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IF x is a positive integer, what is the units digit of

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IF x is a positive integer, what is the units digit of  [#permalink]

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New post Updated on: 07 Sep 2016, 10:05
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If x is a positive integer, what is the units digit of \((24)^{(2x+1)}(33)^{(x+1)}(17)^{(x+2)}(9)^{(2x)}\)

a. 4
b. 6
c. 7
d. 8
e. 9

How to solve for 33 and 17 when we dont know value of x ? Please help me understand

Originally posted by deepthit on 07 Sep 2016, 10:02.
Last edited by Bunuel on 07 Sep 2016, 10:05, edited 1 time in total.
Edited the question.
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Re: IF x is a positive integer, what is the units digit of  [#permalink]

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New post 07 Sep 2016, 11:25
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To find the units digit of the above (24)^(2x+1)(33)^(x+1)(17)^(x+2)(9)^(2x) , find the units digit of each term possible .

24^2x . 24 --> Units digit of (24^2)^X = 6^X = 6 multiplied by last digit of 24 = 4
33^x . 33 --> Units digit of 33^x . 3 --> 3,9,7,1 multiplied by 3
17^x. 17^2 --> Units digit of 17^x. 9 (units digit of 7^2)--> 7,9,3,1 multiplied by 9
9^2x --> Units digit of 81^x = 1

If you observe 2nd and 3rd expression above and multiply both you will always get 1 for units digit of 33^x multiplied by 17^x ( because 3*7, 9*9,7*3,1*1 all end in 1 for the same value of x) . Thus you have 3 and 9 from 2nd and third expression above.
So the units digit of the whole expression = Units digit of 4*3*9*1 which is 8 . Answer Choice D
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Re: IF x is a positive integer, what is the units digit of  [#permalink]

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New post 07 Sep 2016, 11:37
Hope you are clear with 24 and 9.

Coming to 33 and 17,

Units digits of powers of 33 can be - 3, 9, 7, 1 and repeats further in the same order.
Units digits of powers of 17 can be - 7, 9, 3, 1 and repeats further in the same order.

Now look at powers of 33 and 17 i.e. x+1 and x+2 respectively.

If x=1,
units digit value of power of 33 will be - 9
units digit value of power of 17 will be - 3
So, the final product of these two will have 7 as their unit digit.

If x=2,
units digit value of power of 33 will be - 7
units digit value of power of 17 will be - 1
So, the final product of these two will have 7 as their unit digit.

If x=3,
units digit value of power of 33 will be - 1
units digit value of power of 17 will be - 7
So, the final product of these two will have 7 as their unit digit.

If x=4,
units digit value of power of 33 will be - 3
units digit value of power of 17 will be - 9
So, the final product of these two will have 7 as their unit digit.

So 4*7*1 = 8. Hence D.

Hope it is clear
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Re: IF x is a positive integer, what is the units digit of  [#permalink]

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New post 09 Sep 2016, 05:16
I solved it using x = 1 and confirmed the answer for x=5 and x=17.

Got the same Last digit each time. Hence, Ans D.
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IF x is a positive integer, what is the units digit of  [#permalink]

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New post 17 Oct 2016, 16:41
D is correct. Here's why:

If we use x=1, we can create a potential number to determine units digit of

(24^3)(33^2)(17^3)(9^2)

4: 4, 16, 64
3: 3,9
7: 7,49,...3
9: 9,81

Multiply the units digits together --> 4x9x3x1 = 108 :)
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IF x is a positive integer, what is the units digit of  [#permalink]

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New post 23 Jan 2017, 18:04
1
Great Question.
There are two ways to solve this up.
Method 1->
As x is a postive integer and there has to be only one answer =>
Putting x=1 => units digit of the expression must be 8.

Method 2->
Observe that (33)^(x+1) * (17)^(x+2) => (33*17)^x+1 * 17
The units digit of (33*17)^x+1 is 1
The units digit of 17 is 7
Hence the units digit of (33*17)^x+1 * 17 is always 7.
So the units digit of the required expression will be => 4*7*1 => 8.
Hene D.


Similar Question to practise -->
If p is a positive integer, what is the units digit of Z, if Z = \(104^{4p + 1} * 277^{p + 1} * 93^{p + 2} * 309^{6p}\)?
A)0
B)2
C)4
D)6
E)8

B.

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Re: IF x is a positive integer, what is the units digit of  [#permalink]

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