Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
A terminating decimal is defined as a decimal that has a
[#permalink]
Show Tags
22 May 2010, 14:35
4
16
00:00
A
B
C
D
E
Difficulty:
5% (low)
Question Stats:
81% (00:38) correct 19% (01:09) wrong based on 930 sessions
HideShow timer Statistics
A terminating decimal is defined as a decimal that has a finite number of nonzero digits. Examples of terminating decimals are 0.24, 52, and 6.0314. x and y are positive integers. If x/y is expressed as a decimal, is it a terminating decimal?
Theory: Reduced fraction \(\frac{a}{b}\) (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only \(b\) (denominator) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as \(250\) (denominator) equals to \(2*5^3\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\).
Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.
For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be terminating decimal.
(We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced.)
In original question statement (2) says that denominator equals to 2^3=8, hence x/8 will be terminating decimal no matter what the value of x is.
_________________
Re: A terminating decimal is defined as a decimal that has a
[#permalink]
Show Tags
24 Apr 2012, 04:20
2
3
Found this helpful explanation on Mgmat site. Author- Emily Sledge
This rule took a while for me to internalize. It's tough to picture a decimal terminating when the denominator is so huge, such as DWG's example of 43/256. I found it helped me to think about the basic patterns:
Every one of these terminates, and the pattern indicates that would continue to be true for higher powers. The number of decimal places increases along with the powers of 2 or 5, but the number of decimal places will always be finite.
In contrast, any factors other than 2 or 5 in the denominator can quickly be shown to be non-terminating, even for the most basic case (exponent of 1). Higher powers would be even messier: 1/3 = 0.33333(3 repeating) 1/6 = 0.16666(6 repeating) 1/7 = 0.142857(142857 repeating) 1/9 = 0.11111(1 repeating)
(1) Definitely isn't enough, because you can tweak the denominator any way you like to arrive at fraction that simplifies down to say, 2/3 (0.66666...) (2) Is the same thing.
At first glance this question seems really too easy. You need to know what's going on with both x and y in order be able to answer it.
C) jumps out immediately. It's obvious that if you know even the ranges of both x and y you could test each combo out and eventually arrive at an answer so clearly taken together they are sufficient.
It's just a matter of seeing if A, B or D is feasible. I don't think they are for the reasons I gave above. If I only know either the nominator or denominator, I can find a match somewhere down the line that allows to make it so the simplified result ends up to be 2/3 (recurring decimal) or 1/1 (obviously a terminating one).
(1) Definitely isn't enough, because you can tweak the denominator any way you like to arrive at fraction that simplifies down to say, 2/3 (0.66666...) (2) Is the same thing.
At first glance this question seems really too easy. You need to know what's going on with both x and y in order be able to answer it.
C) jumps out immediately. It's obvious that if you know even the ranges of both x and y you could test each combo out and eventually arrive at an answer so clearly taken together they are sufficient.
It's just a matter of seeing if A, B or D is feasible. I don't think they are for the reasons I gave above. If I only know either the nominator or denominator, I can find a match somewhere down the line that allows to make it so the simplified result ends up to be 2/3 (recurring decimal) or 1/1 (obviously a terminating one).
So: C
OA is B
Statement (2): Any number divided by 8 results in a terminating decimal. This is because when a number is divided by 2, the only possible remainders are or 1, 2, 3, 4, 5, 6, and 7 (actually 1/8, 2/8, etc.). These remainders are expressed as .125, .25, .375, .5, .625, .75, and .875, respectively. Therefore x/y is a terminating decimal; SUFFICIENT.
You're supposed to intuitively know that anything ever divided by 8 will result in a terminal decimal.
I messed up in assuming I had control over the denominator (when I said (2) is the same logic as why (1) doesn't work), when it clearly said it was 8 and nothing else.
It's funny, the last DS question I answered here I got right but made a big deal about feeling reluctant to toss out B. I was right to be feeling that way, but just not for the correct question. *sigh*
A terminating decimal is defined as a decimal that has a finite number of nonzero digits. Examples of terminating decimals are 0.24, 52, and 6.0314. x and y are positive integers. If x/y is expressed as a decimal, is it a terminating decimal?
(1) 40 < x < 45
(2) y = 8
B.
any positive integer number divided by 8 gives terminate decimal equal to 5. 1) is very alluring, cause we read 1) and then 2), having in mind "I dont know x, so I cant find out what is the decimal point, thus I need to know the range of numbers for X" Thus c is wrong.
_________________
A terminating decimal is defined as a decimal that has a finite number of nonzero digits. Examples of terminating decimals are 0.24, 52, and 6.0314. x and y are positive integers. If x/y is expressed as a decimal, is it a terminating decimal?
(1) 40 < x < 45
(2) y = 8
1) we don't know anything about y, so Insufficient
2) when you divide anything by 8 the answer will be either an integer, a fraction of a multiple of 0.125. For example 201/8 = 25.125 and 203/8 = 25.375
So in any case, this will always lead to a terminating decimal. Sufficient
Re: A terminating decimal is defined as a decimal that has a
[#permalink]
Show Tags
27 Apr 2016, 14:43
1
In statement 1 x can be 41,42,43 or 44. insufficient as we don't have value of y
In statement 2, clearly y is given as 8 which is the denominator of the fraction x/y. we know that any number which has denominator as 8 will be a terminating decimal
Re: A terminating decimal is defined as a decimal that has a
[#permalink]
Show Tags
13 Sep 2018, 03:22
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
81% (00:38) correct 
