If a

Question

If a<0 and b<0 , is \frac{(a-2p)}{(b-2p)} > \frac{a}{b} ? (1) p>0 (2) a

WoundedTiger · Answer

Took time. We need to find a better way We need to find \frac{(a-2p)}{(b-2p)} > a/b Notice here that the question is asking if we subtract same term from Numerator and Denominator \frac{a}{b} then is the resulting fraction greater than original fraction a/b you will have 4 case here a>b, p>0 a>b, p<0 a0 Clearly St 1 is not sufficient because for p>0, we can have 2 possible cases a>b and b>a and we get different result Consider a=-3, b=-4 (a>b) and p=1 \frac{(-3-2)}{(-4-2)} =-5/-6 > -3/-4 Consider a=-4,b=-3 (b>a) and p=1 \frac{(-4-2)}{(-3-2)} or 6/5 < 4/3 Not sufficient Similarly st 2 is not sufficient with above reasoning as p >0 or p<0 Combining 2 statements we get a0 b=-3,a=-4 and p=1 then Original fraction = 4/3 New fraction = \frac{(-4-2)}{(-3-2)} or 6/5 <4/3 Consider another value of p=1/2 \frac{(-4-1)}{(-3-1)} = or 5/4<4/3 Ans is C

mridupawandas · Answer

any short cut to solve this question...because it took 3 minutes for me to solve it

jwang27 · Answer

Couldn't figure out a way to do this without plugging in numbers. Anyone understand this from a theory perspective?

viktorija · Answer

I did it without plugging in.
I cross multiplied the inequality and got:
b(a-2p)>a(b-2p) <-----both a AND b are negative leaving the inequality sign unchanged
ab-2bp > ab - 2ap <----subtract ab from both sides
-2bp > -2ap <----- divide by (-2)
So, is bp<ap?

(1) p>0, this does not give enough information to answer the question because we don't know anything about b and a.

(2) a<b, this does not give us enough info, because it matters if p is positive or negative.

(1)+(2) Sufficient, the answer to the question (is bp<ap?) is no.

jwang27 · Answer

Interesting approach. I thought about cross multiplying but didn't because without knowing p, we wouldn't know if the value (a-2p) or (b-2p) is positive or negative. It is also possible that one is positive and one is negative.

viktorija · Answer

When I cross multiplied, I basically needed to know if b is negative (which I knew because it's given) and if (b-2p) is negative. That's important to know because at first we multiply by one denominator which is b and then we multiply by the second which is (b-2p). So, I tried both and I got:
is bp>ap, when (b-2p) is negative
OR is bp<ap, when (b-2p) is positive. 
The question stays the same though, because we still need to find which is bigger.

That was the logic behind, but I'm not sure if it's correct.

If a<0 and b<0 , is (a-2p)/(b-2p) > a/b ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards