Is cdef

Question

Is cdef 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.

patanahi · Answer

IMO - "A"

1) cd2e3f4  < 0

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

patanahi · Answer

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

subhashghosh · Answer

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

Answer - C

amit2k9 · Answer

combining 1 and 2
either c or e can be negative. D and E are positive.

Hence C.

siddhans · Answer

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

subhashghosh · Answer

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 ?

siddhans · Answer

crystal clear

Kudos

Spidy001 · Answer

1. Not sufficient

we dont know anything about d and f. all we know is ce0

we dont know anything about c and e.

together

ce0 . so cedf<0 . Sufficient

Answer is C.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards