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## Comment on

Units Digit of Large Powers## Brent,

Could you elaborate on more complicated cycles? (n > 3) I'm still confused on how to find the units digit in those situations after I find the cycle and cycle length.

## Sure thing.

Sure thing.

Let's try the units digit of 7^33

First find the pattern AND the cycle:

7^1 = 7

7^2 = 49

7^3 = --3

7^4 = --1

7^5 = --7

7^6 = --9

7^7 = --3

7^8 = --1

.

.

.

So, the CYCLE = 4

Now focus on the MULTIPLES OF 4 (the cycle)

7^4 = ---1

7^8 = ---1

7^12 = ---1

etc

We want the units digit of 7^33

Since 32 is a multiple of 4, we know that 7^32 = ---1

Since the cycle is 7, 9, 3, 1, 7, 9, 3, 1, etc, we know that the NEXT POWER, 7^33, has units digit 7

Does that help?

Cheers,

Brent

## sir in questions like 234^121

here sir can we make pattern of unit digit(by finding cycle) of 4^121 rather than 234^121 since we are interested only in unit digit?

## Yes, that's correct. The

Yes, that's correct. The units digit of 4^121 will be the same as the units digit of 234^121.

Cheers,

Brent

## Hi Brent,

Is it safe to assume that the cycle ends as soon as you get 1?

Because any no: multiplied by 1 will repeat that units digit?

So I start looking for pattern and as soon as I reach 1 i count the no:?

Thank you,

Ari Banerjee

## Yes, that rule will work for

Yes, that rule will work for powers of integers ending in 1, 3, 7 and 9

Cheers,

Brent

## Hi Brent,

In one of the questions https://gmatclub.com/forum/what-is-the-units-digit-of-the-solution-to-217680.html

You have advised to quickly reach a conclusion as follows:

"These questions can be time-consuming. If you're pressed for time, you can use the following approach to reduce the answer choices to just 2 options in about 5 seconds.

177^(28) - 133^(23) = (odd number)^(some positive integer) - (odd number)^(some positive integer)

= odd - odd"

Please can you advise what are the other rules that we can memorise. e.g. Odd number, even integer etc.

Not sure if there is a video for that later on.

Thanks.

## You can find additional rules

You can find additional rules regarding odd and even integers here: https://www.gmatprepnow.com/module/gmat-integer-properties/video/837

Cheers, Brent

## Ok, Thanks Brent.

## Hi Brent, thanks for this

If 2^x + y = 48, what is the value of y ?

1) x^2 = 81

2) x − y = 2

I thought it would be "both statements ALONE are sufficient" as you can take the square root of x in 1) and thereby find y, and in 2) you can substitute x with 2-y to find y.

However, the solution is that statement 2 is sufficient but 1 is not.

Please help! Again, thanks a lot.

However,

## Be careful; there are TWO

Be careful; there are TWO solutions to the equation x² = 81.

Either x = 9, or x = -9

When we plug both values into the equation 2^x + y = 48, we get TWO possible values for y.

So, statement 1 is not sufficient

## .. of course!! Thanks!

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