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# If x is a positive integer, what is the units digit of 3x?

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Senior Manager
Joined: 29 Jan 2011
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If x is a positive integer, what is the units digit of 3x?  [#permalink]

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22 Jun 2011, 01:54
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68% (00:54) correct 32% (01:02) wrong based on 273 sessions

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If x is a positive integer, what is the units digit of 3x?

(1) x = 10k^2 + 1, where k is a positive integer.
(2) The units digit of x^2 is 1.
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Re: DS MGMAT Units digit  [#permalink]

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22 Jun 2011, 02:31
1
siddhans wrote:
If x is a positive integer, what is the units digit of 3x?

(1) x = 10k^2 + 1, where k is a positive integer.
(2) The units digit of x^2 is 1.

Given:
X is positive integer. We need to find the units digit of 3x.

Rephrased question. What is the units digit of x ?

(1) $$x = 10k^2 + 1$$

So what ever be the value of k, the last digit of $$10k^2$$ will always be 0.
Since K is an integer

[Eg: when k = 2, $$10*2^2 = 40$$
when k = 4, $$10*4^2 = 160$$]

So we can conclude that the last digit of x is 0+1 = 1 Sufficient

(2) Units digit of $$x^2 is 1$$.

According to this statement, the units digit of x could be either 9 or 1.

Eg:
$$19^2$$= 361 (last digit 9) or
$$21^2$$= 441 (last digit 1)

both of which yield different results when multiplied by 3, as per our question stem.

Therefore Insufficient

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Re: If x is a positive integer, what is the units digit of 3x?  [#permalink]

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26 Mar 2012, 19:32
in stmt 1, no matter what variable k is since it is greater than 0 and an integer 10k^2+1 will always be 1 and so 1*3 will be 3.... sufficient
stmt 2 = 11 fits the equation and also 9 fits the equation. so it is insufficient what the unit variable is.
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Re: If x is a positive integer, what is the units digit of 3x?  [#permalink]

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17 Mar 2016, 04:31
siddhans wrote:
If x is a positive integer, what is the units digit of 3x?

(1) x = 10k^2 + 1, where k is a positive integer.
(2) The units digit of x^2 is 1.

statement 1 gives a unique answer because x's unit digit is always 1
statement 2 gives two answers; the unit digit of x is either 1 or 9
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Re: If x is a positive integer, what is the units digit of 3x?  [#permalink]

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24 Nov 2016, 05:13
Nice Question.
Here is what i did =>
We need the units digit of 3x
so we need the unit digit of x and we will multiply it by 3 to get to the units digit of 3x

Statement 1
here since k>0 and an integer.
The units digit of x must be 1
hence the units digit of 3x must be 3
hence sufficient
Statement 2
the units digit of x^2 is 1
so the units digit of x can be 1 or 9
hence the units digit of 3x can be 3 or 7

Hence not sufficient

Hence A
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Re: If x is a positive integer, what is the units digit of 3x?  [#permalink]

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29 May 2017, 11:21
siddhans wrote:
If x is a positive integer, what is the units digit of 3x?

(1) x = 10k^2 + 1, where k is a positive integer.
(2) The units digit of x^2 is 1.

This problem can be quickly solved via creating a table. Yes, you can reason your way through it, but it drains mental energy. The goal is to find the UNIQUE value of the units digit of 3x. This number ranges from 0 to 9, since it's a place value.

Statement 1) x = 10k^2 + 1

Create a table here with columns corresponding to k, 10k^2 +1 = x, and 3x

K | 10k^2 = x | 3x
0 | 1 | 3
1 | 11 | 33
2 | 41 | 123
3 | 91
4 | 161
5 | 251

You can already see the pattern, so no need to finish the table. This statement is sufficient. The units value of 3x = 3.

Statement 2) Units digit of x^2 = 1

Once again, create a table and list three columns: x, x^2, 3x

x | x^2 | 3x
0 | 0 | 0
1 | 1 | 3
2 | 4 | 6
3 | 9 | 9
4 | 16 | 12
5 | 25 | 16
6 | 36 | 18
7 | 49 | 21
8 | 64 | 24
9 | 81 | 27

Only two x values have x^2 values with a 1 in the units digit, so that's good, but unfortunately the units value of 3x for those two x values differ (3 and 7, respectively). Insufficient.
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Re: If x is a positive integer, what is the units digit of 3x?  [#permalink]

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25 Sep 2017, 07:22
siddhans wrote:
If x is a positive integer, what is the units digit of 3x?

(1) x = 10k^2 + 1, where k is a positive integer.
(2) The units digit of x^2 is 1.

St 1

This statement basically tells us that the units digit of X will always be 1 because no matter what K is, and K must be a positive integer, 10k^2 will always be a multiple of 10 and thus have a units digit of 0. If this is true then x will always have a units digit of 1 and if x always has a units digit of 1 then the units digit of 3x will always be 3

St 2

clearly insuff could be 11, 9 ,1 etc

A
Re: If x is a positive integer, what is the units digit of 3x? &nbs [#permalink] 25 Sep 2017, 07:22
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