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# What is the ratio of r to s?

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Manager
Joined: 10 Feb 2011
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What is the ratio of r to s? [#permalink]

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Updated on: 29 Jul 2013, 08:29
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What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7
[Reveal] Spoiler: OA

Originally posted by banksy on 15 Mar 2011, 16:48.
Last edited by Bunuel on 29 Jul 2013, 08:29, edited 1 time in total.
Edited the question.
Director
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Re: 20. (M) What is the ratio of r to s? (1) r + s = 7 (2) r2 [#permalink]

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16 Mar 2011, 16:36
1. Not sufficient

(r , s could be 5 2 or 4 3 so on)

2. Not enough info to derive r/s . Not sufficient.

Together its sufficient to find r and s. Answer C.
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Re: (M) What is the ratio of r to s? (1) r + s = 7 (2) r2 s2 = 7 [#permalink]

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29 Jul 2013, 08:27
For (2), I did the following:

r^2 - s^2 = 7
(r+s)(r-s) = 7
(4+3)(4-3) = 7 <--- I don't see any other possible combination of numbers that would give you 7

Thus, I fail to see how statement 2 is insufficient. Please help!
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Re: (M) What is the ratio of r to s? (1) r + s = 7 (2) r2 s2 = 7 [#permalink]

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29 Jul 2013, 08:32
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Startup wrote:
What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7

For (2), I did the following:

r^2 - s^2 = 7
(r+s)(r-s) = 7
(4+3)(4-3) = 7 <--- I don't see any other possible combination of numbers that would give you 7

Thus, I fail to see how statement 2 is insufficient. Please help!

Notice that we are not told that r and s are integers, so consider $$r^2=7$$ and $$s=0$$ OR $$r^2=8$$ and $$s=1$$...
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Re: What is the ratio of r to s? [#permalink]

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15 Sep 2013, 23:14
Why can't R+S = 7 be solved to (-7/1) = (-S/R) and thus prove sufficiency in Statement 1?
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Re: What is the ratio of r to s? [#permalink]

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16 Sep 2013, 02:07
stevennu wrote:
Why can't R+S = 7 be solved to (-7/1) = (-S/R) and thus prove sufficiency in Statement 1?

First of all: when a DS question asks about the value, then the statement is sufficient ONLY if you can get the single numerical value.

From r + s = 7 we cannot find the single numerical value of r/s, it can take infinitely many values:
...
r=-1 and s=8 --> r/s=-1/8;
r=1 and s=6 --> r/s=1/6;
r=2 and s=5 --> r/s=2/5;
...

Also notice that your example does not satisfy the equation at all: if r=1 and s=-7, then r + s = -6 not 7.

Hope this helps.
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Re: What is the ratio of r to s? [#permalink]

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16 Sep 2013, 20:13
I stumbled upon C) to be the right answer but I'm not quite sure how...
1) r+s=7
2)r^2 - s^2 = 7
(r+s)(r-s)=7
r-s=1

Is the question not asking for r/s = ?
Math Expert
Joined: 02 Sep 2009
Posts: 44599
Re: What is the ratio of r to s? [#permalink]

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17 Sep 2013, 00:34
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Ksterr wrote:
I stumbled upon C) to be the right answer but I'm not quite sure how...
1) r+s=7
2)r^2 - s^2 = 7
(r+s)(r-s)=7
r-s=1

Is the question not asking for r/s = ?

What is the ratio of r to s?

Questions asks to find the value of r/s.

(1) r + s = 7. Infinite pairs of (r, s) satisfies this equations. Not sufficient.

(2) r^2 – s^2 = 7. Infinite pairs of (r, s) satisfies this equations. Not sufficient.

(1)+(2) From (2) we know that (r - s)(r + s) = 7, since from (1) r + s = 7, then (r - s)*7 = 7, which gives r - s = 1. Solving r + s = 7 and r - s = 1 gives r = 4 and s = 3 --> r/s = 4/3. Sufficient.

Hope it's clear.
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Manhattan GMAT CAT Question [#permalink]

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20 May 2014, 21:00
I came across a question in one of my CAT practice exams and I thought I answered it correctly, but it turns out I was wrong. But I have no idea why my solution is not valid as I get the same answer as the solutions manual (just with a different approach). Can someone clarify this for me?

Thank you!

What is the ratio of r to s?

(1) r + s = 7

(2) r^2 – s^2 = 7

I answered (B) - statement 2 is sufficient. My reasoning was:

Numbers: 1, 2, 3, 4, 5, 6 etc
Their perfect square: 1, 4, 9, 16, 25 etc.
There is only one occasion in which the difference between two squared numbers is 7 and this 16-9 or 4^2 - 3^2. Thus the ratio of r/s would be 4/3.
Even if you use -1, -2, -3, -4, -5, -6 etc it makes no difference because you still get 4/3.

