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What is the units digit of integer s? (1) The units digit of [#permalink]
07 Jun 2011, 07:05

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

17% (01:02) correct
83% (01:09) wrong based on 13 sessions

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.

Re: DS Exponents question [#permalink]
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

Re: DS Exponents question [#permalink]
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.

Re: DS Exponents question [#permalink]
08 Jun 2011, 09:11

1

This post received KUDOS

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 _________________

Re: DS Exponents question [#permalink]
11 Jun 2011, 16:20

1

This post received KUDOS

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.

Re: DS Exponents question [#permalink]
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). _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: DS Exponents question [#permalink]
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? _________________

Re: DS Exponents question [#permalink]
12 Jun 2011, 01:29

1

This post received KUDOS

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? _________________

Re: DS Exponents question [#permalink]
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.

Re: DS Exponents question [#permalink]
13 Jun 2011, 22:01

1

This post received KUDOS

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. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

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