PS Number properties

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Sat Sep 19, 2015 5:06 am

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

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Source: Beat The GMAT — Problem Solving | Sat Sep 19, 2015 5:06 am

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Sep 19, 2015 10:08 am

sud21 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

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

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Sep 19, 2015 10:36 am

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

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Sep 19, 2015 11:10 am

sud21 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

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

Brent Hanneson - Creator of GMATPrepNow.com

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Sep 24, 2015 11:10 am

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!

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