On a weekend, 6 college friends went skiing and...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

On a weekend, 6 college friends went skiing and...

by swerve » Fri Jan 19, 2018 6:13 am

On a weekend, 6 college friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?

A. $126
B. $156
C. $218
D. $648
E. $1,728

The OA is C.

Please, can any expert explain this PS question for me? I'm not sure about it. I just need to divide each number by 6 and get the result?. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Jan 19, 2018 6:13 am

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

On a weekend, 6 college friends went skiing and...

by Brent@GMATPrepNow » Fri Jan 19, 2018 7:41 am

swerve wrote:On a weekend, 6 college friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?

A. $126
B. $156
C. $218
D. $648
E. $1,728

If the total cost is divisible by 6, then each of the 6 friends will pay an integer amount.

Take answer choice A ($126) for example.
126 is divisible by 6
$126/6 = $31
So, each person pays an integer amount ($31 each)
ELIMINATE A

The question is basically asking us to find the answer choice that is NOT divisible by 6

CONCEPT #1: A number is divisible by 6 if that number is divisible by 2 AND by 3
We can see that all 5 answer choices are divisible by 2.

CONCEPT #2: A number is divisible by 3 if the SUM OF THE DIGITS of that number is divisible by 3
Take answer choice B ($156) for example.
The sum of the digits = 1 + 5 + 6 = 12
Since 12 is divisible by 3, we can conclude that 156 is divisible by 3
ELIMINATE B

Answer choice C ($218)
The sum of the digits = 2 + 1 + 8 = 11
Since 11 is NOT divisible by 3, we can conclude that 218 is NOT divisible by 3
If 218 is NOT divisible by 3, then 218 is also NOT divisible by 6

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

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 » Fri Jul 26, 2019 11:14 am

swerve wrote:On a weekend, 6 college friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin?

A. $126
B. $156
C. $218
D. $648
E. $1,728

Since the total was divided amongst 6 people, the total must be a multiple of both 2 and 3. Recall that a number is divisible by 2 if its units digit is even, and a number is divisible by 3 if the sum of its digits is divisible by 3.

All of the answer choices are divisible by 2. The only choice that is not a multiple of 3 is C, since 2 + 1 + 8 = 11, which is not divisible by 3.

Answer: C

Scott Woodbury-Stewart
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