Arithmetic

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Arithmetic

by BTGmoderatorRO » Fri Dec 29, 2017 9:04 am

Wonka Bars sell for $1 each. Willy Wonka also accepts three Wonka Bar wrappers in exchange for a Wonka Bar. Violet has $8 and Veruca has $7. If they decide to pool their money together, buy the maximum possible number of Wonka bars and split the bars equally between them, how many Wonka bars will Veruca have?

A) 10
B) 11
C) 15
D) 20
E) 22

OA is B
I want an Expert to do a breakdown of this question. A contribution will be highly appreciated.

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Source: Beat The GMAT — Problem Solving | Fri Dec 29, 2017 9:04 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sun Dec 31, 2017 1:59 pm

Wonka Bars sell for $1 each. Willy Wonka also accepts three Wonka Bar wrappers in exchange for a Wonka Bar. Violet has $8 and Veruca has $7. If they decide to pool their money together, buy the maximum possible number of Wonka bars and split the bars equally between them, how many Wonka bars will Veruca have?

A) 10
B) 11
C) 15
D) 20
E) 22

OA is B
I want an Expert to do a breakdown of this question. A contribution will be highly appreciated.

Hi Roland2rule,
Let's take a look at your question.

Voilet and Veruca have a combined total of $15.
Each Wonka bar cost $1.
Therefore, they can get 15 wonka bars.

Now, 15 Wonka bars will generate 15 wrappers.
3 wrappers can be exchanged with 1 Wonka bar.
Therefore, using 15 wrappers they can get 5 wonka bars.

Now these 5 Wonka bars will generate another 5 wrappers.
Using 3 of the wrappers they will get 1 wonka bar.

2 wrappers already left + 1 more wrapper of the last Wonkabar will make 3 wrappers again to get 1 more wonka bar.

Hence,
total Wonkabars they got = 15 + 5 + 1 + 1 = 22

Voilet and Veruca are splitting the bars equally between them, so Veruca will get 11 bars.

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Aug 25, 2019 5:41 pm

BTGmoderatorRO wrote:Wonka Bars sell for $1 each. Willy Wonka also accepts three Wonka Bar wrappers in exchange for a Wonka Bar. Violet has $8 and Veruca has $7. If they decide to pool their money together, buy the maximum possible number of Wonka bars and split the bars equally between them, how many Wonka bars will Veruca have?

A) 10
B) 11
C) 15
D) 20
E) 22

OA is B
I want an Expert to do a breakdown of this question. A contribution will be highly appreciated.

With a total of $15, they first can buy 15 Wonka bars. Next, with 15 Wonka bar wrappers (after they eat the candy bars), they can exchange for 5 Wonka bars. With the 5 Wonka bars and hence 5 wrappers, they can use 3 wrappers to exchange for 1 bar, and eat that bar and use that wrapper and the remaining 2 wrappers to exchange for 1 more bar. Therefore, in total, they can have a maximum of 15 + 5 + 1 + 1 = 22 bars. Since they split them equally between themselves, each will have 11 bars.

Answer: B

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