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If N is a positive Integer, is the units digit of N equal to

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If N is a positive Integer, is the units digit of N equal to [#permalink] New post 20 Mar 2010, 13:57
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If N is a positive Integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N
(2) N = (2^5)(3^2)(5^7)(7^6)
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Re: DS Question [#permalink] New post 20 Mar 2010, 16:02
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meaglesp345 wrote:
If N is a positive Integer, is the units digit of N equal to zero?

1) 14 and 35 are factors of N
2) N = (2^5)(3^2)(5^7)(7^6)

I need help with an explanation on why # 2 is a sufficient answer.

Thanks for any help.


1) 14 = 2 * 7, 35 = 5 * 7

If a number has prime factors both 2 and 5, then it's divisible by 10 thus the unit digit equal to zero.

2) (2 * 5)^5 = 10,000

10,000 * 3^2 * 5^2 * 7^6

The unit digit has to be 0.

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Re: DS Question [#permalink] New post 24 Mar 2010, 09:20
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Im not sure that Statement 1 is sufficient on it's own. All we know from st1 is that N has prime factors of 2,5,7, and possibly others. From this, N could be 14, or 70 ...

But statement 2 is good because it tells you exactly the value of N. Keep in mind you dont have to figure it out, but you just have to know that if you had time, you could get a value for N and see what its units digit is.
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Re: DS Question [#permalink] New post 24 Mar 2010, 10:11
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I think it's D.

St. 1 : 14 = 2 * 7, 35 = 5 * 7, hence, 2,5,7 are factors of N.
If N=70, 35 * 2 or 14 * 5
If N=105, 35*3, 14 isn't a factor of 105.
If N = 140, 35 * 4, 14 * 10

Thus, when 14 and 35 are factors of N, the unit's digit is always 0 ! Hence, Sufficient.

St.2 : N=(2^5)(3^2)(5^7)(7^6)

As you have 2*5 here, the unit's digit will always be 0. Hence, Sufficient.
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Re: If N is a positive Integer, is the units digit of N equal to [#permalink] New post 10 May 2014, 07:51
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Re: If N is a positive Integer, is the units digit of N equal to [#permalink] New post 30 Jun 2014, 22:41
meaglesp345 wrote:
If N is a positive Integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N
(2) N = (2^5)(3^2)(5^7)(7^6)


Bunnel: If you could throw some light particularly on statement (1), it would be great.

I am still not clear how even statement (2) ensures that unit digit will be zero.
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Re: If N is a positive Integer, is the units digit of N equal to [#permalink] New post 01 Jul 2014, 02:48
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patternpandora wrote:
meaglesp345 wrote:
If N is a positive Integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N
(2) N = (2^5)(3^2)(5^7)(7^6)


Bunnel: If you could throw some light particularly on statement (1), it would be great.

I am still not clear how even statement (2) ensures that unit digit will be zero.


If N is a positive Integer, is the units digit of N equal to zero?

(1) 14 and 35 are factors of N --> N is divisible by 2 and 5, hence it's divisible by 10 --> the units digit must be 0. Sufficient.

(2) N = (2^5)(3^2)(5^7)(7^6). The same here 2 and 5 ensure that N is divisible by 10. Sufficient.

Answer: D.

Hope it's clear.
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Re: If N is a positive Integer, is the units digit of N equal to   [#permalink] 01 Jul 2014, 02:48
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