At a family summer party, each of the x members of the family

Question

At a family summer party, each of the x members of the family chose whether or not to have a hamburger and whether or not to have a hotdog. If 1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog, then how many family members chose NOT to have both.

A. x/21
B. x/10
C. 9x/10
D. 10x/21
E. 20x/21

A. x/21
B. x/10
C. 9x/10
D. 10x/21
E. 20x/21

chetan2u · Accepted Answer

hi..

what is it asking -  person who did not have BOTH.  
WHAT will it include -  who ate any ONE only or NONE : SAME as ALL-BOTH

ALL is x
BOTH is  \frac{1}{7} of \frac{1}{3}  of x= \frac{x}{21}

ans  x-\frac{x}{21}=\frac{20x}{21} 
E

HolaMaven · Answer

Let x=21
 \frac{1}{3} *21 = 7 chose to have hamburger
 \frac{1}{7} of7 = 1 chose to have both
so remaining 20 (i.e.21-1) will not have both.
Option E,  \frac{20*21}{21}  = 20 gives that answer
So  option E

rahulkashyap · Answer

The questions asks for neither x nor y. I believe that some info is missing from this problem.

We have information for both x and y and x and not y.

chetan2u  , could you please help with this

tommh · Answer

I get how it's figured out, but what about the people who chose to have a hotdog and not a hamburger? Do we not need to know this?

X is all the people - let's call this 21
Therefore, 7 chose to have a hamburger and 14 chose not to have a hamburger.
Of this 7, 1 chose to also have a hotdog. This leaves 6 people who only had a hamburger.
Of the 14 who chose not to have a hamburger, how many chose to have a hotdog and not a hamburger? - We don't know this piece of information, so surely it's a proportion of the 20x/21?

monikaranchi26 · Answer

Say, Hamburger = H & Hotdog = D
Given n(H) =X/3 , Total = X
 and n(D) = X- X/3 = 2X/3
Both = X/3 * 1/7 = X/21
Only H = X/3-X/21 = 6X/21
Only D = 2X/3-X/21 =13X/21
We know that, Total = n(H) + n(D) - n(H&B) + Neither
 X = X/3 + 2X/3 - X/21 + Neither
 Neither = X/21
 So, who eat none = only H+ only D + Neither
 = 6X/21+13X/21+X/21
 = 20X/21.

testcracker · Answer

(1/3) * (1/7) = 1/21 = both anything other than both = 1 - (1/21) 20/21 thanks cheers through the kudos button if this helps

BrentGMATPrepNow · Answer

These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach. 
Here's the INPUT-OUTPUT approach.

It might be useful to choose a number that works well with the fractions given in the question (1/3 and 1/7). 
So, let's say there are 21 family members at the party. 
In other words, we're saying that  x = 21

1/3 chose to have a hamburger, and of those 1/7 chose to also have a hotdog.  
1/3 of  21  is 7, so 7 people chose to have a hamburger. 
1/7 of 7 = 1, so  1  person had BOTH a hamburger AND a hotdog.

How many family members chose NOT to have both?  
If  1  person had BOTH a hamburger AND a hotdog, then the remaining  20  people did  not  have BOTH a hamburger AND a hotdog.

So, when we INPUT  x = 21 , the answer to the question is " 20  people did  not  have BOTH a hamburger AND a hotdog"

Now we'll INPUT  x = 21  into each answer choice and see which one yields the correct OUTPUT of  20

A.  21 /21 =  1 . We want an output of  20 . ELIMINATE A.
B.  21 /10 =  2.1 . We want an output of  20 . ELIMINATE B.
C. (9)( 21 )/10 =  18.9 . We want an output of  20 . ELIMINATE C.
D. (10)( 21 )/21 =  10 . We want an output of  20 . ELIMINATE D.
E. (20)( 21 )/21 = =  20 . PERFECT!

Answer: E

HAPPYatHARVARD · Answer

How to get the missing variable? I think the question is missing some data. HI  Bunuel  can you please check this?

ScottTargetTestPrep · Answer

Since x * 1/3 * 1/7 = x/21 of the family members have both a hamburger and a hotdog, 20x/21 of the family members do not have both.

Answer: E

zeniamehta · Answer

No data is missing..Que asks how many people did not have both which includes people who had one (either hamburger or hotdog) + people who had neither (No ham no hotdog)

Hope that helps.

bumpbot · Answer

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At a family summer party, each of the x members of the family

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At a family summer party, each of the x members of the family

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