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

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.

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.

Hi MikeScarn

I totally agree with you. I spent some time to figure out the meaning.

Kindly clarify my understanding amanvermagmat.[/quote][/quote]




Hello PKN

I have edited the question, there was some confusion. Thanks for your input.

[/quote]




Hello PKN

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

Hi amanvermagmat,
Could you please post your explanation for answer option (C) against the amended question?
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

Answer: C

Thank you.
I think my explanation to the original question is still valid.