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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, 08:05

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

27% (01:55) correct
73% (01:06) wrong based on 23 sessions

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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.

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

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.

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
_________________

"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.

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).
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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?
_________________

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?
_________________

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.

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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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

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19 Jun 2015, 11:37

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?

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

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19 Jun 2015, 12:33

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

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