← Back

GMAT Strategy

Mental Math and Estimation

Reduce arithmetic time with structured transformations and estimate before over-calculating.

4 min

Principle

Fast arithmetic should simplify the structure, not invite guessing.

Use transformations that preserve the exact value, then estimate only when an exact value is unnecessary.

Double one factor and halve the other.

Original
18*25
Transform
9*50
Result
450

Divide by 5 by doubling first.

Original
85/5
Double numerator
170
Divide by 10
17

Use difference of squares near a round base.

Expression
52*48
Rewrite
(50+2)(50-2)
Compute
50^2 - 2^2
Result
2496

Square near a convenient base.

Expression
47^2
Rewrite
(50-3)^2
Compute
2500 - 300 + 9
Result
2209

Ending in 5

Numbers ending in 5 have a compact squaring pattern.

For 65^2, multiply 6 by 7 and append 25 -> 4225.

Estimation

Estimate before exact calculation when choices are separated.

  • Round to convenient numbers.
  • Track whether the rounded value is high or low.
  • Use the estimate to eliminate impossible choices.
  • Calculate exactly only if the remaining choices require it.

Mini application

Try this: estimate 398*51 before multiplying exactly.

Aim for the correct magnitude and neighborhood.

Solution

A strong estimate is about 20,000.

400*50 = 20,000. The exact product is slightly above that because 398*51 = 20,298.

Remember this

Simplify first; calculate only as precisely as the question needs.

GMAT efficiency comes from controlled arithmetic, not from doing more arithmetic faster.

Lesson 14 of 32

Lesson complete

Reviewed