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Bunuel
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In a classroom containing only fifth- and sixth-graders, fifth graders 04 Nov 2025, 00:41
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D
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50% (01:17) correct 50% (01:06) wrong based on 195 sessions

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In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3


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D
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In a classroom containing only fifth- and sixth-graders, fifth graders 04 Nov 2025, 03:38
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Let total students be 30 (smart #s)
1/2 students are fifth graders = 15
Students left over = 15
2/3rd of left over are sixth graders = (2/3)*15 = 10
So the fraction of sixth graders to total students = 10/30 = 1/3
E
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In a classroom containing only fifth- and sixth-graders, fifth graders 04 Nov 2025, 04:45
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The question here is about desks,

Let total Desks be - 60
1/2 of the desks are occupied by 5th graders = 30
Desks left over = 30
2/3rd of left over are occupied by 6th graders = (2/3)*30 = 20
Total desks in use = 20+30=50
Sixth-graders are seated in what fraction of the desks in use = 20/50 = 2/5
Answer: D
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In a classroom containing only fifth- and sixth-graders, fifth graders 04 Nov 2025, 05:35
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You could pick a number for the total amount of desks, but that will require you to find a good number that is compatible with both 1/2 and 2/3. For this question that is not a big deal, as the previous posts have demonstrated, but if you want a consistently repeatable and efficient strategy, I recommend working with the fractions given and understanding what the question is saying. Especially since the answer choices are fractions, not whole numbers.

If 1/2 of the desks are filled with fifth graders, then there is only 1/2 of the desks available to sixth graders. Since sixth graders fill 2/3 of the remainder (“the remainder” referring to 1/2 of the seats), sixth graders fill 2/3 of 1/2 of the seats. To calculate that fraction, multiply the two fractions together: 1/2*2/3 = 1/3. Sixth graders fill 1/3 of the seats.

BUT! The question is not asking for the proportion of total seats occupied by sixth graders! It is asking for the fraction of sixth graders IN THE DESKS IN USE. meaning we don’t care about the total number of seats anymore, we only care about the seats being used. If 1/2 (aka 3/6) are being used by fifth graders and 1/3 (aka 2/6) are being used by sixth graders, that means 5/6 are being used, and that is the number we need to compare to. 5 units (sixths) are being used, and the sixth graders are occupying 2 of those units, therefore the proportion of used seats occupied by sixth graders is 2/5.

If you grasp the logic quickly, then the math looks like this: (fraction of seats occupied by sixth graders) / (fraction of seats occupied) = (1/2*2/3) / (1/2 + 1/3) = (2/6)/(5/6) = 2/5

Answer D
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In a classroom containing only fifth- and sixth-graders, fifth graders 04 Nov 2025, 06:05
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It should be D since the question asked about the fraction of the table in use (which is 10 + 15 = 25, thus sixth grader occupy 10/25 = 2/5)
bruhletmein
Let total students be 30 (smart #s)
1/2 students are fifth graders = 15
Students left over = 15
2/3rd of left over are sixth graders = (2/3)*15 = 10
So the fraction of sixth graders to total students = 10/30 = 1/3
E
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In a classroom containing only fifth- and sixth-graders, fifth graders 04 Nov 2025, 21:38
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Bunuel
In a classroom containing only fifth- and sixth-graders, fifth graders are seated in 1/2 of the desks and sixth-graders are seated in 2/3 of the remainder. Sixth-graders are seated in what fraction of the desks in use?

A. 5/6
B. 2/3
C. 3/5
D. 2/5
E. 1/3


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The classroom contains only Fifth and sixth graders.

Since the denominators in the fraction contains 2 and 3. Let’s assume the total number of desks to be LCM (2,3) = 6x

Given that (1/2) are fifth graders, who occupy the seat = (1/2) * 6x = 3x

Remainder of seats unfilled = 6x - 3x = 3x

Sixth graders are seated in (2/3) of the remainder = (2/3) * 3x = 2x

Total desks currently utilised are = 3x + 2x = 5x

Sixth-graders are seated in what fraction of the desks in use?

= 2x / 5x

= 2/5

Option D
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In a classroom containing only fifth- and sixth-graders, fifth graders 05 Nov 2025, 00:13
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Considering total chairs to be 90

charis used by fifth graders = 1/2 of total = 45
chairs used by 6th graders = 2/3 of remaining = 2/3 x45 = 30

fraction of 6th graders chair to total = 30/75 = 2/5 Option D
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