Is cdef

Question

Is cdef < 0?

(1)  cd^2e^3f^4 < 0 
(2)  c^2d^3e^4f^5 > 0

Bowtye · Answer

Ans is C

stmt 1 tells us that either c or e is negative, but does not tell us about d and f. insuff

stmt 2 tells us that either both d and f are positive or both d and f are negative, but does not tell us about c or e. insuff

combining the two, we know that there will always be an odd number of negatives (either 1 negative or 3 negatives), so cdef < 0 . sufficient

TheKingInTheNorth · Answer

Is cdef < 0?
for the equality to hold true either one is negative or 3 is negative out of cdef .

(1) cd2e3f4<0
(2) c2d3e4f5 >0

From Statement one :
c d^2 e^3 f^4 <0

d and f can be -ve or +ve ....
so d^2 and f^4 are both positive .

we are left with c and e .
either one of them must be negative but not both .

lets go the main question now
Is cdef < 0?

d and f positive ... and out of c and e one has to negative . hence the equality holds true .

now lets consider other scenario d and f negative .... and again out of c and e one has to negative but not both . Then also equality holds true .

Hence A sufficient.

From statement 2 :
c^2 d^3 e ^6 f^5 > 0

c and e will always be positive .
if d is negative then ... f has to negative for the equality to hold true.

now to the question : cdef <0
if we consider all possible combination of c,e,d and f from the above statement 2 ... then statement is not sufficient .

Hence Ans is A .

Mo2men · Answer

cdef<o if one letter has negative sign or 3 letters have negative sign.

Statement 1: We can deduce that either c or e is negative. d & f may be positive or negative . We can know because at end both will be positive due to even power (2 & 4)
if C = -, - - ++ , then, cdef <0 ......No
If C= -, - - + -, then, cdef <0.......Yes

Insuf

Statement 2: We can deduce that both d & f are negative. c & e may be positive or negative . We can know because at end both will be positive due to even power (2 & 4)
if C = -, - - +- , then, cdef <0 ......Yes
If C= +, +- +-, then, cdef <0.......No

Insuf

Combined:
We know from (2) that d &f are negative and either e or e is negative. So 3 letter with negative sign.

3 letter are negative and one is positive so cdef<0 is always yes

Answer: C

longfellow · Answer

Answer is C.

1 states c and e have opp signs but does not info about d and f. using b with a, we can confirm the signs.

padman777 · Answer

1st cond gives c and e have opposite signs. but nothing about d and f..
so a not suff
2nd cond gives that d and f hav same sign. no suff
combined two statements give.

c.e.= always neg(as they have opposite signs) and d.f=(always positive due to same signs)
thus product is negxpositive=neg
hence c is the answer

GMATinsight · Answer

Question : Is cdef < 0? i.e. We need to know the sign of product of all 4 variables c, d, e and f Statement 1 : cd^2e^3f^4 < 0 But with even powers the sign of result is always positive so d^2f^4 is always Positive i.e. ce^3 < 0 i.e. ce < 0 But the sign of df is still Unknown, hence, NOT SUFFICIENT Statement 2 : c^2d^3e^4f^5 > 0 i.e. d^3f^5 > 0 i.e. df > 0 But the sign of ce is still Unknown, hence, NOT SUFFICIENT Combining the two statements : i.e. ce < 0 and df > 0 i.e. cdef < 0 SUFFICIENT Answer: Option C

shailendra79s · Answer

For cdef < 0 → either one or three must be < 0
From Statement 1: cd²e³f4^4 < 0 → either c < 0 or e < 0; Insufficient
From Statement 2: c²d³e^4f^5 > 0 → d<0 & f < 0 or d>0 or f>0; Insufficient
Using both the statements, either c<0 or c<o, e<0 & f<0 → cdef<0.
Answer: C

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Asking whether the product cdef is less than zero is equivalent to asking whether one of the following cases holds: exactly three variables are positive (and the other one is not), or exactly one of the variables is positive. So the question can be rephrased this way: “Is there an odd number of positive variables among c, d, e, and f?”

Statement 1: INSUFFICIENT. Even powers of variables reveal nothing about the sign of the variable. Meanwhile, odd powers have the same sign. So this statement can be rephrased as ce < 0, which tells us that either c or e is negative; the other variable is positive. Exactly one of the variables is positive. However, we don’t know anything about the signs of d and f .

Statement 2: INSUFFICIENT. This statement can be rephrased as df > 0, which tells us that either both variables are positive, or neither variable is positive. However, we don’t know anything about the signs of c and e .

Statements 1 and 2 together: SUFFICIENT. Together, we know that either 1 or 3 of the variables are positive. Thus, we can answer the question with a definite “Yes.”

The correct answer is C.

bumpbot · Answer

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Is cdef < 0? (1) cd^2e^3f^4 < 0 (2) c^2d^3e^4f^5 > 0

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