Remainder

[didieravoaka]

Thanks to help.

[[email protected]]

Hi didieravoaka,

This question is ultimately about pattern-matching (and paying attention to the 'units digit' of each calculation). The GMAT won't expect you to calculate 3^19, so let's do some easier calculations instead and look for a pattern:

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81

3^5 = 243

Notice how the units digit is now following a pattern: 3 - 9 - 7 - 1

This pattern will repeat with every 4 calculations that you perform, so you can deduce:

3^19 will be 4 "groups" of (3 - 9 - 7 - 1) and then a 3, a 9 and finally a 7

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

Another idea here:

3¹� =

(3�)� * 3³

Since 3� = 81, we know that (3�)� = 81� = something that ends in 1. So we have

(something that ends in 1) * 3³ =>

(something that ends in 1) * 27 =>

something that ends in 7

[ceilidh.erickson]

First, we have to translate. Any time a question asks "What is the remainder when X is divided by 10?" it's really asking for the UNITS DIGIT.

For example, when 546 is divided by 10 --> 54 remainder 6
when 7247 is divided by 10 --> 724 remainder 7

As Rich showed, units digits of powers will form certain patterns. Establish that pattern, and you can easily find the answer.

Because powers of 3 repeat every 4 powers, then any time 3 is raised to a power that's a multiple of 4, the units digit will be 1. So we know that 3^16 will have a units digit of 1, and we can establish the pattern after that:

3^16 --> 1
3^17 --> 3
3^18 --> 9
3^19 --> 7

[ceilidh.erickson]

Here are a few more examples of "what is the remainder when divided by 10" used as code for "what is the units digit":
https://www.beatthegmat.com/if-r-s-and-t ... tml#548713
https://www.beatthegmat.com/if-n-and-m-a ... tml#544266

[ceilidh.erickson]

And a few more about units digits generally:
https://www.beatthegmat.com/what-is-the- ... tml#544267
https://www.beatthegmat.com/what-is-the- ... tml#554073