Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47898

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
16 Jul 2012, 04:42
Question Stats:
67% (00:47) correct 33% (00:42) wrong based on 1536 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 47898

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
20 Jul 2012, 03:47
SOLUTIONIf the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?I. 8 II. 12 III. 18 (A) II only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III First of all notice that we are asked: "\(xy\) MUST be a multiple of which of the following", not COULD be a multiple. \(x\) is a multiple of 4 > \(x=4m\), for some positive multiple \(m\), so \(x\) could be: 4, 8, 12, ... \(y\) is a multiple of 6 > \(y=6n\), for some positive multiple \(n\), so \(y\) could be: 6, 12, 18, ... So, \(xy=(4m)*(6n)=24mn\), hence \(xy\) is in any case a multiple of 24, which means it must be a multiple of 8 and 12, but not necessarily of 18. For example the least value of \(x\) is 4 and the least value of \(y\) is 6, so the least value of \(xy\) is 24, which is a multiple of both 8 and 12, but not 18. Answer: B. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 22 Jan 2012
Posts: 34

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
16 Jul 2012, 13:10
x=4a y=6b xy=24ab where a,b are integers Hence , xy will always be divisible by 8,12 . B is the answer.




Manager
Status: Juggg..Jugggg Go!
Joined: 11 May 2012
Posts: 222
Location: India
GC Meter: A.W.E.S.O.M.E
Concentration: Entrepreneurship, General Management
GMAT 1: 620 Q46 V30 GMAT 2: 720 Q50 V38

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
16 Jul 2012, 10:53
Could it be A? X multiple of 4, least value = 4 similarly, least value of y=6 LCM of 4&6=12 hence, A 8 can't be unless, x=2(4) or y=2(6) 18 can't be uncless x=3(4) or y=3(6)
_________________
You haven't failed, if you haven't given up!  bschooladmit Visit my Blog www.bschooladmit.wordpress.com
Check out my other posts: Bschool Deadlines 20132014  Bschool Admission Events 2013 Start your GMAT Prep with Stacey Koprince  Get a head start in MBA finance



Intern
Joined: 17 Jun 2012
Posts: 14
GPA: 3.71

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
16 Jul 2012, 14:07
Prime factors of X = 2,2 Prime factors of Y = 2,3
Prime facots of XY = 2,2,2,3..
8 = 2*2*2 12 = 3*2*2
Answer B



eGMAT Representative
Joined: 04 Jan 2015
Posts: 1887

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
27 Apr 2015, 05:55
Hi Guys, Please find below a practice question based on similar lines as the OG question in this thread: If \(a\) is a multiple of 5, \(b\) is a multiple of 8 and \(c\) is a multiple of 10 with \(c\) having no common factor other than 10 with the product \(ab\), then \(\frac{a^3*b^2}{c^2}\) must be a multiple of which of the following? I. 20 II. 40 III. 160 (A) I only (B) I & III only (C) II & III only (D) I & II only (E) I, II & III Please post your analysis along with the answers. The OA and the solution will be posted on May 1, 2015. Regards Harsh
_________________
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 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 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.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 1887

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
Updated on: 01 Apr 2018, 22:26
EgmatQuantExpert wrote: Hi Guys, Please find below a practice question based on similar lines as the OG question in this thread: If \(a\) is a multiple of 5, \(b\) is a multiple of 8 and \(c\) is a multiple of 10 with \(c\) having no common factor other than 10 with the product \(ab\), then \(\frac{a^3*b^2}{c^2}\) must be a multiple of which of the following? I. 20 II. 40 III. 160 (A) I only (B) I & III only (C) II & III only (D) I & II only (E) I, II & III Please post your analysis along with the answers. The OA and the solution will be posted on May 1, 2015. Regards Harsh The correct answer is Option DGivenWe are given three numbers a, b, c such that a is a multiple of 5, b is a multiple of 8 and c is a multiple of 10 with c having no common factors with the product ab other than 10. We are asked to find \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. ApproachWe are given that a is a multiple of 5, so a = 5x. Since b is a multiple of 8, b = \(2^3\)y Also, c is a multiple of 10. So, we can write c = 2*5z. Now, we are given that the only factor that c has in common with the product ab is 10 (which is 2*5). The important inference to draw from this information is that z contains no 2 or 5. We will use the above expressions to find out if \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. Working OutSubstituting the values of a, b and c, we can write \(\frac{(a^3*b^2)}{c^2}\) = \(\frac{((5x)^{3}*(2^{3}*y)^2)}{(2*5z)^2}\) = \(\frac{(5*2^{4}*x^{3}*y^{2})}{z^2}\) which can be simplified to \(\frac{(80x^{3}y^{2})}{z^2}\) . So, we can say that \(\frac{(a^{3}*b^{2})}{c^2}\) will definitely be a factor of 20 and 40. 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 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 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.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 1887

