Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions)
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58377

How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
17 Apr 2015, 05:06
Question Stats:
65% (01:55) correct 35% (02:03) wrong based on 508 sessions
HideShow timer Statistics
How many positive integers less than 250 are multiple of 4 but NOT multiples of 6? (A) 20 (B) 31 (C) 42 (D) 53 (E) 64 Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 300

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
17 Apr 2015, 05:18
Bunuel wrote: How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
(A) 20 (B) 31 (C) 42 (D) 53 (E) 64
Kudos for a correct solution. 248/4=62 Multiples of 4 which are a multiple of 6 will be of the form 2*2*3=12n where n>0 240/12=20 6220=42 Answer: C




Intern
Joined: 11 Sep 2013
Posts: 21

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
18 Apr 2015, 13:49
Multiples of 4 less than 250 = {4,8,12,......248} = 62 numbers
Multiples of 4 which are multiples of 3 too ={12,24,36.....240} = 20 numbers
So required number= 6220 = 42
Choice C



Manager
Joined: 15 May 2014
Posts: 62

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
19 Apr 2015, 04:37
Positive integers multiple of 4 < 250 \(\,=\,\frac{2484}{4}\,+1\,=\,62\) Positive integers multiple of 12 (LCM of 4 & 6) < 250 \(\,=\,\frac{24012}{12}\,+1\,=\,20\)
Positive integers < 250 multiple of 4 but NOT multiples of 6 \(\,=\,62\,\,20\,=\,42\)
Or
Multiples of 4 <250 \(\,=\,\frac{250}{4}\,=\,62.5\) In multiples of 4 <250 i.e. 4, 8, 12, 16, 20, 24.... every third term is multiple of 6
Positive integers < 250 multiple of 4 but NOT multiples of 6 \(\,=\,62.5\,\,\frac{1}{3}\,*62.5\) \(\,=\,62.5\,20.8\)
\(\,=\,41.7\,\approx{42}\)
Answer C



Math Expert
Joined: 02 Sep 2009
Posts: 58377

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
20 Apr 2015, 04:55
Bunuel wrote: How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
(A) 20 (B) 31 (C) 42 (D) 53 (E) 64
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTIONThis is the type of question that most people can get with unlimited time. You can simply go through every possible number from 1 to 249 and see if each number meets the criteria. Apart from going crosseyed halfway through, you will also spend an atrocious amount of time on a question clearly designed to reward you for using logic. Let’s look at this question logically and see what we can determine. Firstly, it only cares about positive integers, so we can disregard zero. This is helpful because a lot of questions hinge on whether or not zero is included, but that won’t matter in this instance. Furthermore, only integers matter, and we’re looking for multiples of 4 but not 6. Your initial pass on a question like this might look might concentrate on the multiples of 4 and you might write (part of) the following sequence down: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100… After writing a couple of dozen numbers, you may try to figure out the pattern and extrapolate from there. Numbers divisible by 6 are to be eliminated, so you could rewrite this sequence: 4, 8, 16, 20, 28, 32, 40, 44, 52, 56, 64, 68, 76, 80, 88, 92, 100… Even with this, we have a long sequence of numbers, some of which are crossed off, and less than halfway through the entire sequence. Perhaps approaching the question from a more strategic approach would yield dividends: The number must be divisible by 4 but not by 6. Calculating the LCM gives us 12, which means that every 12th number will be divisible by both of these numbers. We want the integers to be divisible by four, but not by six, so 12 is out. Along the way, we stop by 4 and 8, both of which are divisible by four but not by six. So every 12 numbers, our count goes up by two, and we start the pattern again. 112 will give two numbers that work. 1324 will give two more numbers that work. 2536 gives two more, 3748 gives two more and 4960 gives two more as well. Thus, through 60 numbers, we have 10 elements that are divisible by 4 and not 6. From here, it might be easier to go up in bounds of 60, so we know that 61120 gives 10 more numbers. 121180 and 181240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice C is correct here. There are other ways to get the right answer, but the fastest ones all hinge on pattern recognition. Figuring out that every 12 numbers gives two more answers can take us from 1 to 240 in one shot (20 sequences x 2). Alternatively, once finding 4 elements at 24, you can probably easily envision multiplying the total by 10 and getting to 240 straight away (like warping over worlds in Super Mario Bros). Timing is one of the key elements being tested on the GMAT, and one of the goals of the exam is to reward those who have good time management skills. Given 10 minutes, almost everyone would get the correct answer to this question, but the exam wants to determine who can get it right in a fraction of that time. On the GMAT, as in business, timing is everything.
_________________



