Is a/b <0
A) a^2/b^3>0
B) ab^4<0
OAC
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Is a/b <0
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Question stem, rephrased:rsarashi wrote:Is a/b <0
A) a^2/b^3>0
B) ab^4<0
Do a and b have DIFFERENT SIGNS?
Statement 1: a²/b³ > 0
This inequality is valid only if a and b are both NONZERO.
Since the square of a nonzero value must be POSITIVE, b²/a² > 0.
Since b²/a² > 0, both sides of the inequality can safely be multiplied both by b²/a²:
(a²/b³)(b²/a²) > 0(b²/a²)
1/b > 0.
The inequality in blue implies that b>0.
No information about a.
INSUFFICIENT.
Statement 2: ab� < 0
This inequality is valid only if a and b are both NONZERO.
Since a nonzero value raised to an even exponent must be POSITIVE, b� > 0.
Since b� > 0, both sides of the inequality can safely be divided both by b�:
(ab�)/b� < 0/b�
a < 0.
No information about b.
INSUFFICIENT.
Statements combined:
Statement 1 implies that b>0.
Statement 2 implies that a<0.
Thus, a and b have different signs.
SUFFICIENT.
The correct answer is C.
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Jay@ManhattanReview
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Hi rsarashri,rsarashi wrote:Is a/b <0
A) a^2/b^3>0
B) ab^4<0
OAC
We have to determine whether a/b is less than 0. A number less than 0 is a negative number.
Thus, for a/b to be negative, EITHER a has to be positive and b to be negative OR b has to be positive and a to be negative.
This means that if a/b < 0, a and b must be of opposite signs.
Statement 1: a^2/b^3 > 0
Irrespective of a being positive or negative, a^2 is positive, so we do not have any information on a. Since a^2/b^3 > 0 (Positive), it implies that b^3 must be positive, this means that b is positive.
If a and b both are positive, the answer is NO. However, a is negative and b is positive, the answer is Yes. No unique answer. Insufficient!
Statement 2: ab^4 < 0
Like we discussed in Statement 1, irrespective of b being positive or negative, b^4 is positive, so we do not have any information on b. Since ab^4 < 0 (Negative), it implies that a must be negative.
If a and b both are negative, the answer is NO. However, a is negative and b is positive, the answer is Yes. No unique answer. Insufficient!
Statement 1 & 2:
From Statement 1, we know that b is positive and from Statement 2, we know that a is negative, thus, a and b are of opposite signs. Sufficient.
The correct answer: C
Hope this helps!
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