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Is the positive integer n a multiple of 24?

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by amirhakimi » Fri Nov 01, 2013 11:55 pm
Is the positive integer n a multiple of 24?

(1) n is a multiple of 4.
(2) n is a multiple of 6.

Answer is E

[spoiler]24=3x2x2x2[/spoiler]

[spoiler](1) 4=2x2 Not Sufficient[/spoiler]
[spoiler](2) 3=3x2 Not Sufficient[/spoiler]

[spoiler](1)&(2) Although it might be tricky to infer that if n has 2x2 and 3x2 as factors, it should have 3x2x2x2 as factors, 4&6 have factor 2 in common and n can be 12 which is not multiple of 24. n can also be 24 which is multiple of 24. Not Sufficient [/spoiler]

Can we create this general rule? ---> In order for A to be divisible by X, while A is dividable by Y, Z, LCM of Y,Z should be dividable by X
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by theCodeToGMAT » Sat Nov 02, 2013 12:05 am
To find: "n" multiple of 24
24 x _ = "n"

Statement 1:
"n" is a multiple of 4
4 x A = n
A can be any number as we don't have any specific value of "n"
INSUFFICIENT


Statement 2:
"n" is a multiple of 6
6 x B = n
B can be any number as we dont have any specific value of "n"
INSUFFICIENT

Combining...
4 x A = n
6 x B = n
"n" can be
12 -> Not a multiple of 24
24 -> yes a multiple of 24
INSUFFICIENT

Answer [spoiler]{E}[/spoiler]
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by amirhakimi » Sat Nov 02, 2013 12:10 am
Thanks for the reply, but my question is this:

Can we create this general rule? ---> In order for A to be divisible by X, while A is dividable by Y, Z, LCM of Y,Z should be dividable by X

It was kinda CR post ;)
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by theCodeToGMAT » Sat Nov 02, 2013 12:19 am
amirhakimi wrote:Thanks for the reply, but my question is this:

Can we create this general rule? ---> In order for A to be divisible by X, while A is dividable by Y, Z, LCM of Y,Z should be dividable by X

It was kinda CR post ;)
Yes!.. the rule makes sense.

but, for GMAT, avoid making generalized rules; rather apply simple mathematics... You may end up spending 1 minute extra on the question, but you won't be confused between complex rules.
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by amirhakimi » Sat Nov 02, 2013 12:32 am
I just wanted to make sure whether if my logic was right. Thanks my friend :)
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by theCodeToGMAT » Sat Nov 02, 2013 3:12 am
amirhakimi wrote:I just wanted to make sure whether if my logic was right. Thanks my friend :)
You are welcome!
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by [email protected] » Sat Nov 02, 2013 6:14 pm
Hi amirhakimi,

In these types of multiple/factor questions, sometimes the fastest way to get to the correct answer is to TEST Values. Here's how:

We're asked if N is a multiple of 24? This is a YES/NO question.

Fact 1: N is a multiple of 4

If N = 4, then the answer to the question is NO.
If N = 24, then the answer to the question is YES.
Fact 1 is INSUFFICIENT.

Fact 2: N is a multiple of 6

If N = 6, then the answer to the question is NO.
If N = 24, then the answer to the question is YES.
Fact 2 is INSUFFICIENT.

Combined, N is a multiple of 4 AND a multiple of 6:

If N = 12, then the answer to the question is NO.
If N = 24, then the answer to the question is YES.
Combined, INSUFFICIENT.

Final Answer: E

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by Matt@VeritasPrep » Sat Nov 02, 2013 11:07 pm
amirhakimi wrote:Can we create this general rule? ---> In order for A to be divisible by X, while A is dividable by Y, Z, LCM of Y,Z should be dividable by X


I like the thought process here, but I'd phrase this as "If the integer K is divisible by the integers L and M, then K is also divisible by the LCM of L and M." The GMAT loves to test divisibility, so this is a great property to know.
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