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Nikhil54321
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Quant Question [#permalink] New post   26 Jun 2017, 03:35
Hi All,

I started preparing for GMAT. I have a query in quant.

For 7200 number, I solved for below questions

1. Number of factors = 2^5.3^2.5^2 = 54
2. Number of odd factors = 3.3 = 9
3. Number of even factors = 54-9 = 45
4. Number of perfect squares = 12

Now I want to find out number of factors which are multiples of 120 for 7200 number ? Can somebody help me in solving this ?
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abhimahna
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Quant Question [#permalink] New post   26 Jun 2017, 03:46
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Hi Nikhil54321 ,

In order to find the number of factors which are multiple of 120 for 7200, you can follow the below approach:

120 = 2^3 * 3 * 5

7200 = 2^5 * 3^2 * 5^2

In order to find multiples of 120, just take 2^3, 3 and 5 out of the powers of 7200.

So, I can say number of factors of 7200 which are multiples of 120 are 2^2 * 3^1 * 5^1

= 3 * 2 * 2 = 12.

Let me know in case of any concern. :)
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Quant Question [#permalink] New post   26 Jun 2017, 04:12
Hi Abhi,

Thanks for your reply !!!

I didn't understand these two points

In order to find multiples of 120, just take 2^3, 3 and 5 out of the powers of 7200.

[/b]So, I can say number of factors of 7200 which are multiples of 120 are 2^2 * 3^1 * 5^1


Hilighted part I didn't understand. Can you please elaborate ?
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Quant Question [#permalink] New post   26 Jun 2017, 04:19
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Nikhil54321 wrote:
Hi Abhi,

Thanks for your reply !!!

I didn't understand these two points

In order to find multiples of 120, just take 2^3, 3 and 5 out of the powers of 7200.

[/b]So, I can say number of factors of 7200 which are multiples of 120 are 2^2 * 3^1 * 5^1


Hilighted part I didn't understand. Can you please elaborate ?


Hi Nikhil54321 ,

What I meant was in order to find the factors which are multiples of 120, just take the prime factors required to make 120 out of 7200.

So, I have three 2s , one 3 and one 5 in 120.

I will take these out of the prime factors of 7200.

Now, after taking them out you can calculate the number of factors of pending prime factors.

The final result I will get will all be the multiples of 120.

Let me know in case of further concerns.
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Re: Quant Question [#permalink] New post   26 Jun 2017, 04:34
Got it.. Thank you :)
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Nikhil54321
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Re: Quant Question [#permalink] New post   26 Jun 2017, 05:35
One more doubt. How to calculate for not divisible.

Suppose 7200 is the number and factors are 2^5.3^2.5^2

number of factors divisible by 75 = 2^5.3^1 = 12

I want to calculate number of factors not divisible by 75 ?

Thanks in Advance !!!
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Re: Quant Question [#permalink] New post   26 Jun 2017, 06:02
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Nikhil54321 wrote:
One more doubt. How to calculate for not divisible.

Suppose 7200 is the number and factors are 2^5.3^2.5^2

number of factors divisible by 75 = 2^5.3^1 = 12

I want to calculate number of factors not divisible by 75 ?

Thanks in Advance !!!


Hi Nikhil54321 ,

Number of factors NOT divisible by 75 = Total Factors - Number of factors divisible by 75

I hope it makes sense. :)
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Re: Quant Question [#permalink] New post   26 Jun 2017, 06:07
Yeah bro.

You are right.

Thank you :)
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Re: Quant Question [#permalink]
26 Jun 2017, 06:07

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