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

It is currently 22 Aug 2019, 09:25

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
S
Joined: 17 Jul 2014
Posts: 111
GMAT ToolKit User CAT Tests
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 19:36
How many even divisors of 1600 are not multiples of 16?
how many factors of 1600 are not multiples of 16 or are not divisible by 16
Factors of 1600 = \(2^6\) * \(5^2\) = 21 factors
1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600

How many numbers are divisible by 16

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800, 1600,

Total numbers not divisible by 16 - 12

D is the answer
Intern
Intern
avatar
B
Joined: 19 Mar 2012
Posts: 22
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 20:02
answer is 4 as 1600 is 2^6 and 5 ^2, hence 2, 4, 8 and 10, 20 and 40 are not multiples of 16
Director
Director
User avatar
D
Joined: 28 Jul 2016
Posts: 543
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 20:29
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 = \(2^6 *5^2\)

now for multiple of 16
min power of 2 should be 4
hence any divisor with power less than 4 of 2 will not be acceptable
Also given it should be even thus there should be at-least 2

so possible such numbers will be of the form
\((2^1 +2^2 + 2^3)(5^0 +5^1 +5^2)\)

total such divisors will be (3) *(3)
= 9
Thus C
Manager
Manager
User avatar
S
Joined: 27 Mar 2018
Posts: 73
Location: India
GMAT ToolKit User
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 20:48
1
1600=2^6 * 5^2

Total possible factors(or divisors)= (6+1)*(2+1) = 21
Odd factors of 1600 are 1, 5 and 25.

Hence total even divisors of 1600= 21-2 = 18

Let's list the multiples of 16 or 2^4
\(\frac{2^6*5^2}{2^4}\) => 2^2 * 5^2

Possible factors= (2+1)*(2+1) = 9

(16,32,64,80,160,320,400,800,1600)

Hence option C.
_________________
Thank you for the kudos. You are awesome! :)
Manager
Manager
User avatar
S
Joined: 12 Jan 2018
Posts: 112
How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post Updated on: 15 Jul 2019, 21:41
1
Prime Factorisation of 1600,
1600=\(2^{6}\)*\(5^{2}\)
No. of factors of 1600 = 7*3=21

No. of even factors of 1600(Reduce the power of 2 by 1 and find the no. of factors) = 6*3=18

But 16=\(2^{4}\)
Therefore,
No.of factors of 1600 which are multiples of 16= No. of factors of \(2^{2}\)*\(5{2}\) = 3*3=9
Thus,
No.of even factors of 1600 which are NOT multiples of 16= 18-9=9

Ans. C
_________________
"Remember that guy that gave up?
Neither does anybody else"

Originally posted by aarkay on 15 Jul 2019, 21:32.
Last edited by aarkay on 15 Jul 2019, 21:41, edited 1 time in total.
Manager
Manager
User avatar
S
Joined: 29 May 2019
Posts: 98
CAT Tests
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 21:36
1
How many even divisors of 1600 are not multiples of 16?

1600 = 2^6 * 5^2

We are looking for even divisors, so 2^0 can not be there.
And it should not be a multiple of 16 so 2^4/5/6 can not be there.

We can take 2^1/2/3 and 5^0/1/2

So the answer will be: 3 * 3 = 9
Answer: C

_________________
Pick yourself up, dust yourself off, and start again.

Success is the sum of all small efforts.

MAKE IT HAPPEN :)
Manager
Manager
avatar
G
Joined: 18 May 2019
Posts: 162
GMAT ToolKit User Premium Member
How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 21:47
1
One way to approach this problem is find the prime factorization of 1600. I split 1600 into 16x100

16=2^4 and 100= (2^2)*(5^2)
So 1600=(2^4)*{(2^2)*(5^2)}
Even factors 1600 which are not multiples of 16 are all even factors less than 16 and even factors greater than 16 but not divisible by 16.
All factors of 1600 greater than 200 are multiples of 16. Hence the goal is to find even factors of 1600 up to 200 which are not multiples of 16. This yields the ff set:
{2,4,8,10,20,40,50,100,200}
There are therefore 9 even factors of 1600 which are not multiples of 16.

Hence the answer is C.

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 24 Jan 2019
Posts: 103
Location: India
Concentration: Strategy, Finance
GPA: 4
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 15 Jul 2019, 21:56
1
How many even divisors of 1600 are not multiples of 16?

Here, divisor can have maximum 3 as power of 2 and minimum 1. (Because it is even.)

