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# Arithmetic Aptitude :: Simplification

Home > Arithmetic Aptitude > Simplification > General Questions

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21. 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

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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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22. 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

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

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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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24. What is the unit's digit of 21^3 *21^2*34^7*46^8*77^8 ?

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Explanation:

Here is no explanation for this answer

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25. What is the value of ( (x^2012 + x^2011 +.........+ x+1)^2 - x^2012) / (x^2011 +x^2010..........+x+1)

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Explanation:

Here is no explanation for this answer

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26. If pq=28 where p and q are whole numbers then which of the following will be (p2 - q2)?

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Explanation:

Solution: pq=28

So possible factors of 28 are (1,28) (7,4) (14,2)

Now going for option verification with the factors we get 28^2-1^2 = 783 hence option c is the answer.

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27. what is vale of a if a is integer?
1. a^4=1
2. a^3+1=0

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Explanation:

a^3+1=0=> a^3=-1

if a^3 is -1 then a must be (-1)^3=-1
(-1)^4 = 1
=> a=-1.

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28. 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:

2^a = 2*2 + a ......(i)
=> a^3 = 2*a + 3 .....(ii)
=> 4 + a = 2a + 3
=> a=1.

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29. Company A rented a truck \$1000 per month. company B purchased the same type of truck for \$35000.in addition company B paid \$120 monthly maintenance charges. What is relative cost to the competing company for this type of truck after 6 years of operation.

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Explanation:

A's total cost to be spent for 6 years= 6*12*1000 = Rs 72,000
B's total cost + monthly maintenance = 35000+(6*12*120) = Rs 43,640
Relative cost= 72000-43640
= Rs. 28,360

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30. As a mean encouraging company employee to use public transportation,employee is offer a \$0.60 per side discount bus fare. John has spend \$30000 per week from monday to friday.How much cost pay after the discount?

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Explanation:

Employee is offered discount per side = \$0.60.
So both side total disccount = \$0.60*2 = \$1.20
So, for 5 days = 1.20*5= \$6
Total amout = (30000-6) = \$29994

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