4 ways to avoid lengthy calculations

By Brent Hanneson - December 1, 2020 

I’ve already noted that the GMAT test-makers aren’t trying to reward the human calculators out there (more here). If anything, the test-makers reward number sense, which means there are often times when we can avoid performing lengthy calculations.

In this article, we’ll examine 4 common strategies that will allow you (in some cases) to skip the painful calculations and reach the correct answer in a matter of seconds.

Estimation 

Let's say the correct answer to a particular question requires us to calculate the product (4918)(316). Here, it would be great if we could simply round the two values to 5,000 and 300 to get (5,000)(300) = 1,500,000. However, before we can use this simple estimation technique, we must check the answer choices to see whether they're sufficiently spread apart to allow for estimation.

For example, if the answer choices are...

A) 154,088

B) 354,088

C) 854,088

D) 1,554,088

E) 3,540,088

...then the numbers are sufficiently spread apart, in which case answer choice D is the only option that’s reasonably close to our estimation of 1,500,000.

On the other hand, if the answer choices are...

A) 1,554,088

B) 1,564,088

C) 1,574,088

D) 1,584,088

E) 1,594,088

...then our estimation of 1,500,000 won't help, since every answer choice is approximately 1,500,000.

Does this mean we have to calculate (4918)(316)?

Probably not. There's likely another way to avoid performing this calculation, which brings us to the next strategy.

Follow the units digits

If we’re required to calculate (378)(2234), and the answer choices are...

A) 844,450

B) 844,452

C) 844,454

D) 844,456

E) 844,458

... then we can focus on the units digits of the two numbers of the product (378)(2234). Since 8 x 4 = 32, we know that the units digit of the product (378)(2234), must be 2,  which means the correct answer is B.

A little bit more, a little bit less

For this strategy, pretend you're asked to find the best approximation of a satellite's speed, which happens to equal 1200/0.329. Let’s also say the answer choices are:

A) 386

B) 412

C) 1996

D) 3554

E) 3647

Aside: It’s worth noting that, when the GMAT asks us to find an approximate value, there’s usually a shortcut alternative to performing lengthy calculations. 

In this example, answer choices A & B and answer choices D & E are too close to allow for effective estimation. However, if we recognize that 0.329 is just a little bit less than 1/3, we can make the following mental calculations:

We know that 1200/(1/3) = (1200)(3) = 3600. So, 1/3 divides into 1200 a total of 3600 times.

Since 0.329 is just a little bit less than 1/3, we know that 0.329 will divide into 1200 a little bit more than 3600 times. In other words, the correct answer will be a little bit bigger than 3,600, which means the correct answer must be E.

Divisor rules

To introduce this last strategy, let’s say we need to evaluate the product (828)(721), and the answer choices are:

A) 593,238

B) 594,418

C) 596,988

D) 597,658

E) 598,778

First, you’ll need to know your divisibility rules.

For example, if a number is divisible by 4, then its last two digits will form a number that’s divisible by 4. This means 828 is divisible by 4, since 28 is divisible by 4.

If 828 is divisible by 4, then the product of 828 and 721 must also be divisible by 4.

When we check the last two digits of each answer choice, we see that answer choice C is the only one that's divisible by 4. So, the correct answer must be, C.  

Here are a few practice questions where the above strategies apply:

• https://gmatclub.com/forum/if-0-497-mark-has-the-value-of-one-dollar-wha...

• https://gmatclub.com/forum/a-certain-stock-exchange-designates-each-stoc...

• https://gmatclub.com/forum/a-small-business-invests-9-900-in-equipment-t...

• https://gmatclub.com/forum/what-is-the-sum-of-odd-integers-from-35-to-85...