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# By the start of the lunch break of a conference, 3/8 of the original

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
By the start of the lunch break of a conference, 3/8 of the original  [#permalink]

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01 Jan 2018, 10:33
00:00

Difficulty:

35% (medium)

Question Stats:

70% (02:23) correct 30% (01:21) wrong based on 12 sessions

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By the start of the lunch break of a conference, 3/8 of the original participants had already left. By the end of the conference, 1/3 of the original participants remained. Approximately what percentage of the original participants left between lunch and the end of the conference?

A. 25%
B. 29%
C. 37%
D. 63%
E. 67%

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Posts: 3574
By the start of the lunch break of a conference, 3/8 of the original  [#permalink]

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01 Jan 2018, 15:26
1
Bunuel wrote:
By the start of the lunch break of a conference, 3/8 of the original participants had already left. By the end of the conference, 1/3 of the original participants remained. Approximately what percentage of the original participants left between lunch and the end of the conference?

A. 25%
B. 29%
C. 37%
D. 63%
E. 67%

Assign values and calculate

Use LCM of denominators
Let original participants be $$x = 24$$

$$\frac{3}{8}$$ leave before lunch:

$$\frac{3}{8} * 24 = 9$$ left before lunch

$$(24 - 9) = 15$$ remain until the lunch break

At the end, $$\frac{1}{3}$$ of original $$24$$ remain
$$\frac{1}{3} * 24 = 8$$ remain until the end

How many left the conference between lunch and the end of the conference?

At the lunch break: 15 people were there
At the end: 8 people were there

$$(15 - 8) = 7$$ left the conference between lunch and the end of the conference

Approximately what percentage of original participants left between lunch and the end of the conference?

$$\frac{7}{24} = .29xxx \approx {29}$$ percent

Assign values and estimate/eliminate

From the numbers above, 7 of 24 remain.

$$\frac{7}{24}$$ = what percent?

Compare: $$\frac{8}{24} = 33.33$$ percent
$$\frac{7}{24}$$ is a lower percentage than $$\frac{8}{24}$$= 33.33%

Answers C, D, and E are out.

Answer A, 25 percent, would be exactly $$\frac{6}{24}$$
$$\frac{7}{24}$$ is a higher percentage than $$\frac{6}{24}$$

Answer A, too low, is out. By POE:

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By the start of the lunch break of a conference, 3/8 of the original   [#permalink] 01 Jan 2018, 15:26
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