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When positive integer m is multiplied by positive integer n, the units

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Bunuel
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When positive integer m is multiplied by positive integer n, the units [#permalink] New post   02 Feb 2015, 07:28
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When positive integer m is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?

I. 8
II. 15
III. 30

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above
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E
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chetan2u
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   02 Feb 2015, 09:47
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sterling19 wrote:
Let's test a few combinations with positive integers:

1*3 = 3
11*3 = 33
9*7 = 63

None of these products have factors of 8, 15, or 30. The correct answer is E.


ans E..
we can tell the ans w/o using examples..
the units digit of product m*n is 3..
this means m and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   09 Feb 2015, 04:40
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Bunuel wrote:
When positive integer m is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?

I. 8
II. 15
III. 30

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

E. In this units digit property problem you should recognize that an integer that ends in 3 cannot be divisible by any even numbers (the products of which are always even) nor by any multiples of 5 (the products always end in 0 or 5), so none of the proposed values can be factors of n.
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   02 Feb 2015, 09:08
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Let's test a few combinations with positive integers:

1*3 = 3
11*3 = 33
9*7 = 63

None of these products have factors of 8, 15, or 30. The correct answer is E.
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   02 Feb 2015, 10:58
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chetan2u wrote:
sterling19 wrote:
Let's test a few combinations with positive integers:

1*3 = 3
11*3 = 33
9*7 = 63

None of these products have factors of 8, 15, or 30. The correct answer is E.


ans E..
we can tell the ans w/o using examples..
the units digit of product m*n is 3..
this means m and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out


Kudos to you, sir! That is a much smarter way of handling this problem.
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   02 Mar 2015, 15:47
Well, the way I did it was this:

m*n = .....3.

So, m*n could be:
3, 13, 23, 103, 143, 1053 etc etc.

None of these numbers can be divided by 8, 15 0r 30. So ANS E
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   14 Mar 2016, 05:11
Excellent Question..
So here n can end with a one or a three
so not 10 nor 5 nor 15 can have them as the multiple..
The Question Stumped me initially..
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   27 Jun 2017, 17:09
Bunuel wrote:
When positive integer m is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?

I. 8
II. 15
III. 30

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

Kudos for a correct solution.


We don't necessarily have to pick numbers - instead we could examine the units digits patterns for 8 15 30

For 8 we have the pattern 8 4 2 6 - so 8 times any integer must result in a number with any of the 4 numbers as its ones digit

For 15- well we don't necessarily have to multiply because 15 times any integers will either end in 0 or 5

For 30- 30 by any integers will result in a number with 0 as its units digit

Thus
"E"
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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   15 Feb 2018, 12:38
Expert Reply
Hi All,

This question can be solved with Number Properties or by TESTing VALUES. Here's how you can answer it quickly by TESTing VALUES.

We're told that M and N are both POSITIVE INTEGERS and the UNITS DIGIT of their product is 3. We're asked which of the following are factors of N.

Since the units digit is 3, the simplest pair of values would be....

M = 1
N = 3

(or vice-verse)

None of the numbers (8, 15 or 30) are factors of 3, so the correct answer should stand out...

Final Answer:
Show Spoiler
E


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Re: When positive integer m is multiplied by positive integer n, the units [#permalink] New post   11 Mar 2021, 01:21
Bunuel wrote:
When positive integer m is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?

I. 8
II. 15
III. 30

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

Kudos for a correct solution.


This is a good question. The best approach to this question is via statements I, II, III:

I: 8 = \(2^3\)
As 8 has 2 as its factor, all the multiple of 8 will be multiple of 2. Therefore, 3 can't be the unit digit of m*n if n=8.


II: 15 = \(3*5\)
As 15 has 5 as its factor, all the multiple of 15 will have 5 or 0 as unit digit. Therefore, 3 can't be the unit digit of m*n if n=15.


III: 30 = \(2*3*5\)
As 30 has 2 & 5 as its factor, all the multiple of 30 will have 0 as unit digit. Therefore, 3 can't be the unit digit of m*n if n=30.

Correct answer is E
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