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1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60%

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1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   31 May 2019, 11:00
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1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y > 0, how many integer values can x take?

A. 10
B. 20
C. 35
D. 13
E. 30
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nick1816
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   31 May 2019, 12:39
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x.........y
....60....
1.........3

\(\frac{x-60}{60-y}\)=3/1
x+3y=240...(1)
x=240-3y=3(80-y)

We have 2 constraints
1. x=<100
2. x>y
Also, x will be a multiple of 3

x can be 99,96.....63
At x=60, y=60....Hence x can't take value equal to 60 or lower than 60.
Total number of integer values x can take= [\(\frac{99-63}{3}\)]+1=13



DisciplinedPrep wrote:
1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

A. 10
B. 20
C. 35
D. 13
E. 30
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KarishmaB
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   13 Jun 2019, 03:51
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DisciplinedPrep wrote:
1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

A. 10
B. 20
C. 35
D. 13
E. 30


1 part x% alcohol + 3 parts y% alcohol -> 60% alcohol

Since x > y, x must be greater than 60% and y must be less than 60% so that they average out to 60.
The maximum value of x can be 100% (the entire solution can be alcohol).
So x can take any integer value from 61 to 100.

But it seems that the intent of the question is that x and y both should be integer values.

y --- 60 --------- x

Since we are mixing 1 part x with 3 parts y, average will be 1 unit away from y and 3 units away from x.
So if y = 59, x = 63
if y = 58, x = 66
and so on...
x will take values from 63% to 99% i.e. (3*21) to (3*33)
This means (33 - 21 = )12 + 1 = 13 multiples of 3

Check this post for the scale method of weighted avgs:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -averages/
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   31 May 2019, 21:30
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Question is clear but OA is surprising.

The equation on which question depends is

x + 3y = 4*60

So we can start x with 61, which is integer value. We don't bother about Y. Y can take any value integer or not.

So IMHO answer is (100-61)+1 , which is 40.

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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   31 May 2019, 20:43
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nick1816 wrote:
x.........y
....60....
1.........3

\(\frac{x-60}{60-y}\)=3/1
x+3y=240...(1)
x=240-3y=3(80-y)

We have 2 constraints
1. x=<100
2. x>y
Also, x will be a multiple of 3

x can be 99,96.....63
At x=60, y=60....Hence x can't take value equal to 60 or lower than 60.
Total number of integer values x can take= [\(\frac{99-63}{3}\)]+1=13



DisciplinedPrep wrote:
1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

A. 10
B. 20
C. 35
D. 13
E. 30


I don't get it. x and y are concentration in percent. 3 and 1 are the value of units.
the 2 equations will be
1x + 3y = ?
x+y=60.

So we have to find to the value of x for which it is greater than y and the first equation gives a valid number.
right?
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Mohammad Ali Khan
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   31 May 2019, 23:14
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nick1816 wrote:
x.........y
....60....
1.........3

\(\frac{x-60}{60-y}\)=3/1
x+3y=240...(1)
x=240-3y=3(80-y)

We have 2 constraints
1. x=<100
2. x>y
Also, x will be a multiple of 3

x can be 99,96.....63
At x=60, y=60....Hence x can't take value equal to 60 or lower than 60.
Total number of integer values x can take= [\(\frac{99-63}{3}\)]+1=13



DisciplinedPrep wrote:
1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

A. 10
B. 20
C. 35
D. 13
E. 30



Why x has to be less than or equ. 100? i could not understand. please guide??
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bhupendersingh27
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   21 Nov 2020, 10:09
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if Y is not integer than X=61% and Y=179/3% will work, in that case there can be 40 integer values for x.
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   12 Jun 2019, 17:51
Mohammad Ali Khan wrote:
nick1816 wrote:
x.........y
....60....
1.........3

\(\frac{x-60}{60-y}\)=3/1
x+3y=240...(1)
x=240-3y=3(80-y)

We have 2 constraints
1. x=<100
2. x>y
Also, x will be a multiple of 3

x can be 99,96.....63
At x=60, y=60....Hence x can't take value equal to 60 or lower than 60.
Total number of integer values x can take= [\(\frac{99-63}{3}\)]+1=13



DisciplinedPrep wrote:
1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

A. 10
B. 20
C. 35
D. 13
E. 30



Why x has to be less than or equ. 100? i could not understand. please guide??


Maximum value of aclhogol in unit is 100%
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rwcg2d
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   20 Nov 2020, 16:35
Where does the question state that Y must also be an integer? Wouldn't a combination of X = 31, Y = 29/3 still work?
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   20 Nov 2020, 21:36
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rwcg2d wrote:
Where does the question state that Y must also be an integer? Wouldn't a combination of X = 31, Y = 29/3 still work?



Hi rwcg2d, these values will not give an overall 60% by volume by alcohol.

1 unit of 31% alcohol will have 0.31 units of alcohol

3 units of 29/3 % alcohol will have 0.29 units of alcohol

Total 4 units, of which Total alcohol = 0.6

The % is (0.6/4) * 100 = 15%

Hope this helps

Arun Kumar
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   23 Nov 2020, 08:15
bhupendersingh27 wrote:
if Y is not integer than X=61% and Y=179/3% will work, in that case there can be 40 integer values for x.


I agree, Y doesn’t have to be an integer here.
Not sure where that is coming from.

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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink] New post   15 May 2022, 20:45
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Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% [#permalink]
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