Integer Bouncer

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Sun Jul 20, 2008 5:47 am

In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?
(1) 16x is an integer.
(2) 8x is an integer.

am totally stumped...

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Source: Beat The GMAT — Data Sufficiency | Sun Jul 20, 2008 5:47 am

VP_Tatiana: GMAT Instructor; Posts: 189; Joined: Thu May 01, 2008 10:55 pmFollowed by: 1 member; Location: Seattle, WA; Thanked: 25 times; GMAT Score:750+

by VP_Tatiana » Sun Jul 20, 2008 10:04 am

You guys are right; the digit after the decimal point is the tens digit, not the units digit. My bad and thanks for the correction!

Last edited by VP_Tatiana on Sun Jul 20, 2008 2:05 pm, edited 1 time in total.

Tatiana Becker | GMAT Instructor | Veritas Prep

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ildude02: Master | Next Rank: 500 Posts; Posts: 320; Joined: Sun Jan 13, 2008 10:00 pm; Thanked: 10 times

by ildude02 » Sun Jul 20, 2008 11:45 am

The answer is B. 8x will always yield a non zero tenth digit.

I see in Tatianas explanation, she considered 0.50s' tenth digit as 0, but the tenth digit is non-zero which is 5. I beleive for decimals, there is no unit digit and it begins with tenth digit. Correct me if I'm wrong.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sun Jul 20, 2008 12:43 pm

ildude02 wrote:The answer is B. 8x will always yield a non zero tenth digit.

I see in Tatianas explanation, she considered 0.50s' tenth digit as 0, but the tenth digit is non-zero which is 5. I beleive for decimals, there is no unit digit and it begins with tenth digit. Correct me if I'm wrong.

You're 100% correct.

If 8x is an integer, and x must be between 0 and 1, then the smallest possible value of x is .125. Every possibly value has a non-zero tenths digit (which is indeed the digit directly to the right of the decimal - the "tens" digit is actually two to the LEFT of the decimal place).

If 16x is an integer, then the smallest possible value of x is .0625, which does have a tenths digit of 0. Of course, x could also be .125, with a non-zero tenths digit; hence, (1) is insufficient.

(2) is sufficient, (1) is not: choose (B).

As a quick review:

2,436.789

2 is the thousands digit
4 is the hundreds digit
3 is the tens digit
6 is the units (or ones) digit
7 is the tenths digit
8 is the hundredths digit
9 is the thousandths digit

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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cunu: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon Dec 10, 2007 3:41 am

by cunu » Mon Jul 21, 2008 1:47 am

how about 8 (.5) = 4.0 ?

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Mon Jul 21, 2008 4:26 am

@cunu,
had the same doubt...but stuart is spot on...dont look at the answer that ur getting first..u have stated that 8*0.5=4....here, 5 is in the tenths place which is nonzero......dun worry about the answer...

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