Each of the 1,800 households that participated in a survey owned

Question

Each of the 1,800 households that participated in a survey owned either one car, two cars, or no cars. If 740 of the households owned only one car and at least 1/3 of the households owned two cars, what is the greatest possible value of the ratio of the number of households that owned no cars to the number of households that owned two cars?

A. 17/30
B. 23/30
C. 9/10
D. 1
E. 30/23

A. 17/30
B. 23/30
C. 9/10
D. 1
E. 30/23

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divyadna · Answer

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gmatophobia · Answer

Required Ratio = No Car / Two Car

Households with one car = 740

Households with two cars >= 600

To maximize ratio minimize the denominator and maximize the numerator.

Min. households with two cars = 600

Max. household with two cards = 1800 - (600 + 740) = 460

Required Ratio =  \frac{460 }{ 600} = \frac{23}{30}

Option B

meowmeowmeow22 · Answer

Hi  gmatophobia ,

Could you please explain how the max household with 2 cars is 460? Thank you.

divyadna · Answer

Posted from my mobile device

Kinshook · Answer

Given: Each of the 1,800 households that participated in a survey owned either one car, two cars, or no cars.

Asked: If 740 of the households owned only one car and at least 1/3 of the households owned two cars, what is the greatest possible value of the ratio of the number of households that owned no cars to the number of households that owned two cars?

Total number of households = 1800
Number of households owning only 1 car = 740
Number of households owning 2 cars = y >= 1800/3 = 600
Let the number of households owning 0 car = x

740 + y + x = 1800
y >=600

Ratio of number of households that owned no cars to the number of households that owned two cars = x/y
To maximize the ratio of x/y, we have to maximise x and minimise y.

y = 600
x = 1800 - 600 - 740 = 460
x/y max = 460/600 = 23/30

IMO B

Each of the 1,800 households that participated in a survey owned

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Each of the 1,800 households that participated in a survey owned

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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