1600 = 2^6 * 5^2

total possibilities for the power of 2 = 3 (1, 2, 3)
total possibilities for the power of 5 = 3 (0, 1, 2)

So, total even divisors satisfying the given condition = 9


ANSWER: C
Manager
Manager
avatar
S
Joined: 10 Nov 2014
Posts: 59
Location: United States
Concentration: Marketing, Strategy
Schools: Goizueta '22, IIM
How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post Updated on: 16 Jul 2019, 00:19
1
How many even divisors of 1600 are not multiples of 16?

(A) 4
(B) 6
(C) 9
(D) 12
(E) 18

Soln:

Divisors of 1600 are

1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600

Even divisors of 1600, that are not multiple of 16 are
2,4,8, 10,20,40,50,100,200


Correct Ans C

Originally posted by komals06 on 15 Jul 2019, 23:57.
Last edited by komals06 on 16 Jul 2019, 00:19, edited 4 times in total.
Senior Manager
Senior Manager
avatar
P
Joined: 18 Jan 2018
Posts: 308
Location: India
Concentration: General Management, Healthcare
Schools: Booth '22, ISB '21, IIMB
GPA: 3.87
WE: Design (Manufacturing)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 00:03
How many even divisors of 1600 are not multiples of 16?

1600 is divisible by 16 ,
==> 16*10*10
= 16 * 2^2 * 5*2

So total multiple of number with out 16 = (2+1)(2+1) = 3*3 = 9
Odd divisors = (2+1) = 3
even divisors = 9-3 = 6

Option B is answer
Manager
Manager
User avatar
G
Joined: 18 Jun 2013
Posts: 141
Location: India
Concentration: Technology, General Management
GMAT 1: 690 Q50 V35
GPA: 3.2
WE: Information Technology (Consulting)
Reviews Badge
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 01:19
How divisors does 1600 have?

1600 = 2^4 * 2^2 * 5^2 = 2^6 * 5^2 = 7 * 3 = 21

Now how even divisors does 1600 have?

We know 1600 = 2^6 * 5^2
=> 5, 25, 1 are the only odd divisors of 1600
=> 1600 has 18 even divisors

Now, which divisors of 1600 are not multiples of 16?
=> This would include any divisor which does not have a 16 or 2^4 in it's powers.

Lets list these out as the number is small

1 -> We saw above.
5 -> We saw above.
25 -> We saw above.
2 -> Divisor of 1600 and does not have 16 in it.
4 -> Divisor of 1600 and does not have 16 in it.
8 -> Divisor of 1600 and does not have 16 in it.
2 * 5 -> Divisor of 1600 and does not have 16 in it. Adding a 5 in it as 5 is also a divisor of 1600.
4 * 5 -> Divisor of 1600 and does not have 16 in it. Adding a 5 in it as 5 is also a divisor of 1600.
8 * 5 -> Divisor of 1600 and does not have 16 in it. Adding a 5 in it as 5 is also a divisor of 1600.
2 * 5 * 5 -> Divisor of 1600 and does not have 16 in it. Adding a 25 in it as 25 is also a divisor of 1600.
4 * 5 * 5 -> Divisor of 1600 and does not have 16 in it. Adding a 25 in it as 25 is also a divisor of 1600.
8 * 5 * 5 -> Divisor of 1600 and does not have 16 in it. Adding a 25 in it as 25 is also a divisor of 1600.

Hence answer is 12.

Answer: D
Manager
Manager
avatar
B
Joined: 07 Jul 2019
Posts: 54
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 01:28
1
To solve this problem, we need to apply prime factorization here. 1600 can be written as 2 to the power of 6 and 5 to the power of 2. Since we need even factors that are not multiples of 16, we can exclude 2 to the power of 4, 2 to the power of 5, 2 to the power of 6, 5 to the power of one, and 5 to the power of two. Overall factors are (6+1)*(2+1)=21. We will subtract multiples of 16, which are 1, 2^4, 2^5, 2^6, 5^1, 5^2, 2^4*5^1, 2^4*5^2, 2^5*5^1, 2^5*5^2, 2^6*5^1, and 2^6*5^2, totally 12 factors. 21-12=9 (C)
Director
Director
avatar
P
Joined: 20 Jul 2017
Posts: 636
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 01:43
1
Formula: If \(N = 2^a*3^b*5^c*7^d*\) . . . . .
Number of total divisors = (a + 1)*(b + 1)*(c + 1)*(d + 1)* . . . .


