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# If p Is a positive Integer, what is the units digit of p?

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If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:14
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GMATbuster's Weekly Quant Quiz#8 Ques #6

If p Is a positive Integer, what is the units digit of p?
1) p is divisible by 14, 15, 16, and n.
2)$$\frac{p}{(17(25!) )}$$= k, where k Is an Integer.

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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:31
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1
If p Is a positive Integer, what is the units digit of p?
1) p is divisible by 14, 15, 16, and n.
2)p(17(25!))p(17(25!))= k, where k Is an Integer.

Concept: if a number is divisible by 5 and 2 then the unit digit has to be 0.

By that logic:

Stat1:
P is div by 14(2) 15(5)
Since we have a 2 and 5

We can say it is sufficient

Stat 2:

Since P is divisible by the product of 17*25!
We can say the last digit has to be 0.

We can say it is sufficient

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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:34
1
The answer for this question is A
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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:19
From statement 1:

LCM of 16 and 15 is 240. Hence irrespective of the other number N. Unit digit of P will always be zero.
A is sufficient.

From statement 1:

$$\frac{p}{17*25!}$$
Then p must be 17*25! or 34*25!

Unit digit is not always the same.
Insufficient.

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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:42
Answer for this question will be A.
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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:53

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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:56
Stmt 1: p has 2 and 5 as factors. So, units digit will have 0. Hence sufficient.

Stmt 2: Again, p is divisible by 2 and 5, so units digit will have 0. Hence sufficient.

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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 10:59
Statement 1:

If it has to be divisible by both 16 and 15 then units digit has to be 0 as common multiple for these 2 nos is 240. Hence Unit digit of P will always be zero.
Sufficient.

Statement 2

$$\frac{p}{17*25!}$$
Then p can be
17*25!
34*25!
68*25!
etc

So, Unit digit is not sa,e.
Insufficient.

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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 11:01
OPTION A

1) LCM OF all the values will end in 0
2) P CAN BE 17 OR 25!. SO IT CAN END IN 0 OR 7
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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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10 Nov 2018, 11:15
statement1::

lcm of 14,15,16,n = 1080n
so p is divisible by 1080n
this implies unit digit has to be 0
hence, a is sufficient

statement 2:

25! contains trailing zeros
this also implies p must have unit digit 0
hence st 2 is sufficient

both statements are sufficient individually so ans :: D
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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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09 Mar 2019, 00:47
nitesh50 wrote:
If p Is a positive Integer, what is the units digit of p?
1) p is divisible by 14, 15, 16, and n.
2)p(17(25!))p(17(25!))= k, where k Is an Integer.

Concept: if a number is divisible by 5 and 2 then the unit digit has to be 0.

By that logic:

Stat1:
P is div by 14(2) 15(5)
Since we have a 2 and 5

We can say it is sufficient

Stat 2:

Since P is divisible by the product of 17*25!
We can say the last digit has to be 0.

We can say it is sufficient

I too followed your approach, but OA is A. I dont know why? can anyone explain....
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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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09 Mar 2019, 19:42
The OA shall be D.

The typo has been removed.

Thanks for the update.

kiran120680 wrote:
nitesh50 wrote:
If p Is a positive Integer, what is the units digit of p?
1) p is divisible by 14, 15, 16, and n.
2)p(17(25!))p(17(25!))= k, where k Is an Integer.

Concept: if a number is divisible by 5 and 2 then the unit digit has to be 0.

By that logic:

Stat1:
P is div by 14(2) 15(5)
Since we have a 2 and 5

We can say it is sufficient

Stat 2:

Since P is divisible by the product of 17*25!
We can say the last digit has to be 0.

We can say it is sufficient

I too followed your approach, but OA is A. I dont know why? can anyone explain....

Posted from my mobile device
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Re: If p Is a positive Integer, what is the units digit of p?  [#permalink]

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12 Mar 2019, 04:48
gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#8 Ques #6

If p Is a positive Integer, what is the units digit of p?
1) p is divisible by 14, 15, 16, and n.
2)$$\frac{p}{(17(25!) )}$$= k, where k Is an Integer.

From statement 1, p must have a 0 in units place because it has 5 in 15 and at least a 2 in 14 or 16 , so the answer for units digit of p is 0
1 is sufficient
From statement 2, 25! has a 0 in its units place and p/(17*25!) is an integer so again units digit of p must have a 0.
2 is sufficient
Re: If p Is a positive Integer, what is the units digit of p?   [#permalink] 12 Mar 2019, 04:48
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