If abcd is not equal to zero ,is abcd

Question

Hi Mike,

I tried solving the below DS question and solved as given below. Could you please explain where I am going wrong, as the correct answer to this question is C.

If abcd is not equal to zero ,is abcd <0 ?

1) a/b > c/d

2) b/a > d/c

Statement 1:

a/b > c/d --> Multiplying both sides by b --> a > cb/d --> Multiplying both sides by d --> ad > bc --> Multiplying both sides by bc --> abcd > (cd)^2

Since Square of any number is positive, hence (cd)^2 is > 0, Therefore abcd > 0. Statement 1 is sufficient.

Statement 2:

b/a > d/c --> Multiplying both sides by a --> b > ad/c --> Multiplying both sides by c --> bc > ad --> Multiplying both sides by ad --> abcd > (ad)^2

Since Square of any number is positive, hence (ad)^2 is > 0, Therefore abcd > 0. Statement 2 is sufficient.

Hence answer is D.

14101992 · Answer

Hey meetthedevil , Consider a case a=1, b=2, c=1 and d=4. As per statement 1, a/b>c/d ---> 1/2 > 1/4 ---> True As per statement 2, b/a>d/c ---> 2/1 > 4/1 ---> Not True Hence, we know there can be examples like the above one that will make the answer D wrong. In inequalities, do not multiply L.H.S denominator to R.H.S numerator or vice-versa without carefully looking at the conditions given in the questions. The negatives and positive values can play a huge role in inequality questions. ---------------------------------------- P.S. Don't forget to give kudos

mikemcgarry · Answer

Dear meetthedevil , I'm happy to respond. :-)

I would say this is a flawed question. :-)

You see, the statements are not compatible with each other. If the inequality a/b > c/d is true, then it is impossible for the inequality b/a > d/c to be true. The question would not be flawed if the inequalities were " greater than or equal to ," as opposed to simply " greater than ." The problem with your approach is as follows. Suppose we know ad > bc . Now, we want to multiply both sides of the inequality by bc. But, is bc positive or negative? If we multiply by a positive, then the direction of the inequality remains the same. If bc is negative, then we reverse the order of the inequality. Because we don't know whether bc is positive or negative, we don't know which way the inequality points after we multiply. To 14101992 , I would say: the point is not to pick numbers that make some statements true and some statements false. On GMAT DS, we have to assume that the statements themselves are true, and we have to pick numbers consistent with this. Unfortunately, in this flawed question, there is no way to pick one set of numbers that would satisfy both statements. Does all this make sense? Mike :-)

14101992 · Answer

mikemcgarry

Take a condition where a and b are positive and one of c and d is negative. So, we will have a/b>c/d and b/a>d/c.
For ex. a=1, b=1, c=-1 and d=1. So, 1/1>-1/1 (True) and 1/1>1/(-1) is also true.

This will give us that abcd<0 is possible only if statement 1 and 2 both are true.

Hope this makes sense! :p

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P.S. Don't forget to give Kudos