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04 Jul 2025, 07:55
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Statement (1): The probability that a randomly selected vehicle is either a minivan or runs on gasoline is 2/5.
P(M or G) = 2/5
Using the Addition Rule for Probabilities:
P(M or G) = P(M) + P(G) - P(M and G)
So, 2/5 = P(M) + P(G) - P(M and G)
We also know that P(M) = P(M and G) + P(M and E)
And P(G) = P(M and G) + P(S and G)
Substituting these into the equation:
2/5 = (P(M and G) + P(M and E)) + (P(M and G) + P(S and G)) - P(M and G)
2/5 = P(M and G) + P(M and E) + P(S and G)
Alternatively, and often more simply for "or" probabilities in a 2x2 table, P(M or G) is the sum of all cells except the one that is neither M nor G.
So, P(M or G) = 1 - P(S and E)
2/5 = 1 - P(S and E)
P(S and E) = 1 - 2/5
P(S and E) = 3/5
Now we know P(S and E) = 3/5. However, we still have no information about P(M and G).
For example:
If P(M and G) = 1/5, then 3/5 > 1/5 (Yes)
If P(M and G) = 4/5, then 3/5 > 4/5 (No)
Since we can get both "Yes" and "No", Statement (1) alone is not sufficient.
Statement (2): The probability that a randomly selected vehicle is either a sedan or runs on electricity is 5/8.
P(S or E) = 5/8
Similar to Statement (1), P(S or E) is the sum of all cells except the one that is neither S nor E.
So, P(S or E) = 1 - P(M and G)
5/8 = 1 - P(M and G)
P(M and G) = 1 - 5/8
P(M and G) = 3/8
Now we know P(M and G) = 3/8. However, we still have no information about P(S and E).
For example:
If P(S and E) = 1/8, then 1/8 > 3/8 (No)
If P(S and E) = 4/8, then 4/8 > 3/8 (Yes)
Since we can get both "Yes" and "No", Statement (2) alone is not sufficient.
Combining Statement (1) and Statement (2):
From (1), we found P(S and E) = 3/5.
From (2), we found P(M and G) = 3/8.
Now we need to compare them: Is P(S and E) > P(M and G)?
Is 3/5 > 3/8?
To compare, find a common denominator (e.g., 40):
3/5 = (3 * 8) / (5 * 8) = 24/40
3/8 = (3 * 5) / (8 * 5) = 15/40
Is 24/40 > 15/40?
Yes, this is definitively true.
Since combining both statements allows us to definitively answer the question with a "Yes", and neither statement alone was sufficient, the correct GMAT Data Sufficiency option is (C).
The final answer is C
P(M or G) = 2/5
Using the Addition Rule for Probabilities:
P(M or G) = P(M) + P(G) - P(M and G)
So, 2/5 = P(M) + P(G) - P(M and G)
We also know that P(M) = P(M and G) + P(M and E)
And P(G) = P(M and G) + P(S and G)
Substituting these into the equation:
2/5 = (P(M and G) + P(M and E)) + (P(M and G) + P(S and G)) - P(M and G)
2/5 = P(M and G) + P(M and E) + P(S and G)
Alternatively, and often more simply for "or" probabilities in a 2x2 table, P(M or G) is the sum of all cells except the one that is neither M nor G.
So, P(M or G) = 1 - P(S and E)
2/5 = 1 - P(S and E)
P(S and E) = 1 - 2/5
P(S and E) = 3/5
Now we know P(S and E) = 3/5. However, we still have no information about P(M and G).
For example:
If P(M and G) = 1/5, then 3/5 > 1/5 (Yes)
If P(M and G) = 4/5, then 3/5 > 4/5 (No)
Since we can get both "Yes" and "No", Statement (1) alone is not sufficient.
Statement (2): The probability that a randomly selected vehicle is either a sedan or runs on electricity is 5/8.
P(S or E) = 5/8
Similar to Statement (1), P(S or E) is the sum of all cells except the one that is neither S nor E.
So, P(S or E) = 1 - P(M and G)
5/8 = 1 - P(M and G)
P(M and G) = 1 - 5/8
P(M and G) = 3/8
Now we know P(M and G) = 3/8. However, we still have no information about P(S and E).
For example:
If P(S and E) = 1/8, then 1/8 > 3/8 (No)
If P(S and E) = 4/8, then 4/8 > 3/8 (Yes)
Since we can get both "Yes" and "No", Statement (2) alone is not sufficient.
Combining Statement (1) and Statement (2):
From (1), we found P(S and E) = 3/5.
From (2), we found P(M and G) = 3/8.
Now we need to compare them: Is P(S and E) > P(M and G)?
Is 3/5 > 3/8?
To compare, find a common denominator (e.g., 40):
3/5 = (3 * 8) / (5 * 8) = 24/40
3/8 = (3 * 5) / (8 * 5) = 15/40
Is 24/40 > 15/40?
Yes, this is definitively true.
Since combining both statements allows us to definitively answer the question with a "Yes", and neither statement alone was sufficient, the correct GMAT Data Sufficiency option is (C).
The final answer is C
04 Jul 2025, 07:58
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S1 Insufficient no info abut the Sedan
S2 Insufficient since no info about the Minivan
S1+S2 While the information provided can be used to establish total probability, it is not sufficient to apportion the probability hence E
S2 Insufficient since no info about the Minivan
S1+S2 While the information provided can be used to establish total probability, it is not sufficient to apportion the probability hence E
Bunuel
04 Jul 2025, 08:58
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The answer is choice A.
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Harsha
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