If a, b, c, d are non zero integers, is a/b + c/d greater than 2?

This is how I tried and got it correct.

Given : Is a/b + c/d greater than 2.

Stat 1: a > b we consider both +ve or -ve or one positive and one negative or some fractions like a = 1/2 and b = 1/3 , etc many cases possible.

From this statement we don't know anything about c and d.

Stat 2: c > d we consider both +ve or -ve or one positive and one negative or some fractions like d = 1/2 and c = 1/3 , etc many cases possible.

From this statement we don't know anything about a and b.

Stat 1 + Stat 2 : Even if we both statements we can plug some numbers and we'll get < 2 or > 2 values and incorrect.

Both statements has many considerations and can't get any unique result.

Hence E is the correct answer.

What would be the fastest way to reach the conclusion that E) is correct?
Just by plugging numbers? If yes, in general, which numbers should I choose?

PTD1995

I think the fastest way would be to understand how a > b affects a/b in different scenarios

For a>b or c>d ->
I) a/b > 1 -> when numerator is greater than denominator and both are positive
II) a/b <0 -> when a is positive and b is negative (still a>b)
III) 0<a/b<1 -> when both are negative (a=-4 b=-5)

Therefore above statement will be true only if we are given that a,b,c,d all are positive along with the 2 statements given.

Hope it helps

Hi Bunuel, this is a GMATPREP question from official practice exam 6

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Added the tag. Thank you!

If a, b, c, and d are nonzero integers, is ​a/b + ​c/d​ greater than 2 ?

(1) a > b
(2) d > c

Ans) So a,b,c,d are integers and none of them are 0. Let me take some nos.

(1) a>b
so let a=2 and b=1. No constraint on c,d so let c,d=1.
a/b + c/d = 2/1 + 1/1 = 3 > 2

let's keep a=2 and b=1. Let c=-1 and d=1.
a/b + c/d = 2/1 + (-1)/1 = 2-1 = 1 <2

St 1 is not sufficient

(2)d>c
so let d=2 and c=1. No constraint on a,b so let a,b=1.
a/b + c/d = 1/1 + 1/2 = 1.5 < 2

let's keep d=2 and c=1. Let a=8 and b=2.
a/b + c/d = 8/2 + 1/2 = 4.5 > 2

St 2 is not sufficient

Combining both statments, a>b and d>c
so let a=2,b=1,d=2,c=1
a/b + c/d = 2/1 + 1/2 = 2.5>2

let a=2,b=1,d=2,c=-1
a/b + c/d = 2/1 + (-1)/2 = 1.5<2

So the answer is E as both statements are not sufficient! <3