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# Bob finishes the first half of an exam in two-thirds the time it takes

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Math Expert
Joined: 02 Sep 2009
Posts: 54369
Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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02 Nov 2015, 08:53
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:15) correct 18% (01:33) wrong based on 100 sessions

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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

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Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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02 Nov 2015, 09:24
x + 2x/3 =60

x =36

therefore, 1st half = 36*2/3 =24
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Re: Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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02 Nov 2015, 09:36
2/3x + x = 1
5x = 3
x = 3/5

2/3 * 3/5 = 2/5

2/5 * 60 = 24 minutes
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Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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02 Nov 2015, 10:02
Bunuel 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

My Solution:

Let time taken to finish the second half = T2

Then time taken to finish the first half, T1 = $$\frac{2T2}{3}$$

Total time = 1hr

Therefore, T1+T2---->$$\frac{2T2}{3}$$+T2=1

Solving we get T2=$$\frac{3}{5}$$ & T1=$$\frac{2}{5}$$

Question: T1 in minutes = $$\frac{2}{5}$$*60=24

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Re: Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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02 Nov 2015, 12:04
2nd part of the exam - x
1st part, 2/3 of x

total - 5x/3, and we know that this is 1 hour or 60 minutes.
x = 60*3/5 = 36 minutes.
1st part thus is 2/3*36 = 24 minutes.
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Re: Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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02 Nov 2015, 12:41
Bunuel 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

Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 2/3's the time of the second half (3/3's), we can "see" that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 2:5 and the second half is 3:5). With each fifth of an hour being 12 minutes (60/5), the first half of the exam would have taken 24 minutes. Correct answer is B.
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Joined: 27 Jul 2017
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Re: Bob finishes the first half of an exam in two-thirds the time it takes  [#permalink]

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27 Jul 2017, 18:57
First half: T1 -> Known
Second Half: T2 -> Unknown =X
2/3X+X = 1
2X+3X
--------- = 1
3

5X/3=1
5X=3
X=3/5
Verify: 2/3 * 3/5 + 3/5 = 1
2/5+3/5 = 1
5/5=1
1=1

T1: 2/5*60 = 24
T2: 3/5*60 = 36
Verify: 24+36 = 60

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Re: Bob finishes the first half of an exam in two-thirds the time it takes   [#permalink] 27 Jul 2017, 18:57
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