**Arithmetic Practice Problems With Solutions :**

Here we are going to see some practice questions of the math topic "Arithmetic".

To find question from 1 to 6, please visit the page "SHSAT Arithmetic Practice".

To find question from 7 to 10, please visit the page "SHSAT Arithmetic Practice Problems".

**Question 11 :**

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

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

**Solution :**

u^{-4} = 16

u^{-4} = 2^{4}

u^{4} = 1/2^{4}

u = 1/2

Hence the value of u is 1/2.

**Question 12 :**

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

**Solution :**

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

Hence the answer is 5/11.

**Question 13 :**

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

(A) rp + 2 (B) - |rp| (C) r^{2}p^{2} - 10

(D) -(r + p)^{2 } (E) (r + p)^{3}

**Solution :**

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 14 :**

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})

**Solution :**

= 5^{a} + 5^{a + 1}

= 5^{a} + 5^{a }⋅ 5

= 5^{a}(1 + 5)

= 5^{a}^{ }⋅ 6

= 6⋅5^{a}

**Question 15 :**

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

**Solution :**

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

Hence the answer is 55.

After having gone through the stuff given above, we hope that the students would have understood, "Arithmetic Practice Problems With Solutions".

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