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:

If x is a positive integer, is the remainder 0 when 3^(x + [#permalink]
20 Sep 2008, 06:42

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x is a positive integer, is the remainder 0 when 3^(x + 1) is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient

Guys I usually employ the sequence of unit number reps technique in such questions(3,9,7,1,3,9,7,1) . Is there a quicker way to solve such questions ?

Last edited by Nihit on 20 Sep 2008, 07:37, edited 1 time in total.

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient

Guys I usually employ the sequence of unit number reps technique in such questions(3,9,7,1,3,9,7,1) . Is there a quicker way to solve such questions ?

Shouldn't the question read:

If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?

If so, and if you know that the units digit of powers of 3 repeats in blocks of four, Statement 1 is clearly sufficient; there is no need to do any calculation. Remember that on yes/no DS questions, we don't care whether the answer is yes or no, we only need to be sure we can get an answer. If you know that the units digit of 3^(4n+2) will always be the same for any positive integer n, you're done. Statement 2 is clearly insufficient. A. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient

Guys I usually employ the sequence of unit number reps technique in such questions(3,9,7,1,3,9,7,1) . Is there a quicker way to solve such questions ?

A 1) tells us that x is even, thus 3*x will be even and 3*x + 1 will be odd. remainder will never be 0

If x is a positive integer, is the remainder 0 when 3x + 1 is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient

Guys I usually employ the sequence of unit number reps technique in such questions(3,9,7,1,3,9,7,1) . Is there a quicker way to solve such questions ?

I get D as my answer.

First of all, the question is asking whether we will get a remainder of zero when 3x+1 is divided by 10. 3x+1 will be divisible by 10 if 3x/10 and 1/10 are divisible by 10 or the sum of their remainders will give us 10.

Obviously, 1/10 will give us a remainder of 1, so we will need a remainder of 9 from 3x/10 so that the sum of the remainders will be 10. This will be the case when x=3.

(1) so (3(4n+2) +1)/10 ---> (6(2n+1) + 1)/10

this means (even + odd)/10 = odd/10, and we know that only even numbers can be divided by 10 with zero remainders. So the answer is no ---> suff.

(2) x>4, and we know that only 3 can be used in x to give us a remainder of 9 so that when added to the remainder of 1 from 1/10, the total sum will be 10, hence is not divisible by 10. the answer is no. ---> Suff.

If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?

If so, and if you know that the units digit of powers of 3 repeats in blocks of four, Statement 1 is clearly sufficient; there is no need to do any calculation. Remember that on yes/no DS questions, we don't care whether the answer is yes or no, we only need to be sure we can get an answer. If you know that the units digit of 3^(4n+2) will always be the same for any positive integer n, you're done. Statement 2 is clearly insufficient. A.

Ian can you throw more light on your concept here ??

Thanks _________________

"You have to find it. No one else can find it for you." - Bjorn Borg

If x is a positive integer, is the remainder 0 when 3^(x + 1) is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

The question has been edited since I posted my response above, but there's no way that what I've quoted above is the right version of the question. Of course the remainder is not 0 when 3^(x+1) is divided by 10; 3^(x+1) is an odd number. You wouldn't need to bother looking at the statements. So, as I posted above, I'm pretty sure the question should read

\(3^x + 1\) _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

If x is a positive integer, is the remainder 0 when 3^(x + 1) is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

The question has been edited since I posted my response above, but there's no way that what I've quoted above is the right version of the question. Of course the remainder is not 0 when 3^(x+1) is divided by 10; 3^(x+1) is an odd number. You wouldn't need to bother looking at the statements. So, as I posted above, I'm pretty sure the question should read

If x is a positive integer, is the remainder 0 when 3^(x + 1) is divided by 10? (1) x = 4n + 2, where n is a positive integer. (2) x > 4

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient

Guys I usually employ the sequence of unit number reps technique in such questions(3,9,7,1,3,9,7,1) . Is there a quicker way to solve such questions ?

(3^X+1) WILL NEVER BE DIVISIBLE BY 10..WHATEVER BE THE VALUE OF X(+VE INTEGER) MY ANS D