
Here the term is 860^x and it will be same as 6^x.
Since the last non-zero digit is 6 here and 6 to any power will have last digit as 6 only, the value of x will not affect the last non-zero digit of entire term..
6^1=6.....
6^2=36.... Last digit 6
6^3=216.... Last digit again 6
Sufficient

D


what if x=1/2...then LAST non-zero digit 860^x wont be 6
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7440
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 10:35
sandaki wrote:
chetan2u wrote:
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)
Ki
(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)



Hi..

Q should have mentioned that x and and y are positive integers

We are looking for last non zero digit...
It will depend on the last non-zero digit of each term
Example...
260*3*40 would depend on 6*3*4...
260^4*27^6*800^567 would depend on 6^4*7^6*8^567
Let's see the statements..

(1) \(x = 10, y = 18\)
X and y are given, so we will be able to find exact value of equation.
Sufficient

(2) \(y^2 - 36y + 324= 0\)
This equation comes down to (y-18)^2=0 or y=18..
But what about x? This is the tricky part.

We are looking for LAST non-zero digit of each term.
Rest all terms are known except x as y is 18
Here the term is 860^x and it will be same as 6^x.
Since the last non-zero digit is 6 here and 6 to any power will have last digit as 6 only, the value of x will not affect the last non-zero digit of entire term..
6^1=6.....
6^2=36.... Last digit 6
6^3=216.... Last digit again 6
Sufficient

D


what if x=1/2...then LAST non-zero digit 860^x wont be 6



Hi..
Yes, you are right.
Pl look at the coloured portion above.
Not only fraction but also negative integer.

It has to be ONLY POSITIVE integer
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

BSchool Forum Moderator
User avatar
V
Joined: 28 Mar 2017
Posts: 1212
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 11:02
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)

(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)


We don't even need choices in this question ...... if it's given in the question that x and y are positive number.
Since 860's last non zero digit will always be 6 only; likewise, 1525's last digit will always be 5 irrespective of the values of x and y.

Easy D.
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!
Preparing for RC my way
RC Summary Activity - New Project to imporve RC Skills
Bloomberg's US Bschool Ranking

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant | 2. e-GMAT's ALL SC Compilation | 3. LSAT RC compilation | 4. Actual LSAT CR collection by Broal | 5. QOTD RC (Carcass) | 6. Challange OG RC | 7. GMAT Prep Challenge RC

Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2616
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 12:01
2
gmatexam439 wrote:
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)

(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)


We don't even need choices in this question ...... if it's given in the question that x and y are positive number.
Since 860's last non zero digit will always be 6 only; likewise, 1525's last digit will always be 5 irrespective of the values of x and y.

Easy D.




Nopes.
Not so easy.
Firstly, i too thought the same when i first saw this question.
Easy D.


But there is a trap here.
Let us examine it closely.
Let us consider that both x and y are greater then zero and positive integers.
Let us remove the zero from the 860^x to make it 86^x (as the last digit would be zero.)

Now you see that the last term of the product i.e ((1525)^y will always end with 5.
Hence the last digit of the entire product would still be zero as 5*even ends with zero.
So we need the digit previous to that.
For that we need the value of x.


So D is sufficient.
But your logic wasn't all right.



Off course i might be wrong.

chetan2u is my approach correct ?




P.S => I dont really think this is a GMAT-type question.


Regards
Stone Cold
_________________

Give me a hell yeah ...!!!!!

MBA Dating:- B-SCHOOL with the MOST ATTRACTIVE Women
MBA Recruiting:- EMPLOYMENT AND SALARY STATISTICS AT TOP B-SCHOOLS IN THE US! (2018)
MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!
The MOST AFFORDABLE MBA programs!
STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)
AVERAGE GRE Scores At The Top Business Schools!

