It is currently 20 Apr 2018, 19:12

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If k is a positive integer such that 5,880k is a perfect square, what

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44588
If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 20 Mar 2018, 23:19
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (00:38) correct 33% (01:37) wrong based on 46 sessions

HideShow timer Statistics

1 KUDOS received
Manager
Manager
avatar
B
Joined: 14 Feb 2018
Posts: 120
Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 21 Mar 2018, 00:49
1
This post received
KUDOS
IMO D

5880 = 2^3 * 7^2 * 3 * 5

Therefore, to make it a perfect square, the minimum value of k should be = 2 * 3 * 5 = 30

Thus, D.

Sent from my Lenovo K53a48 using GMAT Club Forum mobile app
Manager
Manager
User avatar
G
Joined: 16 Sep 2016
Posts: 206
WE: Analyst (Health Care)
Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 21 Mar 2018, 02:32
Bunuel wrote:
If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?

(A) 2
(B) 6
(C) 15
(D) 30
(E) 140


Bunuel there seems something wrong with the question. Is the integer at hand 5,880*k or 5,880k which is a concatenation of 5,880 & k. Is this an ambiguity or am I making a mistake in reading it properly.

Please advise.

Best,
Gladi
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44588
Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 21 Mar 2018, 02:46
Gladiator59 wrote:
Bunuel wrote:
If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?

(A) 2
(B) 6
(C) 15
(D) 30
(E) 140


Bunuel there seems something wrong with the question. Is the integer at hand 5,880*k or 5,880k which is a concatenation of 5,880 & k. Is this an ambiguity or am I making a mistake in reading it properly.

Please advise.

Best,
Gladi


5,880k is 5,880*k, so 5,880 multiplied by k (also recall that multiplication sign is often omitted). It cannot be a five-digit integer 5880k because if it were it would have been explicitly mentioned.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2273
Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 22 Mar 2018, 15:47
Bunuel wrote:
If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?

(A) 2
(B) 6
(C) 15
(D) 30
(E) 140



We are given that 5,880k is a perfect square. We must remember that all perfect squares break down to unique prime factors, each of which has an exponent that is a positive multiple of 2. So, let’s break down 5,880 into its prime factors to determine the minimum value of k.

5,880 = 588 x 10 = 12 x 49 x 10 = 2^3 x 3^1 x 5^1 x 7^2

So, in order for 5,880k to be a perfect square, k must contain the factors 2 x 3 x 5 = 30 (so that 5,880k = 2^4 x 3^2 x 5^2 x 7^2), so 30 is the smallest possible value of k.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

Expert Post
1 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 995
If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 25 Mar 2018, 13:31
1
This post received
KUDOS
Expert's post

Solution



    • \(5880* k\) can be written in prime factorization form as \(2^3 * 3 *5 * 7^2 * k\).

    • Since \(5880 * k\) is a perfect square, hence \(5880 * k=n^2\), where \(n\) is any integer.
      o \(n^2 = 2^3 * 3 * 5 * 7^2 * k\)

      o After taking square root on both the sides, we can write:
        o \(n= 2*7* \sqrt{(2*3*5*k)}\)
        oFor \(n\) to be an integer,\(\sqrt{(2 * 3 * 5 * k)}\) must be a perfect square.
          oHence,\(k = 2 * 3 * 5 *\) (square of any positive integer)
      .

    • The least possible value of the square of a positive integer is 1.
      o Hence, k=2 * 3 * 5 = 30
    .

Answer: D
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Director
Director
User avatar
P
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 699
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge
Re: If k is a positive integer such that 5,880k is a perfect square, what [#permalink]

Show Tags

New post 26 Mar 2018, 00:22
Bunuel wrote:
If k is a positive integer such that 5,880k is a perfect square, what is the least possible value of k?

(A) 2
(B) 6
(C) 15
(D) 30
(E) 140


The rule says, " A perfect square always has even number of powers of prime factors".

Prime factorisation of 5880 = 2^3*3^1*5^1*7^2

Therefore, to make 5880 a perfect square we need to multiply it by a set of 2*3*5 = 30

Hence (D)
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Re: If k is a positive integer such that 5,880k is a perfect square, what   [#permalink] 26 Mar 2018, 00:22
Display posts from previous: Sort by

If k is a positive integer such that 5,880k is a perfect square, what

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


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.