CAT 2019 Quant Question with Solution 43

Question:
The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?

  1. 4
  2. 3.5
  3. 4.5
  4. 5
Show Answer

Correct Answer: Option: 3

Let a be the average of 20 numbers whose average does not exceed 5.

Let b be the average of rest of the 10 numbers. Clearly, b>5 i.e. the average of these numbers exceeds 5.

Therefore,

$30\times 5=20a+10b$

$\Rightarrow 2a+b=15$

$\Rightarrow b=15-2a$

Going by the options, we can say that when a=4.5, b=6 which satisfies all the conditions.


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