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Number Properties w/ Remainders

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Source: — Data Sufficiency |
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by sindhu b » Tue Jul 20, 2010 11:17 pm
IMO D
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by Stuart@KaplanGMAT » Tue Jul 20, 2010 11:41 pm
aznmexicana wrote:What is the remainder when the positive integer x is divided by 6?

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
2) When x is divided by 12 the remainder is 3
Like many DS questions, you can solve either by applying concepts or picking numbers. The question is straightforward, so let's dive into the statements.

1) Two key pieces of information.

When x is divided by 2 the remainder is 1 - therefore, x must be odd.
when x is divided by 3, the remainder is 0 - therefore, x must be a multiple of 3.

So, x is an odd multiple of 3: 3, 9, 15, 21, ...

Every one of these numbers gives a remainder of 3 when you divide by 6. Same answer every time, therefore sufficient.

2) Easiest just to pick numbers: 3, 15, 27, 39, ...

Again, we see that all possible values give a remainder of 3 when you divide by 6. Same answer every time, therefore sufficient.

Each statement is sufficient alone: choose (D).
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by thebigkats » Thu Dec 02, 2010 3:52 pm
agreed. It was pretty straightforward.
1. when X is divided by 3, remainder = 0 means that when you divide it by 6, remainder is either 0 or 3. However given that dividing by 2 gives 1, it must be 3
2. second choice is straightforward. anything that is divided by 12 with remainder of X will have remainder of X or (X-6 if X >=6) when divided by 6. So dividing by 6 will also give us 3

Either one works
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by bvosalik » Sat Jan 29, 2011 3:27 am
aznmexicana wrote:What is the remainder when the positive integer x is divided by 6?

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
2) When x is divided by 12 the remainder is 3
Can you please post also the options A-D? thank you :-)
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by diehard_gmat » Sat Jan 29, 2011 3:46 am
bvosalik wrote:Can you please post also the options A-D? thank you :-)
For GMAT Data Sufficiency Quant problems, there are five answer choices, not four. And the answer choices are always same. The answer choices are,
  • (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 to answer the question asked, and additional data are needed.
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by aleph777 » Mon Jan 31, 2011 2:09 pm
I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
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by GMATGuruNY » Mon Jan 31, 2011 2:14 pm
aleph777 wrote:I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
Looking at the list of values that satisfy statement 1: 3, 9, 15, 21...

When 3 is divided by 6, the result is 0 R3.
When 9 is divided by 6, the result is 1 R3.
When 15 is divided by 6, the result is 2 R3.

Since R=3 in every case -- including when x=3 -- sufficient.
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by thebigkats » Mon Jan 31, 2011 2:16 pm
aleph777 wrote:I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
Hi:
When x=3, the remainder upon dividing by 6 = 3. So it is known. Note that the Q says that no is divisible by 3 but not by 2. So it is 3, 9, 15 ... etc. (difference of 6 in consecutive entries). So the remainder when divided by 6 would always be same

So it is D
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by aleph777 » Mon Jan 31, 2011 2:16 pm
Wow... I don't know what I was just thinking. Thanks, Mitch.
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by bvosalik » Wed Feb 02, 2011 2:04 am
diehard_gmat wrote:
bvosalik wrote:Can you please post also the options A-D? thank you :-)
For GMAT Data Sufficiency Quant problems, there are five answer choices, not four. And the answer choices are always same. The answer choices are,
  • (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 to answer the question asked, and additional data are needed.
thank you very much
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by gmatmachoman » Fri Feb 04, 2011 2:24 am
aleph777 wrote:I'm a little confused regarding statement 1.

I followed through the same logic as everyone else, but I chose B rather than D, because I thought if x = 3, then statement 1 is insufficient. Why isn't this the case?
My guess is u would have thought :


1) When x is divided by 2 the remainder is 0, and when x is divided by 3, the remainder is 1

instead of :

1) When x is divided by 2 the remainder is 1, and when x is divided by 3, the remainder is 0
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by sallywoo » Fri Feb 11, 2011 10:44 am
makes sense! thanks guys!
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by cuty » Sat Mar 26, 2011 10:32 pm
IMO D
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by saurabh2525_gupta » Sat Aug 06, 2011 12:18 am
The answer is D.

We can take values and check with them.
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