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A survey was conducted on 500 households and it was found that 70% of them have a two-wheeler and 50% have a four-wheeler. What percentage of the households who have a four-wheeler do not own a two-wheeler?
(1) 350 households have at most one vehicle between a two-wheeler and a four-wheeler
(2) The number of households who do not have either a two-wheeler or a four-wheeler is 50
(1) 350 households have at most one vehicle between a two-wheeler and a four-wheeler
(2) The number of households who do not have either a two-wheeler or a four-wheeler is 50
23 May 2024, 05:18
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Filling in a 3x3 matrix with the info provided in the question stem and with anything that can be worked out:
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & ~ & ~ & 70 \\ \hline
no Two & ~ & ~ & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
(1) 350 households have at most one vehicle between a two-wheeler and a four-wheeler
If 350 households have at most one vehicle, then 150 households have both. 150 out of 500 is 30%,
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & 30 & ~ & 70 \\ \hline
no Two & ~ & ~ & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
which means that \(50 - 30 = 20\)% of households have a four-wheeler and no two-wheeler
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & 30 & ~ & 70 \\ \hline
no Two & 20 & ~ & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
So 40% of households that have a four-wheeler do not have a two-wheeler.
SUFFICIENT
(2) The number of households who do not have either a two-wheeler or a four-wheeler is 50
50 is 10% of 500.
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & ~ & ~ & 70 \\ \hline
no Two & ~ & 10 & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
Which means that \(30-10 = 20\)% of the households have a four-wheeler but no two-wheeler
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & ~ & ~ & 70 \\ \hline
no Two & 20 & 10 & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
So 40% of households that have a four-wheeler do not have a two-wheeler.
SUFFICIENT
ANSWER D
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & ~ & ~ & 70 \\ \hline
no Two & ~ & ~ & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
(1) 350 households have at most one vehicle between a two-wheeler and a four-wheeler
If 350 households have at most one vehicle, then 150 households have both. 150 out of 500 is 30%,
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & 30 & ~ & 70 \\ \hline
no Two & ~ & ~ & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
which means that \(50 - 30 = 20\)% of households have a four-wheeler and no two-wheeler
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & 30 & ~ & 70 \\ \hline
no Two & 20 & ~ & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
So 40% of households that have a four-wheeler do not have a two-wheeler.
SUFFICIENT
(2) The number of households who do not have either a two-wheeler or a four-wheeler is 50
50 is 10% of 500.
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & ~ & ~ & 70 \\ \hline
no Two & ~ & 10 & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
Which means that \(30-10 = 20\)% of the households have a four-wheeler but no two-wheeler
\begin{tabular}{|l|l|l|l|}
\hline
~ & Four & no Four & Total \\ \hline
Two & ~ & ~ & 70 \\ \hline
no Two & 20 & 10 & 30 \\ \hline
Total & 50 & 50 & 100 \\ \hline
\end{tabular}
So 40% of households that have a four-wheeler do not have a two-wheeler.
SUFFICIENT
ANSWER D
29 May 2024, 16:02
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Nidzo
Can you please explain how statement one is sufficient.
What I understand is : at most 350 have 1 vehicle, means (exactly 1 vehicle 350, none 0), may be (exactly 1 vehicle 349, none 1)... (exactly 1 vehicle 1, none 349)....... Correct me if I am wrong.
OR
Here we are looking at the pre-condition (no disucussion of none, so we by default consider it 0).
PLEASE HELP ME here
Bunuel , need your help
