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Problem Solving (PS) | What is the sum of all positive integer xs such that 24/(12 - x)

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24/ (12 -x ) has to be an integer.
Hence 12 - x ) has to be a factor of 24.

How many factors does 24 have ?

24 = 2^3 *3 = 4 * 2 = 8 ..The factors are => 2^0 , 2^1 , 2^2 , 2^3 , 3 , 2.3 , 2^2*3 and 2^3*3.

12- x has to equal to each one of them till it becomes zero. The denominator can never be zero.

12-x = 2^0
12-x = 1
x = 11
Same way , 12-x = 2
x=10
x= 9 , 8 , 6 and 4

Adding them = 48
C is the answer­

Statistics : Posted by sayan640 • on 30 Mar 2023, 09:45 • Replies 2 • Views 742



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