There are a certain number of male and female students in a classroom.

Question

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.

conquerthegmat · Answer

1) Not enough
2) Not enough
combined:
The weight can be 80.1, 80.2, 80.3, ...., so it still cannot be answered

werty_123 · Answer

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

Bunuel · 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.

So, statement (1) alone is not sufficient.

jade529415 · Answer

“all weights are rounded to the nearest 1kg ” does not mean that they are integers.

PeachSnapple1 · Answer

The prompt said     and    . 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.

Morina · Answer

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 · Answer

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.

minionbaba · Answer

Hi Bunuel , I was also confused around this, but the OA is treating this as a requirement that each student has an integer weight hence there can be MAX 6 Males & MAX 6 Females. (Highlighted in blue below) Attached is the SS of Official Explanation. Can you please help share some insights how to deal in some ambiguous question language? Thank you! https://gmatclub.com/forum/download/file.php?id=88718 GMAT-Club-Forum-fq3p32fm.png

egmat · Answer

Hi minionbaba,

Your instinct that the wording is doing something tricky is right, but let me untangle one thing first: the answer is  E  no matter how you read "rounded to the nearest 1 kg." The interpretation question you're stuck on never actually decides the problem.

First, the rounding language.

"All weights are rounded to the nearest 1 kg" is a  reporting  convention - it tells you how the numbers would be displayed, not that each student's true weight must be a whole number. So jade529415 is right: it does  not  force integer weights, and there is no built-in cap of  6  males and  6  females. A weight like  80.4  kg is perfectly allowed; it would just be reported as  80 .

But here's the key move for a doubt like this: test whether the ambiguity even matters.

In Data Sufficiency, before agonizing over an interpretation, check both readings against the question. If the answer is the same either way, the ambiguity is a non-issue.

If weights need NOT be integers:  the count of students and their exact weights are both wide open. Average is undetermined.  Not sufficient .

If weights MUST be integers (the strict reading):  males still have  6  possible values (80-85), females  6  (70-75), but you still don't know  how many  students there are or  which  values they take - males could all sit at  80 , or spread out. Average still swings.  Not sufficient .

Either way, neither statement pins down the actual distribution of weights, so even combined they can't fix the average. That's exactly Bunuel's point about statement (2): equal counts don't tell you the weights aren't clustered at one end of each range.

So the takeaway for ambiguous wording:  don't try to settle the interpretation in your head and then solve. Carry both interpretations into the statements and see if they lead to different answers. If they don't - as here - the wording was a distraction, and you've saved yourself the worry.

Answer: E

There are a certain number of male and female students in a classroom.

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GMAT Data Sufficiency (DS) Questions

There are a certain number of male and female students in a classroom.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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