Q] If x,y,a,b are all positive Integers and x^3 + y^3 = a^3 + b^3, then is xy>89
1] a^3 + b^3 = 1729
2] x^2 = x^3
Suggest best approach to tackle this questions
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First condition is not sufficientStarDust845 wrote:Is the answer A?
Calista.
Here is a clue
a^3 + b^3 = x^3+y^3 = 1729...a,b could be 12,1 or 10,9

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Q] If x,y,a,b are all positive Integers and x^3 + y^3 = a^3 + b^3, then is xy>89
since all the nos are +ve so we have
1] a^3 + b^3 = 1729
largest +ve nos that can be considered here is 12 coz 12 ^3 =1728(we need sum as 1729)
hence we have 12,1 are possible values
we can also evaluate some other cubes like 10, 9 which will also give the same sum
8^3 & 7^3 and cubes of all numbers below 9 will not work coz we cannot pair them with any other value within 12
so we have two possibilities 12,1 (12) & 10,9 (90) INSUFF
2] x^2 = x^3
only nos which satisfies this is 1
hoever value of y can be anything INSUFF
combine x^3+y^3 =1729 & x =1 so y must be 12 here to satisfy stmt 1
SUFF
C
since all the nos are +ve so we have
1] a^3 + b^3 = 1729
largest +ve nos that can be considered here is 12 coz 12 ^3 =1728(we need sum as 1729)
hence we have 12,1 are possible values
we can also evaluate some other cubes like 10, 9 which will also give the same sum
8^3 & 7^3 and cubes of all numbers below 9 will not work coz we cannot pair them with any other value within 12
so we have two possibilities 12,1 (12) & 10,9 (90) INSUFF
2] x^2 = x^3
only nos which satisfies this is 1
hoever value of y can be anything INSUFF
combine x^3+y^3 =1729 & x =1 so y must be 12 here to satisfy stmt 1
SUFF
C
Regards
Samir
Samir

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