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Simplification Questions

Home > Quantitative Aptitude > Simplification > General Questions
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Choose the correct option.

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


A2

B1

C0

D-2

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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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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What is the remainder of (16937^30)/31 ?


A5

B0

C1

D6

Answer: Option C

Explanation:

Solution: Means you have to get the digit at unit's place. 



Divide 16937 by 31 we will get remainder as 11



Now any power of 11 will yield 1 at its unit position hence 1 is the answer.

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If a - b = 3 and a^2 + b^2 = 29, find the value of ab


A10

B12

C15

D18

ENone of these

Answer: Option A

Explanation:

2ab = (a^2 + b^2) - (a - b)^2
= 29 - 9 = 20
ab = 10.

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If m=2- _/3
Find the value of:
(m^6+m^5+m^4+1)/m^3


A(61 - 5?3)

B(61 - 5?2)

C(60 - 5?3)

DNone fo these

Answer: Option A

Explanation:

m = (2 - ?3)
=> 1/m = (2 + ?3)

(m^6+m^5+m^4+1)/m^3
= m^3 + m^2 + m + 1/m^3
= (m + 1/m)^3 - 3(m +1/m) + m(m+1)
= 4^3 - 3*4 + (2-?3)(3-?3)
= 64 - 12 + 9 - 5?3
= (61 - 5?3)

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Solution for XY(Z+1)-ZY = XY is


AZ=0,Y=1

BX=1,Y=1

CX=0,Y=0

DX=1,Z=0

Answer: Option D

Explanation:

Simplifying, XY(Z+1)-ZY = XY
we get, XYZ + XY - ZY = XY
=> XYZ - ZY + XY = XY
=> XYZ - ZY = 0
=> XYZ = ZY
=> XZ = Z
=> XZ - Z=0
=> Z(X-1)=0
Above implies that either Z=0 or X-1=0 => x = 1

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P ( x ) = ( x999 + x998 + x997 + . . . . + x + 1)2 - x999Q ( x ) = x998 + x 997 + . . . . + x + 1The reminder when P ( x ) is divided by Q ( x ) is


Ax + 1

B0

C1

Dx-1

Answer: Option B

Explanation:

Solution: ((x^999 x^998 ... x 1)^2-x^999)/(x^998 x^997 ... x 1)



=> ((x^999 x^998 ... x 1)^2-x^999)/(x^999 x^998 ... x 1)-x^999 or,



=>(x^998 ... x 2)^2-1/(x^998 ... x 2)-1 [taking x^999 as common and cancelling it]



we can now use the identity a^2-b^2=(a b)*(a-b)



using this we can see that p(x) is clearly divisible by q(x)



i.e. p(x)/q(x)= (x^999 x^998 ... x 1) x^999



so the remainder will be 0

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In this question, A^B means A raised to power B. If x^2*y*z < 0, then which one of the following statements must also be true?
I. yz < 0
II. z < 0
III. x < 0


AI only

BIII only

CI & II only

DNone of the above

Answer: Option A

Explanation:

Solution: x^2 will always be positive no matter whatever be the value of x



So to satisfy this condition x^2*y*z < 0 => yz<0 because x^2 will always be positive.

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What is the value of (222224*444445*222221+666668)/222222^2


A444444

B444447

C222224

D444222

Answer: Option B

Explanation:

Let 222222 =x now the expression becomes

(((x+2)*(2x+1)*(x-1)) (3x+2))/x^2

Now solve it by algebra multiplication,addition and division.



we will get 2x+3 i.e 444447

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