Arithmetic Aptitude :: Simplification

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If (x + 1/x)^2 = 3 then (x^3+1/x^3) is equal to


A3

B2

C1

D0

Answer: Option D

Explanation:

(x + 1/x)^2 = 3 => (x + 1/x) = √3
Now (x^3+1/x^3) = (x+1/x)^3-3x*1/x(x+1/x)
=> ( √3)^2 -3?3) = (3√3-3√3) = 0

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2 / 105

Choose the correct option.

(0.1*0.1*0.1 + 0.02*0.02*0.02)/(0.2*0.2*0.2 + 0.04*0.04*0.04) is equal to


A0.125

B0.25

C0.5

D0.855

Answer: Option A

Explanation:

Lets assume 0.1 as a so 0.2 will be 2a
and 0.02 as b so 0.04 will be 2b
Simplify the give equation
(a*a*a + b*b*b)/(2a*2a*2a+2b*2b*2b) => (a^3+b^3)/(8*a^3+8*b^3)
=> (a^3+^3)/8(a^c+b^3) = 1/8 = 0.125

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3 / 105

Choose the correct option.

If (a^2 + b^2 + 1/a^2 + 1/b^2) = 4, then the value of (a^2 + b^2) will be


A1

B2

C1 1/2

D2 1/2

Answer: Option B

Explanation:

Given (a^2 + b^2 + 1/a^2 + 1/b^2) = 4
Simplify the above eq.
=> a^2 + 1/a^2 +b^2 + 1/b^2 = 4
=> (a-1/a)^2 + 2 + (b - 1/b)^2 + 2 = 4
=> (a-1/a)^2 + (b - 1/b)^2 = 0
=> (a - 1/a) = 0; (b - 1/b) = 0
=> a = b = (+-)1
so (a^2+b^2) = 1+1 = 2

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if (x + 1/x) = 2, then the value of (x^100 + 1/x^100) is:


A2

B1

C0

D-2

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Answer: Option A

Explanation:

Quick Approach
for x =1 given eq. will be satisfy. (1+1/1)=2
so (x^100 + 1/x^100) = (1^100 + 1/1^100) = 2

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5 / 105

Choose the correct option.

if (2x + 2/x) = 1, then the value of (x^3 + 1/x^3) is


A13/8

B11/8

C-11/8

D-13/8

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Answer: Option C

Explanation:

(2x + 2/x) = 1
=> (x + 1/x) = 1/2
(x^3+1/x^3) = (x+1/x)^3-3x*1/x(x+1/x)
= (1/2)^3-1/2 = (1/8 - 3/2) = (1-12)/8= -11/8

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6 / 105

Choose the correct option.

If A:B = 2:3, B:C = 4:5 and C:D = 5:9,then A:D is equal to


A11:17

B8:27

C5:9

D2:9

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Answer: Option B

Explanation:

A/B*B/C*C/D= 2/3*4/5*5/9
=> A/D = 8/27

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if x^3 + 3x^2 + 3x = 7, then x is equal to


A2

B1

C'-1

D_/6

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Answer: Option B

Explanation:

x^3 + 3x^2 + 3x = 7
Adding both side 1
=> x^3 + 3x^2 + 3x + 1= 7 +1
=> (x+1)^3=2^3
=> x+1 = 2 => x =1

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8 / 105

What is the value of [(3x+8Y)/(x-2Y)]; if x/2y=2?


A10

B12

C5

D20

Answer: Option A

Explanation:

3x+8y)/( 2y(x/2y - 1))   \\ take 2y as a common



(3x + 8y)/ (2y (1))    \\substitue (x/2y = 2) as in question



3x/2y + 8y/2y



3*2 + 4        \\ substitute (x\2y =2) as per condition



6 + 4



10

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9 / 105

Choose the correct option.

For what values of 'm' is y = 0, if y = x^2 + (2m + 1)x + m^2 - 1? x is a real number.


Am >= -2

Bm < 0

Cm = 0

Dm >= -1.25

Answer: Option D

Explanation:

Here is no explanation for this answer

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Choose the correct option.

If 2x-y=4 then 6x-3y=?


A15

B12

C18

D10

Answer: Option B

Explanation:

Solution:   2x-y=4 



Multiply both sides by 3 then it will be 6x-3y=12  

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