What is the ratio of r to s?

Question

(1) r + s = 7
(2) r^2 – s^2 = 7

Spidy001 · Answer

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.

Startup · Answer

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!

Bunuel · Answer

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 ...

stevennu · Answer

Why can't R+S = 7 be solved to (-7/1) = (-S/R) and thus prove sufficiency in Statement 1?

Bunuel · Answer

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.

Ksterr · Answer

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 = ?

Bunuel · Answer

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.

Answer: C.

Hope it's clear.

zsoltvigh · Answer

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!

WoundedTiger · Answer

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

PerfectScores · Answer

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.

RaviRamisetti · Answer

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!

Bunuel · Answer

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.

Nunuboy1994 · Answer

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

bumpbot · Answer

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What is the ratio of r to s?

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