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Integers

by parulmahajan89 » Thu Feb 27, 2014 10:01 pm
what is the remainder when positive integer is divided by 6?

1) When X is divided by 2, remainder is 1 and when X is divided by 3, remainder is 0
2) When X is divided by 12, remainder is 3

My only question here is X should result in same value for both statements so when divided by 6, we get accurate value right?
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Source: — Data Sufficiency |
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by theCodeToGMAT » Thu Feb 27, 2014 10:33 pm
Let "x" be the positive integer.

To find: Remainder of x/6

Statement 1:
x/2 => r=1 ... x can be 1, 3, 5, 7 etc..
x/3 => r=0 ... x can be 3, 6, 9, 12, etc
Combining facts..
x can be 3, 9, 15, etc
For all these cases.. when x/6.. the remainder is 3
SUFFICIENT

Statement 2:
x/12 => remainder is 3
x can be 3, 15, 27, 39, 51, etc
For all these cases.. when x/6.. the remainder is 3
SUFFICIENT

Answer [spoiler]{D}[/spoiler]
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by [email protected] » Fri Feb 28, 2014 12:06 am
Hi parulmahajan89,

Since Fact 2 focuses on numbers that are divided by 12, you have to be careful about your assumptions. While all numbers that are divisible by 12 ARE divisible by 6, the opposite is NOT true (a number that is divisible by 6 is not necessarily divisible by 12).

The numbers 6, 18, 30, etc. are NOT valid TEST Values for Fact 2.

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by Brent@GMATPrepNow » Fri Feb 28, 2014 7:00 am
parulmahajan89 wrote: My only question here is X should result in same value for both statements so when divided by 6, we get accurate value right?
You're absolutely right, parulmahajan89.
Data Sufficiency (DS) questions should yield the same values. In other words, DS questions will not contradict each other.

For example, the following would NEVER be a true DS question:
What is the value of x?
(1) 2x = 8
(2) x + 3 = 9
In this example, statement 1 tells us that x = 4 and statement 2 tells us that x = 6. Since these results contradict each other, this could never be a true DS question.

If you're interested, we have a free video titled "Useful Contradictions" that addresses what it means if you believe you've spotted a contradiction in a DS question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1104

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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