Aug 18 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Aug 19 08:00 AM PDT  09:00 AM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R1.**Limited for the first 99 registrants. Register today! Aug 20 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) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 57025

How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:00
Question Stats:
53% (01:40) correct 47% (01:51) wrong based on 243 sessions
HideShow timer Statistics
How many even divisors of 1600 are not multiples of 16? (A) 4 (B) 6 (C) 9 (D) 12 (E) 18
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Director
Joined: 03 Jun 2019
Posts: 812
Location: India

How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 09:24
How many even divisors of 1600 are not multiples of 16? (A) 4 (B) 6 (C) 9 (D) 12 (E) 18 \(1600=(2^6)(5^2)\) Total no of divisors of 1600 = (6+1)*(2+1) = 7*3 = 21 Out of which 1, 5 & 25 are odd divisors Total no of even divisors 0f 1600 = 213 = 18 \(1600 = 16 (2^2)(5^2)\) No of divisors which are multiple of 16 = (2+1)*(2+1) = 3*3=9 all are even No of even divisors which are not multiple of 16 = 18  9 = 9 Alternatively, \(2^0, 2^4, 2^5 & 2^6\) are not allowed Only \(2^1, 2^2 & 2^3\) are allowed = 3 ways \(5^0, 5^1 , 5^2\)are allowed = 3 ways Total no of even divisors not multiple of 16 = 3*3 =9 IMO C
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. My GMAT Resources:  Efficient Learning
Originally posted by Kinshook on 15 Jul 2019, 08:34.
Last edited by Kinshook on 15 Jul 2019, 09:24, edited 5 times in total.




Manager
Joined: 29 Nov 2018
Posts: 144
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:17
How many even divisors of 1600 are not multiples of 16?
(A) 4 (B) 6 (C) 9 (D) 12 (E) 18
1600 can be written as 2^6 * 5^2 now even divisors of 1600 which are not multiple of 16 include: 2,2*5,2*25,4,4*5, 4*25, 8, 8*5, 8*25
hence 9 Answer = C



Senior Manager
Joined: 05 Mar 2017
Posts: 253
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Entertainment and Sports)

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:22
How many even divisors of 1600 are not multiples of 16?
(A) 4 (B) 6 (C) 9 (D) 12 (E) 18
Fairly simple question
You need to look for multiples below 16 first like 2, 4, 8, 10 and then some like 20, 40, 100, 400, etc.
The answer is C 9.



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4464
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:32
FACTORS OF 1600 ; 2^6*5^2 AND FACTORS OF 16; 2^4 SO 1600/16 ; 2^6*5^2/2^4 ; 2^2*5^2 ; 3*3 ; 9 IMO C How many even divisors of 1600 are not multiples of 16? (A) 4 (B) 6 (C) 9 (D) 12 (E) 18
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.



Intern
Joined: 26 May 2018
Posts: 45

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:34
Answer is B. Even divisor of 1600 are: 1600/2=800, 1600/4=400, 1600/8=200, 1600/16.. 20, 32, 40, 50, 64,80,and 100 then divide those results by 16 and the total Multiples of 16 are 6. Total divisors of 1600 are 12. so 126=6



Manager
Joined: 31 May 2018
Posts: 183
Location: United States
Concentration: Finance, Marketing

How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 08:38
1600 can be written as
1600 = \(2^6\)*\(5^2\) so total number of factors = (6+1)(2+1) = 7*3=21 total number of odd factors = (2+1) = 3 (in counting odd factors we will live all powers of 2)
total numbers of even factors = 213 = 18
1600 = \(2^4\)(\(2^2\)*\(5^2\))=16(\(2^2\)*\(5^2\)) total number of factors divisible by 16 =(2+1)(2+1)=3*3=9
total number of even factors not divisible by 16 = 189 = 9 C is the answer
Originally posted by shridhar786 on 15 Jul 2019, 08:35.
Last edited by shridhar786 on 15 Jul 2019, 08:38, edited 1 time in total.



Senior Manager
Joined: 16 Jan 2019
Posts: 406
Location: India
Concentration: General Management
WE: Sales (Other)

How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 09:13
\(1600 = 2^6*5^2\)
2 cannot take the power 0,4,5,6 since then we either won't get an even factor or we will get a factor divisible by 16. So 2's power can 1,2 or 3  3 options 5's power can be 0,1 or 2  3 options
Therefore the total number of even factors which are not divisible by 16 = 3*3 = 9
Answer is (C)
Originally posted by firas92 on 15 Jul 2019, 08:36.
Last edited by firas92 on 15 Jul 2019, 09:13, edited 1 time in total.



Manager
Joined: 20 Apr 2019
Posts: 81

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:38
C) 9
16, 32, 64, 80, 160, 320, 400, 800, 1600



Senior Manager
Joined: 27 Aug 2014
Posts: 294
Location: Netherlands
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:39
IMO answer is D:
factors of 1600 are: 1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 160 200 320 400 800 1600 out of these removing 16,32,64,80,160,320,800 and 1600, we are left with 12 numbers so D



Manager
Joined: 27 May 2010
Posts: 200

How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 23:24
1600 = 16*10*10 = 2^3*2*(2*5)*(2*5) Even numbers not multiples of 16 can have a maximum of 2^3 as a factor. 2, 2^2, 2^3, 2*5, 2^2*5, 2^3*5, 2*5^2, (2^2)*(5^2), (2^3)*(5^2) 2,4,8,10,20,40,50,100,200 9 numbers Option C Posted from my mobile device
_________________
Please give Kudos if you like the post
Originally posted by prashanths on 15 Jul 2019, 08:39.
Last edited by prashanths on 15 Jul 2019, 23:24, edited 1 time in total.



