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# sqrt{ABC} = 504. Is B divisible by 2?

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Re: sqrt{ABC} = 504 . Is B divisible by 2? 1) C = 168 2) A is a [#permalink]

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30 Sep 2012, 03:49
I hope bunuel shed light on this one..........
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Re: sqrt{ABC} = 504 . Is B divisible by 2? 1) C = 168 2) A is a [#permalink]

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01 Oct 2012, 03:58
I dont know whether my apporach is right or not..

sqrt{ABC}= 504

here, LHS is sqrt and RHS is integer so LHS must be a n integer value when sqrt is removed.

statement 1 : C=168, nothinh about A and B so insufficient.
statement 2 : A is a perfect square

now A is pefect square, we have value of C=168.

so to make it of even number of power, suppose, B=C=168.

so A,B and C all are of even power, so both the statement are together suffice.B=168 is divisible by 2.
(question stem doesnot mention that all the three are distinct numbers. so we can assume B=C)

Am I right in this?

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Re: DS- Perfect squares [#permalink]

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22 Sep 2013, 11:02
anaik100 wrote:
sqrt{ABC}=504.Is B divisible by 2?

(1) C = 168

(2) A is a perfect square

sqrt{ABC}=504
ABC=504^2

1)
we know C but AB r unknown
hence insuff

2)

A is perfect sq

504
2*252=2*2*126=2*2*2*63=2*2*2*3*3*7

A can be =(2*2*3*3)^2 or (2*2)^2 or (3*3)^2
B and C r still not known
hence insuff

1 and 2
C is known
AB168=504^2
AB=3*504
=3*2*2*2*3*3*7

since A is perf sq
A can be (2*2*3*3)
B will be 3*2*7.it is divisible by 2

id A can be (2*2)
B will be 3*2*7*3*3.it is still divisible by 2

hence C

Answer C is based on the assumption that B is an integer, and no such information is given anywhere in the question.
I believe, answer C wont be valid in case, c=168, a=504^2, B=1/168.
Kindly correct if I am wrong. Thanks.

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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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28 Aug 2014, 21:10
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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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28 Aug 2014, 22:44
let us take factors of 504
=2*2*2*7*3*3

LHS has a square root sign. so number of factors double on LHS.
so we require 6 2's, 2 7's and 4 3's to equate LHS to RHS.

statement 1 is clearly insufficient.
statement 2 also insufficient.

1+2 combined,
factors of 168 are 2*2*2*7*3
so balance we require 3 2's, 1 7's and 3 3's to make LHS and RHS equal.
a= 2^2*3^2 and b=2*7*3 satisfy above condition and b is a divisible by 2
a=2^4*3^2 and b=(7*3)/2=21/2 also satisfy above condition but b is not divisible by 2

Hence statements are insufficient.
Ans=E

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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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28 Aug 2014, 23:24
desaichinmay22 wrote:
let us take factors of 504
=2*2*2*7*3*3

LHS has a square root sign. so number of factors double on LHS.
so we require 6 2's, 2 7's and 4 3's to equate LHS to RHS.

statement 1 is clearly insufficient.
statement 2 also insufficient.

1+2 combined,
factors of 168 are 2*2*2*7*3
so balance we require 3 2's, 1 7's and 3 3's to make LHS and RHS equal.
a= 2^2*3^2 and b=2*7*3 satisfy above condition and b is a divisible by 2
a=2^4*3^2 and b=(7*3)/2=21/2 also satisfy above condition but b is not divisible by 2

Hence statements are insufficient.
Ans=E

Yes, you are right.

But if the question mentioned a, b, c as integers - then answer would be C.

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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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29 Aug 2014, 00:38
bazc wrote:
desaichinmay22 wrote:
let us take factors of 504
=2*2*2*7*3*3

LHS has a square root sign. so number of factors double on LHS.
so we require 6 2's, 2 7's and 4 3's to equate LHS to RHS.

statement 1 is clearly insufficient.
statement 2 also insufficient.

1+2 combined,
factors of 168 are 2*2*2*7*3
so balance we require 3 2's, 1 7's and 3 3's to make LHS and RHS equal.
a= 2^2*3^2 and b=2*7*3 satisfy above condition and b is a divisible by 2
a=2^4*3^2 and b=(7*3)/2=21/2 also satisfy above condition but b is not divisible by 2

Hence statements are insufficient.
Ans=E

Yes, you are right.

But if the question mentioned a, b, c as integers - then answer would be C.

That is right. But for this problem, ans has to be E. It is not given that numbers are integers.

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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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14 May 2016, 11:00
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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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16 May 2016, 21:48
why abc => a*b*c???

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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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16 May 2016, 22:14
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vishnu440 wrote:
why abc => a*b*c???

