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# What is the units digit of integer s? (1) The units digit of

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What is the units digit of integer s? (1) The units digit of [#permalink]

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07 Jun 2011, 07:05
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What is the units digit of integer s?
(1) The units digit of $$s^2$$ is double the units digit of s.
(2) The units digit of $$s^3$$ is four times the units digit of s.
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07 Jun 2011, 07:15
dreambeliever wrote:
What is the units digit of integer s?
(1) The units digit of $$s^2$$ is double the units digit of s.
(2) The units digit of $$s^3$$ is four times the units digit of s.

0,1,2,3,4,5,6,7,8,9: Unit digit of s
0,1,4,9,6,5,6,9,4,1: Unit digit of s^2
0,1,8,7,4,5,6,3,2,9: Unit digit of s^3

(1)
0 OR 2 possible.
Not Sufficient.

(2)
0 OR 2 possible.
Not Sufficient.

Combined:
0 OR 2.

Ans: "E"
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07 Jun 2011, 11:51
fluke wrote:
dreambeliever wrote:
What is the units digit of integer s?
(1) The units digit of $$s^2$$ is double the units digit of s.
(2) The units digit of $$s^3$$ is four times the units digit of s.

0,1,2,3,4,5,6,7,8,9: Unit digit of s
0,1,4,9,6,5,6,9,4,1: Unit digit of s^2
0,1,8,7,4,5,6,3,2,9: Unit digit of s^3

(1)
0 OR 2 possible.
Not Sufficient.

(2)
0 OR 2 possible.
Not Sufficient.

Combined:
0 OR 2.

Ans: "E"

is it true that 0^2 is double 0? I suppose it is. Just doesn't seem right logically.

but I know mathematically: 2 x 0 = 0
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07 Jun 2011, 12:10
moneymike wrote:

is it true that 0^2 is double 0? I suppose it is. Just doesn't seem right logically.

but I know mathematically: 2 x 0 = 0

I had the same dilemma before I decided to go with the mathematical interpretation. Let's ask others.
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08 Jun 2011, 09:11
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dreambeliever wrote:
What is the units digit of integer s?
(1) The units digit of $$s^2$$ is double the units digit of s.
(2) The units digit of $$s^3$$ is four times the units digit of s.

IMO D

1.

1,2,3,4,5,6,7,8,9 have squares as 1,4,9,16,25,36,49,64,81

don not consider the odd numbers as the last digit could not be even if s is odd.

hence

2,4,6,8 have squares => 4,16,36,64

only s=2 is the solution. Hence sufficient.

similar statement 2 is also sufficient.

Hence D

2*0 is not double of 0...2*0 is actually 0
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08 Jun 2011, 09:28
i go with E, 0 should be considered

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11 Jun 2011, 03:23
Dont think zero can be considered..IMO D
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11 Jun 2011, 16:20
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OA is D

Here's the original explanation:

"Explanation: Statement (1) is sufficient: the only units digit that doubles
when squared is 2: a number with a units digit of 2, such as 12, has a units
digit of 4 ($$12^2$$ = 144) when squared.

Statement (2) is sufficient: the only units digit that quadruples when cubed
is also 2. A number with a units digit of 2, such as 2, has a units digit of 8
($$2^3$$= 8) when cubed.
Choice (D) is correct."

It does not say anything about 0. I personally think 0 should be considered and ans should be E.

Source: Jeff Sackmann challenge series.
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11 Jun 2011, 23:48
0 is certainly equal to 2*0, so as the question is written, the answer is E, as several people have pointed out above. The question would be more interesting if it specified that the units digit was nonzero (and judging by the (incorrect) OE, that was clearly the intention of the question designer).
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11 Jun 2011, 23:53
IanStewart wrote:
0 is certainly equal to 2*0, so as the question is written, the answer is E, as several people have pointed out above. The question would be more interesting if it specified that the units digit was nonzero (and judging by the (incorrect) OE, that was clearly the intention of the question designer).

Much needed clarification. thanks IanStewart.

Do you believe that GMAT is less likely to put us through such dilemmas?
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12 Jun 2011, 00:28
In the midst of Soo much intelligence I'd like to put in my two bit from a lay mans point of view.
Firstly I got the answer D

Statement 1
If we test numbers 1 through 10 we see only the number 2 satisfies the description. So sufficient

Statement 2
The same logic applies and the only answer is 2 when numbers are tested 1-5.
Hence d. What is the OA.

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12 Jun 2011, 01:29
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IanStewart wrote:
0 is certainly equal to 2*0, so as the question is written, the answer is E, as several people have pointed out above. The question would be more interesting if it specified that the units digit was nonzero (and judging by the (incorrect) OE, that was clearly the intention of the question designer).

yes 0 is certainly equal to 2*0, but don't you think 2*0 is actually 0? not double of 0?
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12 Jun 2011, 02:10
Double of 0 is 0. So from the calculation of fluke ans is D.
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13 Jun 2011, 20:19
IanStewart wrote:
0 is certainly equal to 2*0, so as the question is written, the answer is E, as several people have pointed out above. The question would be more interesting if it specified that the units digit was nonzero (and judging by the (incorrect) OE, that was clearly the intention of the question designer).

How come Zero is "double" of Zero?!

I am (I guess, most of us here are) confused. Please, explain.
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13 Jun 2011, 22:01
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Schawjibb wrote:
[
How come Zero is "double" of Zero?!

I guess I might ask what else double of zero could be. When you double something, you multiply it by 2. If you multiply zero by 2, you get zero.

All of that said, you would never see this kind of wording on the GMAT, so this discussion won't be helpful to anyone. The question is just not worded well.
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13 Jun 2011, 23:41
0,2 creeps in both of a and b.Hence E it is.
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14 Jun 2011, 09:39
Both 0 & 2 satisfy the both statements.
No unique solution.
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Re: What is the units digit of integer s? (1) The units digit of [#permalink]

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19 Jun 2015, 10:37
Regardless of whether ) should be included, I have another query. For Statement 2, 8 when cubed is 512 (unit No of 2) and unit no. of 8 * 4 is 32 (also unit no. 2) so shouldnt it be included as a possible no too?

hoping to get a reply on this one.
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Re: What is the units digit of integer s? (1) The units digit of [#permalink]

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19 Jun 2015, 11:33
Gmatdecoder wrote:
Regardless of whether ) should be included, I have another query. For Statement 2, 8 when cubed is 512 (unit No of 2) and unit no. of 8 * 4 is 32 (also unit no. 2) so shouldnt it be included as a possible no too?

hoping to get a reply on this one.

Hello Gmatdecoder
When task says "The units digit of s3 is four times the units digit of s" it means that four times s will give us one digit result because unit digits can't be equal to 32

So 8 is out of case.
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Re: What is the units digit of integer s? (1) The units digit of   [#permalink] 19 Jun 2015, 11:33
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