-
amina.shaikh309
- Senior | Next Rank: 100 Posts
- Posts: 31
- Joined: Sat Apr 23, 2016 9:06 pm
This is a tough one
let's break it down...Let's rephrase the question first.
Think about cross-multiplying the inequality. a,b,c,d are all positive numbers, so we can do it.
"Is a/b<c/d?" can be expressed also as "Is ad<bc?"
We will see that this expression can be used to give significant examples to support the answer.
Let's consider STATEMENT 1 ALONE.
If (c-a)/(d-b)>0, it means that either both the numerator and the denominator are positive, either they are both negative. But this does not help to answer the question.
Let's take the first case. If they are both positive, then a<c and d>b.
That does not allow us to answer the question! Think about two examples.
If a=2 and c=10, and d=30 and b=2: is 2*30<10*2? No. (60>20)
If a=2 and c=10, and d=5 and b=4: is 2*5<10*4? Yes. (10<40)
Thus STATEMENT 1 ALONE IS NOT SUFFICIENT.
Let's consider STATEMENT 2. Think about (ad/bc) as one single letter, namely x.
The numbers for which x^2 is less than x are the numbers between 0 and 1. Think about 1/2, if it is squared it becomes 1/4, which is less than 1/2.
This means that (ad/bc)<1, and multiplying both sides for bc we get ad<bc, which allows us to answer YES to the initial question. Thus STATEMENT 2 ALONE IS SUFFICIENT.
The answer is B.
