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Solution
1. Answer e = 1/6. Only product of the expressions in the form mentioned in the question is x^2y^2, where b = 1, is the integer. Now total number of ways of selecting two expression out of 4 are 4c2 = 6, so the probability is 1/6
2. Answer B, suppose store sell X copies on Saturday and Y copies on Firday, while for rest of the five days it sells Z copies each. we have X + Y + 5Z = 90, where X>Y>Z.
Case 1. We know that Z = 8 so X + Y = 50 in this case X can have any value, so we cant say whether Y is > or <11>Z
Maximum value of Z in this condition can by 8, making Y =12. If Z = 9 then Y = 7, which is not possible.
So Case 2. is sufficient.
Answer 3.
If (r,s) and (u,v) are equidistance from the center (0,0), then r^2 + s^2 = U^2 + V^2 ( equalising the distances from the origin)
Case 1. r+s = 1, doesnt tell anything about (u,v).. in sufficient
Case 2. though relation between different coordinate points can be formed but it doent give any clue on the distance from the origin.. insufficient.
Using both the conditions. U^2 = 1+r^22r, and V^2 = 1+s^2s
Adding both these equations we have U^2 +v^2 = r^2 + s^2 +2  2(r+s)
From case 1, we have r+s = 1, so the equation will become U^2 + V^2 = r^2 + s^2 .... sufficient.
Amar
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