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# If 75 percent of the guests at a certain banquet ordered dessert, what

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If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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16 Aug 2010, 12:40
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Question Stats:

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If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-75-percent-of-the-guests-at-a-certain-banquet-ordered-des-168096.html
[Reveal] Spoiler: OA

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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16 Aug 2010, 13:01

X=D+C-DandC
D=.75X

1. DandC = .6 x .75X
We can get a relation between C and X

2. DandC = 0.9C
We can again relate C to X

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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16 Aug 2010, 13:12
mainhoon wrote:

X=D+C-DandC
D=.75X

1. DandC = .6 x .75X
We can get a relation between C and X

2. DandC = 0.9C
We can again relate C to X

Posted from my mobile device

No
It is
[Reveal] Spoiler:
C

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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16 Aug 2010, 13:33
From 2 , c/x = 25, doesn't make sense... Perhaps we are assuming that each ordered D or C. That is perhaps an incorrect assumption...
In which case, we will need both the equations to solve for C and X

X = .75X + C - 0.6 x 0.75X + N
X = 0.75X + C - 0.9C + N

.9C =0.45X
C/X = 50%?

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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16 Aug 2010, 16:04
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metallicafan - do you have the Official answer? Personally, I can't think a shorter way that this... (which is pretty much the same as mainhoon)

D = 0.75X

1) D&C = (0.75X) 0.6
Now you have Subset D only as well as subset D&C - Alone not sufficient

2) D&C = 0.9C
Now you have Subset D&C of subset C - Alone not sufficient

But what you do have is D&C = 0.9C = (0.75)(0.6)X which means you can isolate C as a percentage of X.
You need both pieces of info to solve.

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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10 Oct 2010, 23:26
nice q

C

0.9 X = 0.6(75)
X = percent of the guests ordered coffee = 0.6(75)/0.9
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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12 Oct 2010, 02:11
Attachment:
File comment: Solution is in attachment
Coffee&dessert.docx [28.13 KiB]

Hope it helps.

Regards,
Murali.

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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29 Dec 2015, 19:24
got to C as well.

suppose x is # of people.
0.75x - people ordered dessert.

1. 0.6*0.75x => people who ordered coffee and dessert.

2. suppose y people who ordered coffee, 0.9y = people who ordered coffee and desert. not sufficient.

1+2
3/5*3x/4 = 9y/10
we need to find y:
9x/20=9y/10
y=x/2
or 50%

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Re: If 75 percent of the guests at a certain banquet ordered dessert, what [#permalink]

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29 Dec 2015, 22:08
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Expert's post
metallicafan wrote:
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.

If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

Assume there were 100 guests on the banquet. So we have that 75 of them ordered dessert.

(1) 60 percent of the guests who ordered dessert also ordered coffee --> 0.6*75=45 guests ordered both dessert AND coffee, but we still don't know how many guests ordered coffee. Not sufficient.

(2) 90 percent of the guests who ordered coffee also ordered dessert --> 0.9*(coffee) # of guests who ordered both dessert AND coffee. Not sufficient.

(1)+(2) From (1) # of guests who ordered both dessert AND coffee is 45 and from (2) 0.9*(coffee)=45 --> (coffee)=50. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-75-percent-of-the-guests-at-a-certain-banquet-ordered-des-168096.html
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Re: If 75 percent of the guests at a certain banquet ordered dessert, what   [#permalink] 29 Dec 2015, 22:08
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# If 75 percent of the guests at a certain banquet ordered dessert, what

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