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Arithmetic Aptitude :: Simplification

Home > Arithmetic Aptitude > Simplification > General Questions

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Answer: Option A

Explanation:

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BOA (Bank of America) 

2. 2^30 + 2^30 + 2^30 + 2^30 =

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Answer: Option C

Explanation:

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BOA (Bank of America) 

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

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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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4. (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

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

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

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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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Global Edge 

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

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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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Global Edge 

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

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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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Global Edge 

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

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

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Answer: Option A

Explanation:

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TCS