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# What is the highest power of 5 contained in positive integer N? (1)

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What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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Updated on: 10 Aug 2018, 18:58
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What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

(2) N is the product of 100 and an even integer.

Originally posted by amanvermagmat on 05 Aug 2018, 05:20.
Last edited by amanvermagmat on 10 Aug 2018, 18:58, edited 1 time in total.
Edited the second statement to resolve confusion
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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Updated on: 05 Aug 2018, 18:20
What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.
N =100, contains 5^2
N=500, contains 5^3 - NS

(2) N is an even multiple of 100
N =10, contains 5^1
N=1 200, contains 5^2 - NS

(1)+(2) NS

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Originally posted by Hero8888 on 05 Aug 2018, 07:02.
Last edited by Hero8888 on 05 Aug 2018, 18:20, edited 1 time in total.
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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05 Aug 2018, 16:41
amanvermagmat wrote:
What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

(2) N is an even multiple of 100.

(1) N can be 100, 200, 300, 400.... 900.

If N is 100, greatest power of 5 is 2.

If N is 500, greatest power of 5 is 3.

(2) N can still be 100, 200, 300, 400, 500...1000, 1100, 1200, to infinity. All multiples of 100 are even numbers.

Same answers except there is no max number. So greatest power of 5 is infinity.

(1) + (2) We still don't know what N is.

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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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09 Aug 2018, 22:15
1
amanvermagmat wrote:
What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

(2) N is an even multiple of 100.

Question stem:- What is the highest power of 5 contained in positive integer N?
Or, how many fives are there in the factorization of N?

St1:- N is divisible by 100 but not by 1000

Possible values of N: 100,200,...,500,...,900.
All the above terms contain two fives as factors except 500, which has 3nos of fives as factor.
100=5*5*4
200=5*5*8
.
.
500=5*5*5*4

Insufficient , because we found two results w.r.t. question stem.

St2:- N is an even multiple of 100.
Even multiple implies multiplying factor is even.
N=100*k, where k is positive even.
Possible values of N: (100*2=200),(100*4=400),........,(100*10=1000) etc
200=5*5*8
1000=5*5*5*8
Insufficient , because we found more than one results w.r.t. question stem.

Combined, Set N={200,400,600,800} (1. 100<N<1000, 2. N=100k )
All the elements of set N contain $$5*5=5^2$$ as its factor.
So, the highest power of 5 contained in positive integer N is 2.

Ans. (C)
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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10 Aug 2018, 13:01
PKN wrote:
amanvermagmat wrote:
What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

(2) N is an even multiple of 100.

Question stem:- What is the highest power of 5 contained in positive integer N?
Or, how many fives are there in the factorization of N?

St1:- N is divisible by 100 but not by 1000

Possible values of N: 100,200,...,500,...,900.
All the above terms contain two fives as factors except 500, which has 3nos of fives as factor.
100=5*5*4
200=5*5*8
.
.
500=5*5*5*4

Insufficient , because we found two results w.r.t. question stem.

St2:- N is an even multiple of 100.
Even multiple implies multiplying factor is even.
N=100*k, where k is positive even.
Possible values of N: (100*2=200),(100*4=400),........,(100*10=1000) etc
200=5*5*8
1000=5*5*5*8
Insufficient , because we found more than one results w.r.t. question stem.

Combined, Set N={200,400,600,800} (1. 100<N<1000, 2. N=100k )
All the elements of set N contain $$5*5=5^2$$ as its factor.
So, the highest power of 5 contained in positive integer N is 2.

Ans. (C)

What is the source of this question? If it is not a reliable source, maybe change statement 2 to "N is a multiple of 100 and an even integer"

"N is an even multiple of 100." Does not imply that there is a multiplying factor of an even integer.

N is an even multiple of 100. 500 is an even number and is a multiple of 100.
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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10 Aug 2018, 13:18
MikeScarn wrote:
PKN wrote:
amanvermagmat wrote:
What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

(2) N is an even multiple of 100.

Question stem:- What is the highest power of 5 contained in positive integer N?
Or, how many fives are there in the factorization of N?

St1:- N is divisible by 100 but not by 1000

Possible values of N: 100,200,...,500,...,900.
All the above terms contain two fives as factors except 500, which has 3nos of fives as factor.
100=5*5*4
200=5*5*8
.
.
500=5*5*5*4

Insufficient , because we found two results w.r.t. question stem.

St2:- N is an even multiple of 100.
Even multiple implies multiplying factor is even.
N=100*k, where k is positive even.
Possible values of N: (100*2=200),(100*4=400),........,(100*10=1000) etc
200=5*5*8
1000=5*5*5*8
Insufficient , because we found more than one results w.r.t. question stem.

