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71% (00:38) correct
28% (00:31) wrong based on 52 sessions
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\(0 < a < b < c < d\)
Quantity A
Quantity B
\(\frac{c}{d}\)
\(\frac{b}{a}\)
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
Re: 0 < a < b < c < d
[#permalink]
25 Sep 2018, 08:42
2
Carcass wrote:
\(0 < a < b < c < d\)
Quantity A
Quantity B
\(\frac{c}{d}\)
\(\frac{b}{a}\)
A) Quantity A is greater. B) Quantity B is greater. C) The two quantities are equal. D) The relationship cannot be determined from the information given.
We can solve this question using matching operations
Given: Quantity A: c/d Quantity B: b/a
Since d is POSITIVE, we can safely multiply both quantities by d to get: Quantity A: c Quantity B: bd/a
Since a is POSITIVE, we can safely multiply both quantities by a to get: Quantity A: ac Quantity B: bd
Since b > a, we can say: b = some number BIGGER than a Since d > c, we can say: d = some number BIGGER than c
So, we can rewrite Quantity B as follows: Quantity A: ac Quantity B: (some number BIGGER than a)(some number BIGGER than c)
If we compare the products in parts, we can see that Quantity B must be greater