IPMAT 2019 - Quantitative Aptitude Question 49

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IPMAT 2019 - Quantitative Aptitude

Let the sides be x, y, z then 
6(x2 + y2 + z2) = 564
x2 + y2 + z2 = 94
Only solutions possible are 81 + 9 + 4 and 49 + 36 + 9
Hence possible sides are 9, 3, 2 and 7, 6, 3
Hence, volume = 93 + 33 + 23 and 73 + 63 + 33
= 764 and 586

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