It is currently 17 Dec 2017, 06:05

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If positive integer 36y is divisible by 10, which of the following mus

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 298

Kudos [?]: 596 [1], given: 1474

Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

12 Sep 2015, 11:45
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:08) correct 29% (01:26) wrong based on 175 sessions

### HideShow timer Statistics

If positive integer 36y is divisible by 10, which of the following must be true?

I. y^2 is divisible by 25.

II. y^2 is divisible by 100.

III. $$\frac{3y}{15}$$ is an integer.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only
[Reveal] Spoiler: OA

_________________

KUDO me plenty

Last edited by shasadou on 12 Sep 2015, 19:37, edited 1 time in total.

Kudos [?]: 596 [1], given: 1474

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10419

Kudos [?]: 3700 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

12 Sep 2015, 15:02
1
KUDOS
Expert's post

Roman Numeral questions on the GMAT are usually designed in such a way that you can use the answer choices to avoid doing some of the work. Without those answer choices, we're forced to work through all 3 Roman Numerals. Thus, it would help if you include the 5 answer choices.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Kudos [?]: 3700 [1], given: 173 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 10419 Kudos [?]: 3700 [2], given: 173 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink] ### Show Tags 13 Sep 2015, 11:00 2 This post received KUDOS Expert's post HI shasadou, Although the prompt doesn't state it, I think that it is supposed to state that "Y is an INTEGER." Given that, we can use Prime Factorization to deal with this prompt. Again, assuming that Y is an integer, we're told that 36Y is divisible by 10. This means that 36Y must have a "2" and a "5" among its prime factors. 36 = (2)(2)(3)(3), so it has the '2' that we're looking for, but it doesn't have the '5.' This means that the Y must contain at least a "5" (although it could have other prime factors also, including additional 5s). This is all meant to say that Y MUST be a multiple of 5. Since the prompt asks for what MUST be true, we can use Y=5 to assess the Roman Numerals. I. Y^2 is divisible by 25 Y=5 Y^2 = 25, which IS divisible by 25 Any larger multiple of 5 will also be divisible by 25. Roman Numeral 1 is always true. Eliminate Answers B and C. II. Y^2 is divisible by 100 With the work that we did in Roman Numeral 1, we've proven that this is NOT always true. Eliminate Answer D. III. 3Y/15 is an integer Even before we consider the value of Y, we can simplify this fraction.... 3Y/ 15 = Y/5 So, is Y/5 always an integer? We already proved that Y had to be a multiple of 5, so this Roman Numeral is also always true. Eliminate Answer A. If we had dealt with this Roman Numeral immediately after dealing with Roman Numeral 1, then we wouldn't even have had to deal with Roman Numeral 2. There's only one answer that includes Roman Numerals 1 and 3... Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3700 [2], given: 173

Current Student
Joined: 12 Aug 2015
Posts: 298

Kudos [?]: 596 [0], given: 1474

Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

13 Sep 2015, 11:15
EMPOWERgmatRichC wrote:
Although the prompt doesn't state it, I think that it is supposed to state that "Y is an INTEGER."

hi

hecked once again - i fully restated the question, the stimulus does not say y is an integer. if this were a DS variation of the question it would be E. thanks
_________________

KUDO me plenty

Kudos [?]: 596 [0], given: 1474

Non-Human User
Joined: 09 Sep 2013
Posts: 14796

Kudos [?]: 288 [0], given: 0

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

24 Sep 2017, 06:08
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.
_________________

Kudos [?]: 288 [0], given: 0

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1810

Kudos [?]: 990 [0], given: 5

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

26 Sep 2017, 15:39
If positive integer 36y is divisible by 10, which of the following must be true?

I. y^2 is divisible by 25.

II. y^2 is divisible by 100.

III. $$\frac{3Y}{15}$$ is an integer.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

We can create the following expression:

36y/10 = integer

18y/5 = integer

So we see that y must be a multiple of 5.

Thus, Roman numerals I and III must be true.

Roman numeral II, on the other hand, does not have to be true. For instance, we see that y = 5 satisfies the hypothesis that 36y is divisible by 10; but y^2 = 25 is not divisible by 100.

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 990 [0], given: 5

Intern
Joined: 11 Jun 2017
Posts: 33

Kudos [?]: 4 [0], given: 78

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

26 Sep 2017, 17:53
I have a question of

II. y^2 is divisible by 100.

100 = 2^2 X 5^2, as long as y^2 is divisible by 100 means Y has at least factor 2,2,5,5. Hence 36Y can be divided by 10

Is II wrong because it can not co-exist with I ???

Kudos [?]: 4 [0], given: 78

Math Expert
Joined: 02 Sep 2009
Posts: 42648

Kudos [?]: 135946 [0], given: 12716

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

26 Sep 2017, 20:09
NNURP wrote:
I have a question of

II. y^2 is divisible by 100.

100 = 2^2 X 5^2, as long as y^2 is divisible by 100 means Y has at least factor 2,2,5,5. Hence 36Y can be divided by 10

Is II wrong because it can not co-exist with I ???

If positive integer 36y is divisible by 10, which of the following must be true?
_________________

Kudos [?]: 135946 [0], given: 12716

Intern
Joined: 11 Jun 2017
Posts: 33

Kudos [?]: 4 [0], given: 78

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

27 Sep 2017, 04:36
Sorry Bunuel, I still don't get the explanation you provide. Can you please help?

The question is basically asking whether Y contains any 5.

If y^2 is divisible by 100, then y^2 must contains at least multiple of 2 and 5. When we apply Y(2*2*5*5) back, 36Y can be divided by 10.

What am I getting wrong here?

Kudos [?]: 4 [0], given: 78

Math Expert
Joined: 02 Sep 2009
Posts: 42648

Kudos [?]: 135946 [0], given: 12716

Re: If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

27 Sep 2017, 04:50
NNURP wrote:
If positive integer 36y is divisible by 10, which of the following must be true?

I. y^2 is divisible by 25.

II. y^2 is divisible by 100.

III. $$\frac{3y}{15}$$ is an integer.

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Sorry Bunuel, I still don't get the explanation you provide. Can you please help?

The question is basically asking whether Y contains any 5.

If y^2 is divisible by 100, then y^2 must contains at least multiple of 2 and 5. When we apply Y(2*2*5*5) back, 36Y can be divided by 10.

What am I getting wrong here?

It seems that you don't understand the question.

We are told that 36y is divisible by 10, and asked to find which of the options MUST be true. For 36y to be divisible by 10, y (assuming it's an integer) must be a positive multiple of 5, so y could be 5, 10, 15, 20, ...

Is the second option (y^2 is divisible by 100) always true? NO. If y = 5, then y^2 =25, and it's NOT divisible by 100. So, it's not always true.

11. Must or Could be True Questions

For more check Ultimate GMAT Quantitative Megathread
_________________

Kudos [?]: 135946 [0], given: 12716

Intern
Joined: 11 Jun 2017
Posts: 33

Kudos [?]: 4 [0], given: 78

If positive integer 36y is divisible by 10, which of the following mus [#permalink]

### Show Tags

27 Sep 2017, 05:09
Thanks Bunuel!! I finally got it!!! Got confused MUST BE question with DS-style question..

Kudos [?]: 4 [0], given: 78

If positive integer 36y is divisible by 10, which of the following mus   [#permalink] 27 Sep 2017, 05:09
Display posts from previous: Sort by

# If positive integer 36y is divisible by 10, which of the following mus

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.