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A candy company sells premium chocolate at $5 per pound and regular ch

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A candy company sells premium chocolate at $5 per pound and regular ch [#permalink]

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New post 16 Apr 2016, 05:56
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A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?

[A] 1
[B] 2
[C] 3
[D] 4
[E] 5


P.S => Bit modified..
[Reveal] Spoiler: OA

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Last edited by stonecold on 16 Apr 2016, 07:53, edited 1 time in total.
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Re: A candy company sells premium chocolate at $5 per pound and regular ch [#permalink]

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New post 16 Apr 2016, 06:12
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stonecold wrote:
A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?

[A] 1
2
[C] 3
[D] 4
[E] 5


P.S => Bit modifies..


let the number of premium be P and number of regular be R...
so 5P + 4R =31...
[b]clearly P has to ODD to make LHS Odd..
so P can take 1,3,5..
lets check for which values is R an integer..

when P=1
5+4R=31..
4R = 26.. NOT possible

when P=3
5*3+ 4R = 31
4R = 31-15 = 16
R = 4..
Ok

so ans is 3
C
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Re: A candy company sells premium chocolate at $5 per pound and regular ch [#permalink]

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New post 18 Apr 2016, 16:36
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This question is a bit of Special equations with a single set of unique values.

the Equation stands : 5X + 4Y = 31

Subtract multiple of 5 from 31 and check whether the remaining total is divisible by 4

31 - 5 = 26 -> Not divisible by 4
31 - 10 = 21 -> Not divisible by 4
31 - 15 =16 -> Divisible by 4
31 - 20 =11 -> Not divisible by 4
31 - 25 =6 -> Not divisible by 4
31 - 30 =1 -> Not divisible by 4
Any multiple of 5 hereon will give a negative value for regular chocolates bought and hence, inadmissible

Thus Amount spent on regular chocolate= $16
Amount spent on Premium chocolate= $15
Price per premium chocolate = $5
No. Of boxes of premium chocolate bought = 15 / 5 = 3
Correct Option : C
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Re: A candy company sells premium chocolate at $5 per pound and regular ch [#permalink]

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New post 18 Apr 2016, 21:21
stonecold wrote:
A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound in increment of whole pound only.If Barrett buys a pack of candies which costs him $31, how many pounds of premium chocolates are in the box?

[A] 1
[B] 2
[C] 3
[D] 4
[E] 5


P.S => Bit modified..


Check out a discussion of this concept here: http://www.veritasprep.com/blog/2011/06 ... -of-thumb/
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Re: A candy company sells premium chocolate at $5 per pound and regular ch [#permalink]

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New post 19 Apr 2016, 10:25
Obviously, sum of both is 15 and 16, divised by prices of 5 and 4.

Answer is 3
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Re: A candy company sells premium chocolate at $5 per pound and regular ch [#permalink]

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Re: A candy company sells premium chocolate at $5 per pound and regular ch   [#permalink] 23 Dec 2017, 03:40
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