Is b

Question

Is b < 0?

(1) b^3 b

parasma · Answer

Is b < 0? (1) b^3 b Statement-1 b^3 b b= 2, b^2= 4 so condition satisfied but b is not less than 0. b= -2, b^2=4 so condition satisfied & b is less than 0. Statement 2 is insufficient. Combine (1) b^3 b b= -2, b^3b- Satisfied---- OK b= 2, b^3b- Satisfied---- Not Sufficient b= 0.10, b^3b- Not Satisfied---- Not Sufficient So b<0 Sufficient. Answer is C.

sj296 · Answer

Statement 1

b^3 b^3 - b < 0
=> b (b-1)(b+1) < 0

=> b = (-infinity to -1) and (0, 1)

Here we are getting b < 0 as well as b > 0

Statement 1 is insufficient

Statement 2

b^2 > b

=> b^2 - b > 0
=> b(b-1) > 0

=> b = (-infinity to 0) & (1, infinity)

Here again we are getting b <0 and b> 1

Statement 2 is also insufficient

Statement 1 + Satement 2

=> Statement 1 => b = (-infinity to -1) and (0, 1)
=> Statement 2 => b = (-infinity to 0) & (1, infinity)

The intersection of the two will be b = (-infinity to -1). From this we can definitely say that b < 0

Sufficient

Hence, OA should be C

TestPrepUnlimited · Answer

For these types of questions, we can draw four regions on the number line and test which regions will work for each inequality. The four possible regions are b < -1, -1 1. Statement 1: The regions that work are b < -1 and 0 1. Insufficient. Combined: Combined we only have b < - 1 for both. Sufficient. Ans: C

danbrown9445 · Answer

Statement 1 is possible when b is a positive fraction or negative integer
Statement 2 is possible when b is a negative fraction or negative integer or a positive integer

Intersection of 1 & 2 is b = negative integer.

prakashb2497 · Answer

In S2, can we divide both sides by b to get => b>1. If b is greater than 1 then b is not less than 0. Hence sufficient. What is wrong with my approach here?

@bunnel  chetan2u   KarishmaB

Bunuel · Answer

No.

If b is positive, then after dividing by b you get b > 1 (keep the sign when dividing an inequality by a positive number) but if b is negative, then after dividing by b you get b < 1 (flip the sign when dividing an inequality by a negative number)

Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its sign.

chetan2u · Answer

Say b=-2….(-2)^2>-2
If you divide by b, that is -2, it becomes -2>1. Is it so?

Don’t divide unless you know whether the variable is positive or negative.

Gijmaja · Answer

A: x is either 0-1 or <-1.
B: x is either <-1 or >1

Answer C.

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Is b < 0? (1) b^3 < b (2) b^2 > b

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