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# unit digit !

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unit digit ! [#permalink]  23 Jul 2011, 01:56
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Question Stats:

70% (01:39) correct 30% (00:17) 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

Pls explain the trick underlying the above question .
[Reveal] Spoiler: OA

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Re: unit digit ! [#permalink]  23 Jul 2011, 02:02
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

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Re: unit digit ! [#permalink]  23 Jul 2011, 02:50
@Subhash : Can you pls brief a bit .
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Re: unit digit ! [#permalink]  23 Jul 2011, 02:56
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]  23 Jul 2011, 05:42
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]  23 Jul 2011, 14:14

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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Re: unit digit !   [#permalink] 23 Jul 2011, 14:14
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