magical cook wrote:if x and y are positive, 3x>7y?
1) x>y+4
2) -5x<-14y
Let's start by simplifying the question (a great first step in all DS questions):
Is x > (7/3)y?
So, we need information about the relationship between x and y.
(1) x > y + 4
Like many DS yes/no questions, the best way to tackle this is to pick numbers and try to get both a yes and a no answer. Remember, we can only pick numbers that go along with statement (1).
x=10, y=1 (since 10 > 1 + 4). Is 10 > (7/3)1? Yes.
x=10, y=5 (since 10 > 5 + 4). Is 10 > (7/3)5 = 35/3? No.
We can get a yes and a no: insufficient.
(2) -5x < -14y
Let's simplify to isolate x, just as we did with the original question.
Here, when we isolate x we divide BOTH sides by -5. Since we're dividing both sides of an inequality by a negative number, the inequality will flip directions.
So, we get:
x > (14/5)y
In this case we don't need to pick numbers. We know that x and y are positive, so we're not allowed to pick negative numbers. Since the fractions aren't easy to compare, let's estimate with decimals.
(2) x > 2.8y
Q: Is x > 2.33y?
Well, if we know that x is greater than 2.8y and we know that x and y are positive, we can conclude with certainty that x is greater than 2.33 y: sufficient.
(2) is sufficient, (1) is not: choose (b).