\(1600 = 2^6*5^2\)
Total divisors of 1600 = (6 + 1)*(2 + 1) = 7*3 = 21
Number of Odd divisors of 1600 = 1, 5, 5^2 = 3
--> Number of even divisors of 1600 = 21 - 3 = 18

Even divisors that are multiples of 16 = Number of total divisors of 100 [1600 = 16*100]
--> Total divisors of 100 = \(2^2*5^2\) = (2 + 1)*(2 + 1) = 3*3 = 9

So, Even divisors of 1600 that are not multiples of 16 = 18 - 9 = 9

IMO Option C

Pls Hit Kudos if you like the solution
Intern
Intern
avatar
B
Joined: 13 May 2018
Posts: 10
Location: India
GMAT 1: 710 Q49 V38
GRE 1: Q163 V157
GPA: 4
GMAT ToolKit User
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 02:51
A good question in my opinion.

We can write 1600 in prime factorization form as 2^6 x 5^2.
We need to find number of factors which are even but not a multiple of 16 I. E. The power of 2 Shoulf be greater than = 1 and less than = 3. This means that we can have a total of 3x3 factors of 1600 which are not multiple of 16.

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 08 Jul 2019
Posts: 37
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 03:31
1
All factors of 1600=2^6*5^2

Total number of factors of 1600, including 1 and 1600 is (6+1)∗(2+1)=7∗3=21 total factors. 21 includes all odd and multiples of 16 such as 5^1, and 5^2, and 2^4 (16), and 2^5 (32), 2^6(64). Now, we can count factors that are not multiple of 16. Those are 2^1, and 2^1*5^1, and 2^1*5^2, and 2^2, and 2^2*5^1, and 2^2*5^2, and 2^3, and 2^3*5^1, 2^3*5^2, 9 factors, which is C.
Manager
Manager
User avatar
G
Joined: 08 Apr 2019
Posts: 149
Location: India
GPA: 4
CAT Tests
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 04:23
1
Easy one. Factorising 1600, we get 1600 = 2^6 * 5^2

Now, we are given two conditions 1) the divisors must be even and 2) the divisors should not be multiples of 16

Conforming to condition 1), we need to have atleast one 2 for the divisor to be even and conforming to condition 2), we cannot have more than three 2s (four 2s is 2^4 (16) and would make the divisor a multiple of 16).

Thus, we have three allowed powers for 2, i.e. 0, 1 and 2; and three allowed powers for 5, i.e. 0, 1, 2

Multiplying both, 3*3 = we get 9 factors of 1600, in total, which would be even and would not be a multiple of 16.

Hence, (C) is the correct answer choice.
Manager
Manager
avatar
S
Joined: 01 Oct 2018
Posts: 111
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 04:29
1
How many even divisors of 1600 are not multiples of 16?

1. Let's find prime factors of 1600 and 16:
1600: 2^(6)*5^(2)
16: 2^(4)

2. Next step, let's find a possible number of multiple of 16
Must be 2^(4)
Can be 2^(2)*5^(2): 2, 2 2, 2 5 ...
Quantity of variants: 3*3 = 9 ( 3 variant: 2 , 2 2 and no 2; 3 variant: 5, 5 5 and no 5)

3. Let's find the number of odd factors:
Can be:
1. odd: 1,5
2. odd = odd*odd: 5*5
no other variant, so the total number is 3

4. Let's find total number of factors:
2^(6)*5^(2)
#factors= 7*3 = 21

5. Subtract from the total number odd and multiple of 16

21-9-3 = 9

ANSWER C

(A) 4
(B) 6
(C) 9
(D) 12
(E) 18
Intern
Intern
avatar
B
Joined: 18 Jun 2017
Posts: 6
Location: India
Schools: ISB '21
GMAT 1: 600 Q40 V34
GPA: 4
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 04:35
B. 6.

Total number of divisors divisible by 16 (or, in other words, multiple of 16) = 9.
Out of these, odd divisors = 3.
So, even divisors = 9-3 = 6.
Manager
Manager
avatar
B
Joined: 27 Mar 2016
Posts: 110
GMAT ToolKit User
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 04:49
1
My answer is C. I.e 9

1600
Divisors are from combination 2^6 *5^2

To be even divisors it's needs to have 2
Also if it's not a multiple of 16 then it shouldn't have 2^4
So following divisors of 1600 would not be multiple of 16
2
2*5
2*25
2^2
2^2*5
2^2*25
2^3
2^3*5
2^3*25

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 10 Aug 2017
Posts: 29
Re: How many even divisors of 1600 are not multiples of 16?  [#permalink]

Show Tags

New post 16 Jul 2019, 05:26
How many even divisors of 1600 are not multiples of 16?

(A) 4
(B) 6
(C) 9
(D) 12
(E) 18

Answer is C

Posted from my mobile device
GMAT Club Bot
Re: How many even divisors of 1600 are not multiples of 16?   [#permalink] 16 Jul 2019, 05:26

Go to page   Previous    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?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne