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# Of the total number of people who ate in a restaurant one ev

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Of the total number of people who ate in a restaurant one ev [#permalink]  18 Oct 2017, 22:53
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42% (01:41) correct 57% (01:31) wrong based on 7 sessions
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 ev [#permalink]  18 Oct 2017, 23:59
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

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Let us take the value of T = 9 for easy calculation

Now $$\frac{2}{3}$$ of total 9 people ordered salads = $$\frac{2}{3} *9$$ = 6 people

and the $$\frac{1}{3}$$ of the 6 people had Italian dressing = $$\frac{1}{3} *6$$ =2 people

Out of 9 people only 2 of them had Italian dressing = 9-2 =7 people didnot had Italian dressing.

So we need the value to be 7 and looking at the option only E satisfy the above

$$\frac{7}{9}*T$$

i. e $$\frac{7}{9} * 9 =7$$ (As we have taken T= 9 )
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Re: Of the total number of people who ate in a restaurant one ev [#permalink]  19 Oct 2017, 00:36
Even without the need of numbers, the answer is straightforward.

The number of people who eat Italian dressing is $$\frac{2}{3}\frac{1}{6}T = \frac{2}{9}T$$. Thus, those who does not eaten Italian dressing are $$(1-\frac{2}{9})T = \frac{7}{9}T$$.

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Re: Of the total number of people who ate in a restaurant one ev [#permalink]  08 Jan 2018, 11:02
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Expert's post
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 ev [#permalink]  21 May 2018, 23:15
JeffTargetTestPrep wrote:
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

Quite a slick way of solving the problem .KUDOS
Re: Of the total number of people who ate in a restaurant one ev   [#permalink] 21 May 2018, 23:15
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