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

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

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

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

$Now,\: \: \: \: 125=5\times5\times=5^3\Rightarrow \sqrt [3]{125}=5$

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

$\therefore$     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)  $3600=2^3\times5^2\times3^2\times2.$

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

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

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