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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]
  
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  31 May 2019, 11:00
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  33% (03:28) correct 67% (02:46) wrong based on 55 sessions
  
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  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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  Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60%  [#permalink]
  
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  31 May 2019, 12:39
  3
  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
  ##### General Discussion
  Manager
  Joined: 25 Mar 2018
  Posts: 89
  Location: India
  GMAT 1: 640 Q50 V26
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  WE: Analyst (Manufacturing)
  Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60%  [#permalink]
  
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  31 May 2019, 21:30
  2
  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.
  
  Posted from my mobile device
  Veritas Prep GMAT Instructor
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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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  13 Jun 2019, 03:51
  1
  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.veritasprep.com/blog/2011/0 ... -averages/
  _________________
  Karishma
  Veritas Prep GMAT Instructor
  
  Manager
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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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  31 May 2019, 20:43
  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?
  Manager
  Joined: 11 Aug 2017
  Posts: 59
  Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60%  [#permalink]
  
  ### Show Tags
  
  31 May 2019, 23:14
  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??
  Manager
  Joined: 01 Oct 2018
  Posts: 112
  Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60%  [#permalink]
  
  ### Show Tags
  
  12 Jun 2019, 17:51
  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%
  Re: 1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60%   [#permalink] 12 Jun 2019, 17:51
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