Josh, the manager

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Tue May 22, 2012 2:17 am

Josh, the manager of a bookstore cafe, is completing his weekly sales summary. Each customer bought either a cappuccino or a juice and the cafe sold 50% more juice than cappuccino. One third of the customers who did not buy a cappuccino also bought a brownie and 3/4 of the total customers also bought a bagel. If the number of bagels sold was 300 more than three times the number of brownies, how many customers did Josh's cafe serve?

A: 400 B: 800 C: 1200 D: 2000 E; 6000

I got thrown off initially by the somewhat convoluted wordings under testing condition.
Could someone please explain the algebraic approach....thanks.

Source: Princeton Review Test 2.

OA:

D

Source: Beat The GMAT — Problem Solving | Tue May 22, 2012 2:17 am

GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Tue May 22, 2012 2:39 am

We will have to go from answer to question.

I prefer getting it from the last option.
In that way 2000 fits in the question.

C= 800
j= 1200

Brownie = 400
Bagel = 1500

IMO: D

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Tue May 22, 2012 2:40 am

gmatdriller wrote:Josh, the manager of a bookstore cafe, is completing his weekly sales summary. Each customer bought either a cappuccino or a juice and the cafe sold 50% more juice than cappuccino. One third of the customers who did not buy a cappuccino also bought a brownie and 3/4 of the total customers also bought a bagel. If the number of bagels sold was 300 more than three times the number of brownies, how many customers did Josh's cafe serve?

A: 400 B: 800 C: 1200 D: 2000 E; 6000

Source: Princeton Review Test 2.

OA: D

Choosing appropriate variables and forming equations out of the information given,

J = 1.5C -- (1)

(1/3) of J = Brownies -- (2)
(because those who did not buy a Cappuccino, bought a Juice)

(3/4) of (J + C) = Bagels -- (3)

Bagels = 3*Brownies + 300 -- (4)

Substituting Brownies and Bagels from (2) and (3) respectively,
(3/4)*(J + C) = 3*(J/3) + 300
Substituting J = 1.5C from (1),
(3/4)*(5C/2) = (3C/2) + 300
15C/8 - 3C/2 = 300
C = 800

Total = J + C = 2.5*C = 2000

[spoiler](D)[/spoiler] is correct.

Aneesh Bangia
GMAT Math Coach
[email protected]

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Tue May 22, 2012 3:41 am

I have seen my errors and have taken note of them;

Thanks all for your help.

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