What is the ratio of r to s?

[Guest]

What is the ratio of r to s?

(1) r + s = 7

(2) r2 – s2 = 7

I chose option (B),

r2 – s2 = 7
(r+s) (r-s) = 7

either r and s can be +4 and +3 respectively or r and s can be -4 and -3, on both these options ratio of r to s becomes 4/3. Is my understanding wrong? Can anyone explain please, thanks!

[Guest]

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

then,

either

(r+s) = 7 and (r-s) = 1 OR, - I
(r+s) = -7 and (r-s) = -1 OR, -II
(r+s) = 1 and (r-s) = 7 OR, - III
(r+s) = -1 and (r-s) = -7 -IV

From I, r = 4 and s = 3 => r/s = 4/3
From III, r = 4 and s = -3 => r/s = -4/3

Correct ans is D.

[Guest]

I meant C (Both together). :o

[RonPurewal]

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

then,

either

(r+s) = 7 and (r-s) = 1 OR, - I
(r+s) = -7 and (r-s) = -1 OR, -II
(r+s) = 1 and (r-s) = 7 OR, - III
(r+s) = -1 and (r-s) = -7 -IV

From I, r = 4 and s = 3 => r/s = 4/3
From III, r = 4 and s = -3 => r/s = -4/3

Correct ans is D.

hmm.

this is a lot of work; there are at least 2 quick ways to see that statement (2) is insufficient.

one:
note that statement (2) doesn't give any reason why you should have just 4's and 3's.
if r^2 - s^2 = 7, then there's an infinite collection of possible values; for instance, r^2 could be 11 and s^2 could be 4, making r = +/- √11 and s = +/- 2.
or any other values with a difference of seven.

two:
statement (2) only gives information about the SQUARES of r and s. if we only know r^2 and s^2, then it will be impossible to tell whether r and s are positive or negative.
therefore, you're automatically going to have two possible ratios: one in which r and s have the same sign (--> positive ratio), and one in which r and s have opposite signs (--> negative ratio).

either one of these observations constitutes proof that statement (2) is insufficient.

[yousuf_azim]

Dears,

What is the ANS?

BR

[StaceyKoprince]

the answer is C

[davegerstel]

Hi Ron,
Can you please clarify how negative ratios work. For example -4:-3 is that equal to a ratio of 4 to 3?
Thanks,
David

[tim]

That is true. You know two ratios are the same if the fractions they make are equal. In this case we have -4/-3 = 4/3 so the ratios are equal..