Is a^2*b 0?

Question

Is  a^2*b > 0 ?

(1)  |a| = b 
(2)  ab < 0

sumande · Answer

stmt 1: |a| = b => b >= 0. INSUFFICIENT as we cannot say if a^2*b >0, it can be equal to 0.

stmt 2: ab<0. INSUFFICIENT.

Either a<0 or b<0. If a<0 a^2*b >0 and if b<0, a^2*b <0.
combining stmt 1 and 2. b>0 and a<0.
Since, a^2 >0, a^2*b > 0. SUFFICIENT.

Therefore, answer: C
OA?

Caas · Answer

if abs(a)=b then b is always >0 Answer would be A if a and b were not 0 But we never know :-)

So (1) is not suff (2) is not suff neither Therefore C

sachinn · Answer

According to me, the answer is C.

1) |a| = b, which means that b should be positive.
2) says that one of a or b should be negative.

From 1 we know that "b" is positive hence "a" should be negative and we know that a^2*b < 0.

stingraybullray · Answer

1. Insufficient: because a can be either 0 or any other number (+ve or -ve) 
2. Insufficient: because ab < 0 gives us that one of them is -ve but we don't know which.

Combined: Sufficient: because from 1 & 2, b can't be -ve so a should be -ve and so a^2*b is > 0
It is C.

maratikus · Answer

1: insufficient a = b = 1 or a = b = 0 (b >=0)
2: insufficient a = 1, b = -1 or a = -1, b = 1 (a, b are not equal to 0)

1&2: since b >= 0 and b is not equal to zero -> b > 0, a is not equal to 0 -> a^2*b > 0 -> C

jallenmorris · Answer

With respect to 1 & 2...You're saying neither A nor B can = 0 because anything * 0 = 0 and we're told in 2) that ab <0 (which is not zero). Then with 1, b = |a| and the absolute value of A cannot be nagative. So we know from the 2 statements that B is not 0, and it is not negative. That makes a be negative and not zero (not zero from #2).

Thanks. That helps me out a bunch. +1 for you.

GMATBLACKBELT · Answer

1: a can be 0. Insuff.

2: b could be -. INsuff.

Together, suff b/c a is not 0.

rao · Answer

Q. Is a^2*b > 0?
1) |a|=b
2) ab<0

From 1)

b must be possitive. a's value doesn't matter because a^2 is anyways going to be positive. So far 1) is suff but ... we dont know if a is a non zero or not. hence 1) is not suff.

From 2)

either a or b has to be negative. And neither a or b is zero.
if a is -ve and b is +ve then a^2*b > 0
if a is +ve and b is -ve then a^2*b < 0

therefore not sufficient

TOGETHER:

a and b not equal to zero.
b is +ve
a is -ve

Sufficient.

ANSWER: C

goalsnr · Answer

Allen, please help me understand this :
 a^2*b = (a^2)* b ? 
or
 a^2*b = a^(2* b) ?

x97agarwal · Answer

1. If a^(2b) then answer is C

2. If (a^2)b then answer is E

Please tell us which is the case - 1 or 2

jallenmorris · Answer

I've decided that when I get a DS like this, I'm going to consider a few numbers. I'm going to start with the following set:

{-2, -1, -0.5, 0, 0.5, 1, 2}

That should give an good indication as to how the inequality acts with both + and - numbers.

goalsnr · Answer

C 1. a>0,b>0 yes a<0,b> 0 yes a= b =0 no insuff 2.a>0 b<0 no a<0 b>0 yes insuff from 1 and 2 a< 0 b >0 Suff C

hi0parag · Answer

IMO for both cases viz. a^(2b) or (a^2)b the answer is C. the solution: a != 0 and b != 0 (a&b not equal to 0) from ab<0 & b>0 from |a|=b ---1 => a<0 => a^(2b)>0 ---2 & a^2>0 ---3 hence for the case 1. a^(2b) >0 from ---2 2. (a^2)b > 0 from ---1 & 3 Please correct me if i made a mistake.

ryougazilla · Answer

assuming we are working with a^(2b) > 0, and the following assumptions

B is not negative, B = |A|
A is negative since AB< 0

use -2, and -.5 for A. and 2,.5 for B respectively.

A = -2: (-2)^(2*2) = 16
A = -.5: (-.5)^(2*.5) = -.5

answers on both side of 0.....get E

mbawaters · Answer

To prove, we need:
a) find out if a or b or both are zero?
b) Whether b is +ve or -ve.

1) b = |a| means b is non-negative i.e. either +ve or 0 - Insufficient.

2) ab<0 means a & b are not 0. but either a or b is -ve

Combining: we can say that b is +ve and a is -ve.
C.

Celestial09 · Answer

Hello Experts!
Kindly share your views and methods on this question.
Thanks
Celestial

EgmatQuantExpert · Answer

Hi Celestial09 , The question is a classic example where students miss out on the concept that |x| => 0 and not |x| > 0 . Let's analyze the question statement first to see what exactly we need to find. Analyze the given information in the question The question asks us if a^2*b > 0 . We know that a^2 => 0 . To answer the question, we need to know for sure if a and b are not equal to 0 along with the sign of b . Please note that sign of a does not make any difference as a^2 will never be negative. With this understanding, let's evaluate the statements now. Analyze statement-I independently St-I tells us that |a| = b . Since |a| => 0 , it means that b => 0 . Using this information, |a| = b = 0 or |a| = b > 0 . Since the statement does not tell us for sure if a and b are not equal to 0 we can't say if a^2 * b > 0 . Analyze statement-II independently St-II tells us that ab < 0 i.e. a , b have the opposite signs. So, i. If a > 0 , then b < 0 . This would mean a^2 * b < 0 ii. If a < 0 , then b > 0 . This would mean that a^2 * b > 0 as a^2 is positive irrespective of the sign of a . Thus, the statement does not tell us for sure if a^2 * b > 0 . However, the statement tells us about an important nature of both a and b . Since product of a and b is not equal to 0, we can say that neither of a or b is equal to zero. This nature of a and b would be helpful when we combine the analysis from st-I & II Combine analysis from st-I & II St-I tells us that |a| = b => 0 and st-II tells us that b < 0 or b > 0 and a not equal to 0. Combining both the statements, we can say that |a| = b > 0 . Since none of a and b is equal to 0 and b > 0 , we can safely say that a^2 > 0 and b > 0 i.e. a^2* b > 0 . Hence combining both the statements is sufficient to answer our question. Hope its clear! Regards Harsh

Bunuel · Answer

Is a^2*b > 0?

Since a^2 is a non-negative value (0 or positive), then for a^2*b to be positive   a  must not be 0 and  b  must be positive .

(1) |a| = b. Absolute value of a number (|a|) is also a non-negative value (0 or positive), thus this statement implies that  b\geq{0} . Since both a and b can be 0, then this statement is NOT sufficient.

(2) ab < 0. This statement rules out any of the unknowns being 0 but b can be positive as well as negative. Not sufficient.

(1)+(2) Since from (2)  b
eq{0}  then from (1)  b>0 . So, we have that neither of a and b is 0 and b is positive, therefore a^2*b > 0. Sufficient.

Answer: C.

Hope it's clear.

Bunuel · Answer

Similar questions to practice: is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.html if-r-s-and-t-are-nonzero-integers-is-r-5-s-3-t-4-negative-165618.html is-x-2-y-5-z-98341.html Hope it helps.

Is a^2*b > 0?

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Is a^2*b > 0?

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