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

 It is currently 11 Nov 2019, 20:51 ### 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

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.  # How many even divisors of 1600 are not multiples of 16?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58954
How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

12 00:00

Difficulty:   75% (hard)

Question Stats: 51% (01:42) correct 49% (01:52) wrong based on 263 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 This question was provided by Veritas Prep for the Game of Timers Competition _________________
SVP  P
Joined: 03 Jun 2019
Posts: 1834
Location: India
How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

3
2
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 = 21-3 = 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. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com

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.
##### General Discussion
Manager  G
Joined: 29 Nov 2018
Posts: 148
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

1
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
Senior Manager  G
Joined: 05 Mar 2017
Posts: 261
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

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.

GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5245
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

2
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
Intern  B
Joined: 26 May 2018
Posts: 45
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

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 12-6=6
Senior Manager  P
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing
How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

3
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 = 21-3 = 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 = 18-9 = 9

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  P
Joined: 16 Jan 2019
Posts: 498
Location: India
Concentration: General Management
WE: Sales (Other)
How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
$$1600 = 2^6*5^2$$

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

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  B
Joined: 20 Apr 2019
Posts: 108
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

C) 9

16, 32, 64, 80, 160, 320, 400, 800, 1600
Senior Manager  P
Joined: 27 Aug 2014
Posts: 356
Location: Netherlands
Concentration: Finance, Strategy
Schools: LBS '22, ISB '21
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

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  G
Joined: 27 May 2010
Posts: 200
How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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  S
Joined: 03 Aug 2009
Posts: 59
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

A it is , will provide explanation a bit later
Manager  S
Joined: 30 May 2018
Posts: 157
GMAT 1: 710 Q49 V36 GPA: 3.8
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

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  G
Joined: 10 Mar 2019
Posts: 75
Location: Russian Federation
Schools: Haas '21
GPA: 3.95
How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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: 21-3=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
18-9=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  G
Joined: 26 Jan 2016
Posts: 180
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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  B
Joined: 24 Mar 2019
Posts: 22
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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  G
Joined: 22 Nov 2018
Posts: 562
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

1
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  P
Joined: 01 Aug 2017
Posts: 221
Location: India
GMAT 1: 500 Q47 V15 GPA: 3.4
WE: Information Technology (Computer Software)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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  S
Joined: 17 Apr 2018
Posts: 107
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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.

Manager  G
Joined: 28 Feb 2014
Posts: 176
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

### Show Tags

1
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 12-3 = 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 ]

Display posts from previous: Sort by

# How many even divisors of 1600 are not multiples of 16?  