Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS
Solution:
We are given that a, b, c, and d, are positive numbers, and we need to determine:
Is a/b < c/d ?
Since we have all positive numbers, we can cross multiply our inequality. By cross multiplying we obtain:
Is ad < bc ?
Statement One Alone:
0 < (c-a)/(d-b)
From the information in statement one we know that EITHER both c – a and d – b are positive or both are negative.
Case 1:
If both c – a and d – b are positive, then c > a and d > b.
Case 2:
If both c – a and d – b are negative, then c < a and d < b.
Let’s analyze case 1 first. If c = 2, a = 1, d = 2 and b = 1, then ad = 2 and bc = 2, so ad is not less than bc. However, if c = 2, a = 1, d = 3 and b = 2, then ad = 3 and bc = 4, so ad is less than bc.
Without even analyzing case 2, we see that we do not have enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
[(ad)/(bc)]^2 < (ad)/(bc)We can see that the left hand side of the inequality is the square of the right hand side. Since a, b, c and d are positive numbers, (ad)/(bc) is a positive quantity. The only time a positive quantity squared is less than itself is when the quantity is less than 1. So we know that:
(ad)/(bc) < 1
Multiply both sides by bc, we have:
ad < bc
We see that ad is less than bc. Statement two alone is sufficient to answer the question.
Answer: B
