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

 It is currently 16 Oct 2019, 01:19

### 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

# Let x and y be positive integers, and r and s be single-digit positive

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58374
Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

05 Jun 2015, 06:09
1
8
00:00

Difficulty:

55% (hard)

Question Stats:

63% (01:48) correct 37% (02:10) wrong based on 156 sessions

### HideShow timer Statistics

Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58374
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

08 Jun 2015, 05:41
3
2
Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

MANHATTAN GMAT OFFICIAL SOLUTION:

Fractions that have only factors of 2 and 5 in the denominator equate to terminating decimals. Since x/y = r.sss, a non-terminating decimal, y must have some other prime factors besides just 2 and/or 5.

(A) y = 12, 120, 1,200, etc. Prime factors of 12: (2)(2)(3)
(B) y = 15, 150, 1,500, etc. Prime factors of 15: (3)(5)
(C) y = 18, 180, 1,800, etc. Prime factors of 18: (2)(3)(3)
(D) y = 25, 250, 2,500, etc. Prime factors of 25: (5)(5). CANNOT be true—only has 5's and 2's.
(E) y = 27, 270, 2,700, etc. Prime factors of 27: (3)(3)(3)

_________________
##### General Discussion
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

05 Jun 2015, 06:51
1
1
Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

Attachments

Sol6.jpg [ 329.67 KiB | Viewed 2489 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 12 Oct 2014
Posts: 1
GMAT Date: 07-15-2015
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

05 Jun 2015, 23:38
Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option D is correct answer?

Cheers,
Sri
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

05 Jun 2015, 23:50
2
Sri22 wrote:
Bunuel wrote:
Let x and y be positive integers, and r and s be single-digit positive integers. If x/y = r.sss, where the bar below the s indicates that the decimal repeats infinitely, which of the following CANNOT be true?

(A) y = 1.2 × 10^a, where a is a positive integer.
(B) y = 1.5 × 10^b, where b is a positive integer.
(C) y = 1.8 × 10^c, where c is a positive integer.
(D) y = 2.5 × 10^d, where d is a positive integer.
(E) y = 2.7 × 10^e, where e is a positive integer.

Concentrating only on the answer choices, only option D is not a multiple of 3. The rest of them are multiples of 3, thats a common trend in other answer choices. With this logic can we say that Option D is correct answer?

Cheers,
Sri

Hi Sri,

I would say YES, you can conclude it but only in grave situations when you have already given up on question and have to move on with one of the answer choices as selection.
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 12 Feb 2013
Posts: 20
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

06 Jun 2015, 01:00
2
1
For such questions... generally one rule works most of the time
if there is only 2 or 5 or combination of 2 and 5 in denominator, it will always give u a fixed output rather than a never ending one.
You can try few examples

33/5 = 6.6
3333333333/5 = 666666.6 something

1111/2 = 555.5

in all options except D, there is a factor of 3 involved... where as in D only 5 is there (5*5 = 25)
in GMAT you dont need to solve every expression... there might be possibility of other options as correct but first skim through options and then use logic.
I have solved numerous questions of gmat but never felt the need to solve anything for such questions..

yes, if still you want to use logic, then a perfect algebric solution is provided by GMATINSIGHT
Non-Human User
Joined: 09 Sep 2013
Posts: 13161
Re: Let x and y be positive integers, and r and s be single-digit positive  [#permalink]

### Show Tags

19 Mar 2018, 06:42
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: Let x and y be positive integers, and r and s be single-digit positive   [#permalink] 19 Mar 2018, 06:42
Display posts from previous: Sort by