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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.

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.

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)?

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)?

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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“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

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.

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.
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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.
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