The solution states that you need both (answer C) in order to solve the problem (and they come up with 4/3 as well). Now using both statements is perfectly valid but why can't I get away with using only (2)?

Any help would be much appreciated!
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Re: Manhattan GMAT CAT Question [#permalink]

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20 May 2014, 21:56
1
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zsoltvigh wrote:
I came across a question in one of my CAT practice exams and I thought I answered it correctly, but it turns out I was wrong. But I have no idea why my solution is not valid as I get the same answer as the solutions manual (just with a different approach). Can someone clarify this for me?

Thank you!

What is the ratio of r to s?

(1) r + s = 7

(2) r^2 – s^2 = 7

I answered (B) - statement 2 is sufficient. My reasoning was:

Numbers: 1, 2, 3, 4, 5, 6 etc
Their perfect square: 1, 4, 9, 16, 25 etc.
There is only one occasion in which the difference between two squared numbers is 7 and this 16-9 or 4^2 - 3^2. Thus the ratio of r/s would be 4/3.
Even if you use -1, -2, -3, -4, -5, -6 etc it makes no difference because you still get 4/3.

The solution states that you need both (answer C) in order to solve the problem (and they come up with 4/3 as well). Now using both statements is perfectly valid but why can't I get away with using only (2)?

Any help would be much appreciated!

Hello zsoltvigh,

Welcome to Gmatclub..

The Question is discussed here : what-is-the-ratio-of-r-to-s-110947.html#p1267783
As you scroll through the posts in the above link you will find the answer as C and not B....(Hint consider a case where s=0....and see what you get as ratio r/s what-is-the-ratio-of-r-to-s-110947.html#p1251159)

Note that when you have some doubts on questions especially from MGMAT Test or Veritas prep test, use the search option to check if the question has been discussed before.It will get you answers faster than waiting for response.....

If you don't find you are more than welcome to post it on the Forum
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Manager
Joined: 20 Dec 2013
Posts: 124
Re: What is the ratio of r to s? [#permalink]

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20 May 2014, 22:11
banksy wrote:
What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7

Statement I is insufficient:

r = 2, s = 5
r = 1, s = 6

Statement II is insufficient:
(r+s)(r-s) = 7
r = 4, s = 3
r = -4, s = 3

Combining is sufficient:
r + s = 7
(r+s) (r-s) = 7
r - s = 1, r + s = 7
We get definite values of r and s hence answer is C.
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Intern
Joined: 25 Mar 2014
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Re: What is the ratio of r to s? [#permalink]

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20 May 2014, 23:39
It's better to use algerabic forumale rather than picking numbers as the exponent is 2.

Also R power 2 - S power 2 can be written as (R+S)(R-S).

I used statement 1 to deduct R-S.

Then Combine Statement1 and R-S to get the value of R.

Obviously we will get S value from any statement. No need to calculate as its a DS q.

I might belong to that band which assumes given variables are integers though it's not explicitly given.

Kudos!
Math Expert
Joined: 02 Sep 2009
Posts: 44599
Re: Manhattan GMAT CAT Question [#permalink]

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21 May 2014, 01:41
Expert's post
1
This post was
BOOKMARKED
zsoltvigh wrote:
I came across a question in one of my CAT practice exams and I thought I answered it correctly, but it turns out I was wrong. But I have no idea why my solution is not valid as I get the same answer as the solutions manual (just with a different approach). Can someone clarify this for me?

Thank you!

What is the ratio of r to s?

(1) r + s = 7

(2) r^2 – s^2 = 7

I answered (B) - statement 2 is sufficient. My reasoning was:

Numbers: 1, 2, 3, 4, 5, 6 etc
Their perfect square: 1, 4, 9, 16, 25 etc.
There is only one occasion in which the difference between two squared numbers is 7 and this 16-9 or 4^2 - 3^2. Thus the ratio of r/s would be 4/3.
Even if you use -1, -2, -3, -4, -5, -6 etc it makes no difference because you still get 4/3.

The solution states that you need both (answer C) in order to solve the problem (and they come up with 4/3 as well). Now using both statements is perfectly valid but why can't I get away with using only (2)?

Any help would be much appreciated!

Merging similar topics. Please refer to the discussion above.

P.S. please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, 2, and 3. Thank you.
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Posts: 776
Re: What is the ratio of r to s? [#permalink]

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08 Sep 2017, 20:41
banksy wrote:
What is the ratio of r to s?

(1) r + s = 7
(2) r^2 – s^2 = 7

St 1

clearly insuff too many possibilities

St 2

rewrite

(r +s)(r-s) =7

more than one possibility as do not know whether r and s should be integers, negative numbers etc

St 1 and St 2

We have a system of linear equations because

7(r-s) =7

r +s =7
r-s =1

S =3

C
Re: What is the ratio of r to s?   [#permalink] 08 Sep 2017, 20:41
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