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Official PYQ · 2014Set 1 · QGA-9NAT1 mark

GATE CS 2014 Set 1 QGA-9 — General Aptitude

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In a survey, 300300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter?MenWomenOwn vehicleCar4034Own vehicleScooter3020Own vehicleBoth6046Do not own vehicle2050\begin{array}{|l|l|l|l|} \hline & & \text{Men} & \text{Women} \\ \hline \text{Own vehicle} & \text{Car} & 40 & 34 \\ \hline \text{Own vehicle} & \text{Scooter} & 30 & 20 \\ \hline \text{Own vehicle} & \text{Both} & 60 & 46 \\ \hline \text{Do not own vehicle} & & 20 & 50 \\ \hline \end{array}
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Answer: 48

To find the percentage of respondents who do not own a scooter, we can first determine the total number of respondents who do own a scooter.

From the given table, the respondents who own a scooter fall into two categories:

  1. Own only a Scooter:
    • Men = 3030
    • Women = 2020
  2. Own Both (Car and Scooter):
    • Men = 6060
    • Women = 4646

Calculating the total number of scooter owners:

Total Scooter Owners=(30+20)+(60+46)=50+106=156\text{Total Scooter Owners} = (30 + 20) + (60 + 46) = 50 + 106 = 156

Since the total number of respondents is 300300, the number of respondents who do not own a scooter is:

Do not own a scooter=300−156=144\text{Do not own a scooter} = 300 - 156 = 144

Alternatively, this can be calculated directly by summing those who do not own any vehicle and those who own only a car:

Do not own a scooter=(20+50)⏟No vehicle+(40+34)⏟Car only=70+74=144\text{Do not own a scooter} = \underbrace{(20 + 50)}_{\text{No vehicle}} + \underbrace{(40 + 34)}_{\text{Car only}} = 70 + 74 = 144

Now, we calculate the required percentage:

Percentage=(144300)×100=48%\text{Percentage} = \left( \frac{144}{300} \right) \times 100 = 48\%

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