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21 Sep 2019, 16:02
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A
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Difficulty:
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Question Stats:
50% (02:23) correct
50%
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wrong
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Khalil drove 120 kilometers in a certain amount of time. What was his average speed, in kilometers per hour, during this time?
(1) If Khalil had driven at an average speed that was 5 kilometers per hour faster, his driving time would have been reduced by 20 minutes.
(2) If Khalil had driven at an average speed that was 25% faster, his driving time would have been reduced by 20%.
DS01951.01
(1) If Khalil had driven at an average speed that was 5 kilometers per hour faster, his driving time would have been reduced by 20 minutes.
(2) If Khalil had driven at an average speed that was 25% faster, his driving time would have been reduced by 20%.
DS01951.01
29 Sep 2019, 19:42
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gmatt1476
We know that the distance is 120. Let r be his average speed. The original question: r=?
1) At the old speed, his driving time is 120/r. At the new speed, his driving time would be 120/(r+5). We can set up an equation about his new driving time, which is 1/3 hour less than his old driving time.
\(\frac{120}{r+5}=\frac{120}{r}-\frac{1}{3}\)
\(360r=360r+1800-r^2-5r\)
\(r^2+5r-1800=0\)
Since c/a is negative for the quadratic equation above, its two roots have different signs. However, only its positive root applies to the context of the problem.
Thus, we could get a unique value to answer the original question. \(\implies\) Sufficient
2) At his new speed, his driving time would be 120/(1.25r). We can set up an equation about his new driving time, which is 20% less than his old driving time.
\(\frac{120}{\frac{5}{4}r}=\frac{4}{5}\cdot \frac{120}{r}\)
The above equation is an identity. Since r can be any positive number, we can't get a unique value to answer the original question. \(\implies\) Insufficient
Answer: A
21 Sep 2019, 16:41
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given : \(vt = 120\)
from statement (1), \((v+5)(t-\frac{1}{3}) = 120\)
\(v + 5 = 15t = 15(\frac{120}{v})\)
so \(t = 3\) and \(v = 40\) ---> sufficient
from statement (2), \((\frac{5}{4})v*(\frac{4}{5})t = 120\) ---> no use because the fractions cancel each other (insufficient)
from statement (1), \((v+5)(t-\frac{1}{3}) = 120\)
\(v + 5 = 15t = 15(\frac{120}{v})\)
so \(t = 3\) and \(v = 40\) ---> sufficient
from statement (2), \((\frac{5}{4})v*(\frac{4}{5})t = 120\) ---> no use because the fractions cancel each other (insufficient)
