Model 3 Simplification based on cube & cube root Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 4 EXERCISES
The following question based on simplification topic of quantitative aptitude
(a) 64
(b) 81
(c) 343
(d) 125
The correct answers to the above question in:
Answer: (a)
343 = 7 × 7 × 7
125 = 5 × 5 × 5
81 = 3 × 3 × 3 × 3
64 = 8 × 8 = 4 × 4 × 4
We see that 343 and 125 are only perfect cubes of 7 and 5 respectively.
81 is only a perfect square of 9. 64 is a perfect square of 8 as well as a perfect cube of 4.
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Read more problems based on cubes and roots Based Quantitative Aptitude Questions and Answers
Question : 1
The sum of the cubes of the numbers 22, –15 and –7 is equal to
a) 0
b) 6930
c) 3
d) 9630
Answer »Answer: (b)
Here, 22 - 15 - 7 = 0
We know that
$a^3 + b^3 + c^3$ = 3abc,
if a + b + c = 0
$(22)^3 + (–15)^3 + (–7)^3$
= 3 × 22 × (–15) (–7) = 6930
Question : 2
The square of a natural number subtracted from its cube is 48. The number is :
a) 4
b) 8
c) 5
d) 6
Answer »Answer: (a)
Let number be x
According to question,
$x^3 - x^2$ = 48 ⇒ ∴ x = 4
Question : 3
$√^3{0.000125}$ is equal to
a) 0.005
b) 0.5
c) 0.05
d) 0.15
Answer »Answer: (c)
$√^3{0.000125} = √^3{0.05 × 0.05 × 0.05}$
= 0.05
Question : 4
By what least number should 4320 be multiplied so as to obtain a number which is a perfect cube ?
a) 80
b) 40
c) 60
d) 50
Answer »Answer: (d)
4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= $2^3 × 3^3 × 2^2 × 5$
Required number = 2 × 5 × 5 = 50
Question : 5
The sum of the squares of 2 numbers is 146 and the square root of one of them is $√5$. The cube of the other number is
a) 1441
b) 1111
c) 1331
d) 1221
Answer »Answer: (c)
First number = $(√5)^2 = 5$
Let the second number be x.
$x^2 + 5^2 = 146$
$x^2$ = 146 –25 = 121
$x = √{121} = 11$
Cube of 11 =1331
Question : 6
$√^3{{72.9}/{0.4096}}$ is equal to :
a) 13.6
b) 0.5625
c) 182
d) 5.625
Answer »Answer: (d)
$√^3{{72.9}/{0.4096}} = √^3{{729000}/{4096}}$
= $√^3{(90)^3/(16)^3} = 90/16 = 45/8 = 5.625$
GET simplification PRACTICE TEST EXERCISES
Model 1 Simplification using VBODMAS
Model 2 Simplification based on square & square root
Model 3 Simplification based on cube & cube root
Model 4 Simplification with continued fraction
simplification Shortcuts and Techniques with Examples
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