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 [#permalink]

Show Tags

15 Aug 2009, 18:32

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

100% (01:01) correct
0% (00:00) wrong based on 2 sessions

HideShow timer Statistics

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

Please, show your logic. Thanks, -----------------------------

Q32: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? (1) x = 3n + 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.

Last edited by TriColor on 16 Aug 2009, 09:36, edited 1 time in total.

If x is a positive integer, is the remainder 0 when (3x + 1)/10? - divisibility by 10 means 3x+1 has zero as a last digit.

(1) x = 3n + 2, where n is a positive integer. Let's just substitute x for this expression: 3*(3n+2) + 1 = 9n + 7. In order to have 0 as a last digit. 9n must end with digit 3, otherwise our expression cannot be divisible by 10. It's possible for n=7: 9*7=63. Therefore, the expression can be divisible by 10 (n=7) and cannot be divisible by 10 (n=6). Insufficient.

(2) x > 4 Insufficient along and doesn't add any support to first statement. _________________

Please, show your logic. Thanks, -----------------------------

Q32: If x is a positive integer, is the remainder 0 when (3x + 1)/10? (1) x = 3n + 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.

Agree with E. 1) if x=3n+2, then 3x+1 = 9n+7. If n=7 , then 9n+7/10 will have 0 as remainder. For other values remainder will be other than 0. Not suff. 2) x>4. Now, we need to find some multiple of 3 to which when 1 is added the result is divisible by 10. x can be 33 in which case remainder is 0 , for some other values remainder will not be 0. Not suff.

Combining, we have 9n+7 / 10 where n>2/3. So n can take any value which might satisfy the equation. E.

Hello, I have correcter the question... X should be the exponent of 3... Sorry about the mistake. -----------------------------

Q32: If x is a positive integer, is the remainder 0 when (3^x + 1)/10? (1) x = 3n + 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.

EDITED: Sometimes I also make silly mistakes... I corrected my post.

it is old DS-trap here. After good preparation you can solve this in 10-15 sec. Here is a pattern:

1. The question about divisibility/last digit 2. The question contains exponent a^x 3. x can be periodical (x=a*x+b, one of the statement). In other words, something like: each 4th number and so on. 4. other statement is obviously insufficient.

Where is a key? Just write out last digit for a few consecutive numbers of exponent:

3^x x=0: 1 x=1: 3 x=2: 9 x=3: 7 x=4: 1 period:4

Let's consider any other example:

7^x x=0: 1 x=1: 7 x=2: 9 x=3: 3 period:4

6^x x=0: 1 x=1: 6 x=2: 6 x=3: 6 period:1 (need to check for x=0)

2^x x=0: 1 x=1: 2 x=2: 4 x=3: 8 x=4: 6 x=3: 2 period:4 (need to check for x=0)

So, for any a^x exponent there is a pattern and GMAC is trying to trick you here. But if you can instantly recognize the DS-pattern, you in a few second will "feel" that answer is A and will spend next 10 seconds to check match between 3^x period for last digit (here it is 3) and period for one statement, (3n+2) has period 4. They don't equal. So the answer is E. You even may not know the answer (divisible or not) you only know for sure that last digit of 3^x+1 is always the same. _________________

great problem. guys, can anyone write down a general rule on how to determine a last digit when a number raised to power? Thanks! I took the right approach but could not avoid using a calculator

great problem. guys, can anyone write down a general rule on how to determine a last digit when a number raised to power? Thanks! I took the right approach but could not avoid using a calculator

Its just same as Walker mentioned. You gotta remember the pattern for 3 , 4, 6, 7, 9 and 11 powers of x. I have not seen any others being tested

great problem. guys, can anyone write down a general rule on how to determine a last digit when a number raised to power? Thanks! I took the right approach but could not avoid using a calculator

You don't need to do all math here. Let's say, you want to see last digit of 353^x. The main rule here:

last digit of 353^x is equal to last digit of 3^x. So, you can always cut all digits but last.