If a and b are two real numbers, is ab < 6? (1) |a-2| < 1 (2) |b+3|

Here is the OE

Solution:
Step 1: Analyse Question Stem
a and b are two real numbers.
We need to find if a* b < 6 or not.
We don’t know anything about a and b, so let’s analyse each statement and see if we can find if a* b < 6 or not.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: |a – 2| < 1

⟹ -1 < a – 2 < 1

⟹ -1 + 2 < a – 2 +2 < 1 + 2

⟹ 1 < a < 3

We know the range of a, however, don’t know anything about b. Hence, statement 1 is not sufficient and we can eliminate answer options A and D.

Statement 2: |b + 3| < 5

⟹ -5 < b + 3 < 5

⟹ -5 – 3 < b + 3 – 3 < 5 - 3

⟹ -8 < b < 2

We know the range of b, however, don’t know anything about a. Hence, statement 2 is also not sufficient and we can eliminate answer B.

Step 3: Analyse Statements by Combining
From statement 1: 1 < a < 3

From statement 2: -8 < b < 2

Multiplying the extreme values of a and b, we get

1 x – 8 = -8

1 x 2 = 2

3 x -8 = -24

3 x 2 = 6

Thus, the range of a*b will be:

-24 < a*b < 6

We can clearly see that the value of a*b is always less than 6. Hence the correct answer is Option C.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.