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# sqrt(abc) = 504. Is B divisible by 2? (1) C = 168 (2) A is a

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Director
Joined: 26 Feb 2006
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sqrt(abc) = 504. Is B divisible by 2? (1) C = 168 (2) A is a [#permalink]  16 Jun 2007, 13:35
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sqrt(abc) = 504. Is B divisible by 2?
(1) C = 168
(2) A is a perfect square
VP
Joined: 10 Jun 2007
Posts: 1465
Followers: 6

Kudos [?]: 133 [0], given: 0

Re: DS: Sqrt [#permalink]  16 Jun 2007, 13:47
Himalayan wrote:
sqrt(abc) = 504. Is B divisible by 2?
(1) C = 168
(2) A is a perfect square

I got C.
sqrt(abc) = 504
=> abc = 504^2 = 2^6 * 3^4 * 7^2

(1) c = 168 = 2^3 * 3 * 7
Therefore, ab = 2^3 * 3^3 * 7
we cannot determine if b is divisible by 2 here. Say a = 2^3, b won't be divisible by 2. Say a = 3^3, b will be divisible by 2. INSUFFICIENT.

(2) a is a perfect square. We cannot dertermine the divisibility of b here. since a can be anything. INSUFFICIENT.

Together, we know ab = 2^3 * 3^3 * 7 and a is a perfect square. In this case, a can be 2^2, 3^2, or 6^2. In every case, b will be divisible by 2 since we have 2^3. SUFFICIENT.
VP
Joined: 08 Jun 2005
Posts: 1147
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Re: DS: Sqrt [#permalink]  16 Jun 2007, 14:15
bkk145 wrote:
Himalayan wrote:
sqrt(abc) = 504. Is B divisible by 2?
(1) C = 168
(2) A is a perfect square

I got C.
sqrt(abc) = 504
=> abc = 504^2 = 2^6 * 3^4 * 7^2

(1) c = 168 = 2^3 * 3 * 7
Therefore, ab = 2^3 * 3^3 * 7
we cannot determine if b is divisible by 2 here. Say a = 2^3, b won't be divisible by 2. Say a = 3^3, b will be divisible by 2. INSUFFICIENT.

(2) a is a perfect square. We cannot dertermine the divisibility of b here. since a can be anything. INSUFFICIENT.

Together, we know ab = 2^3 * 3^3 * 7 and a is a perfect square. In this case, a can be 2^2, 3^2, or 6^2. In every case, b will be divisible by 2 since we have 2^3. SUFFICIENT.

Perfect ! I second (C) well done bkk145

Senior Manager
Joined: 21 Jun 2006
Posts: 287
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sqrt(abc) = 504. Is B divisible by 2?
(1) C = 168
(2) A is a perfect square

Together sufficient
abc = 504*504
ab = 504*504/168
= 3*504
= 3*168*3
= 3*3*4*4*7*3*2

a is 3 or 4, which leaves B divisible by 2
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