December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST. December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3292

If m is the square of integer n and m is divisible by 98, m must also
[#permalink]
Show Tags
11 Oct 2012, 16:51
Question Stats:
63% (01:26) correct 37% (01:32) wrong based on 212 sessions
HideShow timer Statistics
If m is the square of integer n and m is divisible by 98, m must also be divisible by: I. 28 II. 196 III. 343 (A) I only (B) II only (C) I & II only (D) II & III only (E) I, II, and III I would like to know why the answer (see spoiler) and not B here we go: 98 has factors : 2 7 and 7 so : \(2^1\) and \(7^2\) But at the same time \(n\) \(=\) \(m^2\) so m is a perfect square so we need \(2^2\) and \(7^2\) at least28 = \(2^2\) and \(7\) 196 =\(2^2\) and \(7^2\) 343 = \(7^3\) Please explain i'm struggling a lot the last days with this concept
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Math Expert
Joined: 02 Sep 2009
Posts: 51100

Re: If m is the square of integer n and m is divisible by 98, m must also
[#permalink]
Show Tags
11 Oct 2012, 17:03
carcass wrote: If m is the square of integer n and m is divisible by 98, m must also be divisible by: I. 28 II. 196 III. 343 (A) I only (B) II only (C) I & II only (D) II & III only (E) I, II, and III I would like to know why the answer (see spoiler) and not B here we go: 98 has factors : 2 7 and 7 so : \(2^1\) and \(7^2\) But at the same time \(n\) \(=\) \(m^2\) so m is a perfect square so we need \(2^2\) and \(7^2\) at least28 = \(2^2\) and \(7\) 196 =\(2^2\) and \(7^2\) 343 = \(7^3\) Please explain i'm struggling a lot the last days with this concept Given: \(m=n^2\) (not \(n=m^2\) as you've written) and \(m\) is a multiple of \(98=2*7^2\). Now, since \(m\) is a perfect square than it must have even powers of its primes, thus \(m\) must be divisible by \(2^2*7^2=196\) and naturally by all the factors of 196, which are: 1, 2, 4, 7, 14, 28, 49, 98 and 196. Answer: C. 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



Board of Directors
Joined: 01 Sep 2010
Posts: 3292

Re: If m is the square of integer n and m is divisible by 98, m must also
[#permalink]
Show Tags
11 Oct 2012, 17:54
Bunuel wrote: carcass wrote: If m is the square of integer n and m is divisible by 98, m must also be divisible by: I. 28 II. 196 III. 343 (A) I only (B) II only (C) I & II only (D) II & III only (E) I, II, and III I would like to know why the answer (see spoiler) and not B here we go: 98 has factors : 2 7 and 7 so : \(2^1\) and \(7^2\) But at the same time \(n\) \(=\) \(m^2\) so m is a perfect square so we need \(2^2\) and \(7^2\) at least28 = \(2^2\) and \(7\) 196 =\(2^2\) and \(7^2\) 343 = \(7^3\) Please explain i'm struggling a lot the last days with this concept Given: \(m=n^2\) (not \(n=m^2\) as you've written) and \(m\) is a multiple of \(98=2*7^2\). Now, since \(m\) is a perfect square than it must have even powers of its primes, thus \(m\) must be divisible by \(2^2*7^2=196\) and naturally by all the factors of 196, which are: 1, 2, 4, 7, 14, 28, 49, 98 and 196. Answer: C. Hope it's clear. Sorry for typo Of course, factor foundation rule
_________________
COLLECTION OF QUESTIONS AND RESOURCES Quant: 1. ALL GMATPrep questions Quant/Verbal 2. Bunuel Signature Collection  The Next Generation 3. Bunuel Signature Collection ALLINONE WITH SOLUTIONS 4. Veritas Prep Blog PDF Version 5. MGMAT Study Hall Thursdays with Ron Quant Videos Verbal:1. Verbal question bank and directories by Carcass 2. MGMAT Study Hall Thursdays with Ron Verbal Videos 3. Critical Reasoning_Oldy but goldy question banks 4. Sentence Correction_Oldy but goldy question banks 5. Readingcomprehension_Oldy but goldy question banks



Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 377

Re: If m is the square of integer n and m is divisible by 98, m must also
[#permalink]
Show Tags
30 Nov 2016, 08:55
prime factorization of 98: (2)(7^2) > to make this into a perfect square we need to multiply by another 2, which will give us the overall number of 196.
m= 196 n=14 (i.e. 14^2 = 196)
so, m must be divisible by 196 and 28 because it has prime factors that can be combined to create those values.
Thus, C is the answer.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4273
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If m is the square of integer n and m is divisible by 98, m must also
[#permalink]
Show Tags
30 Nov 2016, 10:11
carcass wrote: If m is the square of integer n and m is divisible by 98, m must also be divisible by:
I. 28 II. 196 III. 343
(A) I only (B) II only (C) I & II only (D) II & III only (E) I, II, and III \(m = n^2\) \(\frac{m}{98} = \frac{n^2}{98}\) Remainder is 0 Least possible values of \(n^2 = 196\) , so \(m = + 7\) Further \(196 = 7^2*2^2\) We find 196 is divisible by both 28 & 196 , but not divisible by 343 ( Coz 343 = 7^3 ) Hence our answer will be (C) I & II only
_________________
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 )



VP
Joined: 09 Mar 2016
Posts: 1211

If m is the square of integer n and m is divisible by 98, m must also
[#permalink]
Show Tags
06 Oct 2018, 06:42
carcass wrote: If m is the square of integer n and m is divisible by 98, m must also be divisible by:
I. 28 II. 196 III. 343
(A) I only (B) II only (C) I & II only (D) II & III only (E) I, II, and III
if m is dvisibe by 98, it means (in my oinion ) that m must be at least 98*2 = 196 and square root of which, is 14 196 is divisible by 28 and 196 i wonder if my reasoning is correct




If m is the square of integer n and m is divisible by 98, m must also &nbs
[#permalink]
06 Oct 2018, 06:42






