Maths / Cube and Cube Roots / Properties of Cubes of Numbers

QUESTION
 

Which of the following options is INCORRECT ?

OPTIONS
A. 

Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. The numbers will be 5, 10, 15.

B. 

The digit in the units place for the cube of a four digit number of the form xyz8 is 2.

C. 

The smallest number by which 3600 be divided to make it a perfect cube is 450.

D. 

None of these

Right Option : D

EXPLANATION
Explain TypeExplanation Content
Text

(A) Let the numbers be x, 2x and 3x Sum of cubes of the numbers = 4500

therefore : : (x)^3+(2x)^3+(3x)^3=4500

Rightarrow : : : : : x^3+8x^3+27x^3=4500

Rightarrow : : : : 36x^3=4500 Rightarrow x^3=frac {4500}{36}=125 Rightarrow x=sqrt [3]{125}

Now,: : : : 125=5times5times=5^3Rightarrow sqrt [3]{125}=5

therefore : : : x=sqrt [3]{125}=5

therefore     Required numbers are 5, 10 and 15.

(B)  Since the unit's place of xyz8 is 8.

therefore     Unit's place digit of cube xyz8 is 2.

(C)  3600=2^3times5^2times3^2times2.

To make it a perfect cube, it must be divided by

         5^2times3^2times2: i.e., 450.

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