If ab 9, is a

Question

If ab > 9, is a < 1?
 
(1) b < 9
(2) 1 < b < 8

AbhishekGopal · Answer

Hi Bunuel,

Could you please tell me how you got B as the answer choice?

I got D as the answer.

Bunuel · Answer

________________________
Pleas post your solution.

NandishSS · Answer

Hi, (1)b < 9 Consider b=-8 and a=-2 & ab>9 is a < 1--Yes Now Consider b=4 and a=4 & ab>9 is a < 1--No So Statement 1 is not suff (2) 1 < b < 8 In this case consider extreme b=7.99 then to prove ab>9 a has to be greater than 1, hence gives ans no hence suff Hence B

HKD1710 · Answer

Hi AbhishekGopal , Here is how D is incorrect: ab > 9 ab/9 > 1 a(b/9) > 1 stmt-1: b < 9 if b < 9 then b/9 < 1 a*something-less-than-1 > 1 shows that a has to be greater than 1 i.e. a > 1. so you say this sentence is fine. is this sufficient? stmt-2: 1 < b < 8 again it means b/9 < 1 and reasoning is same a*something-less-than-1 > 1 shows that a has to be greater than 1. but wait we are getting the same answer from both the statements but are the ranges provided for b by both the statements SAME? No! in stmt-1 b can be -ve also. all right so if b is negative then a also has to be -ve for a(b/9) > 1 to be true. which means a < 1. so this proves that stmt-1 is not sufficient. I wanted to prove two things here: #1. If i followed the process of evaluating the statement very carefully then i would not have gotten into the trap initially in statement-1. but now that i was trapped: #2. Take help from the other statement. Great, this told me that there was sometthing fishy about statement-1. Trap - We generally forget to test the -ve values. Learning!

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If ab > 9, is a < 1? (1) b < 9 (2) 1 < b < 8

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