Pizza Problem

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MBALA2009: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Wed May 07, 2008 12:08 pm; Location: Toronto, Canada

by MBALA2009 » Tue Jun 03, 2008 6:51 pm

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

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Source: Beat The GMAT — Problem Solving | Tue Jun 03, 2008 6:51 pm

athinabean: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Thu Apr 17, 2008 11:33 am

by athinabean » Tue Jun 03, 2008 8:24 pm

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.

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kishore: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Fri Dec 21, 2007 2:58 pm; Location: Fremont , California; Thanked: 3 times

by kishore » Tue Jun 03, 2008 8:33 pm

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

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singhpradeep: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Jun 03, 2008 10:30 pm; Location: noida,new delhi

by singhpradeep » Wed Jun 04, 2008 4:24 am

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8177; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Dec 05, 2017 5:25 pm

MBALA2009 wrote: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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: Pizza Problem

by Brent@GMATPrepNow » Fri Feb 07, 2020 7:08 am

MBALA2009 wrote: ↑
Tue Jun 03, 2008 6:51 pm
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

Brent Hanneson - Creator of GMATPrepNow.com

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