BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

4 and 2 unique property?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Sun Jun 27, 2010 9:25 pm
Thanked: 2 times

4 and 2 unique property?

by ashblog02 » Sat Nov 06, 2010 9:11 pm
Any decimal that has a finite number of non-zero digits is a terminating decimal. for example, 24, 0.82, 5.096 are three terminating decimals. If r & s are positive integers and the ratio of r/s is expressed as a decimal, is r/s a termnating decimal?

1] 90<r<100
2] s=4

a. statement 1
b. statement 2 (ans)
c. both together
d. each statment alone
e. neither statement

I understood the ans for option 1 but why is option b sufficient? does 4 have a unique property that it does not result in terminating decimals where as 3 does??
or i ws thinking of 6 it does have recurring decimals numbers but then 2 does not, is this a unique property to some integers?
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1460
Joined: Tue Dec 29, 2009 1:28 am
Thanked: 135 times
Followed by:7 members

by selango » Sat Nov 06, 2010 10:24 pm
stmt2,

s=4

r/s=r*1/4

=r*0.25

Whatever values of r, the result is decimal with finite number of integers.

So B is sufficient.

whenever a odd number is divided by 2^n,it result in decimal with finite number of integers.
Last edited by selango on Wed Nov 10, 2010 7:30 pm, edited 1 time in total.
--Anand--
Top
User avatar
GMAT Instructor
Posts: 1031
Joined: Thu Jul 03, 2008 1:23 pm
Location: Malibu, CA
Thanked: 716 times
Followed by:255 members
GMAT Score:750

by Brian@VeritasPrep » Wed Nov 10, 2010 12:03 pm
Great explanation, Selango - if I can just tack on a little bit, this is one case in which it may be particularly helpful to be able to think of division problems in a few ways.

Let's consider the possibility of 11 divided by 4. We could express that as:

11/4 (a fraction)

2 and 1/4 (a mixed number, in which we'll take the number of times that 4 goes in evenly to 11, and then take what's left and divide back by 4 as a fraction)

2 remainder 1 (much like the mixed number but we leave the remainder as is and don't divide it back in)

2.25 (we take the mixed number and actually calculate it to a decimal place)


The GMAT likes to test your flexibility with these ways of expressing division, and this problem is a good example. r/s, if s = 4, is r/4. With that, to find the decimal we'd take whatever the remainder is and divide it back by 4. Those possibilities are:

No remainder --> Nothing after the decimal place.
Remainder 1 --> 1/4 ---> .25
Remainder 2 --> 1/2 ----> .5
Remainder 3 --> 3/4 ---> .75

Had they asked about a different value of s, we could try the same thing until we either found a repeating and a terminal decimal or recognized that we wouldn't. Say that s were 6, we'd have:

Remainder 1 ---> 1/6 ---> .166666......
Remainder 2 ---> 2/6 ---> 1/3 ---> .333333..........
Remainder 3 ----> 3/6 ---> 1/2 ----> .5

Now we have both a terminal decimal (.5) and a repeating decimal (.16666...), so this one wouldn't be sufficient.



I'd say that this question is much more about your ability to recognize the concept behind division than it is about knowing particular rules for numbers - once you know the concept the trial-and-error for the division shouldn't be that time-consuming or difficult, but the real catch is recognizing that if they're asking about division in a more conceptual framework you should be thinking about that relationship between remainder, fraction, and decimal.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
Top
Post new topic Post Reply
• Page 1 of 1