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When we think of averages, we usually rush into formulas like:
Average = Total / Number of Items
While that's technically correct, it’s not always the smartest way to approach average problems on the GMAT—especially under time pressure.
Instead, think of averages as a balance point.
Just like on a see-saw: if some items are below the average, others must be proportionally above it to maintain the balance.
Let’s see how this idea works.
Basic Example Using 2 Numbers:
More Than 2 Numbers:
To bring the average back to 80, the fourth number must be +10 above 80 = 90.
This lets you solve quickly without calculating full totals. Instead of:
GMAT Practice Problem :
In a business statistics class, the average score of 15 students is 73.6. The average score of the top 40% of students is 89.2, and the average score of the bottom 20% of students is 52.4. What is the average score of the remaining students?
A. 68.6 B. 71.2 C. 74.3 D. 76.5 E. 78.1
In a class of 15 students, the average score is 73.6
Total deviation so far = 93.6-63.6 = +30.0
To balance:
Correct answer: A.
This deviation method saves a few seconds and reduces calculation errors—time you can reinvest in harder problems!
Common Mistake to Avoid: Don't forget: Total deviation must equal ZERO for the balance to work. Every negative deviation must be offset by positive deviations.
Master this technique and you'll solve average problems in less time with greater accuracy!
Average = Total / Number of Items
While that's technically correct, it’s not always the smartest way to approach average problems on the GMAT—especially under time pressure.
Instead, think of averages as a balance point.
Just like on a see-saw: if some items are below the average, others must be proportionally above it to maintain the balance.
Let’s see how this idea works.
Basic Example Using 2 Numbers:
- Let’s say the average of two numbers is 80.
- If one number is 70, that’s 10 below average.
- To balance the average at 80, the other number must be 10 above average, which is 90.
More Than 2 Numbers:
- Let’s say the average of 4 numbers is 80.
- Three numbers are:75,70, 85
- What must the fourth number be?
- -5 (from 75)
- –10 (from 70)
- +5 (from 85)
To bring the average back to 80, the fourth number must be +10 above 80 = 90.
This lets you solve quickly without calculating full totals. Instead of:
- Finding total sum = average × number of items
- Subtracting known values
- Solving for missing value
GMAT Practice Problem :
In a business statistics class, the average score of 15 students is 73.6. The average score of the top 40% of students is 89.2, and the average score of the bottom 20% of students is 52.4. What is the average score of the remaining students?
A. 68.6 B. 71.2 C. 74.3 D. 76.5 E. 78.1
In a class of 15 students, the average score is 73.6
- Top 40% (6 students) average 89.2
- → each is 15.6 above average
- → total = 6*15.6 = +93.6
- Bottom 20% (3 students) average 52.4
- → each is 21.2 below average
- → total = 3* (-21.2) = -63.6
Total deviation so far = 93.6-63.6 = +30.0
To balance:
- The remaining 6 students must total -30.0 in deviation.
- So each is( -5.0 )
- → average score of the remaining 6 students = 73.6 - 5 = 68.6
Correct answer: A.
This deviation method saves a few seconds and reduces calculation errors—time you can reinvest in harder problems!
Common Mistake to Avoid: Don't forget: Total deviation must equal ZERO for the balance to work. Every negative deviation must be offset by positive deviations.
Master this technique and you'll solve average problems in less time with greater accuracy!
