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# Of the total number of people who ate in a restaurant one evening, 2/3

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Math Expert
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Of the total number of people who ate in a restaurant one evening, 2/3  [#permalink]

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20 Oct 2017, 00:12
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Difficulty:

15% (low)

Question Stats:

81% (01:26) correct 19% (02:09) wrong based on 93 sessions

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Of the total number of people who ate in a restaurant one evening, 2/3 ordered salads. Of those who ordered salad, 1/3 had Italian dressing on their salad. If the total number of people who ate in the restaurant that night was T, which of the following expressions represents the number of people who did not eat any Italian dressing at the restaurant that evening?

(A) 2/9*T
(B) 1/3*T
(C) 1/2*T
(D) 2/3*T
(E) 7/9*T

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Re: Of the total number of people who ate in a restaurant one evening, 2/3  [#permalink]

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20 Oct 2017, 02:13
People who ate something else than salad = 1/3*T
People who ordered salads without italian dressing = T*2/3*(1 - 1/3) = T*2/3*2/3 = T*4/9

People who did not eat italian dressing in sum = 1/3T + 4/9T = 7/9 T -> Answer E
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Re: Of the total number of people who ate in a restaurant one evening, 2/3  [#permalink]

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20 Oct 2017, 04:29
No. of people who ate salad = $$\frac{2T}{3}$$
No. of people who ate salad with Italian dressing = $$\frac{2T}{3}*\frac{1}{3}$$
No. of people who did not eat salad with Italian dressing = $$\frac{2T}{3}*\frac{2}{3}$$ = $$\frac{4T}{9}$$
No. of people who did not eat any Italian dressing = (T- $$\frac{2T}{3}$$)+$$\frac{4T}{9}$$
= $$\frac{1T}{3}$$+ $$\frac{4T}{9}$$ = $$\frac{7T}{9}$$

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Re: Of the total number of people who ate in a restaurant one evening, 2/3  [#permalink]

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20 Oct 2017, 04:38
Lets say T = 9
Those who ordered Salads = 2/3 * 9 = 6
Those who had Italian dressing = 1/3 * 6 = 2

Those who did not have Italian dressing = 7 . So if you put T=9, answer should be 7

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Re: Of the total number of people who ate in a restaurant one evening, 2/3  [#permalink]

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24 Oct 2017, 06:16
Bunuel wrote:
Of the total number of people who ate in a restaurant one evening, 2/3 ordered salads. Of those who ordered salad, 1/3 had Italian dressing on their salad. If the total number of people who ate in the restaurant that night was T, which of the following expressions represents the number of people who did not eat any Italian dressing at the restaurant that evening?

(A) 2/9*T
(B) 1/3*T
(C) 1/2*T
(D) 2/3*T
(E) 7/9*T

There were T people at the restaurant and (1/3) x (2/3) x T = (2/9)T had Italian dressing on their salads. Thus, in terms of T, the number of people who did not have Italian dressing on their salads is:

T - (2/9)T = (7/9)T

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Re: Of the total number of people who ate in a restaurant one evening, 2/3 &nbs [#permalink] 24 Oct 2017, 06:16
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