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

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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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Explaination:

Let total no. of pizza sold = 168

1/8 of the pizzas sold in one week were mushroom, so mushroom pizza = 1/8 . 168 = 21

Remaining pizza = 168 - 21 = 147

1/3 of the remaining pizzas sold were pepperoni, so pepperoni pizza = 147/3 = 49

If 49 implies to n, then 21 implies to 21n/49 = 3n/7
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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The crux of the question is 1/3 of the remaining pizzas sold were pepperoni

So Lets say Total = x
Mushroom Pizza = m = x/8
Therefore x = 8m
Pepperoni Pizaa = n = (1/3)(7x/8) = 24x/7 [1/8th were mushroon so rest pizzas are 7/8th]
Therefore x= 24n/7

Now 8m = 24n/7
m= 3n/7

Difficulty level - 600
Time Taken - 1:07

Bunuel can you please guide me on how to insert fractions and special symbols in a reply ? I think I have to insert pics.
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
wow the gmat certainly goes out of their way to trick you... i kept thinking 1/3 sold was pizza, not the remaining of the 1/8... sigh
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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In such questions, representing the given information visually in a rough tree structure reduces the chances of making an error:

Given: $$\frac{7t}{24}=n$$
=> $$t=\frac{24n}{7}$$
=> $$\frac{t}{8} = \frac{3n}{7}$$
=> Number of Mushroom pizzas sold = $$\frac{3n}{7}$$

Hope this helped!

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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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pepo wrote:
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

Is possible to solve this question plugging a number for "n"?
Thanks!

Hi,

yes it is pssible to solve this Q by plugging values for either 'n' or TOTAL..
better would be TOTAL, since taking value of 'n' would mean working backwards..

so take total as LCM of 8 and 3 as we have two fractions 1/8 and 1/3..
LCM is 24, so take Total =24..
Mushroom= 3... this should be the answer from the choices
so remaining = 24-3=21
therefore n= 1/3 of 21= 7..

Now substitute n as 7 in choices, the choice which gives you answer as 3 is the CORRECT answer

Only B gives you 3, so the correct answer
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
Total T

Mushroom = 1/8T

Pep = 1/3 * 7/8T

Pep = n

So, 1/3 * 7/8T = n ; 7/8T = 3n

1/8 = 3/7 * n
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
Bunuel wrote:

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

Let, Total Pizza = x

Mushroom Pizza = (1/8)*x

Remaining Pizza = x-(1/8)x = (7/8)x

Pepperoni Pizza = (!/3) of remaining pizzas = (1/3)* (7/8)x = (7/24)x

Given, n = (7/24)x i.e. x = 24n/7

Mushroom PIzzas = (1/8)*(24 n/7) = 3n/7

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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

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

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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
Bunuel wrote:

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

Clue 1: "1/8 of the pizzas sold in one week were mushroom" = 1/8 P = Mushroom which means 7/8 P = NOT_Mushroom

Clue 2: "1/3 of the remaining pizzas sold were pepperoni" = 1/3 (NOT_Mushroom) = R => 1/3 * 7/8 * P = R

Clue 3: "if n of the pizzas sold were pepperoni" = 1/3 * 7/8 * P = n

Clue 4: "how many were mushroom" means 1/8 P = ? i.e. you dont care about the value of P you care about the whole thing "1/8 * P"

Take equation 3 and rearrange it:

( 7 * P) / (3 * 8) = n =>

(divide both sides with 7) => P/ (3*8) = n/7 =>

(multiply both sides with 3) 1/8 * P = 3n/7

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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
Bunuel wrote:
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

Let uring the week 24 pizzas were sold..

So, Mushroom pizzas soldd = 3 ; remaining Pizzas = 21

Peperroni Pizza = 7 ; remaining pizzas is 14

Now, n = 7 , so no of Mushroom Pizzas sold is $$\frac{3n}{7}$$

Hence, correct answer must be (B) $$\frac{3n}{7}$$
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
Weirdly worded question. Almost as bad as the clock that strikes question.

Anyway, once I got past the wording, I did the following:

8/8 is total pizza sold
1/8 is mushroom sold
8/8 - 7/8 = the remainder

1/3 x 7/8 = pepperoni = 7/24
7/24 = n

when you go to plug in 7/24 into the answer choices... 3/8 x 7/24 does not equal 1/8

However, with 3/7 x 7/24 = 3/24 = 1/8 = mushroom

Therefore, the answer is (B) 3/7 n
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

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

Cheers,
Brent
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
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

Let x be the number of pizzas sold.

x/8 = mushroom

1/3 x 7x/8 = 7x/24 = pepperoni

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

24n/7 / 8 = 3n/7

B.
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Re: At a certain pizzeria, 1/8 of the pizzas sold in one week were [#permalink]
Video solution here (2:59):

A key habit is to read carefully! A common mistake on word problems is to misread the "OF ____" part; here, we must not overlook the word "1/3 of the REMAINING pizzas."

0:16: Method 1 — Pick a number for the total pizzas, "T". We use the Least Common Multiple (LCM) of 8 and 3, which is 24.

1:42: Method 2 — Fast Algebra. It's essential to get very fluent translating words to equations.
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