GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 14:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The values of x and y vary with the value of z so that each

Author Message
Director
Joined: 29 Aug 2005
Posts: 744
The values of x and y vary with the value of z so that each  [#permalink]

### Show Tags

07 Apr 2009, 15:58
1
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:01) correct 0% (00:00) wrong based on 9 sessions

### HideShow timer Statistics

The values of x and y vary with the value of z so that each additive increase of 2 in the value of z corresponds to the value of x increasing by a factor of 2 and the value of y increasing by a factor of 3. If x and y are positive for each z>0, what is the value of x/(x+y) when z=12?

(1) When z=6, x=5y
(2) z=0, x =y+1

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1527
Re: x and y vary with the value of z  [#permalink]

### Show Tags

07 Apr 2009, 23:00
botirvoy wrote:
The values of x and y vary with the value of z so that each additive increase of 2 in the value of z corresponds to the value of x increasing by a factor of 2 and the value of y increasing by a factor of 3. If x and y are positive for each z>0, what is the value of x/(x+y) when z=12?

(1) When z=6, x=5y
(2) z=0, x =y+1

I've seen this in GMATFocus, but among the several thousand real GMAT questions I've seen, I've yet to see anything all that similar to this question, so there are probably more important problems to study. Still, the idea here is this:

-According to the stem, if we add 2 to z, x will double, and y will triple. So, to take an example, suppose when z = 6 that x = a, and y = b. Then when z = 8 (we add two to z), x = 2a (x doubles), and y = 3b (y triples). Similarly, if we add two again to z -- that is, when z = 10 -- then again x doubles and y triples; we have x = 2^2 * a, and y = 3^2 * b. Similarly, when z = 12, x = 2^3 * a and y = 3^3 * b, and so on.

-Using Statement 1, if z = 6, we know that x = 5y. If y = b when z = 6, then x = 5b. So working as above, when z = 12, x = 2^3 * 5b, and y = 3^3 * b. From there, you can work out x/(x+y), because the b will cancel.

-Using Statement 2, we know that x = y + 1 when z = 0. If y = d when z = 0, then x = d+1. Using the same logic as above, you can determine that when z = 12, x will be equal to 2^6 * (d + 1), and y will be equal to 3^6 * d. Now if you try to calculate x/(x+y), d will not cancel; we would need to know the value of d to calculate x/(x+y) here.

So the first statement is sufficient, the second not. The question is really just a convoluted way of testing whether you understand that ratios are based on multiplication and division, and not on addition, and uses what are known as 'logarithmic scales' to test that idea. It's a much more complicated version of question 99 in the PS section of OG11, which tests 'logarithmic scales' in a much more straightforward way - the question in the OG is in a much more common format than the above, and is worth understanding.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Senior Manager
Joined: 01 Mar 2009
Posts: 338
Location: PDX
Re: x and y vary with the value of z  [#permalink]

### Show Tags

07 Apr 2009, 23:10
Ian has explained it all. It took me a minute to figure out the ratio but once that's figured out the solution is quite easy. A nice problem though. Thanks for posting.

_________________
In the land of the night, the chariot of the sun is drawn by the grateful dead
VP
Joined: 05 Jul 2008
Posts: 1198
Re: x and y vary with the value of z  [#permalink]

### Show Tags

08 Apr 2009, 08:12
IanStewart wrote:
botirvoy wrote:
The values of x and y vary with the value of z so that each additive increase of 2 in the value of z corresponds to the value of x increasing by a factor of 2 and the value of y increasing by a factor of 3. If x and y are positive for each z>0, what is the value of x/(x+y) when z=12?

(1) When z=6, x=5y
(2) z=0, x =y+1

I've seen this in GMATFocus, but among the several thousand real GMAT questions I've seen, I've yet to see anything all that similar to this question, so there are probably more important problems to study. Still, the idea here is this:

-According to the stem, if we add 2 to z, x will double, and y will triple. So, to take an example, suppose when z = 6 that x = a, and y = b. Then when z = 8 (we add two to z), x = 2a (x doubles), and y = 3b (y triples). Similarly, if we add two again to z -- that is, when z = 10 -- then again x doubles and y triples; we have x = 2^2 * a, and y = 3^2 * b. Similarly, when z = 12, x = 2^3 * a and y = 3^3 * b, and so on.

-Using Statement 1, if z = 6, we know that x = 5y. If y = b when z = 6, then x = 5b. So working as above, when z = 12, x = 2^3 * 5b, and y = 3^3 * b. From there, you can work out x/(x+y), because the b will cancel.

-Using Statement 2, we know that x = y + 1 when z = 0. If y = d when z = 0, then x = d+1. Using the same logic as above, you can determine that when z = 12, x will be equal to 2^6 * (d + 1), and y will be equal to 3^6 * d. Now if you try to calculate x/(x+y), d will not cancel; we would need to know the value of d to calculate x/(x+y) here.

So the first statement is sufficient, the second not. The question is really just a convoluted way of testing whether you understand that ratios are based on multiplication and division, and not on addition, and uses what are known as 'logarithmic scales' to test that idea. It's a much more complicated version of question 99 in the PS section of OG11, which tests 'logarithmic scales' in a much more straightforward way - the question in the OG is in a much more common format than the above, and is worth understanding.

Yeah very different Q from what we have seen so far.

If x and y are positive for each z>0, what is the value of x/(x+y) when z=12?

What relevance does this have? B gives us a value of X for Z=0.
Director
Joined: 29 Aug 2005
Posts: 744
Re: x and y vary with the value of z  [#permalink]

### Show Tags

09 Apr 2009, 14:28
Thank you everyone!
OA A.
Current Student
Joined: 13 Jan 2009
Posts: 311
Location: India
Re: x and y vary with the value of z  [#permalink]

### Show Tags

13 Apr 2009, 19:01
I liked this question.
Non-Human User
Joined: 09 Sep 2013
Posts: 11013
Re: The values of x and y vary with the value of z so that each  [#permalink]

### Show Tags

04 Jul 2017, 11:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: The values of x and y vary with the value of z so that each   [#permalink] 04 Jul 2017, 11:20
Display posts from previous: Sort by
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}