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# If x is a positive integer, is the remainder 0 when 3^(x +

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If x is a positive integer, is the remainder 0 when 3^(x + [#permalink]  20 Sep 2008, 06:42
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.
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Re: remainder ! [#permalink]  20 Sep 2008, 07:16
Nihit wrote:
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 ?

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.
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Re: remainder ! [#permalink]  20 Sep 2008, 07:16
Nihit wrote:
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
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Re: remainder ! [#permalink]  20 Sep 2008, 07:25
Nihit wrote:
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.

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Re: remainder ! [#permalink]  20 Sep 2008, 07:30
IanStewart wrote:

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
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Re: remainder ! [#permalink]  25 Sep 2008, 11:01
I am also getting D.

It is straight forward.

Any power to 3 gives 3, 7, 9 or 1 as last digit of the number.

For example,
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

so last digits are 3, 9, 7 and 1 and they are repeating.

So, no number will be divisible by 10 so there will be never remainder is 0.

So both statements are individually sufficient. Hence, it is D.
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Re: remainder ! [#permalink]  25 Sep 2008, 15:34
Nihit wrote:
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

$$3^x + 1$$
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Re: remainder ! [#permalink]  25 Sep 2008, 17:12
IanStewart wrote:
Nihit wrote:
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

$$3^x + 1$$

Yep, The way the Q is posted the answer is D.
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Re: remainder ! [#permalink]  26 Sep 2008, 03:44
Nihit wrote:
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
Re: remainder !   [#permalink] 26 Sep 2008, 03:44
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