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Intern  Joined: 26 Feb 2010
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If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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Question Stats: 78% (01:19) correct 22% (01:27) wrong based on 342 sessions

### HideShow timer Statistics 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)
Math Expert V
Joined: 02 Sep 2009
Posts: 56373
Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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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.

Hope it's clear.
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GMAT 3: 740 Q49 V41 Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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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.

D
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Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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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: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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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 zero?  [#permalink]

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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)

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.
Intern  Joined: 26 Jun 2011
Posts: 6
Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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Bunuel wrote:
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.

Hope it's clear.

I opted B.

Bunnel..I am having doubts with statement 1. It just says 14 & 35 are factors of N, but it doesn't specify whether they are the only factors. If they aren't, then 1 isn't sufficient on its own. How can we infer that they are the only factors, when it's not clearly specified.
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Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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Feluram wrote:
Bunuel wrote:
patternpandora wrote:
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.

Hope it's clear.

I opted B.

Bunnel..I am having doubts with statement 1. It just says 14 & 35 are factors of N, but it doesn't specify whether they are the only factors. If they aren't, then 1 isn't sufficient on its own. How can we infer that they are the only factors, when it's not clearly specified.

The question asks whether the units digit of N equals to zero. From (1) N is divisible by 2 and 5, hence it's divisible by 10, which means that the units digit of N is 0. We don't care about other factors of N at all.
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Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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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)

Bunuel

When you say N is divisible by 2 and 5

If you take apart 14 and 35 say- 2 x 7 x 5 x 5 - is this correct method for making that conclusion?
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Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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Nunuboy1994 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)

Bunuel

When you say N is divisible by 2 and 5

If you take apart 14 and 35 say- 2 x 7 x 5 x 5 - is this correct method for making that conclusion?

N is divisible by 14, so it's divisible by 2.
N is divisible by 35, so it's divisible by 5.

Thus, it's divisible by 10.

Generally if a positive integer is divisible by positive integers x and y, then it must be divisible by the least common multiple of x and y. So, N above must be divisible by the LCM(14, 35), so by 70.
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Re: If N is a positive Integer, is the units digit of N equal to zero?  [#permalink]

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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)

We need to determine whether the units digit of a positive integer N is zero. If N has a units digit of zero, then N must be divisible by 10. In other words, N must be divisible by both 2 and 5.

Statement One Alone:

14 and 35 are factors of N.

Since 14 is divisible by 2 and 35 is divisible by 5, N is divisible by both 2 and 5, and thus it has a units digit of zero. Statement one alone is sufficient. We can eliminate answer choices B, C, and E.

Statement Two Alone:

N = (2^5)(3^2)(5^7)(7^6)

We see that N is divisible by both 2 and 5 and thus has a units digit of zero. Statement two alone is also sufficient.

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