If ab < 7, is b < 1?
1. a > 7
2. b < 7
My question is, may I add these inequalities in the way I did or was I just lucky with this approach, and "number picking" is the right approach for these questions to solve them in general? OA explanation suggests number picking for both statements. I feel this is much clearer. Thanks for your comments and help.
Statement 1: 7 < a This tells me "a" is a positive number bigger than 7.
If I add 7 < a to ab < 7, I will get:
ab + 7 < 7 + a deducting on both sides 7
ab < a Normally, I couldn't divide by "a", cause I wouldn't know "a's" sign. But here we are told it is positive and bigger than 7. So I divide by "a" know the inequality sign will not flip.
b < 1 This is what we wanted to prove. SUFFICIENT
Statement 2: This just tells me b is smaller than 7. It could be bigger or smaller than 1.
If I add b < 7 to ab < 7, I will get:
ab + b < 14 I could factor out "b"
b (a +1) < 14 However, this still doesn't help me in anyway to figure out if "b" is smaller than 1. If "a" was say 10 and "b" was 2, then we'd have 22 < 14 which is wrong. If "a" was say 10 and "b" was -1, then we'd have -22 < 14 which would be right. INSUFFICIENT
Most of the inequality questions, its better to use numbers and solve them, but it also depends on how difficult is the problem.
Here, I guess assumption of numbers is not required as this particular question is fairly simple.
Sometimes, we have 3-5 variables, and at that time, it is advisable to use the numbers to solve it faster.
One more important thing, use numbers to ELIMINATE
options and NOT TO SELECT
options. It is more of a negative strategy.
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