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Is p divisible by 168?

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by melguy » Mon Oct 31, 2016 8:01 pm
Is p divisible by 168?

P is divisible by 14
P is divisible by 12

Prime factorization of 168 = 2 x 2 x 2 x 3 x 7

Statement 1

p
------
2 x 7

We only know that p is divisible by 2 and 7.
Not sufficient

Statement 2

p
------
2 x 2 x 3

We only know that p is divisible by two 2's and a 3.
Not sufficient

Combine

We know that p is divisible by 2, 2, 2, 3 and 7 so answer should be C but why is the answer E ?

Thanks
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by crackverbal » Mon Oct 31, 2016 10:28 pm
Hi Melguy,

Your approach is right.

But while combining both the statements you have made a small error.

Combining statement I and II,

Since P is divisible by both 14 and 12, we have to find the LCM of 14 and 12.

LCM of 14 and 12 is 84. That is P should have minimum 2 two's , one three and one seven then only it is divisible by both 14 and 12.

Now P = 84 not a multiple of 168.but divisible by both 14 and 12.

But P could be 168 as well as it is divisible by both 14 and 12. which is also a multiple of 168.

So different answers.

So combined not sufficient.So the answer is E.

Hope it is clear.
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by fiza gupta » Tue Nov 01, 2016 12:22 am
168 => 2*2*2*3*7

1) p is divisible by 14
14 => 2*7
INSUFFICIENT

2) p is divisible by 12
12=> 2*2*3
INSUFFICIENT

combining 1 and 2
x is divisible by 14 and 12
LCM = 2*7 and 2*2*3
= 2*2*3*7 = 84
p is divisible by 84 but by 168 may or may not be
INSUFFICIENT
so E
Fiza Gupta
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by melguy » Tue Nov 01, 2016 12:43 am
I missed the LCM part!

Thanks everyone for your input.
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by [email protected] » Tue Nov 01, 2016 9:54 am
Hi melguy,

You've already defined the detail that you originally missed, so I won't rehash any of that here. However, I do want to point out a Number Property rule that you'll likely face one time on the Official GMAT:

When dealing with two EVEN numbers, the LCM will be HALF of the product of those two numbers:

For example:

The LCM of 4 and 6 is NOT 24... it's 12... (4)(6)/2 = 12
The LCM of 2 and 6 is NOT 12... it's 6... (2)(6)/2 = 6
The LCM of 10 and 20 is NOT 200... it's 100... (10)(20)/2 = 100

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by Scott@TargetTestPrep » Wed Nov 02, 2016 7:33 am
melguy wrote:Is p divisible by 168?

P is divisible by 14
P is divisible by 12
We need to determine whether p/168 = integer.

Statement One Alone:

p is divisible by 14.

The information in statement one is not sufficient to determine whether p/168 = integer. For instance, if p = 14, then p/168 is not an integer; however if p = 168, then p/168 is an integer. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

p is divisible by 12.

The information in statement two is not sufficient to determine whether p/168 = integer. For instance, if p = 12, then p/168 is not an integer; however if p = 168, then p/168 is an integer. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information in statements one and two we see that p is a common multiple of 12 and 14. Since 12 = 2^2 x 3^1 and 14 = 2^1 x 7^1, we see that the least value of p (i.e., the LCM of 12 of 14) is 2^2 x 3^1 x 7^1 = 4 x 3 x 7 = 84.

However, we still do not have enough information to answer the question. For instance, if p = 84, then p/168 is not an integer; however if p = 168, then p/168 is an integer.

Answer: E

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