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a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?

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a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 15 Jan 2012, 23:43
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a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?


(1) \(\frac{c}{b} = \frac{2}{d}\)

(2) \(b^3*a^4*c = 27*a^4*c\)

solution here http://www.platinumgmat.com/gmat-practi ... xplanation

brief expl from me
1 - clearly not suff, and we got that cd=2b
2 - clearly not suff, and we got that |b^3|=27 cause what if c negative? so we can't say for sure that b=3 like stated in OA. Am I right?
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post Updated on: 16 Jan 2012, 02:30
3
a, b, c, and d are integers; abcd >< 0; what is the value of cd?
1) c/b = 2/d
2) b^3*a^4*c = 27*a^4*c

SOLUTION:

statement 1: c/b = 2/d
cd = 2b, we don't know the value of b. so. we can't find the value of cd.
NOT SUFFICIENT

statement 2 : b^3*a^4*c = 27*a^4*c
==> a^4 * c (b^3-27) = 0
it means, a^4 =0 or c =0 or b^3 =27 so, b = 3
so, here we can get different values of cd.
NOT SUFFICIENT

after combining both statement , we can get value of cd = 2b =6

Hence the ans is C.

I HOPE IT WILL BE HELPFUL.
PS: EDITED after bunuel explanation
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Originally posted by 321kumarsushant on 16 Jan 2012, 01:09.
Last edited by 321kumarsushant on 16 Jan 2012, 02:30, edited 2 times in total.
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 16 Jan 2012, 02:11
2
a, b, c, and d are integers; abcd≠0; what is the value of cd?

(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Not sufficient.

(2) b^3*a^4*c = 27*a^4*c --> as \(a\) and \(c\) does not equal to zero we can safely reduce both parts by \(a^4*c\) --> \(b^3=27\) --> \(b=3\). Not sufficient.

(1)+(2) As from (1) \(cd=2b\) and from (2) \(b=3\) then \(cd=2b=6\). Sufficient.

Answer:C.

As for your question:
Runner2 wrote:
2 - clearly not suff, and we got that |b^3|=27 cause what if c negative? so we can't say for sure that b=3 like stated in OA. Am I right?


Odd roots have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

So \(\sqrt[3]{27}=3\) and not \(-3\) --> \(3^3=27\) and \((-3)^3=-27\).

Hope its' clear.
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 16 Jan 2012, 02:33
@bunuel
thanks for explanation. it looks that my mind was somewhere else while solving the question. many times i misses an obvious point , main reason never to the 51 in Quant. i will have to focus more.

anyway, i have edited my explanation.
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 16 Jan 2012, 03:19
thanks for explanation, you should agree very stupid and easy question, I should sleep more not to make such mistakes....
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 21 Jan 2012, 13:45
a, b, c, and d are integers; abcd >< 0; what is the value of cd?

1) c/b = 2/d

c = (2*b)/(d)
not sufficient

2) b^3*a^4*c = 27*a^4*c

b^3 = 27
b = 3

not sufficient.

1 + 2

c = (2*3)/d
c = (6)/d
cd = 6

sufficient.

sufficient.
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 17 May 2012, 08:22
1
Bunuel wrote:
a, b, c, and d are integers; abcd≠0; what is the value of cd?

(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Sufficient.
.



Bunuel, i think what you meant here is Not Sufficient. Correct?
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 13 Sep 2012, 07:12
1
Bunuel wrote:
a, b, c, and d are integers; abcd≠0; what is the value of cd?

(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Sufficient.

(2) b^3*a^4*c = 27*a^4*c --> as \(a\) and \(c\) does not equal to zero we can safely reduce both parts by \(a^4*c\) --> \(b^3=27\) --> \(b=3\). Not sufficient.

(1)+(2) As from (1) \(cd=2b\) and from (2) \(b=3\) then \(cd=2b=6\). Not sufficient.

Answer:C.

As for your question:
Runner2 wrote:
2 - clearly not suff, and we got that |b^3|=27 cause what if c negative? so we can't say for sure that b=3 like stated in OA. Am I right?


Odd roots have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

So \(\sqrt[3]{27}=3\) and not \(-3\) --> \(3^3=27\) and \((-3)^3=-27\).

Hope its' clear.


Hi Bunuel,

There is a slight typing error in the explanation.
Statement "(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Sufficient."
should read
"(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Insufficient."

Correct me if i am wrong.
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 13 Sep 2012, 07:18
fameatop wrote:
Bunuel wrote:
a, b, c, and d are integers; abcd≠0; what is the value of cd?

(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Sufficient.

(2) b^3*a^4*c = 27*a^4*c --> as \(a\) and \(c\) does not equal to zero we can safely reduce both parts by \(a^4*c\) --> \(b^3=27\) --> \(b=3\). Not sufficient.

(1)+(2) As from (1) \(cd=2b\) and from (2) \(b=3\) then \(cd=2b=6\). Not sufficient.

Answer:C.

As for your question:
Runner2 wrote:
2 - clearly not suff, and we got that |b^3|=27 cause what if c negative? so we can't say for sure that b=3 like stated in OA. Am I right?


Odd roots have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).

So \(\sqrt[3]{27}=3\) and not \(-3\) --> \(3^3=27\) and \((-3)^3=-27\).

Hope its' clear.


Hi Bunuel,

There is a slight typing error in the explanation.
Statement "(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Sufficient."
should read
"(1) c/b = 2/d --> \(cd=2b\), we don't know the value of \(b\) to get the single numerical value of \(cd\). Insufficient."

Correct me if i am wrong.


Thank you. Typo edited.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 10 Nov 2014, 10:46
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Bunuel, I think there is a typo- the option (c) i.e, (1)+(2) is 'sufficient', right?
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 16 Sep 2016, 16:37
D is correct. Here's why:

(1) x^(2) yz = 12xy --> xz = 12

SUFFICIENT

(2) (z/4) - (3/x) --> xz = 12

SUFFICIENT
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd?  [#permalink]

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New post 12 Jan 2019, 09:19
law258, that looks like a different problem from the one in this post.
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Re: a, b, c, and d are integers; abcd ≠ 0; what is the value of cd? &nbs [#permalink] 12 Jan 2019, 09:19
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