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x is divided by 6

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x is divided by 6

by sk8ternite » Tue Jul 14, 2009 1:04 pm
What is the remainder when the positive integer x is divided by 6?
(1) When x is divided by 2, the remainder is 1l and when x is divided by 3, the remainder is 0.
(2) When x is divided by 12, the remainder is 3.

Answer is d. Why not c




Statement 1: Cause when 3 is divided by 6, remainder is 6, but when 9 is divided by 3, remainder is 3
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Re: x is divided by 6

by Stuart@KaplanGMAT » Tue Jul 14, 2009 2:00 pm
sk8ternite wrote:What is the remainder when the positive integer x is divided by 6?
(1) When x is divided by 2, the remainder is 1l and when x is divided by 3, the remainder is 0.
(2) When x is divided by 12, the remainder is 3.

Answer is d. Why not c


Statement 1: Cause when 3 is divided by 6, remainder is 6, but when 9 is divided by 3, remainder is 3
First, when 3 is divided by 6, the remainder is 3, not 6, since

3/6 = 0 with 3 left over.

In fact, when you divide by integer n, the greatest possible remainder is n-1, so there's no way that any integer divided by 6 would leave you with a remainder of 6.

For example, if you divide by 4, the possible remainders are 0, 1, 2 and 3; if you divide by 6 the possible remainders are 0, 1, 2, 3, 4 and 5.

(2) is much simpler, so let's start here: x/12 has remainder of 3.

Therefore, x = 3, 15, 27, 39, ...

For each of these numbers, when we divide by 6, we get a remainder of 3: sufficient.

(1) x/2 has remainder 1 and x/3 has remainder 0.

Let's break those up into two different statements:

x/2 has remainder 1... therefore, x is odd.

x/3 has a remainder 0... therefore, x is a multiple of 3.

Together: x is an odd multiple of 3, i.e. 3, 9, 15, 21, 27, ...

For each of these numbers, when we divide by 6, we get a remainder of 3: sufficient.

Each of (1) and (2) are sufficient alone: choose D.
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by Nina1987 » Fri Jan 08, 2016 12:25 am
Is there an algebraic approach to this problem? i am always confused whether to take an algebraic approach or number testing approach esp on remainder prblems. I don't want to make this decision in the exam hall. If I want to go in the exam hall with one approach which one it should be for remainder problems? Thanks
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by GMATGuruNY » Fri Jan 08, 2016 4:43 am
sk8ternite 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.
Statement 1:
When x is divided by 2, the remainder is 1.
In other words, x is 1 more than a multiple of 2:
x = 2a + 1, where a is a nonnegative integer.
Implication:
x is ODD.

When x is divided by 3, the remainder is 0.
In other words, x is a MULTIPLE OF 3:
x = 3b.

Since x must be an ODD MULTIPLE OF 3, options for x:
3, 9, 15...
When any value in this list is divided by 6, the remainder is 3.
SUFFICIENT.

Statement 2:
When x is divided by 12, the remainder is 3.
In other words, x is 3 more than a multiple of 12:
x = 12c + 3, where c is a nonnegative integer.
Options for x:
3, 15, 27...
When any value in this list is divided by 6, the remainder is 3.
SUFFICIENT.

The correct answer is D.

I suggest that you also check my posts below:
https://www.beatthegmat.com/remainder-of ... 54799.html
https://www.beatthegmat.com/when-positiv ... 82655.html
https://www.beatthegmat.com/ds-number-sy ... 13871.html
https://www.beatthegmat.com/remainder-t187461.html
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by [email protected] » Fri Jan 08, 2016 9:50 am
Hi Nina1987,

Business Schools tend to prefer applicants who are flexible thinkers, which is one of the reasons why GMAT questions can often be solved in a variety of ways. To that end, one of your goals should be to develop more than just one set of skills. From what you asked, it sounds like you want to stick with an 'algebraic approach' to most questions. While that's fine, it will likely limit how high you score in the Quant section and could cause some serious pacing problems (since sometimes the 'math way' to approach a question takes far longer than a 'Tactical way' to approach that same question).

1) How long have you been studying?
2) How have you scored on your practice CATs (including the Quant and Verbal Scaled Scores)?
3) What is your goal score?

GMAT assassins aren't born, they're made,
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Contact Rich at [email protected]
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by Matt@VeritasPrep » Fri Jan 08, 2016 1:39 pm
Nina1987 wrote:Is there an algebraic approach to this problem? i am always confused whether to take an algebraic approach or number testing approach esp on remainder prblems. I don't want to make this decision in the exam hall. If I want to go in the exam hall with one approach which one it should be for remainder problems? Thanks
Yes, there's a general approach to problems like this, detailed here. If you can follow that, it's easy to use, but if not, Mitch's approach of making lists and see what they have in common works well in a pinch, especially under test conditions.
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