Manager
Joined: 03 Aug 2009
Posts: 58

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:40
A it is , will provide explanation a bit later



Manager
Joined: 30 May 2018
Posts: 146
Location: Canada
GPA: 3.8

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:43
D
Factorize 1600, we get 16000 = 2^6*5^2. So total no of factors can be (6+1)*(2+1) = 21.
Now, estimate the factors that are multiple of 16. Now, 1600 can be written as 1600 = 16*(2^2*5^2)
From above, total possible divisors of 1600, which are also multiple of 16 are (2+1)*(2+1) = 9
So, total factors that are NOT multiple of 16 should be 21  9 = 12.



Manager
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
GPA: 3.95

How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
Updated on: 15 Jul 2019, 09:50
How many even divisors of 1600 are not multiples of 16?
1600= 2^6*5^2 Total factors = (6+1)*(2+1)=7*3=21 Odd factors are: 1, 5, 25 Then even factors: 213=18
To find the Number of factors that multiples of 16 we need to exclude it from 1600. Thus we have 100=2^2*5^2 Number of factors that multiples of 16 = (2+1)*(2+1)=9
To find the number of even factors that are not multiples of 16, just subtract 9 from total even factors 189=9
IMO C
Originally posted by ancored on 15 Jul 2019, 08:44.
Last edited by ancored on 15 Jul 2019, 09:50, edited 1 time in total.



Manager
Joined: 26 Jan 2016
Posts: 178

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:45
1600 = 2^6*5^2 No of Factors of 1600 = (6+1)*(2+1)=7*3=21 factors Now, 3 factors multiples of 5 are definitely not multiples of 16 In case of multiples of 2, 2,4&8 are not multiples of 16 but 2^4 onward are multiples of 16. So 3 factors here as well Now 3*3=9 factors are not multiple of 16 but remaining 4*3=12 are multiples of 16. So 9 is the answer, hence C
_________________
Your Kudos can boost my morale..!!
I am on a journey. Gradually I'll there..!!



Intern
Joined: 24 Mar 2019
Posts: 22

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:46
We can find the answer by using this
Number of divisors =(2^1+2^2+2^3)(5^0+5^1+5^3) =(3)*(3) =9
Posted from my mobile device



Director
Joined: 22 Nov 2018
Posts: 532
Location: India
GMAT 1: 640 Q45 V35 GMAT 2: 660 Q48 V33

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:47
How many even divisors of 1600 are not multiples of 16? 1600 is not divisible by 3 and any multiple of 3 Even factors of 16 lower than 16 must be multiples of 1600 so 2,4,8 (3 factors other than 1 and 16 itself) 1600 can be factorized into 2^3*5^2*2^3. So factors of 200 that are factors of 1600 are 10,20,40,50,100,200 (5*2,25*2,5*4,5*24,5*8,25*8 based on prime factorization of 200) IMO C  9  2,4,8,10,20,40,50,100,200.
_________________
Give +1 kudos if this answer helps..!!



Manager
Joined: 01 Aug 2017
Posts: 223
Location: India
Concentration: General Management, Leadership
GPA: 3.4
WE: Information Technology (Computer Software)

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:47
How many even divisors of 1600 are not multiples of 16? (A) 4 (B) 6 (C) 9 (D) 12 (E) 18 Factors of 1600 are  \(2^6 * 5^2\) \(16 = 2^4\) There fore maximum powers of 2 can be only 3. Total number of factors such that 1600 are not multiples of 16 = Number of factors of \(2^3 * 5^2\) = (3+1) * (2+1) = 12. Total number of even factors such that 1600 are not multiples of 16 = Number of even factors of \(2^3 * 5^2\) = (2+1) * (2+1) = 9. Ans  C
_________________
If it helps you please press Kudos!
Thank You Sudhanshu



Manager
Joined: 17 Apr 2018
Posts: 108

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:50
1600 = 2^6 X 5^2 not divisible by 16 implies the max power of 2 will be 3.
==> 2^3 X 5^2 number of total factors for this is (3+1)(2+1) = 12 12 factors include (1,5,25) as factors too.
Remove 3 odd factors 12 3 = 9 even factors that are not multiple of 16.
Hence, C is the answer.



Manager
Joined: 28 Feb 2014
Posts: 136
Location: India
Concentration: General Management, International Business
GPA: 3.97
WE: Engineering (Education)

Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
Show Tags
15 Jul 2019, 08:55
Prime factorization 1600 is 2^6 x 5^2 No of factors not divisible by 16 which has prime factorization as 2^3 x 5^2 is 4x3 = 12
No of odd factors in the above factorization are 3
No of even factors which are not multiples of 16 are 123 = 9
C is correct.




Re: How many even divisors of 1600 are not multiples of 16?
[#permalink]
15 Jul 2019, 08:55



Go to page
1 2 3 4 5
Next
[ 87 posts ]



