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# Arithmetic Aptitude :: Simplification

Home > Arithmetic Aptitude > Simplification > General Questions

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81. [6/4 + 4/9] of 3/4 divide 5/3 * 5/4 - 1/3

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Explanation:

[6/4 + 4/9 ] of 3/4 divides 5/3 *5/4-1/3
=[35/18] of 3/4 divides 25/12-1/3
=35/24 divides 21/12
=35/24/21/12
=35/24*12/21
=5/6

Workspace

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82. If 13 = 13w/(1-w) ,then (2w)2 =

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Explanation:

13 = 13w/(1-w)  solving this we get w=1/2

now finding the value of the square of 2w that is 1

Workspace

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83. If the operation,^ is defined by the equation x ^ y = 2x + y,what is the value of a in 2 ^ a = a ^ 3

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Explanation:

Solution:  2 ^ a = a ^ 3  => 2*2 a  = a*a 3   =>  4 a= a2 3

Solving we get a=1 and a=-1

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84. Q is not equal to zero and k = (Q * n - s)/2.What is n?

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Explanation:

Solution:  k = (Q * n - s)/2  Make n the subject of formula

2k=  (Q * n - s)  ⇒  2k s  = Q *n

n= (2k s)/Q

Workspace

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85. If a=2, b=3, c=6
Find the value of c/(a+b)-(a+b)/c

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Explanation:

6/(2+3)-(2+3)/6
=6/5-5/6
=(36-25)/30
=11/30

Workspace

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86. 3/p = 6,3/q = 15.

Find p-q.

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Explanation:

p= 3/6 =1/2
q= 3/15 =1/5
p-q= (1/2) - (1/5)
p-q= 3/10

Workspace

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87. If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?

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Explanation:

Solution: 9x-3y= 12 ⇒y=3x-4
Putting this value in 3x-5y=7 ⇒ 3x- 5(3x-4)=7 ⇒  3x-15x 20=7  ⇒ 13=12x  ⇒x=13/12

Therefore y= -3/4

Putting value of x and y in the equation 6x-2y we get answer as 8.

Workspace

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88. Find the last digit of the following expression:
4+9^2+4^3+9^4+4^5+9^6+....+9^100

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Explanation:

Last digit of 4^1 = 4 ; 4^3 = 4 ; 4^5= 4....
So, 99 = 1+(n-1)*2 n = 50 i.e. 4+4+4....50 times i.e. 4*50 = 200 (last digit 0)
Similarly, last digit of 9^2=1 ; 9^4 = 1....
So, 100 = 2+(n-1)*2 n=50 i.e. 9+9+9+....50 times i.e. 9*50 = 450 (last digit 0)
So, 200+450 = 650 i.e. last digit is '0'.

Workspace

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89. What is the unit digit of(2^3)^123456

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Explanation:

(2^3^)^123456=2^3*123456=2^370368
2 cycle size=4
so,370368/4=remainder(0)
2 unit values=2,4,8,6
so,ans is 6

Workspace

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90. A number 2088 by what if we divide the number it will become a perfect square?

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