Data Sufficiency

What is the ratio of 2x to 3y?

(1) The ratio of x2 to y2 is equal to 36/25.

(2) The ratio of x5 to y5 is greater than 1.

OA C

find 2x/3y?
st(1) x^2/y^2=36/25 or x/y=|6|/|5| Not Sufficient
st(2) x^5/y^5>1 or x/y>1 Not Sufficient
Combined st(1&2): x/y>1 and x/y=|6|/|5| translates into x/y=6/5 with 2x/3y=12/15=4/5
c

dell2 wrote:What is the ratio of 2x to 3y?

(1) The ratio of x2 to y2 is equal to 36/25.

(2) The ratio of x5 to y5 is greater than 1.

OA C

Hey there,

First off, for simplicity's sake, I'd just rephrase this question to myself as "what is the ratio of x to y?", and then as "what is x/y?", and forget about the coefficients. (This is safe to do because (2x)/(3y) = (2/3)(x/y), so certainly if we knew x/y, we'd easily be able to just multiply that by 2/3 to answer the actual question.)

So:

Q: What is x/y?

Statement (1) (alone) pulls the classic "squares" trick: know that x^2 = 36 and y^2 = 25 simply tells us that x = +6 or -6 and that y = +5 or -5. So that's almost enough to answer the question (and say the ratio x/y is 6/5) -- except of course not quite, because if one of those variables is negative and the other one is positive, then the ratio of x/y = -6/5. So from this statement we emerge with two possibilities for the answer: 6/5 if the variables have the same signs; -6/5 if they have different signs.

Statement (2) (alone) pulls the classic inequality trick. It tells us that x^5/y^5 > 1. Clearly, this will not be sufficient in itself to determine the specific value of x/y, but let's see how far we can take it. If we manipulate this inequality by multiplying both sides through by y^5, we don't know if we're multiplying by a positive number (in which case the > stays as it is) or a negative number (in which case the > changes to a <). So we come out with two scenarios: x^5 > y^5 IF y^5 is positive, and x^5 < y^5 IF y^5 is negative. Since raising a number to an odd power maintains the original sign of the number, we can rephrase these two possibilities as x^5 > y^5 IF y is positive, and x^5 < y^5 IF y is negative.

Now let's combine the statements. We've got that x must equal +6 or -6 and that y must equal +5 or -5, AND that if y is positive, x^5 must be greater than y^5, and that if y is negative, x^5 must be less than y^5. So, in combination, if y = +5, x^5 must be greater than 5^5, so x MUST be positive -- specifically, +6. And if y = -5, x^5 must be less than (-5)^5, so x MUST be negative -- specifically, -6. So x/y will equal either 6/5 or -6/-5, BOTH OF WHICH simplify to 6/5 since the two negatives cancel each other out in the latter case. So we've got our definitive answer.

Ian, this q. mathematically has no sense. That's why I've introduced a very short solution. Technically, yes the ratio can be negative. BUT mathematically, if we take the ratio as a relationship of two values, it's meaningless to point negative values in the nominator and/or denominator. I don't see any use of the negative ratios in a real life at all. That a/(-b)=(-a)/b may confuse users of an inverse function here. When one value rises in a positive direction the other value may decrease in a negative direction does not mean that the same value decreases in a negative direction with the positive rise of another.

Ian Stewart wrote:This is the kind of prep company question I hate, because it misleads test takers about what is tested on the GMAT. On the GMAT, ratios always only involve positive quantities. If the question designer wanted to allow for negative values of x and y, he or she should not have used the word 'ratio' in the question at all, but instead should have asked for the value of the fraction 2x/3y. The 'trap' in this question is not one you will ever see on the actual test.

For option 1 , the answer will always be 6/5 right??
How can it be -6/5.
In gmat , when we take a square root, whatever is the root is always positive right??
@pemdas :
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What is the ratio of 2x to 3y?

(1) The ratio of x2 to y2 is equal to 36/25.

(2) The ratio of x5 to y5 is greater than 1.

OA C
==> Since we have 2 variables (x, y) in the original condition, we need 2 equations to match the number of variables and since both conditions (1) and (2) have 1 equation each, C is likely the answer. Once we solve directly using (1) & (2),
we get x==+6, -6, y=+5,-5, and using (2) we get x=6, y=5 or x=-6, y=-5. Both leads to 2x:3y=12:15=4/5, thus the condition is sufficient. Therefore the answer is C. "‹


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