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.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
16 Sep 2014, 01:08
Kudos
Bookmarks
If \(x\) and \(y\) are positive integers, is \(10^x - y\) divisible by 9 ?
(1) \(y\) is divisible by 3
(2) \(10^x + y\) is not divisible by 9
(1) \(y\) is divisible by 3
(2) \(10^x + y\) is not divisible by 9
16 Sep 2014, 01:08
Kudos
Bookmarks
Official Solution:
If \(x\) and \(y\) are positive integers, is \(10^x - y\) divisible by 9 ?
Note that for any positive integer \(x\), \(10^x\) will have a digit sum equal to 1, so it will not be divisible by 3.
(1) \(y\) is divisible by 3.
In this case, \(10^x - y\) = (something not divisible by 3) - (something divisible by 3) = (something not divisible by 3). Since \(10^x - y\) is not divisible by 3, it is also not divisible by 9. Sufficient.
(2) \(10^x + y\) is not divisible by 9.
If \(y = 1\), the digit sum of \(10^x + y\) will be 2, so it won't be divisible by 9, but \(10^x - y\) will have only 9s as its digits, so it will be divisible by 9. However, if \(y = 2\), the digit sum of \(10^x + y\) will be 3, so it won't be divisible by 9, but \(10^x - y\) will have some number of 9s followed by an 8, so it won't be divisible by 9 either. Not sufficient.
Answer: A
If \(x\) and \(y\) are positive integers, is \(10^x - y\) divisible by 9 ?
Note that for any positive integer \(x\), \(10^x\) will have a digit sum equal to 1, so it will not be divisible by 3.
(1) \(y\) is divisible by 3.
In this case, \(10^x - y\) = (something not divisible by 3) - (something divisible by 3) = (something not divisible by 3). Since \(10^x - y\) is not divisible by 3, it is also not divisible by 9. Sufficient.
(2) \(10^x + y\) is not divisible by 9.
If \(y = 1\), the digit sum of \(10^x + y\) will be 2, so it won't be divisible by 9, but \(10^x - y\) will have only 9s as its digits, so it will be divisible by 9. However, if \(y = 2\), the digit sum of \(10^x + y\) will be 3, so it won't be divisible by 9, but \(10^x - y\) will have some number of 9s followed by an 8, so it won't be divisible by 9 either. Not sufficient.
Answer: A
23 May 2017, 06:21
Kudos
Bookmarks
Dear Sir,
I am having a doubt which might sound silly. Hence my apologies.
From the question, i understand is ((10^x)-y)/9?
Is it okay if I re-write this way: (10^x/9)-y/9 since they will have comment denominator?
Is that case, since x and y are positive, wouldn't the stem of the question itself denotes that it is not divisible by 9?
I am having a doubt which might sound silly. Hence my apologies.
From the question, i understand is ((10^x)-y)/9?
Is it okay if I re-write this way: (10^x/9)-y/9 since they will have comment denominator?
Is that case, since x and y are positive, wouldn't the stem of the question itself denotes that it is not divisible by 9?