Combined, Set N={200,400,600,800} (1. 100<N<1000, 2. N=100k )
All the elements of set N contain $$5*5=5^2$$ as its factor.
So, the highest power of 5 contained in positive integer N is 2.

Ans. (C)

What is the source of this question? If it is not a reliable source, maybe change statement 2 to "N is a multiple of 100 and an even integer"

"N is an even multiple of 100." Does not imply that there is a multiplying factor of an even integer.

N is an even multiple of 100. 500 is an even number and is a multiple of 100.

If the multiplying factor is even, then it is named as "EVEN MULTIPLE".
For example even multiple of 100 :- 100*2,100*4 etc
For example:- 100*3,100*5 etc are not even multiple of 100.
I don't find ambiguity in the question.
This is a high quality question.

Kindly clarify my understanding amanvermagmat.
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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10 Aug 2018, 17:08
PKN , I completely understand what you're saying dude. Hold your horses.

But what I am saying is that there is indeed ambiguity as far as the English being used.

I read it as "N is even and a multiple of 100." Therefore I don't think this is a high quality question. GMAC does not try to trick people on the Quant section with use of English.

70% of people have gotten it wrong so far.

Hello MikeScarn

I have edited the question. This was NOT intended to be a play of words (there was no intention to Trick based on English words usage). My understanding is simply that even multiple of X means = X multiplied by an even number.

But I understand that it was causing confusion, so I have edited the second statement now, there should be clarity now. Thanks for your input.
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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10 Aug 2018, 17:38
MikeScarn wrote:
PKN , I completely understand what you're saying dude. Hold your horses.

But what I am saying is that there is indeed ambiguity as far as the English being used.

I read it as "N is even and a multiple of 100." Therefore I don't think this is a high quality question. GMAC does not try to trick people on the Quant section with use of English.

70% of people have gotten it wrong so far.

Hi MikeScarn

I totally agree with you. I spent some time to figure out the meaning.
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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10 Aug 2018, 18:54
Kindly clarify my understanding amanvermagmat.[/quote][/quote]

Hello PKN

I have edited the question, there was some confusion. Thanks for your input.
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What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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10 Aug 2018, 19:50
1
amanvermagmat wrote:
Kindly clarify my understanding amanvermagmat.
[/quote]

Hello PKN

I have edited the question, there was some confusion. Thanks for your input.[/quote]

Hi amanvermagmat,
It would be a great learning for me.

Thanking you.

Thanks MikeScarn And Mo2men.
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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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11 Aug 2018, 02:19
PKN wrote:

Hi amanvermagmat,
It would be a great learning for me.

Thanking you.

Thanks MikeScarn And Mo2men.

Hi PKN

You are welcome

I will share my thoughts

What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

This means the number is 100, 200, 300.......900.

Let N = 500=5 *100= 4 * 5^3........Power of 5 = 3

Let N= 1200 = 4*25= 4 *5^2..........Power of 5 = 2 (Please Note any number multiple of 100 until 900, except 500, has 5 with power of 2)

Insufficient

(2) N is the product of 100 and an even integer.

N = 100 * Even Number

Let N = 100 * 2 = 200...............Power of 5 = 2

Let N = 100 * 10 = 1000............Power of 5 = 3

Let N = 100 * 150 = 15,000.......Power of 5 = 3

Let N = 100 * 200 = 20,000.......Power of 5 = 4

Insufficient

Combine 1 & 2

Numbers are 200,400,600 & 800...........All has 5 with power of 2

Sufficient

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Re: What is the highest power of 5 contained in positive integer N? (1)  [#permalink]

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11 Aug 2018, 02:23
Mo2men wrote:
PKN wrote:

Hi amanvermagmat,
It would be a great learning for me.

Thanking you.

Thanks MikeScarn And Mo2men.

Hi PKN

You are welcome

I will share my thoughts

What is the highest power of 5 contained in positive integer N?

(1) N is divisible by 100 but not by 1000.

This means the number is 100, 200, 300.......900.

Let N = 500=5 *100= 4 * 5^3........Power of 5 = 3

Let N= 1200 = 4*25= 4 *5^2..........Power of 5 = 2 (Please Note any number multiple of 100 until 900, except 500, has 5 with power of 2)

Insufficient

(2) N is the product of 100 and an even integer.

N = 100 * Even Number

Let N = 100 * 2 = 200...............Power of 5 = 2

Let N = 100 * 10 = 1000............Power of 5 = 3

Let N = 100 * 150 = 15,000.......Power of 5 = 3

Let N = 100 * 200 = 20,000.......Power of 5 = 4

Insufficient

Combine 1 & 2

Numbers are 200,400,600 & 800...........All has 5 with power of 2

Sufficient

Thank you.
I think my explanation to the original question is still valid.
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Re: What is the highest power of 5 contained in positive integer N? (1) &nbs [#permalink] 11 Aug 2018, 02:23
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