At a certain pizzeria, 1/8 of the pizzas sold in one week were mushroom

[BTGModeratorVI]

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

Source: Official Guide
Answer: B

[Jay@ManhattanReview]

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

Source: Official Guide
Answer: B

Say x numbers of pizzas were sold; thus, the no. mushroom pizzas sold = x/8; the remaining pizzas = x – x/8 = 7x/8

=> the no. pepperoni pizzas sold = 1/3 of 7x/8 = 7x/24

=> 7x/24 = n => x = 24n/7

=> the no. mushroom pizzas sold = x/8 = (24n/7)/8 = 3n/7

The correct answer: B

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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

Source: Official Guide
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

[Scott@TargetTestPrep]

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

Source: Official Guide
Answer: B

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