If the ratio of w to x to y is 1 : 2 : 3, what is the value of w + x?

Question

(1) x - w = 5

(2) 3y - 2w = 35

Kudos for a correct  solution .

Lucky2783 · Accepted Answer

easy one (who says nothing comes or free, this kudo will be almost free :-)

) . option A: Given \frac{w}{x} = \frac{1}{2} , we can substitute x=5+w to get all w,x,y . SUFFICIENT. option B: Given \frac{w}{y} = \frac{1}{3} , we can substitute y= \frac{(35+2w)}{3} to get all w,x,y . SUFFICIENT. Answer : D .

AmoyV · Answer

Let a be the multiple of the ratio.

1. 2a-a=5
a=5

w+x=a+2a=3a=3(5)=15---->Sufficient

2. 3y-2w=35
9a-2a=35
a=5

w+x=3a=15--->Sufficient

Answer: D

FightToSurvive · Answer

option 1: w/x = 1/2 , hence x = 2w. Substitute in St 1. one gets the answer . SUFFICIENT.

option 2: y/w is given. Substitute in St 1. one gets the answer . SUFFICIENT.

Hence D.

Hope its clear.

FightToSurvive · Answer

Sorry typo error:

"option 2: y/w is given. Substitute in St 2. one gets the answer . SUFFICIENT."

D is the answer

minwoswoh · Answer

Rule to Memorize : a three-part ratio is actually a set of 3 variables and 2 equations.

In this case
- Equation 1: 2w = x
- Equation 2: 3x = 2y

One might mistakenly think that 3w = y is a third equation. It is not. It is a just a conclusion derived by the other 2 equations.

How to approach this problem  
Therefore, if we get a new linear equation in any of the statements, we can reach w + x.
And that is what both statements separately provide.

Correct Answer = D

EMPOWERgmatRichC · Answer

Hi All,

It looks like everyone is comfortable with the Algebra involved in this question, which is good (you'll use those skills on a number of questions on Test Day). You don't actually have to do Algebra though to solve this problem (if you recognize the pattern in the original ratio).

We're given the ratio:

W:X:Y
1:2:3

So the 3 variables COULD be...
1, 2 and 3
2, 4 and 6
3, 6 and 9
4, 8 and 12
5, 10 and 15
Etc.

Notice how the "spread" in each option is unique. For example, the ONLY time that Y and W differ by 2 is in the first option (as the variables get bigger, the "spread" gets bigger). We can use THAT knowledge to our advantage.

We're asked for the value of W + X.

Fact 1: X - W = 5

The ONLY time that X-W = 5 is in the 5th option. As X gets bigger, the difference between X and W gets bigger.
W+X = 5+10 = 15
Fact 1 is SUFFICIENT

Fact 2: 3Y - 2W = 35

This is just another relationship between 2 variables, so we KNOW there's only ONE way for 3Y-2W to = 35. It's the 5th option.
W+X = 5+10 = 15
Fact 2 is SUFFICIENT

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

the ratios are w:x:y= 1:2:3..
let the common term in all three be t..
so w=t; x=2t; y=3t..
lets look at the statements now..
(1) x - w = 5..
2t-t=5... so w,x,y=5,10,15... sufficient to find w+x=15

(2) 3y - 2w = 35..
3*3t-2*t=7t=35 ..t=5 
same as statement 1 from here onwards... sufficient
ans D..

buddyisraelgmat · Answer

Hi Rich Nice approach - I believe you're saying the answer is D ( not B as you've mentioned in the spoiler)

Thanks

EMPOWERgmatRichC · Answer

Hi buddyisraelgmat,

You are correct. Thanks for the heads up; I've edited my post.

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION: abcratio_text.PNG

pulak1988 · Answer

w:x = 1:2 so, x = 2w
w:y = 1:3 so y= 3w.

so now both statements give us a value of w, which can be used for finding other values. hence both stments can be used to find w+x, no need to solve any equation.

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If the ratio of w to x to y is 1 : 2 : 3, what is the value of w + x?

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