Inequalities

[sparkle6]

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

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


[spoiler]Answer: B, but I feel it is D[/spoiler]

[Ian Stewart]

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

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


[spoiler]Answer: B, but I feel it is D[/spoiler]

Statement 1 is not sufficient here. You might, just looking at the inequality in the question, quickly ask when 3x would be greater than 7y. Since 3 is smaller than 7, that won't be true unless x is quite a bit bigger than y. Using Statement 1, we know that x is more than 4 greater than y. If y is a small number (say y = 1 and x = 6), then the answer to the question is 'yes', but if we make x and y both large numbers (and somewhat close together), we can make the answer 'no'. For example, if x=200 and y=100, then Statement 1 is true, and the answer to the question is 'no'. So Statement 1 is not sufficient.

For Statement 2, we want to know if x > (7/3)y, or in decimal terms, if x > 2.666...*y. We can multiply by -1 on both sides of the inequality in Statement 2 (reversing the inequality because we multiplied by a negative) to get

5x > 14y
x > (14/5)y
x > 2.8y



Since y is positive, 2.8y is greater than 2.666...*y, so Statement 2 is sufficient.

[knight247]

1) x > y + 4
This can be re written as x-y>4
Lets assume x-y=5 as this satisfies the above inequality

x could be 10 and y could be 5 in which case 3x<7y

Lets assume x-y=20

x could be 22 and y could be 2 in which case 3x>7y

We get conflicting outcomes when we plug in different values. Hence this statement is INSUFFICIENT.

(2)-5x < -14y Multiplying by -1 on both sides 5x>14y or x>2.8y and multiplying both sides by 3 we have 3x>8.4y. Obviously 3x would be greater than 7y. SUFFICIENT.

Hence B