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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] New post 23 Jul 2011, 00:56
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63% (01:52) correct 38% (00:47) wrong based on 112 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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Re: unit digit ! [#permalink] New post 23 Jul 2011, 01:02
The unit's digit of 6^15 = 6
The unit's digit of 7^4 = 1
The unit's digit of 9^3 = 9

So the The unit's digit of product = 6 - 1 - 9

.........6
........10
-------------
6

Answer - C
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Re: unit digit ! [#permalink] New post 23 Jul 2011, 01:50
@Subhash : Can you pls brief a bit .
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Re: unit digit ! [#permalink] New post 23 Jul 2011, 01:56
AnkitK wrote:
@Subhash : Can you pls brief a bit .


What I've done here is - take the unit's digit of all the individual numbers into consideration because the unit's digit of the sum of the digits will be decided ultimately by the unit's digit of all the individual numbers.

Thereafter, if you see the expression, I've grouped together positive and negative numbers.

6^15 is a very big number and much > 7^4 + 9^3.

So you need to visualize it as (xxxx6 - 10), and 6 can borrow 1 easily from left side because it's very big number.

HTH.

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Re: unit digit ! [#permalink] New post 23 Jul 2011, 04:42
As subhashgosh did, let me just add visual to it.
Interesting to see that 6^15 is large number something like XXXXXXXX6
7^4 = 2401
9^3 = 729
Now subtract
XXXXXXXX6
- 2401
--------------------------
xxxxxxxxxx5

xxxxxxxxxx5
- 729
--------------------------
xxxxxxxxxxx6

Unit digit = 6

OA C.
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Re: unit digit ! [#permalink] New post 23 Jul 2011, 13:14
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Answer is C.

6^15 will always result in a unit digit of 6.

unit digit of 7^4 = 7*7 = 49. 7*9 = 63. 7*3=21---> Unit digit of 21 = 1.

Unit digit of 9^3 = 9*9 = 81. 9*1 = 9 --->unit digit of 9 is 9.

6-1 = 5. 5 - 9 = 4----> THIS IS WRONG. because remember, when subtracting a bigger number from a smaller number, you add 10 to the smaller number.

In this case, you add 10 to 5, which gives us 15. 15 - 9 = 6.
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What is the units digit of 6^15 - 7^4 - 9^3? [#permalink] New post 19 May 2012, 17:04
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink] New post 19 May 2012, 18:36
Answer is 6.

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] New post 19 May 2012, 23:15
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] New post 20 May 2012, 06:55
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink] New post 21 May 2012, 17:04
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] New post 21 May 2012, 17:37
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] New post 21 May 2012, 18:56
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] New post 21 May 2012, 19:12
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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] New post 22 May 2012, 00:43
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] New post 22 May 2012, 03:36
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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] New post 22 Nov 2013, 10:01
AnkitK wrote:
What is the units digit of 6^15 - 7^4 - 9^3?

A) 8
B) 7
C) 6
D) 5
E) 4


6-1-9 = -4. Bottow 10
Units digit is then 6.

Answer is C

Hope it helps
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Re: What is the units digit of 6^15 - 7^4 - 9^3? [#permalink] New post 26 Feb 2014, 00:57
6^15 - 7^4 - 9^3

Rewrite as 6^15 - (7^4 + 9^3 )

6^15 would give units digit as 6

7^4 would give units digit as 1

9^3 would give units digit as 9

(7^4 + 9^3 ) gives 9+1 = 10 so 0 is the units digit

6^15 - (7^4 + 9^3 ) gives 6-0 = 6 as the units digit

Answer = C
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Re: What is the units digit of 6^15 - 7^4 - 9^3?   [#permalink] 26 Feb 2014, 00:57
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