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
01 May 2015, 06:58
Sometimes, students get confused between questions of the following 2 types: Type 1 Sample Question: If P and Q are positive integers, is the product PQ a multiple of 24? (1) P is a multiple of 4 (2) Q is a multiple of 6
(Note: the question above is a PS question of Type 1) Type 2 Sample Question:
Is the positive integer n a multiple of 24?
(1) n is a multiple of 4. (2) n is a multiple of 6.
(OG QR2 DS 115. Open discussion of this question is available here: http://gmatclub.com/forum/isthepositiveintegernamultipleof109886.html)When these two types of Questions are put side by side, it’s easy to see the difference between them: In Type 1 questions, the information is given about two distinct integers and the question is asked about the product of these two integers.
In order to answer the Sample Type 1 question given here, here’s what we should do:
From St. 1, P is of the form 4k And from St. 2, Q is of the form 6m So, PQ is of the form 4k*6m = 24*something. Therefore, by combining the two statements, we are able to answer the question.In Type 2 questions, both pieces of information are about the same integer n, and the question is also asked about n.
In order to answer the Sample Type 2 question given here, here’s what we should do:
From St. 1, n is of the form 4k. Prime factorize this. We get: n = \(2^{2}k\) From St. 2, n is of the form 6m. Prime factorize this. We get: n = 2*3m Combining the two statements, we see that n is of the form 2^{2}*3*something.
So, we can say for sure that n is divisible by 12 but cannot be definitive about divisibility by 24.
Therefore, the correct answer is E.
The mistake that some students make is that they solve Type 2 questions by using the approach for Type 1 questions. Please beware of this mistake! Hope this discussion was useful for you! Best Regards Japinder
_________________
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 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 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.egmat.com



Director
Joined: 10 Mar 2013
Posts: 561
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
21 Jun 2015, 04:02
bschooladmit wrote: Could it be A? X multiple of 4, least value = 4 similarly, least value of y=6
LCM of 4&6=12 hence, A 8 can't be unless, x=2(4) or y=2(6) 18 can't be uncless x=3(4) or y=3(6) You can not count LCM this way if you have 2 variables, there sets don't overlap > See MGMAT NUmber Properties Chapter 6  Poblem Set Ex. 4&5 For your solution you need question like this > X is a multiple of 4 and X is a multiple of 6 (One variable)
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12175
Location: United States (CA)

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
Updated on: 08 Jul 2015, 11:00
Hi Mo2men, It looks like I completely misread that question (it goes to show that a tired brain can impact anyone's performance). Kudos for catching it. 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
CoFounder & 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!***********************



SVP
Joined: 26 Mar 2013
Posts: 1777

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
08 Jul 2015, 04:16
EMPOWERgmatRichC wrote: Hi All, In these types of questions, it often helps to focus on the SMALLEST possible value that fits all of the given facts. You'll find that larger and larger multiples of this initial number MIGHT be a multiple of certain numbers, but the smallest number is NOT a multiple of those numbers... We're told that X and Y are positive integers, that X is a multiple of 4 and Y is a multiple of 6. We're asked what (X)(Y) MUST be a multiple of... The smallest multiple of 4 and 6 is 12 (not 24). From here, it doesn't take much basic math to see that ALL multiples of 12 are multiples of 4 and 6, but we're going to focus on the number 12 since it's the smallest number that 'fits' Is 12 a multiple of 8? NO. Is 12 a multiple of 12? YES. Is 12 a multiple of 18? NO. There's only one answer that fits... Final Answer: GMAT assassins aren't born, they're made, Rich Hi Rich, This question is #23 from diagnostic test in OG#13. Solution is B in OG13 page 55. The question asks which is multiple of XY; I mean which is the multiple of the product of two numbers: x=4k, y=6m so xy=24km 8 & 12 is multiple of 24 Answer is B.



