Cinnia wrote:Bob finishes the first half of an exam in two-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
A) 20
B) 24
C) 27
D) 36
E) 40
Could someone please explain how to solve this one? I got a completely different number from the actual answer.
Thank you in advance.
Plug in a value to determine the ratio.
Let second half = 3 minutes.
Then first half = (2/3)*3 = 2 minutes.
Thus, first half : second half = 2:3.
Since 2+3 = 5, 2 of every 5 minutes -- meaning 2/5 of the time -- is spent on the first half of the exam.
(2/5)*60 = 24.
The correct answer is
B.
Another approach:
Plug in the answers, which represent the time spent on the first half.
Since the time spent on the first half is 2/3 the time spent on the second half, less time is spent on the first half than on the second half.
Thus, the correct answer must be less than (1/2)*60 = 30.
Eliminate D and E.
Answer choice C: 27 minutes spent on the first half
Thus, 60-27 = 33 minutes is spent on the second half.
2/3 * 33 = 22.
Doesn't work, since C says that the time spent on first half is 27 minutes.
Eliminate C.
Answer choice B: 24 minutes spent on the first half
Thus, 60-24=36 minutes is spent on the second half.
(2/3)*36 = 24. Success!
The correct answer is
B.
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