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The average mark of a class of n students is 64. When eight new students with an average mark of 73 join the class, the new average of the entire class is a whole number. Find the number of students now in the class, given that n lies between 25 and 60.
  • a)
    44
  • b)
    32
  • c)
    36
  • d)
    72
Correct answer is option 'C'. Can you explain this answer?
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The average mark of a class of n students is 64. When eight new studen...
Let ‘x’ be the increase in the average 


For ‘x’ to be a whole number 72 (= 9 * 8) should be divisible by (n + 8) 

From the choices it can be said that 36 and 72 are two such factors. But 72 does not lie within the range. 

∴ number of students in class are 36.
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The average mark of a class of n students is 64. When eight new studen...
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The average mark of a class of n students is 64. When eight new studen...
Let's assume that there are n students in the class initially.

Average of n students = 64

Total marks of n students = 64n

Now, when 8 new students with an average score of 73 join the class, the new average becomes a whole number.

Let's assume that after the 8 new students join, the total number of students in the class becomes x.

So, the new average = (64n + 73*8)/x

We know that the new average is a whole number. Therefore, (64n + 73*8) should be divisible by x.

64n + 73*8 = 584 + 64n = 8*73 + 64n

So, we need to find a value of n such that 8*73 + 64n is divisible by x.

Let's check the options given:

Option A: 44 students

8*73 + 64*44 = 3752, which is not divisible by 44. Therefore, option A is not correct.

Option B: 32 students

8*73 + 64*32 = 3072, which is divisible by 32. Therefore, option B could be correct.

Option C: 36 students

8*73 + 64*36 = 3456, which is divisible by 36. Therefore, option C is correct.

Option D: 72 students

8*73 + 64*72 = 5408, which is not divisible by 72. Therefore, option D is not correct.

Therefore, the correct answer is option C, i.e., there are 36 students in the class now.
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