Today's tough question.. Help!

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yumi2012: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Mon Jul 23, 2012 1:59 pm; Thanked: 1 times

by yumi2012 » Sun Aug 18, 2013 8:26 pm

An eccentric casino owner decides that his casino should only use chips in $5 and $7 denominations. Which of the following amount cannot be paid out using these chips?

A. $31
B. $29
C. $26
D. $23
E. $21

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Source: Beat The GMAT — Problem Solving | Sun Aug 18, 2013 8:26 pm

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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 » Sun Aug 18, 2013 9:06 pm

yumi2012 wrote:An eccentric casino owner decides that his casino should only use chips in $5 and $7 denominations. Which of the following amount cannot be paid out using these chips?

A. $31
B. $29
C. $26
D. $23
E. $21

To determine the amount that CANNOT be paid out, we'll eliminate the amounts that CAN be paid out.

When we scan the 5 answer choices, we can see that we can eliminate 3 of them almost immediately.
We can pay out $21 using three $7 chips, so ELIMINATE E.
Since $26 is $5 greater than $21, we can pay out $26 using three $7 chips and one $5 chip. ELIMINATE C.
Since $31 is $10 greater than $21, we can pay out $31 using three $7 chips and two $5 chips. ELIMINATE A.

This leaves us with B and D.
We can pay out $29 using two $7 chips, and three $5 chips so ELIMINATE B.

By the process of elimination (POE), the correct answer must be D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Sun Aug 18, 2013 11:55 pm

yumi2012 wrote:An eccentric casino owner decides that his casino should only use chips in $5 and $7 denominations. Which of the following amount cannot be paid out using these chips?

A. $31
B. $29
C. $26
D. $23
E. $21

So every amount can be represented by N = 5a + 7b where a and b are whole numbers.

31 = 10 + 21
29 = 15 + 14
26 = 5 + 21
21 = 21

Choose D

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Aug 19, 2013 3:17 am

yumi2012 wrote:An eccentric casino owner decides that his casino should only use chips in $5 and $7 denominations. Which of the following amount cannot be paid out using these chips?

A. $31
B. $29
C. $26
D. $23
E. $21

Make a list of the MULTIPLES OF 5 and the MULTIPLES OF 7 less than 30:
5, 10, 15, 20, 25, 30
7, 14, 21, 28.

Determine the four answers answer choices that CAN be yielded by the list of values above.
A: 31 = 10+21
B: 29 = 15+14
C: 26 = 5+21
E: 21 = 21.

The correct answer is D.

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tarik: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Tue May 21, 2013 10:22 am

by tarik » Mon Aug 19, 2013 1:22 pm

Got it on time by elimination.

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