Is ab 0 (2) b

Question

Is  ab < \frac{1}{ab} ?

(1)  ab > 0 
(2)  b < 0

arnimavarshney10 · Answer

Option A is wrong because ab can be a non-integer number.

chetan2u · Answer

In such questions, take all quantities on one side ab < \frac{1}{ab} ab - \frac{1}{ab}<0 \frac{(ab)^2-1}{ab}<0 Two cases a) ab>0, then (ab)^2-1<0 or -10 or ab<-1 or ab>1. Thus, range is ab<-1. (1) ab > 0 We cannot say whether ab>1. Insufficient (2) b < 0 Nothing much Insufficient Combined Nothing new Insufficient E

Gauravji21 · Answer

St 1: ab > 0
If both are negative. Let a=-2, b= -3, ab = 6, 1/ab = 1/6..
Answer to the question is : No

If a= 1/2, b = 1/3, ab = 1/6
1/ab = 6
Answer to the question is: Yes
St 1 is insufficient aa we are not getting unique answer.

St 2: b<0
Let a = 4, b= -2
ab = -8, 1/ab = -1/8 which is greater than -8.. answer to question is Yes.

Let a= -4, b=-2
ab = 8, 1/ab = 1/8 which is less than ab=8
Answer to the question is No

Hence St2 is insufficient.

Combining both statements,
ab>0 and b<0
=> both a and b are negative.

Let a= -2, b=-3
ab= 6, 1/ab = 1/6
Answer to question is No

Let a=-1/2 b =-1/3
ab= 1/6, 1/ab = 6
Answer to the question is Yes

We are not getting a unique answer. Hence, together also the statements are insufficient.

Hence, E is the answer.

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Gauravji21 · Answer

How you have arrived at Range as .. ab < -1 ?
If we combine the range of ab based on both the conditions, ab is ranging from - infinity to + infinity.

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Is ab < 1/ab? (1) ab > 0 (2) b < 0

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