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

It is currently 20 Nov 2018, 07:44

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50714
If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 20 Mar 2018, 22:19
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:13) correct 41% (01:41) wrong based on 55 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
G
Joined: 14 Feb 2018
Posts: 387
Re: If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 20 Mar 2018, 23:49
1
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
PS Forum Moderator
User avatar
P
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 383
GMAT 1: 740 Q50 V40
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 21 Mar 2018, 01:32
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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50714
Re: If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 21 Mar 2018, 01:46
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

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 22 Mar 2018, 14:47
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

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2203
If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 25 Mar 2018, 12:31
1

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
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



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

VP
VP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1312
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge CAT Tests
Re: If k is a positive integer such that 5,880k is a perfect square, what  [#permalink]

Show Tags

New post 25 Mar 2018, 23:22
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)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

GMAT Club Bot
Re: If k is a positive integer such that 5,880k is a perfect square, what &nbs [#permalink] 25 Mar 2018, 23:22
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.