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03 Jul 2025, 19:08
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The correct answer choice is (B) Statements 2 is sufficient but statement 1 is not sufficient
The question base provides very little information about the proportions or possibly probability of the car types and fuel types beyond stating the variety. The question then asks about sedans on electricity and minivans on gasoline, so one must figure out the proportions of those vehicles using the statements, if possible.
Statement 1 provides information about the probability of selecting a minivan OR runs on gasoline, which means it could be minivans of either gasoline or electric, and vehicles that run on gasoline of which could be sedans or minivans. There is not further information on the breakdowns of these types. All we know is that this 2/5 figure does NOT include Electric Sedans, so that must be the other 3/5. Therefore the 3/5 figure is larger than 2/5 for sure and it answers our question.
Statement 2 provides information about 5/8 being sedans OR running on electricity. However we don't know if this includes sedans running on gasoline and minivans running on electricity, so we cannot use this statement to answer our question.
The question base provides very little information about the proportions or possibly probability of the car types and fuel types beyond stating the variety. The question then asks about sedans on electricity and minivans on gasoline, so one must figure out the proportions of those vehicles using the statements, if possible.
Statement 1 provides information about the probability of selecting a minivan OR runs on gasoline, which means it could be minivans of either gasoline or electric, and vehicles that run on gasoline of which could be sedans or minivans. There is not further information on the breakdowns of these types. All we know is that this 2/5 figure does NOT include Electric Sedans, so that must be the other 3/5. Therefore the 3/5 figure is larger than 2/5 for sure and it answers our question.
Statement 2 provides information about 5/8 being sedans OR running on electricity. However we don't know if this includes sedans running on gasoline and minivans running on electricity, so we cannot use this statement to answer our question.
03 Jul 2025, 20:41
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To check: P (sedan AND electricity) > P (minivan AND gasoline)
(1) The probability that a randomly selected vehicle is either a minivan or runs on gasoline is 2/5.
P (minivan OR gasoline) = 2/5
P (neither minivan nor gasoline) = 1 - P(minivan or gasoline) = 2/5
= 1 - 2/5
= 3/5
Since there are only 2 types of vehicles and fuel types, if it is not a minivan that means it is a sedan, and if it is not running on gasoline, then it must be running on electricity.
So, P (neither minivan nor runs on gasoline) = P (sedan AND electricity) = 3/5
But question requires us to check if P (sedan AND electricity) > P (minivan AND gasoline)
We have P (minivan OR gasoline) = 2/5 but not P (minivan AND gasoline)
Statement 1 is not sufficient
(2) The probability that a randomly selected vehicle is either a sedan or runs on electricity is 5/8.
P(sedan OR electricity) = 5/8
P(neither sedan nor electricity)= P(minivan AND gasoline) = 1-5/8 = 3/8
Again, we have (sedan OR electricity), but not (sedan AND electricity).
Statement 2 is not sufficient
1 and 2 together
From 1 --- P (sedan AND electricity) = 3/5
From 2 --- P(minivan AND gasoline) = 3/8
since 3/5 is more than 3/8, we can now confirm that P (sedan AND electricity) > P(minivan AND gasoline)
Statement 1 and 2 together are sufficient.
Answer is C
(1) The probability that a randomly selected vehicle is either a minivan or runs on gasoline is 2/5.
P (minivan OR gasoline) = 2/5
P (neither minivan nor gasoline) = 1 - P(minivan or gasoline) = 2/5
= 1 - 2/5
= 3/5
Since there are only 2 types of vehicles and fuel types, if it is not a minivan that means it is a sedan, and if it is not running on gasoline, then it must be running on electricity.
So, P (neither minivan nor runs on gasoline) = P (sedan AND electricity) = 3/5
But question requires us to check if P (sedan AND electricity) > P (minivan AND gasoline)
We have P (minivan OR gasoline) = 2/5 but not P (minivan AND gasoline)
Statement 1 is not sufficient
(2) The probability that a randomly selected vehicle is either a sedan or runs on electricity is 5/8.
P(sedan OR electricity) = 5/8
P(neither sedan nor electricity)= P(minivan AND gasoline) = 1-5/8 = 3/8
Again, we have (sedan OR electricity), but not (sedan AND electricity).
Statement 2 is not sufficient
1 and 2 together
From 1 --- P (sedan AND electricity) = 3/5
From 2 --- P(minivan AND gasoline) = 3/8
since 3/5 is more than 3/8, we can now confirm that P (sedan AND electricity) > P(minivan AND gasoline)
Statement 1 and 2 together are sufficient.
Answer is C
03 Jul 2025, 21:35
Kudos
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we're asked to compare two probabilities:
p(sedan and electric) vs p(minivan and gasoline)
statement 1:
p(minivan or gasoline) = 2/5
use the formula:
p(minivan) + p(gasoline) − p(minivan and gasoline) = 2/5
this gives a relationship, but we can’t isolate either p(minivan and gasoline) or p(sedan and electric)
not sufficient
statement 2:
p(sedan or electric) = 5/8
p(sedan) + p(electric) − p(sedan and electric) = 5/8
again, this gives one equation with three unknowns
not sufficient
combine both:
from 1:
p(minivan) + p(gasoline) − p(minivan and gasoline) = 2/5
from 2:
p(sedan) + p(electric) − p(sedan and electric) = 5/8
note that total probability = 1
p(minivan) = 1 − p(sedan)
p(gasoline) = 1 − p(electric)
use substitution to express everything in terms of sedan, electric, and the two target joint probabilities
you’ll get a solvable system (in ds, dont solve things when you’re sure that they can be solved; time trap is the worst kind of that we see in DI section)
with two equations and two target values, it is possible to determine which is greater
so combined statements are sufficient
final answer is c
p(sedan and electric) vs p(minivan and gasoline)
statement 1:
p(minivan or gasoline) = 2/5
use the formula:
p(minivan) + p(gasoline) − p(minivan and gasoline) = 2/5
this gives a relationship, but we can’t isolate either p(minivan and gasoline) or p(sedan and electric)
not sufficient
statement 2:
p(sedan or electric) = 5/8
p(sedan) + p(electric) − p(sedan and electric) = 5/8
again, this gives one equation with three unknowns
not sufficient
combine both:
from 1:
p(minivan) + p(gasoline) − p(minivan and gasoline) = 2/5
from 2:
p(sedan) + p(electric) − p(sedan and electric) = 5/8
note that total probability = 1
p(minivan) = 1 − p(sedan)
p(gasoline) = 1 − p(electric)
use substitution to express everything in terms of sedan, electric, and the two target joint probabilities
you’ll get a solvable system (in ds, dont solve things when you’re sure that they can be solved; time trap is the worst kind of that we see in DI section)
with two equations and two target values, it is possible to determine which is greater
so combined statements are sufficient
final answer is c
