GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Nov 2019, 11:21

### GMAT Club Daily Prep

#### 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

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

# Any decimal that has only a finite number of nonzero digits

Author Message
TAGS:

### Hide Tags

Director
Joined: 07 Jun 2004
Posts: 552
Location: PA
Any decimal that has only a finite number of nonzero digits  [#permalink]

### Show Tags

30 Sep 2010, 04:28
14
41
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:14) correct 39% (00:59) wrong based on 1122 sessions

### HideShow timer Statistics

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) k = 3

(2) j is an odd multiple of 3.
Math Expert
Joined: 02 Sep 2009
Posts: 58989

### Show Tags

30 Sep 2010, 04:37
8
25
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.)

Questions testing this concept:
700-question-94641.html?hilit=terminating%20decimal
is-r-s2-is-a-terminating-decimal-91360.html?hilit=terminating%20decimal
pl-explain-89566.html?hilit=terminating%20decimal
which-of-the-following-fractions-88937.html?hilit=terminating%20decimal

BACK TO THE ORIGINAL QUESTION:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) $$k = 3$$ --> now, if $$j=3p$$ (j is a multiple of 3) then $$\frac{j}{k}=\frac{3p}{3}=p=integer=terminating \ decimal$$ but if $$j$$ is not a multiple of 3 then reduced fraction $$\frac{j}{k}=\frac{j}{3}$$ won't be a terminating decimal, as denominator has primes other than 2 and/or 5. Not sufficient.

(2) $$j$$ is an odd multiple of 3 --> $$j=3(2k+1)$$, clearly insufficient as no info about the denominator $$k$$.

(1)+(2) $$\frac{j}{k}=\frac{3(2k+1)}{3}=2k+1=integer=terminating \ decimal$$. Sufficient.

_________________
##### General Discussion
Manager
Joined: 14 Jun 2010
Posts: 164

### Show Tags

07 Oct 2010, 01:19
2
But it says the ratio j/k is expressed as a decimal, so how come j=3p ?
I thought answer is A since J has to be a non-multiple of 3 since if it is a multiple of 3, j/k cannot be expressed as a decimal. COrrect me if i am wrong!
Retired Moderator
Joined: 02 Sep 2010
Posts: 723
Location: London

### Show Tags

07 Oct 2010, 01:36
psychomath wrote:
But it says the ratio j/k is expressed as a decimal, so how come j=3p ?
I thought answer is A since J has to be a non-multiple of 3 since if it is a multiple of 3, j/k cannot be expressed as a decimal. COrrect me if i am wrong!

Anser can't be A. Because just knowing that k=3, doesnt tell you much about the decimal. For instance if j and k do not have 3 as a common factor, it will not cancel out and you will not get a terminating decimal which you would if they do have 3 as a common factor.

Eg. j=1, k=3 : Decimal is 0.333333....
j=6, k=3 : Decimal is 2.0
_________________
Senior Manager
Joined: 25 Feb 2010
Posts: 278

### Show Tags

08 Oct 2010, 11:08
psychomath wrote:
But it says the ratio j/k is expressed as a decimal, so how come j=3p ?
I thought answer is A since J has to be a non-multiple of 3 since if it is a multiple of 3, j/k cannot be expressed as a decimal. COrrect me if i am wrong!

Can;t be true..
j can be a multiple of 3.
_________________
GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...
SVP
Joined: 06 Sep 2013
Posts: 1553
Concentration: Finance

### Show Tags

17 Oct 2013, 05:49
Bunuel wrote:
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.)

Questions testing this concept:
700-question-94641.html?hilit=terminating%20decimal
is-r-s2-is-a-terminating-decimal-91360.html?hilit=terminating%20decimal
pl-explain-89566.html?hilit=terminating%20decimal
which-of-the-following-fractions-88937.html?hilit=terminating%20decimal

BACK TO THE ORIGINAL QUESTION:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) $$k = 3$$ --> now, if $$j=3p$$ (j is a multiple of 3) then $$\frac{j}{k}=\frac{3p}{3}=p=integer=terminating \ decimal$$ but if $$j$$ is not a multiple of 3 then reduced fraction $$\frac{j}{k}=\frac{j}{3}$$ won't be a terminating decimal, as denominator has primes other than 2 and/or 5. Not sufficient.

(2) $$j$$ is an odd multiple of 3 --> $$j=3(2k+1)$$, clearly insufficient as no info about the denominator $$k$$.

