In a class with 20 students, a test was administered, scored only in

Question

In a class with 20 students, a test was administered, scored only in whole numbers from 0 to 10. At least one student got every possible score, and the average was 7. What is the lowest score that two students could have received?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Abhishek009 · Accepted Answer

Sum of scores of 20 students is 140

At least one student got every possible score...

So, We have -  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, a, b, c, d, e, f, g, h, i

Now, Sum of score available is =  55 + a + b + c + d + e + f + g + h + i

Maximization and Minimization form now, let 8 students got 10 each, ie a - h got 10 each, so total sum is 80

Thus, 55 + 80 + i = 140

Or,  i = 5 , Answer will be (B) 5

tushki23 · Answer

The answer should be 5.

Total score for 20 students = 20*7 = 140

Since each of the students got atleast one of the score from 0 to 10, so 11 students got 0+1+2+..+10= 55 --- (i)

Remaining score = 140-55 = 85

Since 9 students are remaining, we can maximize the score for 8 students considering 10 marks for each (max score), so total= 80.

9th Student would score = 85-80 = 5

So, the two students with lowest score would be 5 ( one above and another considered in (i))

Diablo21 · Answer

Avg of 20 students = 20
So, total= 140

Now, Sum of 11 students that get each of possible whole no is 0+1+...+10=55

Now, sum of rest 9 students marks= 140-55= 85

For getting lowest 2 students' marks, We have to take max marks for most of students. 
If rest 9 students got 10 marks, then their sum = 90, Not possible
Next will be 8 students got 10 marks and the one left student gets 5 marks. 
I.e. 8*10+1*5=85
This means that lowest possible marks scored by two students will be 5 (as 1 student had already score 5 in first 11 students group)

Posted from my mobile device

mohammadfaraaz123 · Answer

I could be wrong but does anyone find the language of this question problematic ?

"At least one student got every possible score".

"What is the lowest score that two students could have received?" If the correct answer choice is 5 then wouldn't it mean that 5 is the total of minimum marks that two students could have received.

I understand that we are dealing with whole numbers only in this question so last two students could not have gotten equal marks i.e. 2.5. 
Language did throw me off. Does GMAC also frame their question in similar language ?

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