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A train traveled from Station A to Station B at an average

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A train traveled from Station A to Station B at an average

by AAPL » Fri Jun 15, 2018 2:15 pm

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A train traveled from Station A to Station B at an average speed of 80 kilometers per hour and then from Station B to Station C at an average speed of 60 kilometers per hour. If the train did not stop at Station B, what was the average speed at which the train traveled from Station A to C?

(1) The distance that the train traveled from Station A to Station B was 4 times the distance that train traveled from Station B to Station C.
(2) The amount of time it took to the train to travel from Station A to Station B is 3 times the amount of time that it took the train to travel from Station B to Station C.

The OA is D.

Is there a quicker way to see that the distance variable cancels out, rather than going through the entire algebraic calculation? I made the assumption that the variable would remain, and struggle to finish in ~ 2 minutes once I start getting into algebra for DS questions. Thanks.
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Source: — Data Sufficiency |
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edited:

by deloitte247 » Fri Jul 27, 2018 2:37 pm

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Let the distance between station A and B = ab Km
Let the distance between station B and C = bc Km
Then (ab/80) Km is the amount of time taken in hours the train took to travel from station A to B.
Also, (bc/60)Km is the amount of time taken in hours the train took to travel from station B to C.

$$We\ now\ have\ to\ find\ the\ value\ of\ \frac{\left(ab+bc\right)}{\frac{ab}{80}+\frac{bc}{60}}$$

Statement 1: The distance that the train traveled from Station A to B was 4 times the distance the train
traveled from B to C.
$$Therefore,\ \frac{\left(ab+bc\right)}{\frac{ab}{80}+\frac{bc}{60}}=\frac{\left(4bc+\ bc\right)}{\frac{4bc}{80}+\frac{bc}{60}}=\frac{\left[bc\left(4+1\right)\right]}{bc\left(\frac{4}{80}+\frac{1}{60}\right)}$$
$$=\frac{\left(4+1\right)}{\frac{4}{80}+\frac{1}{60}}$$
We can get a definite value here. hence, statement 1 is sufficient

Statement 2: The amount of time it took the train to travel from station A to B is 3 times the amount of time taken it took the train to travel from station B to C
$$Therefore,\ \frac{ab}{80}=3\ \left(\frac{bc}{60}\right)$$
$$\frac{ab}{80}=\frac{bc}{20}$$
$$by\ cross\ multiplying,\ we\ have$$
$$20ab=80bc$$
$$In\ ratio\ of\ ab=4bc\ which\ is\ the\ same\ with\ statement\ 1.\ Hence,\ statement\ 2\ is\ sufficient$$

In conclusion, OPTION D is correct because each of statement 1 and 2 is sufficient alone
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