ARITHMETIC PRACTICE PROBLEMS WITH SOLUTIONS

Question 1 :

If u^-4  =  16, what is one possible value of u ?

(A) 4       (B) 2       (C) 1       (D) 1/2       (E) 1/4

Answer :

u^-4  =  16

u  =  16^-1/4

=  (1/16)^1/4

=  1/(16)^1/4

=  1/(2⁴)^1/4

=  1/2

Question 2 :

If a kilogram is equal to approximately 2.2 pounds, which of the following is the best approximation of the number of kilograms in one pound ?

(A) 11/5     (B) 5/8     (C) 5/11     (D) 1/3     (E) 1/5

Answer :

To get rid of decimals in a fraction, multiply the top and bottom by the smaller power of 10 we can.

If you need to move a decimal over 2 places, multiply the top and bottom by 100.

1 kilogram/2.2 pounds  =  x kilograms/1 pound

x  =  1/2.2

=  10/22

=  5/11

Question 3 :

If r is positive, and p is negative, which of the following must be negative ?

(A) rp + 2     (B) -|rp|     (C) r²p² - 10

(D) -(r + p)²     (E) (r + p)³

Answer :

Let us take option B, -|rp|

By multiplying positive and negative number, we get negative number. But the negative is in absolute sign, the answer will be positive.

In front of |rp|, we have negative sign. So the final answer will always be negative.

Question 4 :

If a is a positive integer, then what is the value of 5^a + 5^{a + 1} ?

(A) 6^a    (B) 5^a - 1    (C) 5^2a + 1    (D) (5^a)^a - 1    (E)  6(5^a)

Answer :

  =  5^a + 5^{a + 1}

  =  5^a + 5^a ⋅ 5

  =  5^a(1 + 5)

  =  5^a ⋅ 6

  =  6⋅5^a

Question 5 :

X, Y and Z are points on a line in that order. XY is 20, and YZ is 15 more than XY. What is XZ ?

(A) 25       (B) 35       (C) 45       (D) 55       (E) 65

Answer :

XY  =  20

YZ  =  15 + 20  =  35

From this, we come to know that Y lies between X and Z

XZ  =  XY + YZ

  =  20 + 35

  =  55

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