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

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If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   24 Dec 2020, 01:15
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If A, B, and C are positive integers and \(\sqrt{A*B*C}=504\), is B divisible by 2?

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


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C
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   24 Dec 2020, 05:04
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If A, B, and C are positive integers and \(\sqrt{A*B*C}=504\), is B divisible by 2?

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

504=21*3*8


1. C = 168 = 3*7*8

Does not tell us anything about B. >> Not.Sufficient.

2. A is perfect sq.

Ok so this means \(\sqrt{B*C}\) is also perfect square but what their values are we dont know. >> Not.Sufficient.

Togther, C = 168 and A is perfect sq. so yes B should be such that \(\sqrt{B*C}\) is also perfect sq. and we will get definite Yes or No.

Sufficient.

IMO C
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   24 Dec 2020, 08:07
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504 = \(2^3\) * \(3^2\) * 7

Statement 1:

C=168 = \(2^3\)*3*7. All 2s are gone, nothing left for B.
So, B is not divisible by 2.
Sufficient.

Statement 2:
A is a perfect square, It can be 4, 9, 36, in every case we have a 2 left (min). It can be a factor of B or C.
Insufficient

IMO Option A
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   24 Dec 2020, 08:47
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given, Sqrt (A∗B∗C)=504= (2^3)*(3^2)*7, so A*B*C = (2^6)*(3^4)*(7^2)

Stat1: C = 168 = (2^3)*3*7
So, A*B = (2^3)*(3^3)*(7^1), now, B can be divisible by 2 or not. Not sufficient.

Stat2: A is a perfect square
So, A*B*C = (2^6)*(3^4)*(7^2), now, B can be divisible by 2 or not. Not sufficient.

Combining Stat 1 and 2,
A*B = (2^3)*(3^3)*(7^1), and A is a perfect square, so for B, we have always one 2 left. Sufficient

So, I think C. :)
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   24 Dec 2020, 09:54
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504 = 2*2*2*3*3*7
so A*B*C = 2*2*2*2*2*2*3*3*3*3*7*7

Statement 1: C=168 = 2*2*2*3*7
=> A*B = 2*2*2*3*3*3*7
As we don't know the value of A so this statement is not sufficient.

Statement 2: A is a perfect square
As there are six 2s, four 3s and two 7s so, there are many perfect squares.
So, this statement is also not sufficient.

Combining Statements A and B:
C= 2*2*2*3*7
A*B = 2*2*2*3*3*3*7
If A is a perfect square then it can have maximum of two 2s which means one of the 2 will be left. So, B will always be a multiple of 2.

So, correct answer is C.
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   25 Dec 2020, 00:56
Is the answer E?
Couldn't we just use knowledge of odd/even to figure this one out?
From the stem, we see that the\( \sqrt{ABC}\) gives us 504. This tells us that ABC MUST be an even perfect square.

Statement 1 - C = 168
1. a is even, b is even, c is even YES b is divisible by 2
2. a is odd, b is even, c is even YES
3. a is even, b is odd, c is even NO
Insufficient

Statement 2 - a is a perfect square
This means a could be odd or even, doesn't tell us anything about B

Combined:
Well if b could be even or odd, we don't know.
Insufficient

Answer: E
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   01 Jan 2021, 22:14
Bunuel wrote:
If A, B, and C are positive integers and \(\sqrt{A*B*C}=504\), is B divisible by 2?

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


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Q - is b even
(Abc) = 504 * 504 or abc = even
1) c = 168 even insufficient
2) a is a perfect sq
A can end in
1,4,5,9,6 insufficient
1&2 )
Ab = (504*504/168) or even
Even * even = even
Od * even = even
A can be both od/even
So b has to be even. And divisible by 2
Hence ans C

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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink] New post   29 Aug 2023, 11:45
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Re: If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib [#permalink]
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