Rapid Revision · Quantitative Aptitude
Average questions are sum questions in disguise. Convert every statement to a total, work with totals, convert back at the end.
If you read nothing else tonight, read these 6 lines.
Every formula for averages in one place, each labelled so you know exactly when to reach for it. Screenshot it the night before.
Average
average = sum of terms / number of terms
Recover the total
sum = average x count
The single most useful step: turn an average back into a total.
First n naturals
average of 1..n = (n + 1) / 2
Round-trip speed
avg speed = 2xy / (x + y)
Equal distance each way at speeds x and y. NOT (x+y)/2.
Weighted average
avg = (n1 x a1 + n2 x a2) / (n1 + n2)
Replacement effect
change in average x count = new item - old item
7 cards, each one idea: what it is, a worked example, and the trap to dodge.
The only safe move: turn every average into a total (sum = avg x n), do the arithmetic on totals, then divide back.
Avg of 8 numbers is 20 (sum 160); two numbers averaging 26 leave: new sum 160 - 52 = 108, new avg 108/6 = 18.
Trap: Averages of averages cannot be averaged unless group sizes are equal.
When one member is replaced and the average of n people moves by d, the newcomer differs from the leaver by n x d.
Avg weight of 10 rises by 2 kg when X replaces Y (60 kg): X = 60 + 10 x 2 = 80 kg.
Evenly spaced numbers average to their middle value. For 1 to n the average is (n+1)/2.
Average of 21, 23, 25, 27, 29 = 25 (the middle).
Different group sizes need weights: avg = (n1 x a1 + n2 x a2)/(n1 + n2). The combined average always sits between the two, closer to the bigger group.
30 students avg 40, 20 students avg 60: (1200 + 1200)/50 = 48.
Trap: If your combined average is outside the two group averages, you made an arithmetic slip.
Equal distances at x and y: average speed = 2xy/(x+y), the harmonic mean. Equal TIMES average to (x+y)/2.
60 km/h out, 40 km/h back: 2 x 60 x 40 / 100 = 48 km/h.
Trap: (60+40)/2 = 50 is the bait answer on almost every paper.
One entry was wrong: correct average = wrong average + (correct value - wrong value)/n.
Avg of 20 numbers read as 50 with 83 typed as 38: 50 + 45/20 = 52.25.
When someone joins and the average changes by d, the newcomer's value = old average + (n+1) x d, where n is the old count.
10 people avg 25; a joiner lifts it to 26: joiner = 25 + 11 x 1 = 36.
A recap is not practice. These are the creators we rate for real depth on averages; full credit to each.
Each recap takes 3 minutes; the full set covers everything the first round tests. And when the test is cleared, your resume takes the next screen.
Original content by OptiResume; facts and formulas are common knowledge, the wording is ours. Go-deeper links go to creators we rate; we are not affiliated with them.