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

It is currently 16 Oct 2019, 12:35

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

The sum of the digits of [(10^x)^y]-64=279. What is the

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 173
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post Updated on: 29 Oct 2012, 01:59
3
27
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

59% (02:12) correct 41% (02:14) wrong based on 289 sessions

HideShow timer Statistics

The sum of the digits of [(10^x)^y]-64=279. What is the value of xy ?

A. 28
B. 29
C. 30
D. 31
E. 32

_________________
I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Originally posted by rajathpanta on 28 Oct 2012, 10:18.
Last edited by Bunuel on 29 Oct 2012, 01:59, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: The sum of the digits of [(10^x)^y]-64=79. What is the value  [#permalink]

Show Tags

New post 29 Oct 2012, 01:59
8
13
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=79. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32


The question should read:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32

Also, it should be mentioned that xy is a positive integers.

First of all \((10^x)^y=10^{xy}\).

\(10^{xy}\) has \(xy+1\) digits: 1 and \(xy\) zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of \(10^{xy}-64\) is 279 --> \(9(xy-2)+3+6=279\) --> \(9(xy-2)=270\) --> \(xy=32\).

Answer: E.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope it's clear.
_________________
Most Helpful Community Reply
Intern
Intern
User avatar
Status: Active
Joined: 30 Jun 2012
Posts: 36
Location: India
Re: The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post 29 Oct 2012, 02:26
6
1
As

Question is \((10^x)^y - 64\) . Let say \((10^x)^y\) as Number1
Say Number1 - 64 = Number2 ==>
100 - 64 = 36 [ Number1: No. of zeroes = 2 , Number2: No. of 9's = zero ] and Sum of digits of Number 2 : 9*0 + (3+6) = 1*9 = 9
1000 - 64 = 936 [ Number1: No. of zeroes = 3 , Number2: No. of 9's = 1] and Sum of digits of Number 2 : 9*1 + (3+6) = 9 + 9 = 2*9 = 18
10000 - 64 = 9936 [ Number1: No. of zeroes = 4 , Number2: No. of 9's = 2] and Sum of digits of Number 2 : 9*2 + (3+6) = 18 + 9 = 3*9= 27
100000 - 64 = 99936 [ Number1: No. of zeroes = 5 , Number2: No. of 9's = 3] and Sum of digits of Number 2 : 9*3 + (3+6) = 27 + 9 =4*9= 36


so lets go from right to left for the sum of digits of number2 i.e given as 279
so 279 = 31*9 = 9*30 + (3+6) => Number2: Number of 9's = 30 ==> Number1: Number of zeros = 32

So the Number1 i.e. \((10^x)^y = 10000.....(32 zeroes)\)

Now, as we now, \(10^1\) = 10 (1 zero)
\(10^2\) = 100 (2 zeroes)
\(10^3\) = 1000 (3 zeroes)

same way, 10000.....(32 zeroes) = \(10^32\)

\((10^x)^y = 10^(xy) = 10^32\)
==> xy = 32
_________________
Thanks and Regards!

P.S. +Kudos Please! in case you like my post. :)

General Discussion
Manager
Manager
User avatar
B
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 51
GMAT Date: 10-01-2012
Re: The Sum of the digits of(10^x)^y  [#permalink]

Show Tags

New post 28 Oct 2012, 11:13
1
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.
_________________
I will rather do nothing than be busy doing nothing - Zen saying
Manager
Manager
User avatar
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 173
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: The Sum of the digits of(10^x)^y  [#permalink]

Show Tags

New post 28 Oct 2012, 11:22
Pansi wrote:
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.


Well, It is a multiple of 9. How will you arrive at xy with that approach?

Try finding patterns. (thats the clue)
_________________
I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 563
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: The Sum of the digits of(10^x)^y  [#permalink]

Show Tags

New post 28 Oct 2012, 19:44
1
Pansi wrote:
I spent some time on this question, got stuck and could not move towards a solution - Should not the sum of the digits of the number [(10^x)^y - 64] be a multiple of 9. Please clarify if the question formed the way it is now is the best way. I think I have misinterpreted something here.


Well, simple reason is that the question is incorrect.

rajathpanta wrote:
Well, It is a multiple of 9. How will you arrive at xy with that approach?

Try finding patterns. (thats the clue)


Question is:
10^xy -64 = N,
where sum of digits of N=79

The pattern is like this:

100 -64 = 36
1000 -64 = 936
10000 -64 =9936

or,
1 followed by (n times 0) = (n-2)times 9 followed by 36

Therefore sumof digits on right side is always a multiple of 9 [9s and 6+3 =9]

However in question stem RHS is 79, which is not divisible by 9. And therefore you can not arrive at any of the answer choices given.

Rajathpanta- on a lighter note - if this too is from Aristotle, I'd suggest please change the source of questions. :D

Hope it helps!
_________________
Lets Kudos!!! ;-)
Black Friday Debrief
Intern
Intern
avatar
Joined: 04 Aug 2013
Posts: 6
Re: The sum of the digits of [(10^x)^y]-64=79. What is the value  [#permalink]

Show Tags

New post 24 Nov 2013, 19:36
Hi Bunuel,

Could you please xplain the last bit oft he equations which takes us to a 279?

Thanks


quote="Bunuel"]
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=79. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32


The question should read:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32

Also, it should be mentioned that xy is a positive integers.

