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06 Mar 2005, 17:29
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a, b, c, and d are positive integers less than 10, is 0.ab + 0.cd > 1?
(1) The least value of a, b, c, and d is 4
(2) 0.ab*0.cd > 1/2
(1) The least value of a, b, c, and d is 4
(2) 0.ab*0.cd > 1/2
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06 Mar 2005, 17:47
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state 1....a,b,c,d can be same....if they r all 4...then ans is NO of they r 9 the YES....insuff
state 2.....let's say 0.ab = x....0.cd = y
x*y > 1/2....so 2xy > 1...(1)
now we need to see if x+y > 1........for if (x+y)^2 > 1.....
(x+y)^2 = x2+y2+2xy......we know that x2 and y2 will be < 1 but from eq 1...we now know that 2xy > 1.....sp (x+y)^2 > 1....or x+y > 1...suff...
state 1....a,b,c,d can be same....if they r all 4...then ans is NO of they r 9 the YES....insuff
state 2.....let's say 0.ab = x....0.cd = y
x*y > 1/2....so 2xy > 1...(1)
now we need to see if x+y > 1........for if (x+y)^2 > 1.....
(x+y)^2 = x2+y2+2xy......we know that x2 and y2 will be < 1 but from eq 1...we now know that 2xy > 1.....sp (x+y)^2 > 1....or x+y > 1...suff...
