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12 Days of Christmas GMAT Competition 2025 - Day 2: A survey of 90

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atenim

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17 Dec 2025, 06:04

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A is suff. because debate left will be 32 which can never be more than maths

Bunuel

A survey of 90 students found that each student participates in at least one of two activities: Debate Club or Math Club. Is the number of students who participate in Debate Club greater than the number who participate in Math Club?

(1) 3/5 of the students participate in only Math Club.
(2) 2/9 of the students participate in both Debate Club and Math Club.

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meenumaria

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17 Dec 2025, 06:10

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imo only 1st statement alone is suffiecient
given total 90 students
questions Is no of students in debate> no of students in math club
statement 1 tells us 3/5 of all students only in math club that is 54 students. which is clearly majority so this implies no of students in debate club is not greater than no of students in math club

statement 2 only tell us common studetns are 2/9 that is 20 which dont tell us anything about individual clubs. Henc enot sufficient.

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17 Dec 2025, 07:04

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Lets deep dive into both the statements :

Statements 1: 3/5 of the students participate in only Math club => 60 % in only Math. Based on this, even if all the remaining people join the debate club, they will still be less than the students joining math club.Sufficient

Statement 2: 2/9 of the students participate in both the clubs - Does not give any conclusion of the comparison of math and debate club members. Not sufficient.

Hence, statement 1 alone is sufficient. => A

corporisnobis

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17 Dec 2025, 07:45

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only 1 is sufficient

Bunuel

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asmitatiwari26

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Total students = 90 (everyone is atleast in one club)
From 1 - 3/5*90 = 54 students are only in Math -----(does not tell us anything about Debate club)
From 2 - 2/9*90 = 20 students are in both clubs --- (No info about Math and Debat club alone)
so total students in Math = 54+20 = 74
Students not in only Maths = 90-54 = 36 (Out of these 20 are in both) so only Debate - 36-20 = 16
Total Debat students = 16+20 = 36
since 36<74 , debate club has fewer students

Therefore, Both statement together is suffcient

Bunuel

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17 Dec 2025, 08:40

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1 - 3/5 students, i.e. 90*3/5 = 54, are in only math club. These students are neither in both clubs nor in debate club. This means that maximum 36 students can participate in the debate club only or in both debate and math club.

In both the scenarios students in the debate club will be lower than those in the math club. Hence, the statement is sufficient.

2 - 2/9 are in both clubs, i.e 20 students are in both. This does not specify whether remaining students are in math club or in debate club. Hence, the statement is not sufficient.

Statement 1 alone is sufficient but 2 alone is not sufficient.

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17 Dec 2025, 08:48

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We are given,
Total students = 90
Every student participates in atleast one of the Debate Club(D) or the Math Club (M)

We need to find out if D > M ?
Now,
Statement (1),
3/5 of the students participate in only Math Club

Only M = 0.6 * 90 = 54

=> Only D + Both (M and D) = 90 - 54 = 36
Now, lets assume
Both = x
Only D = 36 - x
Then,
D = (36 - x) + x = 36
Similarly,
M = 54 + x

Now, we can see that
54 + x > 36 always

=> Number of students who participate is Math club is always greater than number of students who participate in Debate club.

Statement (1) is sufficient

Statement 2,
2/9 of the students participate in both clubs

Both = (2/9)*90

Then,
Only D + Only M = 70

Now here we dont really know how only Debate and only Math are split due to which is true between D > M and D < M cant be concluded

=> Statement (2) alone in insufficient

A. Statement(1) alone in sufficient but statement (2) alone is not sufficient

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17 Dec 2025, 08:57

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Option A is Correct

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hershehy

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Correct Answer is C.

I find tabular method the easiest way to solve it.

Given: 90 students, all partake in atleast 1 activity hence the column of neither will have 0.

Statement 1: 3/5 participate in only math club

	Math club	No Math Club	Total
Debate	or here, or could be different numbers	Could be 36 here	36
No debate club	54	0	54
Total			90

Since we know 3/5 participate in ONLY math club which means no debate club, therefore 3/5 *90= 54 students in ONLY MATH club.

Clearly not sufficients. We are left with options B, C and E now.

Statement 2: 2/9 Pariticpate in both club, meaning 2/9*90= 20 students in both M and D club, 0 in neither

	MC	NMC	TOTAL
DC	20
NDC		0
TOTAL			90

Cleary not Enough, We are left with C and E.

Now combining both statements, we have

	Math Club	No Math club	total
Deb club	20	16	36
Ndc	54	0	54
Total	74	16	90

We have all the required data.

Bunuel.

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KunchiGoks

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Conceptual refresh: Two-set (Venn diagram) problem. "At least one" means the students who participate in Debate or Math in any way Debate only, Math only or Both (the Union). Total - Union is neither, but since no student is in neither club, the total here equals the union: Debate Only + Math Only + Both = 90 students.

If exact values were required, we would need at least two of the three Venn regions (Debate only, Math only, Both). However, this is a DS question, so it is enough if we can force a YES or NO to the question: (Debate Only + Both) > (Math Only + Both).

Statement (1): 3 / 5 * 90 = 54 students are in Math Only leaving 90 - 54 = 36 students in (Debate Only + Both) at most since we can determine 36 is < than 54 statement 1 alone is sufficient. Option A.