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There are a certain number of male and female students in a classroom. The weights of the male students range from 80 kg to 85 kg. The weights of the female students range from 70 kg to 75 kg. What is the average (arithmetic mean) weight of all the students in the classroom? All weights are rounded to the nearest 1 kg.

(1) No two students weigh the same.

(2) The number of male students is equal to the number of female students.


Bunuel , karishma , GMATNinja
No two students weigh the same.

Can we infer that all students have different weights? If thats the case and the questions says All weights are rounded to the nearest 1 kg
, then it mean there are only 6 students in total. Hence, A is enough to answer

"No two students weigh the same" means that every student has a unique weight. However, it does not mean there are only 6 students, because the given weight ranges do not require one student per integer value. There could be fewer students, as long as each has a distinct weight within the range. For example, there can be a case where there are two male students, one weighing 80 kg and the other 85 kg.

So, statement (1) alone is not sufficient.
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Bunuel , karishma , GMATNinja
No two students weigh the same.

Can we infer that all students have different weights? If thats the case and the questions says All weights are rounded to the nearest 1 kg
, then it mean there are only 6 students in total. Hence, A is enough to answer




“all weights are rounded to the nearest 1kg ” does not mean that they are integers.
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The prompt said [All weights are rounded to the nearest 1 kg.] and [(1) No two students weigh the same.]. Kinda unambiguous. Are the weights of the students considered before or after rounding up? But in either case, the answer is E because we don't know the exact number of students.
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Statement 1 is NS
But Statement 2 : sin we know that 80<M<85 then m can take values from 81to 84 which the Average will be 82.5~83Kg same for Women ~73K and since both M=w then we can sum (73+83)/2 then we have the average of all students ? so its sufficient. is that correct ?
Bunuel


"No two students weigh the same" means that every student has a unique weight. However, it does not mean there are only 6 students, because the given weight ranges do not require one student per integer value. There could be fewer students, as long as each has a distinct weight within the range. For example, there can be a case where there are two male students, one weighing 80 kg and the other 85 kg.

So, statement (1) alone is not sufficient.
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Statement 1 is NS
But Statement 2 : sin we know that 80<M<85 then m can take values from 81to 84 which the Average will be 82.5~83Kg same for Women ~73K and since both M=w then we can sum (73+83)/2 then we have the average of all students ? so its sufficient. is that correct ?


No, that reasoning is incorrect.

Statement (2) says the number of male and female students is the same, but it does not say that the weights are evenly distributed across each range. The male weights could all cluster near 80 or near 85, and the same for females near 70 or near 75.
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