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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

06 Aug 2009, 22:59

1

This post received KUDOS

A

Statement 1: if u take N=5 and any value for M it will always hold true that is (10^M + N)/3 an integer; becoz 10^M ( let M = any value) will always leave a reminder of 1....and 1+5 = 6 which is divisable by 3 ....sufficient

Statement 2 : if MN is even ...this means (M,N) can be both even or odd (except both being odd at a time)....if taken an example....

at M>=0: \(10^M = {1, 10, 100, 1000....}\) or \(3k+1\) at M<0: 10^M is a fraction and our expression is not an integer.

Now, let's see our statements:

1) N=5 at M>=0: (3k+1 + 5) /3 = k+2 - an integer at M<0: a fraction. insufficient

2) MN is even a) at M=2, N=5 our expression is an integer b) at M=-2, N=-5 our expression in a fraction insufficient

1)&2) N=5 & MN is even --> N=5, M is even For all even M>=0 we will get an integer. Now we have interesting question: Could negative numbers be even or odd? if yes, we can choose M=-2, N=5 and get a fraction. if no, M cannot be negative and two statements are sufficient.

If M and N are integers, is ((10^M)) + N) / 3 an integer?

1. N = 5 2. MN is even

Answer to question is E.

From statement 1 and 2, M has to be Even Positive as N = 5 and MN is even.

Now when 5 is added to 10^M where M is even positive and then divided by 3 it always results into an integer.

Basically the the question ask whether \(10^m+n\) is divisible by 3. Now, in order \(10^m+n\) to be divisible by 3: A. It must be an integer, and B. the sum of its digits must be multiple of 3.

(1) N = 5 --> if \(m<0\) (-1, -2, ...) then \(10^m+n\) won't be an integer at all (for example if \(m=-1\) --> \(10^m+n=\frac{1}{10}+5=\frac{51}{10}\neq{integer}\)), thus won't be divisible by 3, but if \(m\geq{0}\) (0, 1, 2, ...) then \(10^m+n\) will be an integer and also the sum of its digits will be divisible by 3 (for example for \(m=1\) --> \(10^m+n=10+5=15\) --> 15 is divisible by 3). Not sufficient.

(2) MN is even --> clearly insufficient, as again \(m\) can be -2 and \(n\) any integer and the answer to the question will be NO or \(m\) can be 0 and \(n\) can be 2 and the answer to the question will be YES. Not sufficient.

(1)+(2) From \(mn=even\) and \(n=5\) it's still possible for \(m\) to be negative even integer (-2, -4, ...), so \(10^m+n\) may or may not be divisible by 3. Not sufficient.

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

19 Sep 2013, 22:22

Hi,

"I read in a forum that negative numbers cannot be tagged as odd or even. So, if I get a DS question stating that X is a even integer, then it also implies that X>=0."

However, in the question given below, the logic is not holding true. I was considering the right answer to be C), because if MN = even and N =5 , then it implies that M must be odd integer (and hence M is > 0). Can you clarify if the argument above is false?

If M and N are integers, is 10M+N3 an integer? (1) N=5

(2) MN is even

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.EACH statement ALONE is sufficient.Statements (1) and (2) TOGETHER are NOT sufficient.Mark as a guessHide Answer The question does not mention whether M and N are positive. Hence, the statements taken together are not sufficient because the answer is YES if M=2, N=5 and NO if M=−2; N=5.

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

19 Sep 2013, 23:44

SurabhiStar wrote:

Hi,

"I read in a forum that negative numbers cannot be tagged as odd or even. So, if I get a DS question stating that X is a even integer, then it also implies that X>=0."

However, in the question given below, the logic is not holding true. I was considering the right answer to be C), because if MN = even and N =5 , then it implies that M must be odd integer (and hence M is > 0). Can you clarify if the argument above is false?

If M and N are integers, is 10M+N3 an integer? (1) N=5 (2) MN is even

First, every number except zero "0" can be categorized either Even or odd. Secondly, "X is a even integer" does not necessarily mean X>=0. X can be smaller than 0 as well.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

"I read in a forum that negative numbers cannot be tagged as odd or even. So, if I get a DS question stating that X is a even integer, then it also implies that X>=0."

However, in the question given below, the logic is not holding true. I was considering the right answer to be C), because if MN = even and N =5 , then it implies that M must be odd integer (and hence M is > 0). Can you clarify if the argument above is false?

If M and N are integers, is 10M+N3 an integer? (1) N=5 (2) MN is even

First, every number except zero "0" can be categorized either Even or odd. Secondly, "X is a even integer" does not necessarily mean X>=0. X can be smaller than 0 as well.

1. EVEN/ODD

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.

An odd number is an integer that is not evenly divisible by 2.

According to the above both negative and positive integers can be even or odd.

2. ZERO

Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

18 Jan 2015, 11:26

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.
_________________

Re: If M and N are integers, is ((10^M)) + N)/3 an integer? [#permalink]

Show Tags

19 Jan 2015, 00:42

Nice question....

Initially didnt observe that M can be negative....then it looked too easy....well had it come in the early part of real test....i wud have thought im still in easy qtns zone....and put it as A

From statement 1 and 2, M has to be Even Positive as N = 5 and MN is even.

Now when 5 is added to 10^M where M is even positive and then divided by 3 it always results into an integer.

M25-07

Question: Is ((10^M)) + N)/3 an integer? Re-worded: Is (10^M + N) a multiple of 3?

Note that 10^M will be something like 1000... if M is non-negative. Then, 10^M will be of the form (3a+1) because it will leave remainder 1 when divided by 3. If M is negative, 10^M will not be an integer.

Assuming M is non-negative, for 10^M + N to be a multiple of 3, N should be of them form 3n+2.

(1) N = 5 We don't know whether M is non-negative. Not sufficient.

(2) MN is even again, we don't know whether M is non-negative. Not sufficient.

Using both, we know that M is even since N = 5 (odd) but we don't know whether it is non-negative.

Re: If M and N are integers, is (10^M + N)/3 an integer? [#permalink]

Show Tags

05 Nov 2015, 04:44

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.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...