Director
Joined: 23 Jan 2013
Posts: 525

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
16 Aug 2015, 05:35
Multiples of 4 are:
4,8,12,16,20,24,28,32,36  9 numbers
12,24,36 are multiple of 6  3 numbers
so for 62 multiple of 4 we will have 20 multiple of 6
6220=42
C



Manager
Joined: 08 Sep 2012
Posts: 59
Location: India
Concentration: Social Entrepreneurship, General Management
WE: Engineering (Investment Banking)

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
16 Aug 2015, 05:59
Bunuel wrote: How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
(A) 20 (B) 31 (C) 42 (D) 53 (E) 64
Kudos for a correct solution. I solved this differently: List multiples of 4, making groups of 3: 4,8,12, 16,20,24, 28,32,36... Every 3rd multiple is a multiple of 6. So in short, a third of all multiples of 4 will be multiple of 6 Total number of multiples of 4: (2484)/4 +1 = 62. Now, the 62nd multiple is 248; 61st multiple is 244; 60th multiple is 240  a multiple of 12 So upto the 60th multiple we will get proper groups of 3. So 1/3rd of 60 = 20 multiples will be multiple of 6. So total number of multiples = 6220 = 42 Answer is C
_________________
+1 Kudos if you liked my post! Thank you!



Current Student
Joined: 12 Aug 2015
Posts: 2569

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
23 Aug 2016, 11:05
In these Kinda Questions its best to use the set theory Set A => numbers of multiples of 4 => 62 Set B = multiples of 6 We are asked numbers that are only multiples of 4 => Number of elements in set A  number of elements in A intersection B Hence A intersection B => multiples of 12 => 20 Required Value => 6220 => 42 SMASH that C
_________________



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
15 Oct 2016, 21:05
Bunuel wrote: How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
(A) 20 (B) 31 (C) 42 (D) 53 (E) 64
Kudos for a correct solution. Multiples of 4, less than or equal to 250 = [250/4] = 62 Multiples of 6&4 i.e. 12, less than or equal to 250 = [250/12] = 20 Now, Multiples of 4 that are not multiples of 6 = 6220 = 42 Answer: Option C
_________________
Prosper!!!GMATinsightBhoopendra 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 Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Current Student
Joined: 20 Jan 2017
Posts: 51
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
20 Jan 2017, 04:39
1) The number of multiple of 4 but not multiples of 6=the number of multiples of 4the number of multiple of 4 AND 6. 2)The number of multiples of 4=(2484)/4+1=61+1=62 3)The prime factors of 4 are 2*2; the prime factors of 6 are 2*3, thus the prime factors of the numbers that are multiples of 4 AND 6 are 2*2*3=12. 4)The number of multiples of 12=(24012)/12+1=20 5)6220=42



Director
Joined: 24 Oct 2016
Posts: 531
GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
05 Jun 2019, 15:23
Bunuel wrote: How many positive integers less than 250 are multiple of 4 but NOT multiples of 6?
(A) 20 (B) 31 (C) 42 (D) 53 (E) 64
Kudos for a correct solution. # of multiples of 4 = (2484)/4 + 1 = 62 # of multiples of 12 = (240  12) + 1 = 20 ANSWER = 62  20 = 42 (C)
_________________
Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW) Verb Tenses SimplifiedIf you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.



Manager
Joined: 28 Feb 2014
Posts: 171
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)

Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
Show Tags
11 Jul 2019, 20:32
No of multiples of 4 less than 250 are (2484)/4 + 1 = 62
Taking LCM of 4 and 6 is 12. No of multiples of 12 less than 250 are (24012)/12 + 1 = 20
No of multiples of 4 but not of 6 = no of multiples of 4  no of multiples of 12 = 6220 = 42.
C is correct.




Re: How many positive integers less than 250 are multiple of 4 but NOT mul
[#permalink]
11 Jul 2019, 20:32






