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# The cost per kg of rice varies inversely with the square of the quanti

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Math Expert
Joined: 02 Sep 2009
Posts: 61396
The cost per kg of rice varies inversely with the square of the quanti  [#permalink]

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16 Jan 2020, 03:19
00:00

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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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]

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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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Scott@TargetTestPrep.com
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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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The text passage contains a mathematical question related to the cost of rice and its production quantity. The question is about finding the production quantity when the cost per kg of rice is given, based on the inverse relationship between the cost and the square of the quantity produced.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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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
user
The text passage contains a mathematical question related to the cost of rice and its production quantity. The question is about finding the production quantity when the cost per kg of rice is given, based on the inverse relationship between the cost and the square of the quantity produced.

TYPE: SINGLE_QUESTION_WITH_ANSWER