TBT wrote:
If a*b is not equal to 0, is \((\frac{a}{b})> (\frac{b}{a}) \) ?
(1) a=b+10
(2) b > 0
Step 1: Simplify the premise
\((\frac{a}{b})> (\frac{b}{a}) \)
\((\frac{a}{b})- (\frac{b}{a}) > 0 \)
\( \frac{a^2 - b^2 }{ ab } > 0 \)
Step 2: Analyze conditions which can result the inequality
Case 1:
ab > 0If ab > 0, \(a^2 - b^2\) should be positive
Therefore \(a^2 > b^2\)
Taking square on both sides
|a| > |b|
Case 2:
ab < 0If ab > 0, \(a^2 - b^2\) should be negative
Therefore \(a^2 < b^2\)
Taking square on both sides
|a| < |b|
In a nutshell we need to determine two things
1) Whether ab is positive
2) The distance of a and b with respect to 0
Statement 1(1) a=b+10 We know that "a" lies to the right of "b" and is 10 units away. However, we don't know whether both "a" and "b" lie on the same side of 0 or on opposite sides.
Hence we have no way to determine point 1 - "Whether ab is positive".
Hence this statement is not sufficient. We can eliminate A and D.
P.S. - We don't even have to check for point 2.
Statement 2(2) b > 0 This statement tells us that "b" is positive. However, we don't know the nature of "a".
Hence just as in Statement 1, the Statement is not sufficient.
Eliminate B.
CombinedFrom statement 2, we know that "b" is positive.
Statement 1 tells us that "a" lies to the right of "b" , hence is a positive as well.
Let's look at both points now
1) Whether ab is positive - Yes !
2) The distance of a and b with respect to 0 - a lies farther from 0 than b lies. Hence |a| > |b|
Hence case 1 satisfies.
The statements combined are sufficient.
Option C