Thought process on remainders

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 273
Joined: Thu Sep 08, 2011 6:50 am
Thanked: 5 times
Followed by:3 members

Thought process on remainders

by fangtray » Wed May 02, 2012 3:23 pm
If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

a. 8
b. 9
c. 16
d. 23
e. 24

For this question, I made a careless mistake that seems to be easy to make if I use this strategy to solve. Below is my strategy, please let me know if there is a better way to do it or if I did something wrong.

16/y = Q + 1/y
16 = Qy + 1
Qy = 15

so Y could equal 3, 5, 15 and 1.

adds to 24.

OA is 23 because if you divide 16 by 1, you don't get a remainder. But in trying to figure out how to answer the question using the way i show above, it seems easy to get lost and accidentally add that 1 in there... does someone have a better way to do it?
Source: — Problem Solving |

Master | Next Rank: 500 Posts
Posts: 110
Joined: Wed Feb 22, 2012 11:28 pm
Location: India
Thanked: 13 times
Followed by:1 members

by spartacus1412 » Wed May 02, 2012 8:21 pm
answer is 23.

numbers less than 16 which have remiander 1 with 16 are 3, 5, 15
3+5+15 = 23
Its do or die this time!
Practise, practise and practise.

User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Wed May 02, 2012 11:14 pm
Hi,

for the GMAT, your goal is to be as efficient as possible. While you could certainly derive a fancy formula to solve this type of problem, brute force is almost certainly quicker.

Since we want all the numbers that leave a remainder of 1 when divided into 16, what we really want is the factors of 15 that are not ALSO factors of 16. Breaking down 15:

1*15
3*5

Of, those, 3, 5 and 15 are NOT factors of 16. So,

3+5+15 = 23... choose (D)!

Remember: the GMAT is not a high school math test on which you get 1 mark for the answer and 9 for showing your solution - all we care about is filling in the right bubble! On test day, fast and dirty will always beat long an elegant.
fangtray wrote:If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?

a. 8
b. 9
c. 16
d. 23
e. 24

For this question, I made a careless mistake that seems to be easy to make if I use this strategy to solve. Below is my strategy, please let me know if there is a better way to do it or if I did something wrong.

16/y = Q + 1/y
16 = Qy + 1
Qy = 15

so Y could equal 3, 5, 15 and 1.

adds to 24.

OA is 23 because if you divide 16 by 1, you don't get a remainder. But in trying to figure out how to answer the question using the way i show above, it seems easy to get lost and accidentally add that 1 in there... does someone have a better way to do it?
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course