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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 < 14which is wrong. If "a" was say 10 and "b" was -1, then we'd have -22 < 14 which would be right. INSUFFICIENT

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 < 14which 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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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 < 14which is wrong. If "a" was say 10 and "b" was -1, then we'd have -22 < 14 which would be right. INSUFFICIENT

Your approach is correct.

ADDING/SUBTRACTING INEQUALITIES:

You can only add inequalities when their signs are in the same direction:

If \(a>b\) and \(c>d\) (signs in same direction: \(>\) and \(>\)) --> \(a+c>b+d\). Example: \(3<4\) and \(2<5\) --> \(3+2<4+5\).

You can only apply subtraction when their signs are in the opposite directions:

If \(a>b\) and \(c<d\) (signs in opposite direction: \(>\) and \(<\)) --> \(a-c>b-d\) (take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) --> \(3-5<4-1\).

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.
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