[Q] Averages Tricks - 1

Q. 1) The average weight of 4 men is increased by 3 kg when one of them who weighs 120 kg is replaced by another man. What is the weight of the new man?

Weight of new person = Weight of removed person + No. of persons * Increase in Average = 120+3*4
Weight of new person = 132 kg

Q. 2) The average marks obtained by 120 candidates in a certain examination is 35. If the average marks of passing candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the exam?

Such questions are best dealt with allegation formula:
Mean value = 35, Dearer value = 39 and Cheaper = 15
Failed students : Passed students = (Dearer - Mean) : (Mean - Cheaper) = 39 - 35 : 35 - 15 = 4 : 20
No. of students who passed = (5/6) * 120 = 100

Q. 3)

Correct Average = Incorrect average + (Correct value - Incorrect value)/Total observations

Correct Average = 35 + (85 - 45)/20 = 37

Answer: (D)

Q. 4)

Take x = 1

Then A = (1 + 1)/2 = 1

Average of x^3 + 1/x^3 = (1 + 1)/2 = 1

Now put A = 1 in all the four options and check which one is giving '1' as the output

Answer: (D)

Q. 5)

For consecutive numbers:
If the number of terms is odd (e.g. A, B, C), then their average is the middle term(i.e. B).
If the number of terms is even(e.g. A, B, C, D) then their average is (B+C)/2
So here, the average of eight consecutive even numbers = (5th term + 4th term)/2
Given, (5th term + 4th term)/2 = 93
5th term + 4th term = 186
We know, 5th term - 4th term = 2
Adding the equations, we get 5th term = 94
Hence 8th term = 5th term + 2 + 2 + 2 = 100
Answer: (C)

Q. 6)

Average = (8*3 + 20*2 + 26*m + 29*1)/(3 + 2 + m + 1)
17 = (93 + 26m)/(6 + m)
102 + 17m = 93 + 26m
m = 1
Answer: (A)

Q. 7)

Given, (3a + 4b)/2 > 50

3a + 4b > 100

5a > 100  [Since a = 2b]

a > 20

Hence the smallest value of a is 21

Answer: (D)

Q. 8)

Average of six numbers a,b,c,d,e,f = (Average of a,b + Average of c,d + Average of e,f)/3

3.95*3 = 3.4 + 3.85 + x

x = 4.6

Answer: (C)

Q. 9) The average of 11 numbers is 50. The average of first six numbers is 49, and that of last six is 52. Find the sixth result.
This is a common CGL question and a short-cut to solve it is:
Sixth result = 50 + 6{(52 - 50) + (49 - 50)} = 50 + 6(2 - 1) = 56
Answer: 56


Q. 10)

Answer: (B)

Q.11)

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