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2649

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
03 Dec 2016, 23:16
Nice Official Question. Here is what i did in this Question =>
x=4k y=6k' so xy=24k*k"=24z for some integer z. So xy is divisible by 24. RULE => A number is divisible by factors as well as factors of its factors. Notice 8 and 12 are both factors of 24 and 18 is not. Hence 1 and 2 only.
Hence B
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3746
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
04 Dec 2016, 01:23
Bunuel wrote: If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8 II. 12 III. 18
(A) II only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III Let x = 4 , y = 6 ; so xy = 24 ( Multiple of 8 & 12 ) Let x = 8 , y = 6 ; so xy = 48 ( Multiple of 8 & 12 ) Let x = 8 , y = 12 ; so xy = 96 ( Multiple of 8 & 12 ) Try other combinations if you are not convinced , all are Multiple of 8 & 12 , hence, correct answer will be (B)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Manager
Joined: 08 Oct 2016
Posts: 207
Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE: Engineering (Telecommunications)

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
18 Apr 2017, 05:16
As per statement x=4,8,12 y=6,12,18 Take two values ox xy xy=24,96 both can be evenly divided by 8,12 only So Option: B Time taken: 1:20
_________________
Got Q42,V17 Target#01 Q45,V20April End



Intern
Joined: 03 May 2014
Posts: 14

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
20 Aug 2017, 06:38
EgmatQuantExpert wrote: EgmatQuantExpert wrote: Hi Guys, Please find below a practice question based on similar lines as the OG question in this thread: If \(a\) is a multiple of 5, \(b\) is a multiple of 8 and \(c\) is a multiple of 10 with \(c\) having no common factor other than 10 with the product \(ab\), then \(\frac{a^3*b^2}{c^2}\) must be a multiple of which of the following? I. 20 II. 40 III. 160 (A) I only (B) I & III only (C) II & III only (D) I & II only (E) I, II & III Please post your analysis along with the answers. The OA and the solution will be posted on May 1, 2015. Regards Harsh The correct answer is Option DGivenWe are given three numbers a, b, c such that a is a multiple of 5, b is a multiple of 8 and c is a multiple of 10 with c having no common factors with the product ab other than 10. We are asked to find \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. ApproachWe are given that a is a multiple of 5, so a = 5x. Since b is a multiple of 8, b = 23y Also, c is a multiple of 10. So, we can write c = 2*5z. Now, we are given that the only factor that c has in common with the product ab is 10 (which is 2*5). The important inference to draw from this information is that z contains no 2 or 5. We will use the above expressions to find out if \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. Working OutSubstituting the values of a, b and c, we can write \(\frac{(a^3*b^2)}{c^2}\) = \(\frac{((5x)^{3}*(2^{3}*y)^2)}{(2*5z)^2}\) = \(\frac{(5*2^{4}*x^{3}*y^{2})}{z^2}\) which can be simplified to \(\frac{(80x^{3}y^{2})}{z^2}\) . So, we can say that \(\frac{(a^{3}*b^{2})}{c^2}\) will definitely be a factor of 20 and 40. Answer (D) "Since b is a multiple of 8, b = 23y." I am assuming that "23y" is meant to read (2^3)y?



Manager
Joined: 21 Jun 2015
Posts: 51
Location: India
Concentration: Finance, General Management
GPA: 3.32
WE: Programming (Computer Software)

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
13 Sep 2017, 04:21
"Since b is a multiple of 8, b = 23y." I am assuming that "23y" is meant to read (2^3)y?[/quote]
Prime factors of X = 2,2 Prime factors of Y = 2,3
Prime facots of XY = 2,2,2,3.. >24
8 = 2*2*2 12 = 3*2*2
Only 8 and 12 can satisfy this



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
20 Dec 2017, 12:32
Bunuel wrote: If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following?
I. 8 II. 12 III. 18
(A) II only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III Since x is a multiple of 4, x = 4k for some positive integer k. Similarly, since y is a multiple of 6, y = 6m for some positive integer m. Thus, xy = (4k)(6m) = 24km. We see that regardless what k and m are, 24km will always be divisible by 8 and 12, but not necessarily by 18. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 09 Mar 2016
Posts: 746

