Solutions with detailed explanations to compass math test practice questions in sample 12.

What is 1/3 of 300?
Solution
1/3 of 300 is mathematically translated as
1/3 × 300
Simplify
= 300 / 3 = 100

If 2/7 of x is equal to 6, then x =
Solution
"2/7 of x is equal to 6" is mathematically translated as
(2/7) × x = 6
Solve for x
2x = 42
x = 21

What is 15% of 45% of 1.4?
Solution
"15% of 45% of 1.4" is mathematically translated as
15%(45% × 1.4)
Simplify
= (15/100) × (45 / 100 × 1.4)
= (15 × 45 × 1.4) / 10,000
= 945 / 10,000
= 0.0945

What is 2/3 of 1/5 of 12,000?
Solution
"2/3 of 1/5 of 12,000" is mathematically translated as
(2/3)( 1/5 × 12,000) =
Simplify
(2/3)( 1/5 × 12,000) =
= (2/3)(12,000/5)
= (2/3)(2,400)
= 2 × 2,400 / 3
= 1,600

If x% of 23 is 9.2, then x =
Solution
"x% of 23 is 9.2" is mathematically translated as
(x%) × (23) = 9.2
Solve for x
(x / 100) × 23 = 9.2
23 x = 9.2 × 100
x = 40

On a 25 questions Math test, Peter got 60% of the 10 algebra questions correct, 80% of the 10 geometry questions correct and 60% of the 5 trigonometry questions correct. What percentage of all the questions did Peter get correct
Solution
60% of the 10 algebra questions correct
60% * 10 = 6
80% of the 10 geometry questions correct
80% * 10 = 8
60% of the 5 trigonometry questions correct
60% * 5 = 3
Total number of questions
6 + 8 + 3 = 17
Percentage of correct questions
17 / 25 = 0.68 = 68%

If 25% of y is x, then y =
Solution
"25% of y is x" is mathematically translated as
(25 / 100) y = x
Solve for y
25 y = 100 x
y = (100 x) / 25
y = 4x

What fraction subtracted from 1/2 + 4/5 gives 1?
Solution
Let x be the fraction to be subtracted. Hence
(1/2 + 4/5)  x = 1
Solve for x
x = (1/2 + 4/5)  1
x = (5/10 + 8/10)  10/10 = 3/10

One out of 5 of a group of students took a math test, 28% of the same group took a science test and the rest took a history test. What percent of students took a history test?
Solution
One out of 5 may be written as a fraction equal to
1/5
and in percent as
20%
So 20% took math and 28% took science. The percent of those who took history is
100%  20%  28% = 52% of students took history

If one fifth of y + 1 is equal to 2, then y + 2 =
Solution
"one fifth of y + 1 is equal to 2" is mathematically translated as
(1/5)(y + 1) = 2
Multiply both sides by 5
y + 1 = 10
y + 1 + 1 = 10 + 1
y + 2 = 11
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