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Is the integer x divisible by 6?

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Is the integer x divisible by 6?

by siddhans » Wed Jul 20, 2011 3:16 pm
Is the integer x divisible by 6?
(1) x + 3 is divisible by 3
(2) x + 3 is an odd number.

Answer choices:
(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) Either statements are NOT sufficient, but BOTH together are sufficient.
(d) Each statement ALONE is sufficient.
(e) Neither statement Alone is sufficient.


[spoiler]Any one have any insights? Correct Answer: c[/spoiler]
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by Gurpinder » Wed Jul 20, 2011 6:00 pm
Is the integer x divisible by 6?
(1) x + 3 is divisible by 3
(2) x + 3 is an odd number.

(1) x + 3 is divisible by 3
This means that x is also a multiple of 3. Hence x + 3 is a multiple of 3. But x could be 0, 3, 6. If x=3, x is not divisible by 6. Otherwise it is.
Hence Insufficient.

(2) x + 3 is an odd number
This means that x is an even number. X can be 6, or 10. Again insufficient.

Together:
From (1) we know that x is a multiple of 3. Hence X can be 0,3,6,9,12,15,18,21,24,27,30
From (2) we know that x is even. Hence X can be 0,6,12,18,24,30

Hence x is divisible by 6.
Shortcut: All even multiples of 3 will be divisible by 6 because since they are even, they have a "2" in their prime tree and since they are a multiple of 3, they also have a "3" in their prime tree.

Hence (C)
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by siddhans » Wed Jul 20, 2011 9:34 pm
Gurpinder wrote:Is the integer x divisible by 6?
(1) x + 3 is divisible by 3
(2) x + 3 is an odd number.

(1) x + 3 is divisible by 3
This means that x is also a multiple of 3. Hence x + 3 is a multiple of 3. But x could be 0, 3, 6. If x=3, x is not divisible by 6. Otherwise it is.
Hence Insufficient.

(2) x + 3 is an odd number
This means that x is an even number. X can be 6, or 10. Again insufficient.

Together:
From (1) we know that x is a multiple of 3. Hence X can be 0,3,6,9,12,15,18,21,24,27,30
From (2) we know that x is even. Hence X can be 0,6,12,18,24,30

Hence x is divisible by 6.
Shortcut: All even multiples of 3 will be divisible by 6 because since they are even, they have a "2" in their prime tree and since they are a multiple of 3, they also have a "3" in their prime tree.

Hence (C)

How can we say its C?? Does X consists of 0,3,6,9,12.... from 1 and 2 or just 0,6,12,18.... I am confused...What happens when you combine 1 and 2?
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by Gurpinder » Thu Jul 21, 2011 3:09 am
When you combine (1) and (2), it turns out that x is an EVEN multiple of 3. All even multiples of 3 are divisible by 6.
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by siddhans » Thu Jul 21, 2011 4:29 am
Gurpinder wrote:When you combine (1) and (2), it turns out that x is an EVEN multiple of 3. All even multiples of 3 are divisible by 6.
Well but stmt 1 says x + 3 is divisible by 3 ..so x has to be odd in this case ....since if its even its not divisible by 3??
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by krishnasty » Fri Jul 22, 2011 3:09 am
Please counter my explaination.

What if we take x =0 ?
statement 1 : x+3 id divisble by 3 ( 0+3 is indeed disivible by 3). but 0 is not divisble by 6
statement 2 : 0+3 is divisible by 3.but 0 is not divisble by 6

combining both the equations, we can get x =0 ( not divisble) and x = 6 ( divisble).isnt ans should be (E) ??
siddhans wrote:Is the integer x divisible by 6?
(1) x + 3 is divisible by 3
(2) x + 3 is an odd number.

Answer choices:
(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) Either statements are NOT sufficient, but BOTH together are sufficient.
(d) Each statement ALONE is sufficient.
(e) Neither statement Alone is sufficient.


[spoiler]Any one have any insights? Correct Answer: c[/spoiler]
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by Ozlemg » Fri Jul 22, 2011 6:02 am
Well, very tricky!! is this really the sort of thing that the gmat will test??

Answer should be E

0 is a factor of all Numbers (1,2,3.....)
0 is not a divisor of any number (1/0,2/0....)
The more you suffer before the test, the less you will do so in the test! :)
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by Gurpinder » Sat Jul 23, 2011 5:49 am
krishnasty wrote: What if we take x =0 ?
statement 1 : x+3 id divisble by 3 ( 0+3 is indeed disivible by 3). but 0 is not divisble by 6
statement 2 : 0+3 is divisible by 3.but 0 is not divisble by 6
Incorrect!

0/6=0 which is an integer. Hence, 0 is divisible by EVERY number.

Please read Manhattan Number Properties book.
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
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