BTGmoderatorDC wrote: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%.
OA A
Source: Official Guide
Say Khalil drove 120 kilometers in x hours. Thus, the average speed = 120/x kmpl. We have to get the value of 120/x.
Thus, if we get the value of x, we get the answer.
Let's take each statement one by one.
(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.
120 / (120/x + 5) = 60x - 20
6x / (120 + 5x) = 3x - 1
15x^2 + 349x - 120 = 0
Since this is a quadratic equation, x would have two values and we have to get the unique value of x. But solving this quadratic equation is challenging. However, observing closely we find that the two split parts of 349x must be equal to 15x^2 * (- 120), i.e. a negative number. Thus, one of the two split parts of 349x must be negative and the other positive, yielding one value of x as negative and the other positive. Since x cannot be negative, we would have only one positive value of x. Thus, this equation would ensure a unique value of 120/x. Sufficient.
(2) If Khalil had driven at an average speed that was 25% faster, his driving time would have been reduced by 20%.
=> Speed increases to 125% = 125/100 = 5/4, thus, time would reduce to reciprocal of 5/4 = 4/5 = 80%. Or, the driving time would reduce by 20%.
This is not new information. Thus, Statement 2 is insufficient.
The correct answer:
A
Hope this helps!
-Jay
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