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# Albert sells chocolate ice-cream for \$0.15 per cup and

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SVP
Joined: 04 May 2006
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Albert sells chocolate ice-cream for \$0.15 per cup and [#permalink]

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23 May 2008, 02:51
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Albert sells chocolate ice-cream for \$0.15 per cup and vanilla ice-cream for \$0.14 per cup. If Albert earned \$5 during his day's work, what is the least number of vanilla cups he could have sold?

0
5
10
15
20

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Kudos [?]: 1399 [0], given: 1

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4585 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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23 May 2008, 03:12
1
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Expert's post
C

we can write out: 0.15x+0.14y=5 or 15x+14y=500
1. 15x and 500 is divisible by 5, so 14y has to be also divisible by 5
2. It is possible for y=0,5,10,15.... or y=5k where k in an integer.
3. 15x+14*5k=500 --> 3x=100-14k
4. find the least number k that 100-14k is divisible by 3: 100 is not, 86 is not, 72 - is divisible (k=2) and therefore, x=10.
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Kudos [?]: 4585 [1], given: 360

Manager
Joined: 11 Apr 2008
Posts: 153

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Schools: Kellogg(A), Wharton(W), Columbia(D)

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23 May 2008, 05:26
sondenso wrote:
Albert sells chocolate ice-cream for \$0.15 per cup and vanilla ice-cream for \$0.14 per cup. If Albert earned \$5 during his day's work, what is the least number of vanilla cups he could have sold?

0
5
10
15
20

Let,
No. of chocolate ice-cream for \$0.15 per cup = C
No. of vanilla ice-cream for \$0.14 per cup = V

15*C + 14* V = 500 (\$5 total)
So,

Plug options where you get C as an integral value, start from ..0
15*C = 500 X
15*C = 500 - 14*5 = 430 X
15*C = 500 - 14*10 = 360 Done!

Kudos [?]: 68 [0], given: 0

SVP
Joined: 04 May 2006
Posts: 1881

Kudos [?]: 1399 [0], given: 1

Schools: CBS, Kellogg

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23 May 2008, 19:06
walker wrote:
C

we can write out: 0.15x+0.14y=5 or 15x+14y=500
1. 15x and 500 is divisible by 5, so 14y has to be also divisible by 5
2. It is possible for y=0,5,10,15.... or y=5k where k in an integer.
3. 15x+14*5k=500 --> 3x=100-14k
4. find the least number k that 100-14k is divisible by 3: 100 is not, 86 is not, 72 - is divisible (k=2) and therefore, x=10.

Yeah, so cool this reasoning! Many thanks, Walker!
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Re: Albert sells chocolate ice-cream for \$0.15 per cup and [#permalink]

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05 Mar 2017, 05:37
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Re: Albert sells chocolate ice-cream for \$0.15 per cup and   [#permalink] 05 Mar 2017, 05:37
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