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06 Sep 2019, 10:52
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:27) correct
50%
(02:05)
wrong
based on 272
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How much time does Mr. Richards take to reach his office from home?
(1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.
(2) He needs to drive at a constant speed of 25 miles per hour to reach his office just in time if he is 30 minutes late from home.
(1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.
(2) He needs to drive at a constant speed of 25 miles per hour to reach his office just in time if he is 30 minutes late from home.
07 Sep 2019, 12:30
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Bunuel
Tricky question in my opinion.
The fundamental concept here is Velocity = Distance/Time.
So, t = regular time to reach Mr. Richard's house from his house (minutes), d = distance from home to office (miles) and V = regular speed (miles per minutes).
(i) t_initial = 30 and t_final = t + 50.
So, the time requiered is: t_final - t_initial = t +50 - 30 = t + 20.
Also we have V_new = d/(t + 20) --> fundamental relation in the new scenario
On the other hand V_new = 75%*V or 3/4*V, because the velocity is 25% slower than his regular speed
So, V_new = 75%*d/t = d/(t + 20) --> t= 60 Sufficient
(ii) V_new = 25 when t_initial = 30 and t_final = t. So, we have 25 = d/(t - 30). d is unknown, so insufficient
Then the correct answer is (A)
Let me know if you have comments or there is something wrong in my post.
Cheers,
R.
07 Sep 2019, 18:23
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Bunuel
Statement 1:
Mr. Richard takes 20 more min if he drives 25% slower, or at 75% of his regular speed. If he drives at \(\frac{3}{4}\) of his regular speed, this means he will take \(\frac{4}{3}\) of his regular time to complete the trip (since distance is fixed). And as we know, he took an extra 20 min, which is the extra \(\frac{1}{3}\) of his regular time. Therefore his typical driving time is \(20/\frac{1}{3}\) = 60 min so this statement is sufficient. The key here is that speed and time have an inverse relationship when the distance is fixed. Also, note \(\frac{1}{4}\) slower speed translates to \(\frac{1}{3}\) more time used, so we should put these terms in ratios to not confuse ourselves.
Statement 2:
Being 30 min late is not useful information. We only know his speed from this which is insufficient.
Answer: A
