Pizza Problem

[MBALA2009]

Is there a way to answer the follow problem picking numbers?

At a certain pizzeria. 1/8 of the pizzas sold in one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni. If n of the pizzas sold were pepperoni, how many were mushroom?

(A) 3/8n
(B) 3/7n
(C) 7/16n
(D) 7/8n
(E) 3n

Answer: B

[athinabean]

Hi,
How about:
Total pizzas: 24 (works with both 8 and 3 in the fractions)
1/8 mushroom =3
1/3 pepperoni (1/3 of 21 left overleft over) = 7
N=7

So, in B, 3/7*7 is 3 => 3 mushroom pizzas.

hope it helped.

[kishore]

At a certain pizzeria. 1/8 of the pizzas sold in one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni. If n of the pizzas sold were pepperoni, how many were mushroom?


Total Number of Pizza's = x

Mushrooms = 1/8(x)

Pepperoni = 1/3(Remaining Pizza's)
= 1/3(7/8 * x)
= 7/24 (x)
since,n of the pizzas sold were pepperoni

n = 7/24 (x)

This can also be written as

n = 7/3 * 1/8 (x)

n = 7/3 (M) (since Mushrooms, M = 1/8 x)

3n = 7 M

=> 7M = 3n
=> M = 3n/7

3n/7 is the answer

[singhpradeep]

let total pizzas are X
then mushroom are X/8
and peprny are 1/3(X-X/ 8)=7X/24 and this equals to n
so X=24n/7 ie toal pizzas
so mushroom are 24n/7*1/8=3n/7

[Scott@TargetTestPrep]

Is there a way to answer the follow problem picking numbers?

At a certain pizzeria. 1/8 of the pizzas sold in one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni. If n of the pizzas sold were pepperoni, how many were mushroom?

(A) 3/8n
(B) 3/7n
(C) 7/16n
(D) 7/8n
(E) 3n

We can let the total number of pizzas = x

We are given that 1/8 of the pizzas sold in one week were mushroom, which we can represent as (1/8)x.

Next we are given that 1/3 of the remaining pizzas sold were pepperoni and that n of the pizzas sold were pepperoni. Since 1/8 of the pizzas were mushroom, 1 - 1/8 or 7/8 of the pizzas were the remaining pizzas. Thus:

1/3(7/8)x = n

(7/24)x = n

x = (24/7)n

Since x = (24/7)n, the number of mushroom pizzas sold was (1/8)(24/7)n = (24/56)n = (3/7)n

Answer: B

[Brent@GMATPrepNow]

Is there a way to answer the follow problem picking numbers?

At a certain pizzeria. 1/8 of the pizzas sold in one week were mushroom and 1/3 of the remaining pizzas sold were pepperoni. If n of the pizzas sold were pepperoni, how many were mushroom?

(A) 3/8n
(B) 3/7n
(C) 7/16n
(D) 7/8n
(E) 3n

Answer: B

Let T = the total number of pizzas sold

1/8 of the pizzas sold in one week were mushroom
So, T/8 = the total number of mushroom pizzas sold

Aside: 7T/8 pizzas are still unaccounted for.

1/3 of the remaining pizzas sold were pepperoni
So, 1/3 of 7T/8 = number of pepperoni pizza sold
Another words, 7T/24 = number of pepperoni pizza sold

If n of the pizzas sold were pepperoni, how many were mushroom?
In other words, 7T/24 = n

IMPORTANT: We already know that T/8 = the total number of mushroom pizzas sold
So, our job now is to take the equation 7T/24 = n and rewrite it so that we can determine the value of T/8

Take: 7T/24 = n
Multiply both sides by 3 to get: 7T/8 = 3n
Now divide both sides by 7 to get: T/8 = 3n/7

Answer: B

Cheers,
Brent