PS - power

[karthikpandian19]

If a, b, c, and d are numbers such that abd > 0 and acd < 0, which of the following must be negative?


(A) abcd

(B) ab(c^2)d

(C) (a^2)bc(d^2)

(D) (a^3)b(c^2)(d^3)

(E) (a^4)(b^2)(c^2)(d^4)

[eagleeye]

If a, b, c, and d are numbers such that abd > 0 and acd < 0, which of the following must be negative?

We are given:
abd>0 and acd<0
=> (ad)*b>0, and (ad)*c<0.
We can infer one thing easily:
b and c have opposite signs. So bc<0

With that in mind, we need to look for the option that has (b^(odd power)*c^(odd power)).
A quick look at the options rules out B, D, and E. So right answer is between A and C.
We can see that C is the right answer because C is a^2*(bc)*d^2. We have b^1 and c^1 and a^2 and d^2 are always positive in this case.

We could also have ruled out A and have been left with C if we observed that we don't know the sign of ad. It can either be positive or negative. Hence, we don't know if abcd is always negative. And we'd have figured out the answer by elimination.

Let me know if this helps

[karthikpandian19]

A quick look at the options rules out A,B, and D......i hope ur post shld contain E, B, D???

If a, b, c, and d are numbers such that abd > 0 and acd < 0, which of the following must be negative?

We are given:
abd>0 and acd<0
=> (ad)*b>0, and (ad)*c<0.
We can infer one thing easily:
b and c have opposite signs. So bc<0

With that in mind, we need to look for the option that has (b^(odd power)*c^(odd power)).
A quick look at the options rules out A,B, and D. So right answer is between A and C.
We can see that C is the right answer because C is a^2*(bc)*d^2. We have b^1 and c^1 and a^2 and d^2 are always positive in this case.

We could also have ruled out A and have been left with C if we observed that we don't know the sign of ad. It can either be positive or negative. Hence, we don't know if abcd is always negative. And we'd have figured out the answer by elimination.

Let me know if this helps

[eagleeye]

A quick look at the options rules out A,B, and D......i hope ur post shld contain E, B, D???

Yup. It was a typo. Corrected.

[GMATGuruNY]

I posted an explanation here:

https://www.beatthegmat.com/must-be-negative-t95116.html