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

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

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New post 01 Jan 2018, 10:33
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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%
[Reveal] Spoiler: OA

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

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New post 01 Jan 2018, 15:26
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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

Answer B

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:

Answer B) 29 %
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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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