If a

Question

If a < 0 and b < c, which of the following must be true? (A) ab < c (B) ac > b (C) ab > 0 (D) ac < 0 (E) ab > ac

ScottTargetTestPrep · Accepted Answer

Since a is negative and b < c, when we multiply b < c by a, we flip the sign and we have:

ab > ac

Answer: E

ArunSharma12 · Answer

Given: a < 0 b < c case A : a < 0, b > 0, c > 0 case B: a < 0, b < 0, c > 0 case C: a < 0, b < 0 , c < 0 ab - c < 0; not valid for case C ac - b > 0; not valid for case A ab > 0; not valid for case A ac < 0; not valid for case C a*(b-c)> 0 ; valid for all three cases Ans: E

TestPrepUnlimited · Answer

We can think of "a < 0" as "  a  is negative ".

If we want to combine these inequalities there is not much to do, since we only have one useful inequality  b < c .

At best we can multiply both sides of  b < c  by  a  we get  ab > ac  because  a  is negative.

Ans: E

Farina · Answer

Hi can you please explain it further? I tried to plug in different values but got mixed answers plus it was too time consuming

ScottTargetTestPrep · Answer

Plugging numbers is terribly inefficient for this problem because you would have to plug in multiple sets of numbers to test every possibility. It is much easier to use a basic rule of inequalities, and then you won’t need to plug in any numbers at all. One basic rule about inequalities is that whenever you multiply each side of an inequality by a negative number, you need to change the direction of the inequality. For instance, if we have an inequality like 2 < 5 and if we multiply each side by -3, we get -6 on the left hand side and -15 on the right hand side. Notice that -6 is greater than -15, so we need to change the direction of the original inequality and write -6 > -15. Now, instead of the numbers above, let's think in terms of a, b, and c. We have the inequality b < c and we multiply each side by the negative number a. According to the above, we need to change the direction of the inequality and we will obtain ab > ac.

Kinshook · Answer

Asked: If a < 0 and b < c, which of the following must be true?

Since a<0; multiplying by a will reverse the sign in b<c
ab>ac

IMO E

Farina · Answer

Excellent Reply. Thank you very much for your help

ScottTargetTestPrep · Answer

Sure thing!

Yes2GMAT · Answer

ScottTargetTestPrep  Could u explain why option A is incorrect if we were to plug-in numbers? Thanks

ScottTargetTestPrep · Answer

The question is asking for the inequality which MUST be true, so it's enough if we just come up with one example where a, b, and c satisfy the requirements given in the question stem, but ab < c is not satisfied. Just choose both b and c to be negative; for instance, choose a = -1, b = -5, and c = -2. Notice that a < 0 and b < c are both satisfied. However, ab = 5 is not less than c = -2, which means ab < c is not true. This is how you can eliminate answer choice A.

bumpbot · Answer

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If a < 0 and b < c, which of the following must be true?

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