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# What is the units digit of 6^15 - 7^4 - 9^3?

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What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  19 May 2012, 18:04
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51% (01:53) correct 48% (00:48) wrong based on 1 sessions
What is the units digit of 6^15 - 7^4 - 9^3?

A. 8
B. 7
C. 6
D. 5
E. 4
[Reveal] Spoiler: OA

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Last edited by carcass on 20 May 2012, 07:53, edited 1 time in total.
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  19 May 2012, 19:36

Unit digit of 6^15 is 6.
Unit digit of 7^4 is 1.
Unit digit of 9^3 is 9.

Now question is xxx6 - xx1- xx9 = 16 - 10 = 6
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  20 May 2012, 00:15
yes it is C, same method - cyclic unit digits
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  20 May 2012, 07:55
Yup

OA is C

Even though the tricky part is if you assume that 6-1 is -4 so you take the positive value of 4 and then pick E
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  21 May 2012, 18:04
Where am I going wrong...I don't understand the step of 16-10.

I went with 6-1-9, which arrived at (-4), so picked E because closest thing to the answer. I know, dumb reason but still, 16-10? what am I missing?
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  21 May 2012, 18:37
mantazuma wrote:
Where am I going wrong...I don't understand the step of 16-10.

I went with 6-1-9, which arrived at (-4), so picked E because closest thing to the answer. I know, dumb reason but still, 16-10? what am I missing?

Think about it like you're using elementary subtraction and subtracting these.

xxxxxxxx6
xxxxxxxx1
- xxxxxxxx9
__________

After subtracting the first 2 numbers, subtract again:
xxxxxxx5 (result of 6-1)
- xxxxxxx9
__________
xxxxxx6 (result of 5-9)

Not the prettiest but does the job.
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  21 May 2012, 19:56
I'm sorry..but I am still not getting it...how did you get 16? I understood the -10..but not 16
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  21 May 2012, 20:12
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Ok Let me try to explain this.

If you need to subtract 7 from 234 then as you know 7 is greater than 4 so you will take one carry from 10th place integer and you will subtract 7 from 14 to get 7. So result of this subtraction is 227.

Same way we know the last digit of the expression is 6 but this less than 10 so we have take carry from 10th place. So it becomes 16.
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  22 May 2012, 01:43
neetutiwari wrote:
I'm sorry..but I am still not getting it...how did you get 16? I understood the -10..but not 16

see below multiplicity table

4n+1 4n+2 4n+3 4n
1 1 1 1
2 4 8 6
3 9 9 1
4 6 4 6
5 5 5 5
6 6 6 6
7 9 3 1
8 4 2 6
9 1 9 1

All numbers from 1-9 repeat their units digit after a cycle of 4. i.e. 3^2 will have same units digit as 3^6 and form above table we see that 9 would be that digit.

Similarly,
6^15 will have units digit=6
7^4 will have units digit=1
9^3 will have units digit=9

So 6 - 1 - 9 = -4 (+10 from borrow) = 6
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink]  22 May 2012, 04:36
also you can see in this way:

6-9 = -4 but our six is a number in our equation that end with unit digit 5 infact to obtain the number of our answer choices subtracting 9 we have a number that must with unit digit of 5

A) 8 -> to get 8 you have 17 - 9= 8 but unit digit is 7 wrong

B) 7 -> 16-9 = 7 but unit digit is 6

C) 6 -> 15-9= 6
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Re: What is the units digit of 6^15 - 7^4 - 9^3?   [#permalink] 22 May 2012, 04:36
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