3x

[gmat740]

If x and y are positive, is 3x>7y?

1. x> y+4
2. -5x< -14y

[raghavsarathy]

IMO - B

Statement 1

Take x= 11 , y=6
x> y+4

However it does not satisfy x> (7/3)y
Take x= 1000 , y=1
x> y+4 And the condition x> (7/3)y is satisfied

Hence statement 1 is not sufficient

Statement 2

-5x < -14y

Mutiplying both sides by -1 , the sign of the eqn also changes
we get 5x > 14y
x> (14/5)y
Hence x> (7/3)y , the main condition is satisfied.

Hence B

[gmat740]

Yes I did the same thing and my answer was B but the OA is C

I do doubt the OA. I would wait for some more explanations.

[mehravikas]

Answer should be - B

Statement 1 -

x = 10, y = 4

10 > 5 + 4 but 10 < 2.33 * 5

x = 6, y = 1

6 > 1 + 4 and 6 > 2.33 * 1

Insufficient

Statement 2 -

-5x < - 14y = multiply by -1
5x > 14y -> x > 14/5 * y

x > 2.8y therefore x will always be greater than 2.33 y

[gmat740]

Thanks that helps.

This means the OA must have ben wrong.

[tom4lax]

I also got B.

[gmat740]

Thanks Guys.
I feel that the OA was wrong.It has to be B

[Ian Stewart]

Looking only at S2, we have:

-5x < -14y
5x > 14y
3x > (3/5)*14y
3x > 8.4y

So we know that 3x > 8.4y, and we want to know if 3x > 7y. If y is positive, the answer is certainly 'yes', because then 8.4y > 7y. However, if y is negative, 8.4y is less than 7y. We might have:

y = -1
x = -2.5

Then 3x = -7.5 is certainly greater than 8.4y = -8.4, but 3x is not greater than 7y = -7. Statement 2 is not sufficient.

[raghavsarathy]

Looking only at S2, we have:

-5x < -14y
5x > 14y
3x > (3/5)*14y
3x > 8.4y

So we know that 3x > 8.4y, and we want to know if 3x > 7y. If y is positive, the answer is certainly 'yes', because then 8.4y > 7y. However, if y is negative, 8.4y is less than 7y. We might have:

y = -1
x = -2.5

Then 3x = -7.5 is certainly greater than 8.4y = -8.4, but 3x is not greater than 7y = -7. Statement 2 is not sufficient.

Hi Ian. The main statement says that x and y are positive. In such a situation the ans would be B right ?

[Ian Stewart]

Hi Ian. The main statement says that x and y are positive. In such a situation the ans would be B right ?

Good point! When I was writing up my answer, I think I was remembering a different question that didn't have that restriction. Yes, since:

8.4 > 7

then if y is positive, we can multiply on both sides by y without reversing the inequality to get:

8.4y > 7y

so if x > 8.4y, then x certainly must be greater than 7y. So to clarify my post above, if x and y are positive, S2 is certainly sufficient. If you remove that condition from the question, then S2 is not sufficient.