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7440
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 23 Apr 2017, 17:25
1
stonecold wrote:
gmatexam439 wrote:
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)

(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)


We don't even need choices in this question ...... if it's given in the question that x and y are positive number.
Since 860's last non zero digit will always be 6 only; likewise, 1525's last digit will always be 5 irrespective of the values of x and y.

Easy D.




Nopes.
Not so easy.
Firstly, i too thought the same when i first saw this question.
Easy D.


But there is a trap here.
Let us examine it closely.
Let us consider that both x and y are greater then zero and positive integers.
Let us remove the zero from the 860^x to make it 86^x (as the last digit would be zero.)

Now you see that the last term of the product i.e ((1525)^y will always end with 5.
Hence the last digit of the entire product would still be zero as 5*even ends with zero.
So we need the digit previous to that.
For that we need the value of x.


So D is sufficient.
But your logic wasn't all right.



Off course i might be wrong.

chetan2u is my approach correct ?




P.S => I dont really think this is a GMAT-type question.


Regards
Stone Cold


Hi..
You are correct on THAT..
We have some number of 5s in the term...Say 20
If you have less number of 2s in the remaining terms..Say 19 last digit will always be 5..
But if it's more than 20, then ofcourse all the 5s would be converted into 0s and we would require to know digit prior to 0 and the condition we are talking of..

So two cases..
1) number of 5s is less than number of 2s
We will require to know the exact value of y.
2) the number of 5s is MORE than number of 2s..
We don't require exact value as Nonzero digit will be 5 irrespective of value of y.
But yes you have to know that y is less than the power of 2s.
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Intern
Intern
avatar
B
Joined: 12 Jan 2017
Posts: 40
Location: India
Concentration: Operations, Leadership
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 24 Apr 2017, 00:36
chetan2u wrote:
chetan2u wrote:
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)
Ki
(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)



Hi..

Q should have mentioned that x and and y are positive integers

We are looking for last non zero digit...
It will depend on the last non-zero digit of each term
Example...
260*3*40 would depend on 6*3*4...
260^4*27^6*800^567 would depend on 6^4*7^6*8^567
Let's see the statements..

(1) \(x = 10, y = 18\)
X and y are given, so we will be able to find exact value of equation.
Sufficient

(2) \(y^2 - 36y + 324= 0\)
This equation comes down to (y-18)^2=0 or y=18..
But what about x? This is the tricky part.

We are looking for LAST non-zero digit of each term.
Rest all terms are known except x as y is 18
Here the term is 860^x and it will be same as 6^x.
Since the last non-zero digit is 6 here and 6 to any power will have last digit as 6 only, the value of x will not affect the last non-zero digit of entire term..
6^1=6.....
6^2=36.... Last digit 6
6^3=216.... Last digit again 6
Sufficient

D


Hi..
Yes, you are right.
Pl look at the coloured portion above.
Not only fraction but also negative integer.

It has to be ONLY POSITIVE integer


True,
if question had mentioned that x and and y are positive integers,then answer would have been D.

Since it's not mentioned,the answer is A.
Senior Manager
Senior Manager
User avatar
G
Joined: 18 Jun 2016
Posts: 262
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
GMAT ToolKit User Reviews Badge
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 24 Apr 2017, 03:03
sandaki wrote:

True,
if question had mentioned that x and and y are positive integers,then answer would have been D.

Since it's not mentioned,the answer is A.

Because I made this question, I did not anticipate other possible values of x & y, it seems that I have gotten very rusty these past few months. However, I realized the mistake and have fixed the error. The question now mentions that x and y are positive integers.
_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

BSchool Forum Moderator
User avatar
V
Joined: 28 Mar 2017
Posts: 1212
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 24 Apr 2017, 13:59
stonecold wrote:
gmatexam439 wrote:
umg wrote:
What is the last non-zero digit of this expression?

