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) 15
(b) 12
(c) 10
(d) 11
The correct answers to the above question in:
Answer: (c)
We know that
$a^3 + b^3 + c^3$ - 3abc
= (a+b+c)$(a^2+b^2+c^2$ - ab - bc - ca)
= $1/2 (a + b + c) [(a - b)^2 + (b - c)^2 + (c - a)^2 ]$
∴ $√^3{(333)^3 + (333)^3 + (334)^3 - 3 × 333 × 333 × 334}$
= $√^3{1/2 (333 + 333 + 334)[(333 - 333)^2 + (333 - 334)^2 + (334 - 333)^2]}$
= $√^3{1/2 × 1000 × 2} = √^3{1000}$
= $√^3{10 × 10 × 10}$ = 10
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Read more problems based on cubes and roots Based Quantitative Aptitude Questions and Answers
Question : 1
The least number, by which 1944 must be multiplied so as to make the result a perfect cube, is
a) 13
b) 2
c) 6
d) 3
Answer »Answer: (d)
| 2 | 1944 |
| 2 | 972 |
| 2 | 486 |
| 3 | 243 |
| 3 | 81 |
| 3 | 27 |
| 3 | 9 |
| 3 |
1944 = 2×2×2×3×3×3×3×3 = $2^3 × 3^3 × 3^2$
Clearly, 1944 should be multiplied by 3 to make the result a perfect cube.
Question : 2
$√^3{8}/√{16} ÷ √{100/49} × √^3{125}$ is equal to :
a) $4/7$
b) 7
c) $7/100$
d) 1$3/4$
Answer »Answer: (d)
On simplification,
Expression = $2/4 × 7/10 × 5$
= $7/4 = 1{3}/4$
Question : 3
$√^3{{72.9}/{0.4096}}$ is equal to :
a) 13.6
b) 0.5625
c) 182
d) 5.625
Answer »Answer: (d)
$√^3{{72.9}/{0.4096}} = √^3{{729000}/{4096}}$
= $√^3{(90)^3/(16)^3} = 90/16 = 45/8 = 5.625$
Question : 4
$√^3{4{12}/125}$ is equal to
a) 2.4
b) 1.4
c) 1.8
d) 1.6
Answer »Answer: (d)
Expression = $√^3{4{12}/125}$
= $√^3{512/125} = √^3{{8 × 8 × 8}/{5 × 5 × 5}} = 8/5$ =1.6
Question : 5
$(5.5)^3 - (4.5)^3$ is equal to :
a) 75.25
b) 1
c) 74.25
d) 75
Answer »Answer: (a)
$(5.5)^3 - (4.5)^3$
= $(5.5 - 4.5)^3$ + 3 × 5.5 × 4.5 (5.5 - 4.5)
= $(1)^3$ + 74.25(1)
= 1 + 74.25 = 75.25
Question : 6
The value of $(√{{4}^3 + {15}^2})^3$ is :
a) 3943
b) 4913
c) 4193
d) 4313
Answer »Answer: (b)
Expression = $(√{4^3 + {15}^2})^3$
= $(√{64 + 225})^3 = (√289)^3$
= $(17)^3$ = 4913
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
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