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Arithmetic Aptitude :: Simplification

Home > Arithmetic Aptitude > Simplification > General Questions

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

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Answer: Option D

Explanation:

Here is no explanation for this answer

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12. If 2x-y=4 then 6x-3y=?

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Answer: Option B

Explanation:

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13. If x2 < 1/100 and x< 0, What is the tightest range in which x can lie?

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Answer: Option A

Explanation:

Given x2 < 1/100
so, x < 1/10 or x > - 1/10 first statement
also, as per question x < 0 second statement
so, intersection of both statement will be
- 1/10 < x < 0

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14. If A=2/3(B-C) and C=1/2(A+B) and A+B+C=3000, then find C ?

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Answer: Option B

Explanation:

Given, C=1/2(A+B) => 2C=A+B ---- (1)
3A = 2(B-C) ---------- (2)
and (A+B+C) = 3000 ------ (3)

so, by eq. (1) and (2)
3C = 3000
=> C = 1000

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

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Answer: Option C

Explanation:

Here is no explanation for this answer

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16. What is the simplified result of following the steps below in order?

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Answer: Option D

Explanation:

X2-X-6=0
(x-3)(X+2)=0
X=3,-2

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

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Answer: Option A

Explanation:

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

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18. If m^2+m^-2=23;then what is the value of m^3+m^-3?

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Answer: Option A

Explanation:

m^2+m^-2=23
=> (m + m^-1)^2 - 2 = 23
=> (m + m^-1) = 5

m^3+m^-3 = (m + m^-1)^3 - 3(m + m^-1) = 5^3 - 3*5 = 110

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

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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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20. Solution for XY(Z+1)-ZY = XY is

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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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