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03 Jul 2025, 10:40
Kudos
Bookmarks
Let’s define:
M: event that the vehicle is a minivan
S: event that the vehicle is a sedan
G: event that the vehicle runs on gasoline
E: event that the vehicle runs on electricity
We want to know whether: P(S∩E) > P(M∩G)
Statement (1):
That is: P(M U G)=2/5
This does not help in any way determining the required info, NOT SUFFICIENT
Statement (2):
That is: P(S U E)=5/8
This also does not help in any way determining the required info, NOT SUFFICIENT
Combining 1 and 2:
[*]P(M U G)=P(M) + P(G) − P(M∩G) = 5/2
[*]P(S U E)=P(S) + P(E) − P(S∩E)= 5/8
Also, (Note: P(M) + P(S) =1 , P(G) + P(E) = 1)
P(M) + P(G) − P(M∩G) = 1 - P(S) + 1 - P(E) − P(M∩G) = 5/2
P(S) + P(E) = 1/2 − P(M∩G)
Equating this is equation(2)
1/2 − P(M∩G) − P(S∩E)= 5/8
P(M∩G) + P(S∩E) = 9/8 -> Still not sufficient
Answer E
M: event that the vehicle is a minivan
S: event that the vehicle is a sedan
G: event that the vehicle runs on gasoline
E: event that the vehicle runs on electricity
We want to know whether: P(S∩E) > P(M∩G)
Statement (1):
That is: P(M U G)=2/5
This does not help in any way determining the required info, NOT SUFFICIENT
Statement (2):
That is: P(S U E)=5/8
This also does not help in any way determining the required info, NOT SUFFICIENT
Combining 1 and 2:
[*]P(M U G)=P(M) + P(G) − P(M∩G) = 5/2
[*]P(S U E)=P(S) + P(E) − P(S∩E)= 5/8
Also, (Note: P(M) + P(S) =1 , P(G) + P(E) = 1)
P(M) + P(G) − P(M∩G) = 1 - P(S) + 1 - P(E) − P(M∩G) = 5/2
P(S) + P(E) = 1/2 − P(M∩G)
Equating this is equation(2)
1/2 − P(M∩G) − P(S∩E)= 5/8
P(M∩G) + P(S∩E) = 9/8 -> Still not sufficient
Answer E
03 Jul 2025, 10:41
Kudos
Bookmarks
(1) => P(M U G)= 2/5 => Know nothing about S or E => Insufficient
(2) => P(S U E) = 5/8 => Know nothing about M or G => Insufficient
(1)+(2):
P(M U G)= P(M)+P(G)−P(M∩G)=2/5
P(S U E) = P(S)+P(E)−P(S∩E)=5/8
P(M)+P(S)=1
P(G)+P(E)=1
=> Can't determine whether P(S∩E) > P(M∩G) => Insufficient
=> E
(2) => P(S U E) = 5/8 => Know nothing about M or G => Insufficient
(1)+(2):
P(M U G)= P(M)+P(G)−P(M∩G)=2/5
P(S U E) = P(S)+P(E)−P(S∩E)=5/8
P(M)+P(S)=1
P(G)+P(E)=1
=> Can't determine whether P(S∩E) > P(M∩G) => Insufficient
=> E
Bunuel
03 Jul 2025, 10:41
Kudos
Bookmarks
I don't think this question is 505-605. This is not complex but definitely tricky one.
So essentially the question stem asks, is P(sedan & Electricity) > P (Minivan & Gasoline)?
The question is whether \(n/(x+y+m+n) > x/ (x+y+m+n)\)?
Statement 1: says P ( Minivan or Gasoline) = 2/5. This means
\(\\
(x+m+y)/(x+y+m+n) = 2/5. \\
\\
\)
So subtracting from 1,
\(1-2/5 = 3/5 = n/(x+y+m+n)\) which is already more than half.
So for example, if there were 50 cars, 30 cars are Sedans running on electricity.
m+n+y<30 that means x<30.
So sufficient.
Statement 2: says P ( Sedan or Electricity) = 5/8. This means
\((m+n+y)/(x+y+m+n) = 5/8.\)
So subtracting both sides from 1,
\(x /(x+y+m+n) = 3/8.\) This could lead to variety of situations.
Lets say the number of cars are 80, Then 30 cars are running on minivans running on gasolines and we don't know anything about the rest.
It could be
or
So we can't say. Hence not sufficient.
Hence Answer is option A.
So essentially the question stem asks, is P(sedan & Electricity) > P (Minivan & Gasoline)?
| Minivan | Sedan | |
| Gasoline | x | y |
| Electricity | m | n |
Statement 1: says P ( Minivan or Gasoline) = 2/5. This means
\(\\
(x+m+y)/(x+y+m+n) = 2/5. \\
\\
\)
So subtracting from 1,
\(1-2/5 = 3/5 = n/(x+y+m+n)\) which is already more than half.
So for example, if there were 50 cars, 30 cars are Sedans running on electricity.
| Minivan | Sedan | |
| Gasoline | x | y |
| Electricity | m | 30 |
m+n+y<30 that means x<30.
So sufficient.
Statement 2: says P ( Sedan or Electricity) = 5/8. This means
\((m+n+y)/(x+y+m+n) = 5/8.\)
So subtracting both sides from 1,
\(x /(x+y+m+n) = 3/8.\) This could lead to variety of situations.
Lets say the number of cars are 80, Then 30 cars are running on minivans running on gasolines and we don't know anything about the rest.
It could be
| Minivan | Sedan | |
| Gasoline | 30 | 20 |
| Electricity | 20 | 10 |
| Minivan | Sedan | |
| Gasoline | 30 | 5 |
| Electricity | 5 | 40 |
So we can't say. Hence not sufficient.
Hence Answer is option A.
Bunuel
