NEW HERE? LEARN MORE
closeclose
Last visit was: 29 Apr 2024, 10:36 It is currently 29 Apr 2024, 10:36
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If x and y are positive integers, and K equals the decimal equivalent

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29996 [2]
Given Kudos: 799
Location: Canada
Send PM
If x and y are positive integers, and K equals the decimal equivalent [#permalink] New post   Updated on: 02 Sep 2022, 08:19
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

59% (01:27) correct 41% (01:10) wrong based on 49 sessions
Hide Show timer Statistics
If x and y are positive integers, and K equals the decimal equivalent of x/y, is K a terminating decimal?

(1) x is a divisor of 16
(2) y is a multiple of 30
ShowHide Answer
Official Answer
C

Originally posted by BrentGMATPrepNow on 01 Sep 2022, 07:23.
Last edited by BrentGMATPrepNow on 02 Sep 2022, 08:19, edited 1 time in total.
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1426 [0]
Given Kudos: 632
Send PM
If x and y are positive integers, and K equals the decimal equivalent [#permalink] New post   Updated on: 02 Sep 2022, 09:44
BrentGMATPrepNow wrote:
If x and y are positive integers, and K equals the decimal equivalent of x/y, is K a terminating decimal?

(1) x is a divisor of 16
(2) y is a multiple of 30


A fraction is a terminating decimal when the reduced form of the denominator contains only 2's or/and 5's

(1) x is a divisor of 16

We cannot ascertain anything about the denominator.

INSUFF.

(2) y is a multiple of 30

So the denominator is a multiple of \(5*2*3 .\)

We can see we have an extra 3 in the denominator, however we still cannot tell whether this \(3 \) can be reduced/cancelled using the numerator.

Lets say we have numerator as 3 then the fraction becomes \(\frac{3}{5*2*3} = \frac{1}{5*2} \) This is a terminating decimal .
Lets say we have numerator as 2 then the fraction becomes \(\frac{2}{5*2*3} == \frac{1}{5*3}\)This is a NON terminating decimal.

INSUFF.


1+2

Since we can only have 2's ( factors/divisors of 16 ) in the numerator , the 3 in the denominator remains uncancelled.
Thus the fraction remains a non terminating decimal.


SUFF.

Ans C

Hope its clear

( edited after correction in the question)

Originally posted by stne on 01 Sep 2022, 20:58.
Last edited by stne on 02 Sep 2022, 09:44, edited 1 time in total.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29996 [1]
Given Kudos: 799
Location: Canada
Send PM
If x and y are positive integers, and K equals the decimal equivalent [#permalink] New post   Updated on: 02 Sep 2022, 08:35
1
Kudos
Expert Reply
Top Contributor
BrentGMATPrepNow wrote:
If x and y are positive integers, and K equals the decimal equivalent of x/y, is K a terminating decimal?

(1) x is a divisor of 16
(2) y is a multiple of 30

Given: x and y are positive integers, and K equals the decimal equivalent of x/y

Target question: Is K a terminating decimal?

Key Property: If D = the decimal equivalent of the fraction a/b (written in simplest terms), then D will be a terminating decimal only if the prime factorization of b consists of only 2's and/or 5's
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.

Statement 1: x is a divisor of 16
Since we have no information about the denominator (y), statement is not sufficient.
Here are two possible cases that yield conflicting answers to the target question:
Case a: x = 2 and y = 5. In this case, K = x/y = 2/5 = 0.4, which means the answer to the target question is YES, K is a terminating decimal
Case b: x = 2 and y = 3. In this case, K = x/y = 2/3 = 0.666666...., which means the answer to the target question is NO, K is not a terminating decimal
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is a multiple of 30
Here are two possible cases that yield conflicting answers to the target question:
Case a: x = 15 and y = 30. In this case, K = x/y = 15/30 = 1/2 = 0.5, which means the answer to the target question is YES, K is a terminating decimal
Case b: x = 80 and y = 30. In this case, K = x/y = 80/30 = 8/3 = 2.666666...., which means the answer to the target question is NO, K is not a terminating decimal
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x is a divisor of 16, which means x = 1, 2, 4, 8, or 15
Statement 2 tells us that y is a multiple of 30, which means y = (2)(3)(5)(n) for some integer n
Since x cannot be a multiple of 3, the simplified version of the fraction x/y will always have a 3 in the prime factorization of the denominator.
Since we can be certain that x/y will always have a 3 in the prime factorization of the denominator, the decimal equivalent of x/y (aka K) will not be a terminating decimal
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Originally posted by BrentGMATPrepNow on 02 Sep 2022, 07:17.
Last edited by BrentGMATPrepNow on 02 Sep 2022, 08:35, edited 2 times in total.
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1426 [1]
Given Kudos: 632
Send PM
Re: If x and y are positive integers, and K equals the decimal equivalent [#permalink] New post   02 Sep 2022, 08:14
1
Kudos
BrentGMATPrepNow wrote:
BrentGMATPrepNow wrote:
If x and y are positive integers, and K equals the decimal equivalent of x/y, is K a terminating decimal?

(1) x is a divisor of 16
(2) y is a multiple of 30

Given: x and y are positive integers, and K equals the decimal equivalent of x/y

Target question: Is K a terminating decimal?

Key Property: If D = the decimal equivalent of the fraction a/b (written in simplest terms), then D will be a terminating decimal only if the prime factorization of b consists of only 2's and/or 5's
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.

With this in mind, we can jump straight to. . .

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 48 and y = 30. In this case, K = x/y = 48/30 = 16/10 = 1.6, which means the answer to the target question is YES, K is a terminating decimal
Case b: x = 80 and y = 30. In this case, K = x/y = 80/30 = 8/3 = 2.666666...., which means the answer to the target question is NO, K is not a terminating decimal
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E


BrentGMATPrepNow

Perhaps I am missing something, but how is \(48\) or \(80\) divisors/ factors of \(16.\)

They are actually multiples of \(16 \) rather than divisors.

After posting my solution I was wondering about the same thing.

Hope you can clarify.

Thank you.
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6818
Own Kudos [?]: 29996 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: If x and y are positive integers, and K equals the decimal equivalent [#permalink] New post   02 Sep 2022, 08:32
1
Kudos
Expert Reply
Top Contributor
stne wrote:
BrentGMATPrepNow

Perhaps I am missing something, but how is \(48\) or \(80\) divisors/ factors of \(16.\)

They are actually multiples of \(16 \) rather than divisors.

After posting my solution I was wondering about the same thing.

Hope you can clarify.

Thank you.


You're absolutely right!!!
The funny thing is I created that question a couple of weeks ago and noted the correct answer as C.
However, yesterday, when I went to post the question, I mistakenly read statement 1 as "x is a multiple of 16", and incorrectly "updated" the official answer to E.
I have edited my solution accordingly.
Thanks for the heads up!

Kudos for you!!!!!
GMAT Club Bot
gmatclubot
Re: If x and y are positive integers, and K equals the decimal equivalent [#permalink]
02 Sep 2022, 08:32
Moderator:
Bunuel
Math Expert
93014 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions