Latest Elitmus Aptitude Question SOLUTION: 1/x + 1/y = 1/z, if x =12 and y and z are whole numbers. find the no of solutions possible?

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(#M40158236) ELITMUS Numerical Ability question Keep an EYE

1/x + 1/y = 1/z, if x =12 and y and z are whole numbers. find the no of solutions possible?

Asked In Elitmus Avi (7 years ago)

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Amit Kumar Singh  (7 years ago)

AVANTIKA
1/12 + 1/y = 1/z
solving further you will get the equation 12-z=12 * z/y
now z and y are whole numbers so the max value of z would be 12 on LHS .
Form this we conclude that the range of z is from 1 to 12.

Now solving the equation further you will get y = 12*z/12-z
for every z you will get corresponding y . If the corresponding y is a whole no then that will be the solution . Counting all of them for every z = 3,4,6,8,9,10,11 we get corresponding y= calculate from formula
And these 7 combination of z and y are solutions ..

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Amit kumar  (7 years ago)

1/12 + 1/y = 1/z
(y + 12)/12y = 1/z
z(y + 12) = 12y
z(y + 12) - 12y =0
z(y + 12) - 12y -144= -144
z(y + 12) – 12(y -12)= -144
(z-12)(y + 12) = -144
(12-z)(y+12) = 144 = 2^4*3^2
Total number of +ve solution = (4+1)(2+1) = 15
Total Integral Solution = 2*15-1 = 29


Generalization a/x-b/y= 1/n,
1) Number of +ve solution = number of factors of (a*b*n^2)
2) Number of Integral solution = 2* number of factors of (a*b*n^2) -1

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Amit Kumar Singh  (7 years ago)

7 solution

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Avi  (7 years ago)

Amit can you please explain?

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