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18 Jun 2021, 06:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:23) correct
38%
(02:14)
wrong
based on 170
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The speed of two persons \(P_1\) and \(P_2\) are related as \(\frac{S_1^2 + S_2^2}{S_1^2 - S_2^2} = \frac{a^2 + b^2}{a^2 - b^2}\), where a and b are unknown constants. Find the ratio of \(t_1\) and \(t_2\) where \(t_1\) and \(t_2\) are the time taken by \(P_1\) and \(P_2\) to cover the same distance at speeds \(S_1\) and \(S_2\) respectively.
(A) a + b/b
(B) b/a
(C) 2a/b
(D) a/b
(E) (a + b)/(a - b)
(A) a + b/b
(B) b/a
(C) 2a/b
(D) a/b
(E) (a + b)/(a - b)
18 Jun 2021, 07:33
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Bunuel
I assume there's a typo in the question (it doesn't make sense as written), and that equation should read something like (changing the subscripts on some of the S terms) :
\(\frac{S_1^2 + S_2^2}{S_1^2 - S_2^2} = \frac{a^2 + b^2}{a^2 - b^2}\)
Now if you compare the left and right sides, it's easy to see one solution: S_1 = a and S_2 = b. If you factor, you can see that any other solution that looks like S_1 = ka and S_2 = kb will work, for a nonzero constant k. Now the question asks for the ratio of times to cover the same distance, and that will be the reciprocal of the ratio of the speeds traveled to cover that same distance (e.g. if you travel twice as fast, it takes half as long, but if that relationship is not familiar, it can quickly be proven algebraically just using s = d/t). We're asked to find t_1/t_2, which will be the same as S_2/S_1, so will be b/a.
I just guessed which subscript went where - if the order was the opposite of what I guessed, the answer would instead be a/b.
I'll add that I don't think this is a realistic GMAT question, and I would have very little patience for any math book that insisted on writing equations that look like the one below
\(\frac{S_2^2 + S_1^2}{S_2^2 - S_1^2} \)
That's some of the most unnecessarily confusing algebra I've seen recently.
18 Jun 2021, 12:49
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Bunuel
\(\frac{S_1^2 + S_2^2}{S_1^2 - S_2^2} = \frac{a^2 + b^2}{a^2 - b^2}\)
From the above equation, we can figure out: \(S_1 = a, S_2 = b\)
Asked: \(\frac{t_1}{t_2}\)?
As the distance is same.
\(t_1*s_1 = t_2*s_2\)
\(\frac{t1}{t2} = \frac{s_2}{s_1} = \frac{b}{a}\), (B) IMO!
