obligatory brunch

[sanju09]

An auditorium's entry fee is $7 per adult and $3 per child. The obligatory brunch servings inside the auditorium cost $14 per adult and $5 per child. Did the auditorium make more revenue from the children's entry fee than that of the adults, the last Sunday?

(1) There were 4 more children than the adults entered the auditorium the last Sunday.

(2) The auditorium made more revenue from the children's brunch servings than that of the adults, the last Sunday.

[rockeyb]

An auditorium's entry fee is $7 per adult and $3 per child. The obligatory brunch servings inside the auditorium cost $14 per adult and $5 per child. Did the auditorium make more revenue from the children's entry fee than that of the adults, the last Sunday?

(1) There were 4 more children than the adults entered the auditorium the last Sunday.

(2) The auditorium made more revenue from the children's brunch servings than that of the adults, the last Sunday.

This is a Yes / No question so we need a definite yes / no form the answer options any option giving contradictory values will be insufficient .

We need to find if the revenue from children's entry fee was more than adults' entry fees.


(1) There were 4 more children than the adults entered the auditorium the last Sunday.

Lets say there were 2 adults in auditorium so number of children = 6 .

Revenue from adults' entry fees = 14

Revenue from children's entry fees = 18. So the answer is Yes .

But if number of adults = 3 then number of children = 7.

Revenue from adults' entry fees = 21

Revenue from children's entry fees = 21. So the answer is No .

We get both a Yes as well as a No from statement (1) not sufficient .

(2) The auditorium made more revenue from the children's brunch servings than that of the adults, the last Sunday.

Cost of brunch for adults = $14 per adult.

Cost of brunch for children = $5 per child.

Let number of adults = 1

Then no of children has to be at least 3 so that revenue from children's brunch servings is more than that of adults.

If you keep on plugging numbers you will see that number of children will always be 3 times the number of adults present .

Hence Revenue from children's entry fees will be greater than adults' entry fees.

Sufficient . B

[eaakbari]

IMO B

Stem :
Fee Revenue from adult = 7a where a = no. of adults
Revenue from children = 3c where c = noo. of children

We have to determine whether 7a>3c or not

(1)substitute c-a = 4 into the equation we get
4a>12 or a>3
which does not help us
Hence Insuff

(2)
The min ratio for the condition to be satisfied is c:a=3:a
Substituting this in above inequalities we find children revenue is greater
Hence suff

Answer B

Do confirm

[sanju09]

IMO B

Stem :
Revenue from adult = 21a where a = no. of adults
Revenue from children = 8c where c = noo. of children

We have to determine whether 21a>8c or no

(1)substitute c-a = 4 into the equation we get
17a>32
which does not help us
Hence Insuff

(2)
The min ratio for the condition to be satisfied is c:a=3:a
Substituting this in above inequalities we find children revenue is greater
Hence suff

Answer B

Do confirm

If auditorium's entry fee structure is not in proportion to its brunch servings' fee structure, then won't it be chancy to accumulate the two structures all unnecessarily?

[maihan]

I agree with sanju09.

We need to know whether revenue from the children's entry fee is higher than revenue from the adults' entry fee.

The inequality should be 3C > 7A (C and A are number of children and adults, respectively)

From (1), there were 4 more children than the adults entered the auditorium the last Sunday

=> C=A+4. Plug into the inequality, we have 3A+12>7A => A<3.
Hence, if number of adults are <3, the answer is Yes. If number of adults are > or = 3, the answer is No.
=> insufficient.

From (2), the auditorium made more revenue from the children's brunch servings than that of the adults, the last Sunday.
=> 5C>14A => C>3A approximately. Plug into the inequality, we have 3C>3x3A>7A or 3C>9A>7A
Hence, the equality satisfies with all A. The answer is Yes.
=> sufficient.

So I choose B

Please correct me if I'm wrong.

[eaakbari]

IMO B

Stem :
Revenue from adult = 21a where a = no. of adults
Revenue from children = 8c where c = noo. of children

We have to determine whether 21a>8c or no

(1)substitute c-a = 4 into the equation we get
17a>32
which does not help us
Hence Insuff

(2)
The min ratio for the condition to be satisfied is c:a=3:a
Substituting this in above inequalities we find children revenue is greater
Hence suff

Answer B

Do confirm

If auditorium's entry fee structure is not in proportion to its brunch servings' fee structure, then won't it be chancy to accumulate the two structures all unnecessarily?

Thanks for correcting me here sanju, I misread the question. Nevertheless, answer remains the same, shall edit my post