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tricky number properties question

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tricky number properties question

by Brent@GMATPrepNow » Wed May 03, 2017 5:36 am
If a, b and c are integers, and ac/b < 0, then which of the following must be false?

A) ab + ac + bc < 0
B) ca + b > 0
C) bc - a < 0
D) (b-c)(c-a) > 0
E) ca - abc < 0

Answer: E

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by DavidG@VeritasPrep » Wed May 03, 2017 8:45 am
Brent@GMATPrepNow wrote:If a, b and c are integers, and ac/b < 0, then which of the following must be false?

A) ab + ac + bc < 0
B) ca + b > 0
C) bc - a < 0
D) (b-c)(c-a) > 0
E) ca - abc < 0

Answer: E

Source: www.gmatprepnow.com
Difficulty level: 650
If ac/b < 0, there are only two possibilities.

Case 1: ac = negative and b = positive

Case 2: ac = positive and b = negative.

With these types of problems, I like to start with E and work up.

E. Case 1: ca is negative, and b is positive. abc will have to be negative, as we're multiplying a negative and a positive together. Note also that abc will be more negative than ca, as b is a positive integer. So we start with ca, a negative number, and subtract abc, which is more negative. Subtracting a negative is the equivalent of adding a positive, so ca - abc will be positive. In case 1 the statement is not true.

Case 2: ca is positive. and b is negative. abc will still be negative. Now we start with a positive, ca, and subtract a negative, abc, which means we're adding a positive to our original positive, so again, ca - abc will be positive. In case 2, the statement is not true. Therefore E must be false, and is our answer.
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