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y\)

(1) \(x = 10, y = 18\)

(2) \(y^2 - 36y + 324= 0\)


We don't even need choices in this question ...... if it's given in the question that x and y are positive number.
Since 860's last non zero digit will always be 6 only; likewise, 1525's last digit will always be 5 irrespective of the values of x and y.

Easy D.




Nopes.
Not so easy.
Firstly, i too thought the same when i first saw this question.
Easy D.


But there is a trap here.
Let us examine it closely.
Let us consider that both x and y are greater then zero and positive integers.
Let us remove the zero from the 860^x to make it 86^x (as the last digit would be zero.)

Now you see that the last term of the product i.e ((1525)^y will always end with 5.
Hence the last digit of the entire product would still be zero as 5*even ends with zero.
So we need the digit previous to that.
For that we need the value of x.


So D is sufficient.
But your logic wasn't all right.



Off course i might be wrong.

chetan2u is my approach correct ?




P.S => I dont really think this is a GMAT-type question.


Regards
Stone Cold


Thank you stonecold for pointing that out. :) and thank you chetan2u for the explanation !!
_________________

Kudos if my post helps!

Long And A Fruitful Journey - V21 to V41; If I can, So Can You!!
Preparing for RC my way
RC Summary Activity - New Project to imporve RC Skills
Bloomberg's US Bschool Ranking

My study resources:
1. Useful Formulae, Concepts and Tricks-Quant | 2. e-GMAT's ALL SC Compilation | 3. LSAT RC compilation | 4. Actual LSAT CR collection by Broal | 5. QOTD RC (Carcass) | 6. Challange OG RC | 7. GMAT Prep Challenge RC

Intern
Intern
avatar
B
Joined: 03 Jan 2017
Posts: 23
GMAT 1: 680 Q49 V34
What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 28 Apr 2017, 00:14
This question is doing my brain in. Please let me know if my thinking is wrong.

3^327: the last digit of this is 7
4^36: The last digit of this is 6
6^x: The last digit of this is 6
5^y: The last digit of this is 5

Since 7 x 6 x 6 x 5 ends in zero, we need the second last digit of 1525^y. Hence we only need the value of Y to solve the question. Both statements give the value of Y hence D.

Is this correct?
Senior Manager
Senior Manager
User avatar
G
Joined: 18 Jun 2016
Posts: 262
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 750 Q49 V42
GPA: 4
WE: General Management (Other)
GMAT ToolKit User Reviews Badge
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 28 Apr 2017, 13:43
texas wrote:
This question is doing my brain in. Please let me know if my thinking is wrong.

3^327: the last digit of this is 7
4^36: The last digit of this is 6
6^x: The last digit of this is 6
5^y: The last digit of this is 5

Since 7 x 6 x 6 x 5 ends in zero, we need the second last digit of 1525^y. Hence we only need the value of Y to solve the question. Both statements give the value of Y hence D.

Is this correct?

Your answer is correct but the reason (in Red) is wrong.

Here is the safest way to approach such questions

\((573)^3^2^7*(274)^3^6*(860)^x*(1525)^y= (573)^3^2^7*(137*2)^3^6*(86*10)^x*(61*25)^y\)

Notice that 2^(36) will contribute zeros depending upon the value of y.

Hence, if 2y = 36

the last non-zero digit will be decided by

3^(327) * 7^(36) * 6^(x) * 1^(y)
_________________

I'd appreciate learning about the grammatical errors in my posts

Please hit Kudos If my Solution helps

My Debrief for 750 - https://gmatclub.com/forum/from-720-to-750-one-of-the-most-difficult-pleatues-to-overcome-246420.html

My CR notes - https://gmatclub.com/forum/patterns-in-cr-questions-243450.html

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10192
Premium Member
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y  [#permalink]

Show Tags

New post 19 Feb 2019, 10:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y   [#permalink] 19 Feb 2019, 10:00
Display posts from previous: Sort by

What is the last non-zero digit of (573)^(327)*(274)^(36)*860^x*1525^y

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.