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
Pizza Problem
This topic has expert replies
-
- Junior | Next Rank: 30 Posts
- Posts: 11
- Joined: Thu Apr 17, 2008 11:33 am
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.
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.
-
- Senior | Next Rank: 100 Posts
- Posts: 62
- Joined: Fri Dec 21, 2007 2:58 pm
- Location: Fremont , California
- Thanked: 3 times
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
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
-
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Tue Jun 03, 2008 10:30 pm
- Location: noida,new delhi
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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let the total number of pizzas = xMBALA2009 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 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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Let T = the total number of pizzas soldMBALA2009 wrote: ↑Tue Jun 03, 2008 6:51 pmIs 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
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