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16 Dec 2025, 11:23
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1) 3/5 of 90 = 54 students only in Math Club so even if there is no student in both the clubs, debate will not have more than 36 students
So statement 1 is sufficient
2) 2/9 of 90 = 20 students participate in both clubs, no clarity on individual club participation
Debate can be greater than Math and viceversa so not sufficient
Option A
So statement 1 is sufficient
2) 2/9 of 90 = 20 students participate in both clubs, no clarity on individual club participation
Debate can be greater than Math and viceversa so not sufficient
Option A
Bunuel
16 Dec 2025, 11:39
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Quote:
(1) 3/5 of the students participate in only Math Club -> This means 2/5 join only the Debate Club or both. In either case the number of students joining Math Club clearly takes the higher share => Sufficient
(2) 2/9 of the students participate in both Debate Club and Math Club. -> we cannot determine the share of students in either club based on this information => Insufficient
Answer A
16 Dec 2025, 11:57
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The answer is A.
Rephrase for what the question is asking by setting up a double set matrix. I assigned values of x and y to total number of students in debate club and math club, respectively.
The questions asks; if x > y?
Note that the category for students participating in neither is 0.
Statement 1 tells us that 54 are only math, which means that 36 total must be in debate. So x = 36.
If 54 are only math, that means at least 54 are in math, which is greater than 36. So the answer is no.
Statement 2: if 18 students are in both math and debate, we can set up the equation y + x = 110. There is no way to tell which variable is larger from the given information.
So A is correct.
Rephrase for what the question is asking by setting up a double set matrix. I assigned values of x and y to total number of students in debate club and math club, respectively.
The questions asks; if x > y?
Note that the category for students participating in neither is 0.
Statement 1 tells us that 54 are only math, which means that 36 total must be in debate. So x = 36.
If 54 are only math, that means at least 54 are in math, which is greater than 36. So the answer is no.
Statement 2: if 18 students are in both math and debate, we can set up the equation y + x = 110. There is no way to tell which variable is larger from the given information.
So A is correct.