First of all \((10^x)^y=10^{xy}\).

\(10^{xy}\) has \(xy+1\) digits: 1 and \(xy\) zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of \(10^{xy}-64\) is 279 --> \(9(xy-2)+3+6=279\) --> \(9(xy-2)=270\) --> \(xy=32\).

Answer: E.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope it's clear.[/quote]
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58381
Re: The sum of the digits of [(10^x)^y]-64=79. What is the value  [#permalink]

Show Tags

New post 25 Nov 2013, 02:52
1
Shibs wrote:
Hi Bunuel,

Could you please xplain the last bit oft he equations which takes us to a 279?

Thanks


quote="Bunuel"]
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=79. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32


The question should read:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy

A. 28
B. 29
C. 30
D. 31
E. 32

Also, it should be mentioned that xy is a positive integers.

First of all \((10^x)^y=10^{xy}\).

\(10^{xy}\) has \(xy+1\) digits: 1 and \(xy\) zeros. For example: 10^2=100 --> 3 digits: 1 and 2 zeros;

\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. For example: 10^4-49=10,000-49=9,951 --> 4 digits: 4-2=two 9's and 51 in the end;

We are told that the sum of all the digits of \(10^{xy}-64\) is 279 --> \(9(xy-2)+3+6=279\) --> \(9(xy-2)=270\) --> \(xy=32\).

Answer: E.

Similar questions to practice:
the-sum-of-all-the-digits-of-the-positive-integer-q-is-equal-126388.html
10-25-560-is-divisible-by-all-of-the-following-except-126300.html
if-10-50-74-is-written-as-an-integer-in-base-10-notation-51062.html

Hope it's clear.


\(10^{xy}-64\) will have \(xy\) digits: \(xy-2\) 9's and 36 in the and. Threfore the sum of the digits is \(9(xy-2)+3+6=279\).

Hope it's clear.
_________________
Manager
Manager
avatar
B
Status: Student
Joined: 26 Aug 2013
Posts: 167
Location: France
Concentration: Finance, General Management
Schools: EMLYON FT'16
GMAT 1: 650 Q47 V32
GPA: 3.44
Re: The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post 08 Jan 2014, 04:19
1
Hi,

this is my process (edited to be the most efficient possible):

\(1000-64= 936\). Whatever XY is you finish with \(36 ==> 3+6=9\)

Therefore, \(279-9=270\) and \(270/9=30\)

Now you add the last two digits (3 and 6)

Answer is \(30+2=32\)

Hope it helps
_________________
Think outside the box
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2599
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post 30 Jan 2016, 07:00
2
rajathpanta wrote:
The sum of the digits of [(10^x)^y]-64=279. What is the value of xy ?

A. 28
B. 29
C. 30
D. 31
E. 32


Sum of the digits of (10^x)^y - 64 = 279.

We know that (X^a)^b = X^(ab)

Thus, the given form becomes = 10^(xy) - 64.

Now start with xy=2, 10^2 - 64 = 36, sum of the digits = 6+3=9 (realize that the sum of digits is 9*(xy-1))
xy=3 ---> 1000-64=936 = 18 (realize that the sum of digits is 9*(xy-1))
xy=4 ---> 10000-64=9936 = 27 (realize that the sum of digits is 9*(xy-1))
xy=5 ---> 100000-64 = 99936 (realize that the sum of digits is 9*(xy-1))... etc so this is your pattern. The sum of the digits = 9*(xy-1)

Now sum of the digits given = 279.

Thus, based on the pattern above, the sum of the digits must be ---> 9*(xy-1) = 279 ---> xy = 32.

E is thus the correct answer.

Hope this helps.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2513
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post 24 Feb 2016, 18:32
gosh..the structure of the question is hideous...
i solved it this way..
the sum is 279. the last 2 digits must be 3 and 6, or 9. so the rest will be a bunch of 9's. how many 9's? 30.
now, 30 of nines + 36 -> 32 digits +1 since we need to round up - 33 in total, we thus must have 10^32.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15262
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post 27 Mar 2018, 11:43
1
Hi All,

This question has some awkward wording to it, but here's its intent: the number 10^(xy) - 64 has digits that add up to 279.

So, we need to figure out what THAT number is.

Here's what you need to "see" to solve this problem:

IF xy = 3, then 1,000 - 64 = 936 and the sum of digits = 18 = (2)(9)
If xy = 4, then 10,000 - 64 = 9,936 and the sum of digits = 27 = (3)(9)
If xy = 5, then 100,000 - 64 = 99,936 and the sum of digits = 36 = (4)(9)

Notice the pattern? The sum of digits is increasing by 9 every time.

So, how many times does 9 divide into 279? 31 times

As a reminder of the pattern:
xy = 3 --> (2)(9)
xy = 4 --> (3)(9)
xy = 5 --> (4)(9)

So, (31)(9) --> xy = 32

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13210
Re: The sum of the digits of [(10^x)^y]-64=279. What is the  [#permalink]

Show Tags

New post 21 Apr 2019, 07:23
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 Club Bot
Re: The sum of the digits of [(10^x)^y]-64=279. What is the   [#permalink] 21 Apr 2019, 07:23
Display posts from previous: Sort by

The sum of the digits of [(10^x)^y]-64=279. What is the

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





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