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
28 Mar 2018, 11:18
EgmatQuantExpert wrote: EgmatQuantExpert wrote: Hi Guys, Please find below a practice question based on similar lines as the OG question in this thread: If \(a\) is a multiple of 5, \(b\) is a multiple of 8 and \(c\) is a multiple of 10 with \(c\) having no common factor other than 10 with the product \(ab\), then \(\frac{a^3*b^2}{c^2}\) must be a multiple of which of the following? I. 20 II. 40 III. 160 (A) I only (B) I & III only (C) II & III only (D) I & II only (E) I, II & III Please post your analysis along with the answers. The OA and the solution will be posted on May 1, 2015. Regards Harsh The correct answer is Option DGivenWe are given three numbers a, b, c such that a is a multiple of 5, b is a multiple of 8 and c is a multiple of 10 with c having no common factors with the product ab other than 10. We are asked to find \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. ApproachWe are given that a is a multiple of 5, so a = 5x. Since b is a multiple of 8, b = 23y Also, c is a multiple of 10. So, we can write c = 2*5z. Now, we are given that the only factor that c has in common with the product ab is 10 (which is 2*5). The important inference to draw from this information is that z contains no 2 or 5. We will use the above expressions to find out if \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. Working OutSubstituting the values of a, b and c, we can write \(\frac{(a^3*b^2)}{c^2}\) = \(\frac{((5x)^{3}*(2^{3}*y)^2)}{(2*5z)^2}\) = \(\frac{(5*2^{4}*x^{3}*y^{2})}{z^2}\) which can be simplified to \(\frac{(80x^{3}y^{2})}{z^2}\) . So, we can say that \(\frac{(a^{3}*b^{2})}{c^2}\) will definitely be a factor of 20 and 40. Answer (D) Hello there EgmatQuantExpert are these the formulas you are using ? or what?
_________________
In English I speak with a dictionary, and with people I am shy.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 1887

If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
01 Apr 2018, 21:52
dave13 wrote: EgmatQuantExpert wrote: EgmatQuantExpert wrote: Hi Guys, Please find below a practice question based on similar lines as the OG question in this thread: If \(a\) is a multiple of 5, \(b\) is a multiple of 8 and \(c\) is a multiple of 10 with \(c\) having no common factor other than 10 with the product \(ab\), then \(\frac{a^3*b^2}{c^2}\) must be a multiple of which of the following? I. 20 II. 40 III. 160 (A) I only (B) I & III only (C) II & III only (D) I & II only (E) I, II & III Please post your analysis along with the answers. The OA and the solution will be posted on May 1, 2015. Regards Harsh The correct answer is Option DGivenWe are given three numbers a, b, c such that a is a multiple of 5, b is a multiple of 8 and c is a multiple of 10 with c having no common factors with the product ab other than 10. We are asked to find \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. ApproachWe are given that a is a multiple of 5, so a = 5x. Since b is a multiple of 8, b = 23y Also, c is a multiple of 10. So, we can write c = 2*5z. Now, we are given that the only factor that c has in common with the product ab is 10 (which is 2*5). The important inference to draw from this information is that z contains no 2 or 5. We will use the above expressions to find out if \(\frac{(a^3*b^2)}{c^2}\) is a multiple of which of 20, 40 and 160. Working OutSubstituting the values of a, b and c, we can write \(\frac{(a^3*b^2)}{c^2}\) = \(\frac{((5x)^{3}*(2^{3}*y)^2)}{(2*5z)^2}\) = \(\frac{(5*2^{4}*x^{3}*y^{2})}{z^2}\) which can be simplified to \(\frac{(80x^{3}y^{2})}{z^2}\) . So, we can say that \(\frac{(a^{3}*b^{2})}{c^2}\) will definitely be a factor of 20 and 40. Answer (D) Hello there EgmatQuantExpert are these the formulas you are using ? or what? Hey Dave, Happy to help These are not formulas. Understand it like this: If \(a\) is a multiple of \(5\), the possible values of a can be \(5, 10 , 15, 20\).. and so on. Which is \(5*1, 5*2, 5*3, 5*4\) and so on. Thus, we can write \(a\) as \(5x\), where \(x\) is any positive integer. For example: \(a = 40, x =8\) ; if \(a = 100, x = 20\) and so on. This is a general representation of the number \(a\) and not any formula. In a similar way, we can write: \(b\) as \(8y\), where \(y\) is any positive integer, and \(c\) as \(10z\), where \(z\) is any positive integer. We wrote a, b, and c in such a manner to reduce the complexity of the problem by denoting each of them in their general form. Regards.
_________________
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 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 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.egmat.com



SVP
Joined: 08 Jul 2010
Posts: 2132
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If the positive integer x is a multiple of 4 and the
[#permalink]
Show Tags
01 Apr 2018, 22:36
Bunuel wrote: If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following? I. 8 II. 12 III. 18 (A) II only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III Diagnostic Test Question: 23 Page: 23 Difficulty: 550 x = 2^2 y = 2*3 i.e. x*y = 2^2*2*3 = 2^2*3 = 24i.e. x*y must be a Multiple of all factors of 248 and 12 are factors of 24 but 18 is not a factor of 24 hence Answer: option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION




Re: If the positive integer x is a multiple of 4 and the &nbs
[#permalink]
01 Apr 2018, 22:36






