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
The official answer is 23 but I don't understand why it isn't 24.
x*y=15 R 1
3x5=15 R1
5*3=15 R1
15*1=15 R1
1*15=15 R1
3+5+15+1=24
Any help would be greatly appreciated. Thanks!
CAT: Problem Solving Solving - Disagree with Answer- Help?!?
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Just in case anyone else was wondering about this, we have:
(16/y) has remainder 1, or
16 = y*(something) + 1, or
15 = y*(something)
So y is a factor of 15 other than 1 itself. (Remember that any positive integer divided by 1 has remainder 0.)
Hence y = 3, 5, or 15, and the sum of solutions = 3 + 5 + 15 = 23.
(16/y) has remainder 1, or
16 = y*(something) + 1, or
15 = y*(something)
So y is a factor of 15 other than 1 itself. (Remember that any positive integer divided by 1 has remainder 0.)
Hence y = 3, 5, or 15, and the sum of solutions = 3 + 5 + 15 = 23.
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Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
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
==> (x#y)= the remainder after dividing x by y. (16#y)=1 means that the remainder is 1 when you divide 16 by y. Since 16=2^4, dividing it by an odd number would mean the remainder is 1 (except 1). From 16=3*5+1=5*3+1=15*1+1, y=3,5,15 and the sum would be 3+5+15=23. Therefore the answer is D
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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
==> (x#y)= the remainder after dividing x by y. (16#y)=1 means that the remainder is 1 when you divide 16 by y. Since 16=2^4, dividing it by an odd number would mean the remainder is 1 (except 1). From 16=3*5+1=5*3+1=15*1+1, y=3,5,15 and the sum would be 3+5+15=23. Therefore the answer is D
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8