Practice Simplification - quantitative aptitude Online Quiz (set-2) For All Competitive Exams
Q-1) Simplify $√{[(12.1)^2 - (8.1)^2] + [(0.25)^2 + (0.25)(19.95)]}$
(a)
(b)
(c)
(d)
$√{{20.2 × 4}/{0.25 × 20.2}} = √{4/{0.25}}$
= $√{400/25} = √{16}$ = 4
Q-2) Simplification of ${(3.4567)^2 - (3.4533)^2}/{0.0034}$ yields the result :
(a)
(b)
(c)
(d)
? = ${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$
= ${6.9100 × 0.0034}/{0.0034}$ = 6.91
Using Rule 8,
${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$
= ${{3.4567}^2 - {3.4533}^2}/{(3.4567 - 3.4533)}$
= 3.4567 + 3.4533 = 6.91
Q-3) $[2√{54} - 6√{2/3} - √{96}]$ is equal to
(a)
(b)
(c)
(d)
Expression
= $2√{54} - 6√{2/3} - √{96}$
= $2√{9 × 6} - √{{2 × 6 × 6}/3} - √{16 × 6}$
= $2 × 3√{6} - 2√{6} - 4√{6}$ = 0
Q-4) The sum of the cubes of the numbers 22, –15 and –7 is equal to
(a)
(b)
(c)
(d)
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
Q-5) The square of a natural number subtracted from its cube is 48. The number is :
(a)
(b)
(c)
(d)
Let number be x
According to question,
$x^3 - x^2$ = 48 ⇒ ∴ x = 4
Q-6) The least number, by which 1944 must be multiplied so as to make the result a perfect cube, is
(a)
(b)
(c)
(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.
Q-7) By what least number should 4320 be multiplied so as to obtain a number which is a perfect cube ?
(a)
(b)
(c)
(d)
4320 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
= $2^3 × 3^3 × 2^2 × 5$
Required number = 2 × 5 × 5 = 50
Q-8) Which of the following is a perfect square as well as a cube? 343, 125, 81, or 64
(a)
(b)
(c)
(d)
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.
Q-9) The least number, that must be added to 1720 so as to obtain a perfect cube, is
(a)
(b)
(c)
(d)
12 × 12 × 12 = 1728
∴ Required number
= 1728 - 1720 = 8
Q-10) By what least number should 675 be multiplied so as to obtain a perfect cube number ?
(a)
(b)
(c)
(d)
675 = 5 × 5 × 3 × 3 × 3
∴ Required number = 5
Q-11) The sum of $√{0.01} + √{0.81} + √{1.21} + √{0.0009}$ is :
(a)
(b)
(c)
(d)
$√{0.01} + √{0.81} + √{1.21} + √{0.0009}$
= 0.1 + 0.9 + 1.1 + 0.03 = 2.13
Q-12) The value of $√{0.441}/√{0.625}$ is equal to :
(a)
(b)
(c)
(d)
Expression = $√{0.441}/√{0.625}$
= $√{{0.441}/{0.625}} = √{441/625}$
= $21/25$ = 0.84
Q-13) The value of $(√{{4}^3 + {15}^2})^3$ is :
(a)
(b)
(c)
(d)
Expression = $(√{4^3 + {15}^2})^3$
= $(√{64 + 225})^3 = (√289)^3$
= $(17)^3$ = 4913
Q-14) $√^3{{72.9}/{0.4096}}$ is equal to :
(a)
(b)
(c)
(d)
$√^3{{72.9}/{0.4096}} = √^3{{729000}/{4096}}$
= $√^3{(90)^3/(16)^3} = 90/16 = 45/8 = 5.625$
Q-15) 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)
(b)
(c)
(d)
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
Q-16) Simplify : $1+2/{1+3/{1+{4/5}}}$
(a)
(b)
(c)
(d)
? = $1 + 2/{1 + {{3 × 5}/9}} = 1 + 2/{1 + {5/3}}$
= $1 + {2 × 3}/8 = 7/4$
Q-17) Evaluate : ${9|3 - 5|- 5|4|÷10}/{- 3 (5) - 2 × 4 ÷ 2}$
(a)
(b)
(c)
(d)
? = ${9|3 - 5|- 5|4|÷10}/{- 3 (5) - 2 × 4 ÷ 2}$
= ${9 × 2 - 5 × 4 ÷ 10}/{- 15 - 8 ÷ 2}$
= ${18 - 2}/{- 19} = -16/19$
Q-18) $1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110$ = ?
(a)
(b)
(c)
(d)
Using Rule 2,
$1/{5×6} + 1/{6×7} + 1/{7×8} + 1/{8×9} + 1/{9×10} + 1/{10×11}$
= $1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 +1/9 - 1/10 +1/10 - 1/11 +1/11$
= $1/5 - 1/11 ={11 - 5}/55 = 6/55$
Q-19) Simplify : ${2{3/4}}/{1{5/6}} ÷ {7/8} × (1/3 + 1/4) + 5/7 ÷ {3/4} of {3/7}$
(a)
(b)
(c)
(d)
Using Rule 1,
The given expression
${2{3/4}}/{1{5/6}} ÷ {7/8} × (1/3 + 1/4) + 5/7 ÷ {3/4} of {3/7}$
= ${11/4}/{11/6} ÷ {7/8} × ({4+3}/12) + 5/7 ÷ {3/4} of {3/7}$
= $(11/4 × 6/11) ÷ {7/8} × 7/12 + 5/7 ÷ (3/4 × 3/7)$
= ${3/2} ÷ {7/8} × 7/12 + {5/7} ÷ {9/28}$
= ${3/2} × {8/7} × 7/12 + {5/7} ×{28/9}$
= $1 + 20/9 = {9+20}/9 = 29/9 = 3{2}/9$
Q-20) The simplified value of $√{900} + √{0.09} + √{0.000009}$ is
(a)
(b)
(c)
(d)
Expression
= $√{900} + √{0.09} - √{0.000009}$
= 30 + 0.3 - 0.003
= 30.297