Three men sit at a table. One dollar is placed in front of

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Wed Dec 05, 2018 2:40 pm

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Source: EMPOWERgmat

Three men sit at a table. One dollar is placed in front of each of them. When a buzzer sounds, the first man to touch the money in front of him keeps the money that is in front of him, while the other two receive nothing. If none of the three men touches the money in front of them, then the amount of money doubles for the next round. After five rounds of this activity, what is the maximum amount of money that any one man could receive?

A. $4
B. $5
C. $10
D. $15
E. $16

The OA is E

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Source: Beat The GMAT — Problem Solving | Wed Dec 05, 2018 2:40 pm

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Wed Dec 05, 2018 3:25 pm

BTGmoderatorLU wrote:Source: EMPOWERgmat

Three men sit at a table. One dollar is placed in front of each of them. When a buzzer sounds, the first man to touch the money in front of him keeps the money that is in front of him, while the other two receive nothing. If none of the three men touches the money in front of them, then the amount of money doubles for the next round. After five rounds of this activity, what is the maximum amount of money that any one man could receive?

A. $4
B. $5
C. $10
D. $15
E. $16
The OA is E

Let's see what happens if a man waits until the last (5th) round to take the money.

Round #1: $1 placed in front of the man (but he doesn't take it)
Round #2: Now, $2 placed in front of the man (but he doesn't take it)
Round #3: Now, $4 placed in front of the man (but he doesn't take it)
Round #4: Now, $8 placed in front of the man (but he doesn't take it)
Round #5: Now, $16 placed in front of the man, and this time he takes it

So, it's POSSIBLE for 1 man to receive $16, but is is possible to receive MORE THAN $16?
Fortunately, we need not concern ourselves with this question, since $16 is the biggest possible answer choice.

So, the correct answer must be E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Thu Dec 06, 2018 11:20 am

The maximum amount of money collected at the end of the 5 turns will be when the first 4 turns end up in no one touching it.

After 1st: $1 becomes $2
After 2nd: $2 becomes $4
After 3rd: $4 becomes $8
After 4th: $8 becomes $16

Thus the maximum amount of money = $16. E is the correct answer.

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