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# Is cdef < 0? 1) cd2e3f4< 0 2) c2d3e4f5 > 0 (A)

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Is cdef < 0? 1) cd2e3f4< 0 2) c2d3e4f5 > 0 (A) [#permalink]

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04 May 2011, 10:37
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(N/A)

Question Stats:

22% (00:59) correct 78% (00:48) wrong based on 13 sessions

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Is cdef < 0?

1) cd2e3f4< 0
2) c2d3e4f5 > 0

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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04 May 2011, 11:16
1
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IMO - "A"

1) cd2e3f4 [highlight]< 0[/highlight]

we know either c,d,e, or f one of these numbers is negative to claim cd2e3f4 < 0 - sufficient.
2) c2d3e4f5 > 0 - it can be +ve or -ve - not sufficient

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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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04 May 2011, 14:39
the numbers here are exponents to their bases then

c d^2 e^3 f^4 < 0

N/S

2) c^2 d^3 e^4 f^5 > 0
n/s

combined

3) Combined:

c d e f <0
Sufficient

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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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04 May 2011, 20:07
1) c d^2 e^3 f^4 < 0

=> ce < 0, but no information about df

So not sufficient

2) c^2 d^3 e^4 f^5 > 0

=> df > 0, but not information about ce, so not sufficient

(1) + (2)

df > 0 and ce < 0, so cdef < 0, Sufficient

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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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04 May 2011, 20:26
combining 1 and 2
either c or e can be negative. D and E are positive.

Hence C.
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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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22 Jun 2011, 03:20
subhashghosh wrote:
1) c d^2 e^3 f^4 < 0

=> ce < 0, but no information about df

So not sufficient

2) c^2 d^3 e^4 f^5 > 0

=> df > 0, but not information about ce, so not sufficient

(1) + (2)

df > 0 and ce < 0, so cdef < 0, Sufficient

How is ce < 0 in 1 and how is df>0 in 2 ...can you please explain

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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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22 Jun 2011, 04:29
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How is ce < 0 in 1 ?

c d^2 e^3 f^4 < 0

Now d^2 and f^4 will be always > 0, because even powers are always >= 0

And hence => c * e^3 < 0

Again e^3 will have same sign as e.

so c*e^3 < 0 => ce < 0

and how is df>0 in 2 ...can you please explain

c^2 d^3 e^4 f^5 > 0

Here, c^2 * e^4 > 0, being even powers

So d^3*f^5 > 0 as well, because the whole expression is > 0

now d^3 and f^5 will have same sign as d and f respectively.

so df > 0

Is it clear now ?
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Senior Manager
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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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22 Jun 2011, 04:36
subhashghosh wrote:
How is ce < 0 in 1 ?

c d^2 e^3 f^4 < 0

Now d^2 and f^4 will be always > 0, because even powers are always >= 0

And hence => c * e^3 < 0

Again e^3 will have same sign as e.

so c*e^3 < 0 => ce < 0

and how is df>0 in 2 ...can you please explain

c^2 d^3 e^4 f^5 > 0

Here, c^2 * e^4 > 0, being even powers

So d^3*f^5 > 0 as well, because the whole expression is > 0

now d^3 and f^5 will have same sign as d and f respectively.

so df > 0

Is it clear now ?

crystal clear Kudos

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Re: From MitDavidDv: Data Sufficiency Question [#permalink]

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22 Jun 2011, 19:55
1. Not sufficient

we dont know anything about d and f. all we know is ce<0

2. Not sufficient

df>0

we dont know anything about c and e.

together

ce<0 , df>0 . so cedf<0 . Sufficient

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Re: From MitDavidDv: Data Sufficiency Question   [#permalink] 22 Jun 2011, 19:55
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# Is cdef < 0? 1) cd2e3f4< 0 2) c2d3e4f5 > 0 (A)

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