Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 2808:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
May 2909:50 AM PDT
-11:00 AM PDT
Wondering about your chances for top MBA programs? Join ARINGO for a concise Q&A session where we'll evaluate profiles, estimate school prospects, and offer expert tips.
May 2312:00 PM EDT
-11:59 PM EDT
What do András from Hungary, Conner from the United States, Giorgio from Italy, Leo from Germany, and Saahil from India have in common? They all earned top scores on the GMAT Focus Edition using the Target Test Prep course!
May 2805:30 AM PDT
-07:30 AM PDT
This Memorial Day, honor your future with upto 44% off on our GMAT Focus plans and score 99 %ile before R1. Take advantage of the sale & get access to a personalized study plan, 100+ video lessons, 5 mocks & more at prices starting $149. Hurry up!- May 28
08:30 AM PDT
-09:30 AM PDT
Analysing Real MBA Resumes Selected & Rejected by Top Business Schools. Join the Live Expert Analysis Tuesday, May 28th at 8:30 AM PDT - May 30
08:30 AM PDT
-09:30 AM PDT
Ever wondered how to score a perfect 805 on the GMAT? Julia did it, and she’s here to share her journey to an impressive 805 GMAT Focus score! Scoring 805 is an incredible achievement, and Julia’s story is sure to inspire you. - May 31
10:00 AM PDT
-11:00 AM PDT
In this GMAT Success Story episode, we delve into the GMAT journeys of Piyush a petroleum engineer from ISM Dhanbad, India, currently working in the oil and energy sector. 
May 3112:00 PM EDT
-01:00 PM EDT
Think a 100% GMAT Focus Verbal score is out of your reach? TTP will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun. Get 20% off until 5/31.
Jun 0105:30 AM PDT
-07:30 AM PDT
Struggling with shuffling between multiple data sets and question choices? With DI scores now equally weighted, learn how to reduce solving time and boost accuracy on these questions through clever data set analysis. Join us for expert tips!
Jun 0111:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – 1. Learn effective reading strategies 2. Tackle difficult RC & MSR with confidence 3. Excel in timed test environment- Jun 02
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. - Jun 11
05:30 AM PDT
-12:00 PM PDT
Register for the GMAT Club Virtual MBA Spotlight fair, the biggest MBA fair of the year. You will have a chance to hear Admissions directors from almost every Top 20 program speak, network with peers, and more.
Manager
Joined: 13 Feb 2010
Status:Prevent and prepare. Not repent and repair!!
Posts: 146
Given Kudos: 282
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]
![The sum of the digits of [(10^x)^y]-64=279. What is the](https://cdn.gmatclub.com/cdn/files/forum/styles/gmatclub_light/imageset/icon_post_target_unread.png "The sum of the digits of [(10^x)^y]-64=279. What is the")
Updated on: 29 Oct 2012, 01:59
Updated on: 29 Oct 2012, 01:59
4
Kudos
57
Bookmarks
Show timer
00:00
A
B
C
D
E
Difficulty:
65%
(hard)
Question Stats:
58% (02:10) correct
42%
(02:25)
wrong
based on 539
sessions
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
A. 28
B. 29
C. 30
D. 31
E. 32
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.
Last edited by Bunuel on 29 Oct 2012, 01:59, edited 2 times in total.
Renamed the topic and edited the question.
Re: The sum of the digits of [(10^x)^y]-64=79. What is the value
[#permalink]
29 Oct 2012, 01:59
29 Oct 2012, 01:59
8
Kudos
19
Bookmarks
Expert Reply
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
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.
Intern
Joined: 30 Jun 2012
Status:Active
Posts: 31
Given Kudos: 36
Location: India
Re: The sum of the digits of [(10^x)^y]-64=279. What is the
[#permalink]
29 Oct 2012, 02:26
29 Oct 2012, 02:26
9
Kudos
1
Bookmarks
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
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
