If x y 0 and p q 0, then which one of the following expression

Question

If x > y > 0 and p > q > 0, then which one of the following expressions must be greater than 1?

(A)  \frac{x + p}{y + q}

(B)  \frac{x + q}{y + p}

(C)  \frac{x}{p}

(D)  \frac{xq}{yp}

(E)  \frac{yq}{xp}

Source:   Nova GMAT  
Difficulty Level:   550

niks18 · Answer

Given that x, y, p & q are all positive numbers. so we can write the two equations as 
x>y -------(1)
p>q -------(2).

Adding equation 1 & 2, we get
x+p>y+q. As all number are positive, their summation will be positive. Hence we can cross-multiply. So the expression becomes -

\frac{x + p}{y + q}  >1

Hence option  A

Alternatively, you can assume values of x, y, p & q and then substitute them in option to test

niks18 · Answer

Hi  JTR ,

Option E can be written as (y/x)*(q/p)

Now per the question y<x, hence (y/x)<1 and q<p so (q/p)<1
So if you multiply two numbers that are less than 1, the product will never be greater than 1

JTR · Answer

Thanks for the reply. I got it.

Sent from my Moto G Play using  GMAT Club Forum mobile app

pushpitkc · Answer

Assume values for x,y,p,q
Since x > y > 0 and p > q > 0. Let y=q=1 and x=p=2

Evaluating answer options

(1) \frac{x + p}{y + q}  =  \frac{2+2}{1+1}  = 2

(2) \frac{x + q}{y + p}  =  \frac{2+1}{1+2}  = 1

(3) \frac{x}{p}  = \frac{2}{2}  = 1

(4) \frac{xq}{yp}  =  \frac{2*1}{2*1}  = 1

(5) \frac{yq}{xp}  =  \frac{1*1}{2*2}  =  \frac{1}{4}

Only  Option A  has a value greater than 1. Hence, it is the correct answer

ydmuley · Answer

x > y > 0  and  p > q > 0

There two ways with which you can solve this question:

1. Test some values
2. Leverage and solve given information

I will solve by the second method considering it is easy and takes less time.

As -  x > y > 0

and  p > q > 0  we can write -

x > y 
 p> q

x + p > y + q

\frac{x + p}{y + q} > 1  - Dividing both the sides by  y+q 
 
So, without even checking the values we have go the equation which matches tho the first one.

Hence, the answer is A

TimeTraveller · Answer

Since  x>y  and  p>q , for an expression to be greater than  1 , the numerator must contain the larger numbers and the denominator the smaller numbers. Only option A fits this condition. So, Ans - A.

Alternatively,
 x>y 
 p>q 
adding, we get  x+p>y+q , hence their ratio must be greater than  1 .

dave13 · Answer

Hello what is the reason you are dividing by y+q and not by x + p thank you

niks18 · Answer

Hi  dave13

Let’s assume you divide by x+p, so can explain what you will get and how are you going to arrive at the options. Remember our end objective is to get the answer at shortest time

Posted from my mobile device

CAMANISHPARMAR · Answer

Since x,y,p and q are positive & x > y and p > q we have x + p > y + q, therefore option A is correct!

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If x > y > 0 and p > q > 0, then which one of the following expression

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