Question : What is the smallest two-digit perfect cube?
Option 1: 25
Option 2: 27
Option 3: 16
Option 4: 64
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Correct Answer: 27
Solution : ⇒ 251/3 = 52/3 This is not a perfect cube. ⇒ 271/3 = 33/3 = 3 This is a perfect cube. ⇒ 161/3 = 24/3 = 2 × (21/3) This is not a perfect cube. ⇒ 641/3 = 43/3 = 4 This is a perfect cube. Thus, 27 and 64 are perfect cubes of numbers and 27 is the smallest. Hence, the correct answer is 27.
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Question : The radius of two spheres is in the ratio of 1 : 5. What is the ratio of the volume of the two spheres?
Option 1: 8 : 27
Option 2: 1 : 25
Option 3: 1 : 125
Option 4: 1 : 64
Question : The average of a set of 15 consecutive even numbers is 64. What is the difference between the largest and the smallest numbers belonging to this set?
Option 1: 26
Option 3: 25
Option 4: 28
Question : If $\frac{J}{4}=\frac{K}{5}=\frac{L}{3}$, what is the value of $(L + J)^2:(J +K)^2:(K +L)^2$?
Option 1: 25 : 16 : 9
Option 2: 64 : 25 : 81
Option 3: 49 : 81 : 62
Option 4: 49 : 81 : 64
Question : What is the smallest three-digit number when divided by 2, 3, and 4 leaving the remainder 1 in each case?
Option 1: 111
Option 2: 105
Option 3: 101
Option 4: 109
Question : Two successive discounts of 20% and 30% are given while selling an item. What is the ratio of the marked price to the selling price of the item?
Option 1: 25 : 11
Option 2: 25 : 14
Option 3: 28 : 11
Option 4: 27 : 16
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