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08 May 2015, 06:21
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (01:59) correct
18%
(02:20)
wrong
based on 495
sessions
History
Date
Time
Result
Not Attempted Yet
If 2/z = 2/(z + 1) + 2/(z + 9) which of these integers could be the value of z?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Kudos for a correct solution.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Kudos for a correct solution.
General Discussion
Answer is z= 3.
One could easily pick numbers and check this within a minute.
But if we can rewrite the equation as (1/z) - (1/z+1) = 1/z+9. One can see that the left hand side is 1/z(z+1)
(For example 1/4- 1/5 = 1/20; 1/3-1/4 = 1/12; 1/9 - 1/10 = 1/90)
So you get z(z+1) = z+9. Now one can easily see that z=3 (One can also see that LHS is always even so RHS has to be even.So z has to be odd)
Answer : D
One could easily pick numbers and check this within a minute.
But if we can rewrite the equation as (1/z) - (1/z+1) = 1/z+9. One can see that the left hand side is 1/z(z+1)
(For example 1/4- 1/5 = 1/20; 1/3-1/4 = 1/12; 1/9 - 1/10 = 1/90)
So you get z(z+1) = z+9. Now one can easily see that z=3 (One can also see that LHS is always even so RHS has to be even.So z has to be odd)
Answer : D
