Processing math: 100%
Home / Aptitude Tests / Mathematics / Solve the following ...
Solve the following equation: 2(2r1) - ...

Solve the following equation: 2(2r1)53 =  1(r+2)

A.

( -1,52 )

B.

( 1, - 52 )

C.

( 52, 1 )

D.

(2,1)

Correct answer is B

2(2r1)53 =  1(r+2)

2(2r1)1(r+2)  = 53

The L.C.M.: (2r - 1) (r + 2) 

2(r+2)1(2r1)(2r1)(r+2)53

2r+42r+1(2r1)(r+2)53

cross multiply the solution

3 * 5 = (2r - 1) (r + 2) * 5

divide both sides 5

3 =  2r2 + 3r - 2 (when expanded)

collect like terms

2r2 + 3r - 2 - 3 = 0

2r2 + 3r - 5 = 0

Factors are -2r and +5r

2r2 -2r + 5r - 5 = 0

[2r2 -2r] [+ 5r - 5] = 0

2r(r-1) + 5(r-1) = 0

(2r+5) (r-1) = 0

 r = 1 or - 52