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by karthikpandian19 » Wed Jul 04, 2012 9:35 pm
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)
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by eagleeye » Wed Jul 04, 2012 10:34 pm
karthikpandian19 wrote: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 :)
Last edited by eagleeye on Wed Jul 04, 2012 11:13 pm, edited 1 time in total.
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by karthikpandian19 » Wed Jul 04, 2012 11:09 pm
A quick look at the options rules out A,B, and D......i hope ur post shld contain E, B, D???

eagleeye wrote:
karthikpandian19 wrote: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 :)
Regards,
Karthik
The source of the questions that i post from JUNE 2013 is from KNEWTON

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by eagleeye » Wed Jul 04, 2012 11:16 pm
karthikpandian19 wrote: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.
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by GMATGuruNY » Thu Jul 05, 2012 3:14 am
I posted an explanation here:

https://www.beatthegmat.com/must-be-negative-t95116.html
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

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