aspirant1 wrote:If -2<a<11 and 3<b<12 , then which of the following is NOT true?
a. 1<a+b<23
b. -14<a-b<8
c. -7<b-a<14
d. 1<b+a<23
e. -24<ab<152
OA
C
NOTE : If i go by plug in values...its going on for ever!; then i tried to solve the inequalities i.e -6,33,-24,132 what's the next step! I am trying to understand how to solve/approach this problem.
Thanks
Honestly, I'm not at all sure that knowing the rules for every possible iteration is faster than brute force; I'd have just jumped right into the choices.
It's a "which of the following" question, which means that the answer is slightly more likely to be near the bottom (based on historical GMAT stats), so, let's start with (e) and work our way up:
e) -24<ab<152
Only a can be negative, so let's pick the smallest possible a and the biggest possible b to get our smallest value for ab:
(-2)(12) = -24
To maximize ab, let's pick the two biggest values:
(11)(12) = 132
So, we get:
-24 < ab < 132
As papgust points out, if ab < 132 it's certainly less than 152, so (e) must be true: eliminate it.
d) 1<b+a<23
the minimum value of b+a uses the minimum value of each:
(-2) + (3) = 1
if we add the maximum value of both:
11 + 12 = 23
So, we know that:
1 < a + b < 23. As papgust also right points out, (A) and (D) are identical, so eliminate both of them.
c) -7 < b - a < 14
The minimum value of b - a occurs when we minimize b and maximize a:
3 - 11 = -8
We can already see that b-a could be less than or equal to -7, so (c) is NOT a must be true: choose C.
Now, it takes awhile to say all that out loud or to type it up, but if you know how to test each choice you should be able to answer this question by brute force in well under 2 minutes.
* * *
As an aside, if this question were properly worded, it would have read "which of the following is not
necessarily true" instead of just "which of the following is not true"; with it's current wording, there's no correct answer, since it's possible that b-a falls in the range in (c), it's just not a sure thing.
