PS Number properties

[sud21]

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

I only

II only

I and II only

II and III only

None of the above

[theCEO]

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

I only

II only

I and II only

II and III only

None of the above

If the unit digit of m x n = 3, it means m and n are odd;
even x even = even
odd x even = even
odd x odd = odd

if n is odd, it cannot have an even factor
therfore we can eliminate 8 and 30

Multiples of 15 will have unit digits of 5 or 0 always, so we can elimiante 15 as 15 times any number will not have a unit digit of 3

Therefore none of these choices are correct

answer = e

[[email protected]]

Hi sud21,

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 produce 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: E

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

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

It's important to know that the question reads Which of the following ARE factors of n?
It doesn't say, Which of the following COULD BE factors of n?
This means we can quickly eliminate some statements be PLUGGING in numbers.

Rich used m = 1 and n = 3.
We could also use m = 3 and n = 11, or any variety of options.

Since none of the options (8, 15, 30) are factors of 11, the correct answer is E

[Matt@VeritasPrep]

Since the number ends in 3, it's odd, and can't have any even factors (eliminate 8 and 30).

Since the number ends in 3, it doesn't end in 0 or 5, and can't have 5 as a factor (eliminate 15).

We're done!