If ab^3c^4 0, is a^3bc^5 0?

Question

If  ab^3c^4 > 0 , is  a^3bc^5 > 0 ?

(1) b > 0
(2) c > 0

Kudos for a correct  solution .

GMATinsight · Answer

Given:  ab^3c^4 > 0

i.e. a*b must be Positive  
i.e. a and b have same sign

Question  : is  a^3bc^5 > 0

But  a^3b  will always be positive as a and b have same sign

i.e. We only need to find the sign of c to answer the question

Statement 1: b > 0

Sign of c is unknown

Hence,   NOT SUFFICIENT

Statement 2: c > 0

i.e. c is positive therefore  a^3bc^5 > 0  is True

Hence,   SUFFICIENT

Answer: option  B

balamoon · Answer

If ab^3c^4>0, is a^3bc^5>0?

(1) b > 0
(2) c > 0

Explanation -

Stmt 1 - If b is +ve, a is +ve and we do not know about c +ve or -ve. Not Sufficient

Stmt 2 - If c is +ve, both a and b must be +ve or -ve to meet the condition. Sufficient

Ans B
Thanks

Please give me Kudos

ShristiK · Answer

(i) ab^3c^4>0
(ii) a^3bc^5>0?

Here, powers of a and b are odd in both inequalities so, their sign won't change to negative. 
(Notice c^4 will always be positive so multiplication of odd powers of a with odd powers of b will also be always positive to satisfy  (i) ).

However, the power of c changes in both inequalities from even in  (i)  to odd in  (ii) .
Hence, if c is positive  (ii)  will be positive, and if c is negative  (ii)  will be negative.
 
(1) b > 0
 This gives us no information on the sign of c, and consequently, we cannot determine if  (ii)  is positive or negative.  Not Sufficient

(2) c > 0
 This tells us c is positive. Hence  (ii)  is positive.  Sufficient

Press  Kudos  if you like it!

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

Odd exponents do not “hide the sign” of the base. In other words, a and a^3 have the same sign, as do b and b^3, regardless of the signs of a and b. In comparing ab^3c^4 > 0 (the constraint) to a^3bc^5 (the question), the only unknown real difference is between c^4 and c^5. We know that c^4 must be positive (even exponent), so if we want c^5 to be positive, then c needs to be positive also. Our rephrased question is thus “Is c > 0?”
(1) INSUFFICIENT: No information about the sign of c.
(2) SUFFICIENT: Answers the rephrased question directly.
The correct answer is B.

(1) INSUFFICIENT: No information about the sign of c.

(2) SUFFICIENT: Answers the rephrased question directly.

The correct answer is B.

deepthit · Answer

a and b are odd powers in both the expressions. only unknown sign is of c

Statement 2 states C >0 => final value is positive.

HEnce B

anairamitch1804 · Answer

Odd exponents do not “hide the sign” of the base. In other words, a and a^3 have the same sign, as do b and b^3, regardless of the signs of a and b. In comparing ab^3c^4 > 0 (the constraint) to a^3bc^5 (the question), the only unknown real difference is between c^4 and c^5. We know that c^4 must be positive (even exponent), so if we want c^5 to be positive, then c needs to be positive also. Our rephrased question is thus “Is c > 0?”
(1) INSUFFICIENT: No information about the sign of c.
(2) SUFFICIENT: Answers the rephrased question directly.
The correct answer is B.

KSBGC · Answer

If  ab^3c^4>0 is a^3bc^5>0?

1.b>0
2.c>0

kunalcvrce · Answer

from given statement either a>0,b>0 or a<0,b<0 From 1: we cant say anything. From 2: since a and b have same sign Then a*b>0 . and c>0 Therefore a^3bc^5>0 Sufficient B.

Bunuel · Answer

___________________________
Merging topics.

push12345 · Answer

ab^3c^4>0
Simply means a and b have same sign

So for a^3bc^5>0

Since a and b have same sign so only thing we need to know whether c>0 or not

Choice B states this

Posted from my mobile device

rohith2reddy · Answer

Hi,

Given ab^3c^4 > 0. We already know that any integer multiplied to even power is always positive.

Hence from above we already now that b^2 and c^4 are always positive. Hence this inequation input can be simplified to ab>0. This is the given input.
 
Now the question " is a^3bc^5 > 0"?

Again applying above discussed funda, the question can be simplified to is abc>0?

So the question is if ab>0, is abc >o?

From options, it is clear that "option 1 : b >0 " is not sufficient whereas "option 2 : c>0" alone is sufficient to answer.

Hence option "B"

rajmishra88 · Answer

If ab^3c^4 > 0, is a^3bc^5 > 0?

Now coming to first equation: as c^4 term is present, being exponent an even power it has no effect on overall equation.
Hence coming on ab, as ab>0 then definitely a & b are of same sign either both + or both -.

Hence deciding factor is c for the next equation as it has odd exponent, only if its is> 0 then only the whole equation is > 0.

So Statement 2 is true.

Ans. (B)

nide · Answer

ab^3c^4 > 0 gives, ab^3 > 0 i.e., we have ab>0 i. a>0 b>0 ii. a<0 b<0 to find if a^3bc^5 > 0 we already know that ab > 0 which implies a^3b > 0 so if c>0 the a^3bc^5 > 0 is true else false (1) given b>0 ---> insufficient (2) given c>0 ----> sufficient option is B ---------------------------------------- Please leave a kudos:)

MHIKER · Answer

As  ab^3c^4 > 0  so either a & b both are positive or both are negative.

(1) we don't know about a and c.  a^3bc^5  could be  a^3bc^5 > 0  or  a^3bc^5 < 0  with respect to the value of a and c.

(2) As c > 0 and  ab^3c^4 > 0  so a must positive. Then  a^3bc^5 > 0 . Sufficient.

The answer is B.

Malar95 · Answer

Broke it down.

If ab^3c^4 > 0, is a^3bc^5 > 0?

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