(1)+(2) $$\frac{j}{k}=\frac{3(2k+1)}{3}=2k+1=integer=terminating \ decimal$$. Sufficient.

So I guess for this type of questions we can never asume that k>j unless it says so in the question stem. Am I right?
Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 58989

### Show Tags

17 Oct 2013, 08:39
jlgdr wrote:
Bunuel wrote:
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.)

Questions testing this concept:
700-question-94641.html?hilit=terminating%20decimal
is-r-s2-is-a-terminating-decimal-91360.html?hilit=terminating%20decimal
pl-explain-89566.html?hilit=terminating%20decimal
which-of-the-following-fractions-88937.html?hilit=terminating%20decimal

BACK TO THE ORIGINAL QUESTION:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) $$k = 3$$ --> now, if $$j=3p$$ (j is a multiple of 3) then $$\frac{j}{k}=\frac{3p}{3}=p=integer=terminating \ decimal$$ but if $$j$$ is not a multiple of 3 then reduced fraction $$\frac{j}{k}=\frac{j}{3}$$ won't be a terminating decimal, as denominator has primes other than 2 and/or 5. Not sufficient.

(2) $$j$$ is an odd multiple of 3 --> $$j=3(2k+1)$$, clearly insufficient as no info about the denominator $$k$$.

(1)+(2) $$\frac{j}{k}=\frac{3(2k+1)}{3}=2k+1=integer=terminating \ decimal$$. Sufficient.

So I guess for this type of questions we can never asume that k>j unless it says so in the question stem. Am I right?
Cheers
J

Yes, nothing in the stem indicates that k must be greater than j.
_________________
Senior Manager
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 475
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

### Show Tags

25 Oct 2013, 13:36
1
1
This is a GMAT Hacks question of the day. The question reappeared on May 8, 2013. Here is the official explanation in case anyone was interested.

Answer: C Statement (1) is insufficient. If the denominator of the fraction is 3, the decimal would be terminating if the numerator is a multiple of 3. For instance, 6/3 = 2, a terminating decimal. However, if the numerator is not a multiple of 3, it will not be terminating, as in 7/3 = 2.33.

Statement (2) is also insufficient. The important factor in determining whether a fraction is equivalent to a terminating decimal is the denominator. If j = 9, the fraction could be 9/3 (terminating) or 9/7 (not terminating).

Taken together, the statements are sufficient. j/k is equal to (3(integer))/3 = integer. An integer is, as defined in the question itself, a terminating decimal. Choice (C) is correct.

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8346
Location: United States (CA)
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

### Show Tags

16 Jan 2018, 17:55
1
rxs0005 wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?

(1) k = 3

(2) j is an odd multiple of 3.

We need to determine whether j/k is a terminating decimal given that j and k are positive integers. One thing we should keep in mind is that a fraction (in lowest terms and with a denominator greater than 1) can be expressed as a terminating decimal if and only if the denominator comprises prime factors of only 2 and/or 5. For example, 3/10 and 3/15 = 1/5 are terminating decimals, whereas 3/7 and 3/9 = 1/3 are not. On the other hand, if the denominator is 1, the fraction is always a terminating decimal as long as the numerator is an integer.

Statement One Alone:

k = 3

Depending on the value of j, j/k may or may not be a terminating decimal. For example, if j = 1, then j/k = 1/3 is not a terminating decimal. On the other hand, if j = 3, then j/k = 3/3 = 1/1 = 1 is a terminating decimal. Statement one is not sufficient to answer the question.

Statement Two Alone:

j is an odd multiple of 3.

Depending on the value of k, j/k may or may not be a terminating decimal. For example, if j = 3 and k = 7, then j/k = 3/7 is not a terminating decimal. On the other hand, if j = 3, and k = 3, then j/k = 3/3 = 1/1 = 1 is a terminating decimal. Statement two is not sufficient to answer the question.

Statements One and Two Together:

Since j is an odd multiple of 3, and k = 3, j/k is always an odd integer. Thus, j/k is a terminating decimal.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13566
Re: Any decimal that has only a finite number of nonzero digits  [#permalink]

### Show Tags

26 Feb 2019, 04:00
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.
_________________
Re: Any decimal that has only a finite number of nonzero digits   [#permalink] 26 Feb 2019, 04:00
Display posts from previous: Sort by