Hi vishnu440,

abc is always a*b*c, but can be easily mistaken as a 3-digit number..
A 3-digit number will always be mentioned..
say abc is a 3-digit number where a, b are ......etc
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Is B divisible by 2? [#permalink]

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24 Aug 2016, 03:11
If $$\sqrt{ABC}=504$$ . Is B divisible by 2?

(1) C = 168
(2) A is a perfect square
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sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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24 Aug 2016, 04:07
stonecold wrote:
If $$\sqrt{ABC}=504$$ . Is B divisible by 2?

504 can be factorised as follows:
$$\frac{504}{4} = 126\\1+2+6 = 9 \implies 126 = 9 \times 14$$

$$504 = 2^3 \times 3^2 \times 7$$

$$ABC = 2^6 \times 3^4 \times 7^2$$

$$\textbf{(1) } C = 168$$

We know no information about $$B$$ or $$A$$, so it's only possible to prove that $$B$$ is odd.
$$B$$ would only be odd if $$C$$ were divisible by $$2^6 = 64$$
168 is not divisible by 64.

EDIT: stricken through above, we only know one number, even if C were divisible by 64, then $$B=2$$ and $$A = \frac{1}{2}$$ would allow for an even

Insufficient.

----

(2) A is a perfect square

It's trivial to see that there are multiple combinations of squares, If $$A = 2^{3^2}$$, then there would be no twos to distribute.
Otherwise a two may or may not be distributed to B to make it even or odd.

Insufficient

(1+2)

From (1): $$168 = 2^3 \times 3 \times 7 \implies AB = 2^3 \times 3^3 \times 7$$

Prove by counterexample

$$A = 2^4, B=2^{-1} \times 3^3 \times 7 = \text{ odd }$$

Anything without a fractional power of 2 in $$B$$ would be even.

Insufficient

[Reveal] Spoiler:
E

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Last edited by DAllison2016 on 25 Aug 2016, 17:27, edited 1 time in total.

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Re: Is B divisible by 2? [#permalink]

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24 Aug 2016, 04:14
stonecold wrote:
If $$\sqrt{ABC}=504$$ . Is B divisible by 2?

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

Given √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.

Option C is correct answer..

I doubt on the OA...can you share the full official solution if you have or others can try this..

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sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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24 Aug 2016, 04:28
[Reveal] Spoiler: quote
msk0657 wrote:
stonecold wrote:
If $$\sqrt{ABC}=504$$ . Is B divisible by 2?

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

Given √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.

Option C is correct answer..

I doubt on the OA...can you share the full official solution if you have or others can try this..

OA has changed to C now the topics have been merged.

For the OA of E, the numbers do not have to be integers.
Let $$A = 144, B = \frac{21}{2}$$. B is not even.
Let $$A = 4, B = 378$$. B is even.
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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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24 Aug 2016, 07:17
Hi everyone abhimahna DAllison2016 msk0657
here is what i think =>
The ANSWER here should be C

WE aren't told A,B.C are integers.
if the Question would mention that A,B,C are integers then ye => C is fine
Else here E Gotta be true

CC- Bunuel
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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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27 Aug 2016, 02:36
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stonecold wrote:
Hi everyone abhimahna DAllison2016 msk0657
here is what i think =>
The ANSWER here should be C

WE aren't told A,B.C are integers.
if the Question would mention that A,B,C are integers then ye => C is fine
Else here E Gotta be true

CC- Bunuel

Dude,

504 can be written as $$7 * 3^2 * 2^3$$

so, since $$sqrt(ABC) = 504$$, we can say ABC = $$7^2 * 3^4 * 2^6$$

Now, Statement 1 has made it clear that C is an integer.

Now, we also know that A*B = $$7 * 3^3 * 2^3$$

We are not sure if B is even. hence, insufficient.

Now Statement B states that A is a perfect Square. No info about B and C, hence insufficient.

Combining,

We know C and product of A and B.

What do you wanna take the value of A. 1/2, if yes, then take it. I know one thing that in order to make the multiplication of A and B an integer, I MUST have 2 in B.

if you wanna take A = 1/7, again take it ( ) , Since I have the product of A and B even, and A is ODD, I can say B MUST be even.

Also, If I go with the normal integral values, then since I have A a perfect square and 3 2's in the product of A and B, I must infer that B must have atleast one 2 in it.

Hence, sufficient.

Do let me know if you have any doubts.
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Re: sqrt{ABC} = 504. Is B divisible by 2? [#permalink]

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26 Aug 2017, 23:54
The question is quite simple :-

ABC = 504*504
AB = 504*3
We dont know the value of A, therefore the statement A is insufficient

A is a perfect square
But this statement doesnt tell us anything about C or B

Combined,
AB = 504*3
We can assume A to be any perfect square for example 49, 36, 4, 9 etc.

1. 504*3/49 => Not divisible by 2
2. 504*3/9 => 168 => divisible by 2

Not sufficient
E is the answer

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Re: sqrt{ABC} = 504. Is B divisible by 2?   [#permalink] 26 Aug 2017, 23:54

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