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dell2: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Thu Jun 02, 2011 10:28 am

by dell2 » Mon Jun 27, 2011 9:59 am

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

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 27, 2011 9:59 am

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Mon Jun 27, 2011 10:10 am

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

Success doesn't come overnight!

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Ashley@VeritasPrep: GMAT Instructor; Posts: 199; Joined: Tue May 17, 2011 6:06 amFollowed by: 121 members; Location: Cambridge, MA; Thanked: 192 times; GMAT Score:780

by Ashley@VeritasPrep » Mon Jun 27, 2011 10:20 am

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.

Ashley Newman-Owens
GMAT Instructor
Veritas Prep

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Jun 27, 2011 2:42 pm

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 online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Mon Jun 27, 2011 5:10 pm

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.

Success doesn't come overnight!

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shree9975: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Wed Jul 02, 2014 4:04 am

by shree9975 » Wed Aug 19, 2015 2:22 pm

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 :
Please Help!!!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 19, 2015 2:42 pm

shree9975 wrote: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 :
Please Help!!!

Here's how the Official Guide puts it: âˆšn denotes the positive number whose square is n.
So, âˆš(36/25) = 6/5

HOWEVER, the equation âˆš(36/25) = x is NOT EQUIVALENT to the equation xÂ² = 36/25
The equation xÂ² = 36/25 has two solutions: x = 6/5 and x = -6/5
The equation âˆš(36/25) = x has one solution: x = 6/5

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Fri Aug 21, 2015 7:31 pm

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

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. "‹

If you know our own innovative logics to find the answer, you don't need to actually solve the problem.
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