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# If A, B, C are integers and (ABC)^(1/2) = 504

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Retired Moderator
Joined: 12 Aug 2015
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If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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24 Aug 2016, 03:10
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Question Stats:

63% (02:09) correct 37% (01:52) wrong based on 92 sessions

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If A, B, C are integers and $$\sqrt{ABC}=504$$ . Is B divisible by 2?

(1) C = 168
(2) A is a perfect square

Now solve this one=> is-b-divisible-by-224194.html#p1726368
[Reveal] Spoiler: OA

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If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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24 Aug 2016, 04:00
This is how I tried.

Given $$\sqrt{ABC}=504$$.

We write the factor of 504 - 2*2*2*7*3*3

Stat 1: C = 168 then A and B can be 3 or 1. (168*3*1 = 504)...we can't take unique value for A and B.

Stat 2: A is perfect square from the set 2*2*2*7*3*3 , we can take 4 and 9 and also 1..no unique value for A.

Stat 1 + Stat 2: if A is 1 and B = 3 then C = 168. Anyhow 1 is perfect square.

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Re: If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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25 Apr 2017, 09:43
I doubt the correct answer is C.
The question is "IS B DIVISIBLE BY 2?"
We are not looking for the value of B.

Statment 1 is sufficient since B can only be 1 or 3. Whatever the value (1 or 3) B is not divisible by 2.
Statment 2 is insufficient.

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Re: If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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03 May 2017, 23:37
msk0657 wrote:
This is how I tried.

Given $$\sqrt{ABC}=504$$.

We write the factor of 504 - 2*2*2*7*3*3

Stat 1: C = 168 then A and B can be 3 or 1. (168*3*1 = 504)...we can't take unique value for A and B.

Stat 2: A is perfect square from the set 2*2*2*7*3*3 , we can take 4 and 9 and also 1..no unique value for A.

Stat 1 + Stat 2: if A is 1 and B = 3 then C = 168. Anyhow 1 is perfect square.

Even though B cant have a unique value still both the possible values are not divisible by 2

IMO A should be the answer
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Joined: 25 Dec 2016
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Re: If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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04 May 2017, 07:28
I also think answer should be A.
value of B can be 1 or 3 which gives answer as No.
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Re: If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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04 May 2017, 08:06
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KUDOS
Expert's post
stonecold wrote:
If A, B, C are integers and $$\sqrt{ABC}=504$$ . Is B divisible by 2?

(1) C = 168
(2) A is a perfect square

Now solve this one=> http://gmatclub.com/forum/is-b-divisibl ... l#p1726368

Hi stonecold
good Q as so many are making errors..
The value of B can be only 1or 3 is WRONG..

Let's see the Q..

$$\sqrt{ABC}=504$$ MEANS A*B*C=504*504...
So if C =168, A*B=$$\frac{504*504}{168}$$=1512..
So A and B can take various combinations of values..
So statement I is insufficient...
Statement II doesn't give any info alone so again insufficient..

Combined..
A*B=1512=$$3^3*7*2^3$$...
So if A is perfect square, A can have either 2^2 or no 2 in it..
Thus B has to have ATLEAST one 2..
Sufficient

C
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Re: If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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04 May 2017, 08:13
I don't think A is the answer. The first statement says, C = 168:

How can you infer (A =1 and B = 3) or (A = 3 and B = 1). If you do that, you'll get

sq rt (3 * 168 * 1) = 504
sq rt (504) = 504

I got the answer as C by guessing between C & E since A, or D can't be the answers. Following is how:

Statement 1: C = 168
So, sq rt (A * B * 168) = 504
Hence, A*B*168 = 504^2 => A*B = (504^2)/168
Doesn't give is much about B.

Statement 2: A is a perfect sq.
Doesn't give is anything either.

So, A, B and D can't be the answered.

I guessed between C and E.

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Re: If A, B, C are integers and (ABC)^(1/2) = 504 [#permalink]

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04 May 2017, 08:17
chetan2u wrote:
stonecold wrote:
If A, B, C are integers and $$\sqrt{ABC}=504$$ . Is B divisible by 2?

(1) C = 168
(2) A is a perfect square

Now solve this one=> http://gmatclub.com/forum/is-b-divisibl ... l#p1726368

Hi stonecold
good Q as so many are making errors..
The value of B can be only 1or 3 is WRONG..

Let's see the Q..

$$\sqrt{ABC}=504$$ MEANS A*B*C=504*504...
So if C =168, A*B=$$\frac{504*504}{168}$$=1512..
So A and B can take various combinations of values..
So statement I is insufficient...
Statement II doesn't give any info alone so again insufficient..

Combined..
A*B=1512=$$3^3*7*2^3$$...
So if A is perfect square, A can have either 2^2 or no 2 in it..
Thus B has to have ATLEAST one 2..
Sufficient

C

Is there a faster approach other than calculating A*B=$$\frac{504*504}{168}$$=1512? Wouldn't be able to do this question in 2 mins...
Re: If A, B, C are integers and (ABC)^(1/2) = 504   [#permalink] 04 May 2017, 08:17
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