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  # The cost per kg of rice varies inversely with the square of the quanti
  
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  The cost per kg of rice varies inversely with the square of the quanti  [#permalink]
  
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  16 Jan 2020, 03:19
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  Difficulty:
  
  35% (medium)
  
  Question Stats:
  
  79% (01:38) correct 21% (01:54) wrong based on 33 sessions
  
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  The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?
  
  A. 5 million tons
  B. 5.25 million tons
  C. 5.5 million tons
  D. 5.75 million tons
  E. 6 million tons
  
  _________________
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  Posts: 5904
  Location: India
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  Re: The cost per kg of rice varies inversely with the square of the quanti  [#permalink]
  
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  16 Jan 2020, 07:37
  given
  x = 36* 49
  x= 1764
  now
  1764/49 = x^2
  x= 6
  IMO E
  
  Bunuel wrote:
  The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?
  
  A. 5 million tons
  B. 5.25 million tons
  C. 5.5 million tons
  D. 5.75 million tons
  E. 6 million tons
  Target Test Prep Representative
  Status: Founder & CEO
  Affiliations: Target Test Prep
  Joined: 14 Oct 2015
  Posts: 9443
  Location: United States (CA)
  Re: The cost per kg of rice varies inversely with the square of the quanti  [#permalink]
  
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  18 Jan 2020, 12:49
  1
  Bunuel wrote:
  The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?
  
  A. 5 million tons
  B. 5.25 million tons
  C. 5.5 million tons
  D. 5.75 million tons
  E. 6 million tons
  
  Recall that if y varies inversely with x, we let k = the constant of proportionality and we set up the following equation:
  
  y = k * (1/x)
  
  If y varies inversely with the square of x, then the equation is modified to:
  
  y = k * (1/(x^2))
  
  For this question, let’s let c = the cost per kg of rice and q = the quantity produced. Thus, we have:
  
  c = k * (1/(q^2))
  
  36 = k * (1/(7^2))
  
  36 = k * (1/49)
  
  36 * 49 = k
  
  k = 36 * 49 (Note that we do not perform the final multiplication here.)
  
  Now we can let x = the number of millions of tons of rice produced such that the cost was \$49/kg and create the equation:
  
  49 = k * (1/(x^2))
  
  49 = 36 * 49 * (1/(x^2))
  
  1/36 = (1/(x^2))
  
  x^2 = 36
  
  x = 6 million tons
  
  _________________
  
  # Scott Woodbury-Stewart
  
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  Re: The cost per kg of rice varies inversely with the square of the quanti   [#permalink] 18 Jan 2020, 12:49
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explanation: The provided text is a GMAT question related to the concept of inverse variation. It describes a scenario where the cost per kilogram of rice is inversely proportional to the square of the quantity of rice produced in a year. The question provides a specific instance where 7 million tons of rice were produced at a cost of \$36/kg and asks for the production quantity when the cost was \$49/kg. The text includes the question and multiple-choice answers but does not provide the solution or the correct answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
  
   It is currently 22 Feb 2020, 18:27
  
  ### GMAT Club Daily Prep
  
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  # The cost per kg of rice varies inversely with the square of the quanti
  
  Author Message
  TAGS:
  
  ### Hide Tags
  
  Math Expert
  Joined: 02 Sep 2009
  Posts: 61396
  The cost per kg of rice varies inversely with the square of the quanti  [#permalink]
  
  ### Show Tags
  
  16 Jan 2020, 03:19
  00:00
  
  Difficulty:
  
  35% (medium)
  
  Question Stats:
  
  79% (01:38) correct 21% (01:54) wrong based on 33 sessions
  
  ### HideShow timer Statistics
  
  The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?
  
  A. 5 million tons
  B. 5.25 million tons
  C. 5.5 million tons
  D. 5.75 million tons
  E. 6 million tons
  
  _________________
  GMAT Club Legend
  Joined: 18 Aug 2017
  Posts: 5904
  Location: India
  Concentration: Sustainability, Marketing
  GPA: 4
  WE: Marketing (Energy and Utilities)
  Re: The cost per kg of rice varies inversely with the square of the quanti  [#permalink]
  
  ### Show Tags
  
  16 Jan 2020, 07:37
  given
  x = 36* 49
  x= 1764
  now
  1764/49 = x^2
  x= 6
  IMO E
  
  Bunuel wrote:
  The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?
  
  A. 5 million tons
  B. 5.25 million tons
  C. 5.5 million tons
  D. 5.75 million tons
  E. 6 million tons
  Target Test Prep Representative
  Status: Founder & CEO
  Affiliations: Target Test Prep
  Joined: 14 Oct 2015
  Posts: 9443
  Location: United States (CA)
  Re: The cost per kg of rice varies inversely with the square of the quanti  [#permalink]
  
  ### Show Tags
  
  18 Jan 2020, 12:49
  1
  Bunuel wrote:
  The cost per kg of rice varies inversely with the square of the quantity of rice produced in a year. When 7 million tons of rice was produced, its cost was \$36/kg. How much was the production in the year when the cost of rice was \$49/kg?
  
  A. 5 million tons
  B. 5.25 million tons
  C. 5.5 million tons
  D. 5.75 million tons
  E. 6 million tons
  
  Recall that if y varies inversely with x, we let k = the constant of proportionality and we set up the following equation:
  
  y = k * (1/x)
  
  If y varies inversely with the square of x, then the equation is modified to:
  
  y = k * (1/(x^2))
  
  For this question, let’s let c = the cost per kg of rice and q = the quantity produced. Thus, we have:
  
  c = k * (1/(q^2))
  
  36 = k * (1/(7^2))
  
  36 = k * (1/49)
  
  36 * 49 = k
  
  k = 36 * 49 (Note that we do not perform the final multiplication here.)
  
  Now we can let x = the number of millions of tons of rice produced such that the cost was \$49/kg and create the equation:
  
  49 = k * (1/(x^2))
  
  49 = 36 * 49 * (1/(x^2))
  
  1/36 = (1/(x^2))
  
  x^2 = 36
  
  x = 6 million tons
  
  _________________
  
  # Scott Woodbury-Stewart
  
  Founder and CEO
  
  Scott@TargetTestPrep.com
  181 Reviews
  
  5-star rated online GMAT quant
  self study course
  
  See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
  
  If you find one of my posts helpful, please take a moment to click on the "Kudos" button.
  
  Re: The cost per kg of rice varies inversely with the square of the quanti   [#permalink] 18 Jan 2020, 12:49
  Display posts from previous: Sort by
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a GMAT question related to the concept of inverse variation. It describes a scenario where the cost per kilogram of rice is inversely proportional to the square of the quantity of rice produced in a year. The question provides a specific instance where 7 million tons of rice were produced at a cost of \$36/kg and asks for the production quantity when the cost was \$49/kg. The text includes the question and multiple-choice answers but does not provide the solution or the correct answer.
  
  Label: question