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Question 1: How many integers between 1 and 50 contain the digit 3?
Answer: 14
Explanation: There are 14 integers between 1 and 50 that contain
the digit 3: 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43.
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Question 2: |2x + 1| = 3 |x + 5| = 6
What value of x satisfies both of the equations above?
Answer: 1
Explanation: Since |2x + 1| = 3, the value of 2x + 1 is either 3 or -3.
2x + 1 = 3
2x = 2
x = 1
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2x + 1 = -3
2x = -4
x = -2
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The two values of x that satisfy the first equation are 1 and -2.
Since |x + 5| = 6, the value of x + 5 is either 6 or -6.
x + 5 = 6
x = 1
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x + 1 = -6
x = -7
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The two values of x that satisfy the second equation are 1 and -6.
You are asked to find the value of x that satisfies both equations and that value is 1.
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Question 3: The length of rectangle B is 50% longer than the length of rectangle A and
the width of rectangle B is 50% shorter than the width of rectangle A. What is the ratio
between the area of rectangle B and the area of rectangle A?
Answer: .75
Explanation:
The area of rectangle A is AreaA = lA·wA
The area of rectangle B is AreaB = lB·wB = 1.5·lA·.5·wA = .75·lA·wA
The ratio between the area of rectangle B and the area of rectangle A is:
AreaB/AreaA = (.75·lA·wA)/(lA·wA) = .75
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Question 4: If a§b = ab + ba for all real numbers a,b, what is (2§3)§1?
Answer: 18
Explanation:
2§3 = 23 + 32 = 8 + 9 = 17
17§1 = 171 + 117 = 17 + 1 = 18
In conclusion, (2§3)§1 = 18
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Question 5: What is the value of the x + y sum, if x + 2y = 5 and 2x + y = 7 ?
Answer: 4
Explanation:
The easiest way to find x + y is to realize that by adding
the 2 equations, the left term of the addition is a multiple of x + y:
3(x + y) = 12
x + y = 4
You can also solve the system of 2 equations, find x and y and add them,
but this will likely take longer.
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Question 6: If AC and BD are the diagonals of the ABCD rectangle and EAB is equilateral,
what is the value of angle ADE?
Answer: 30o
Explanation:
Rectangles have parallel opposite sides so AD and BC are parallel.
The BD diagonal produces congruent angles: angle ADE is equal to angle CBD.
ABCD is a rectangle so angle ABC is 90o.
ABE is equilateral so angle ABE is 60o.
Angle ADE = Angle CBD = Angle ABC - Angle ABD = 90o - 60o = 30o
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Question 7: The average of a set of 11 numbers is 11. If two numbers are removed
the average of the remaining numbers is 10. What is the sum of the two numbers removed?
Answer: 31
Explanation:
The average of the 11 numbers is equal with the sum of the numbers divided by 11.
11 = (sum of 11 numbers)/11
Sum of 11 numbers = 11·11
Sum of 11 numbers = 121
If x and y are the 2 numbers removed,
[(Sum of 11 numbers) - x - y]/9 = 10
[121 - x - y] = 10·9
[121 - x - y] = 90
x + y = 121 - 90
x + y = 31
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Question 8: Last year, the price of a computer monitor was $300.What is the percent increase in price,
if it is available now at $360?
Answer: 20%
Explanation:
The percent increase in price is the actual change in price,
divided by the original price, and multiplied by 100.
($360 - $300)·100/$300 = 20%
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Question 9: In the x, y plane, what is the area of the triangle created by the x axis, the y axis and the y = (-5/4)x + 5 line?
Answer: 10
Explanation:
y = (-5/4)x + 5 intersects the y axis at x = 0 and y = 5
y = (-5/4)x + 5 intersects the x axis at y = 0 and x = 4
The triangle created by the x axis, the y axis and the y = (-5/4)x + 5 line is a right triangle.
The area of the triangle is A = (1/2)·4·5 = 10.
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Question 10: If a coin is flipped twice, what is the probability that it will land heads at least once?
Answer: .75
Explanation:
The 4 possible combinations are (heads,heads), (heads,tails), (tails,heads) and (tails,tails).
Three of these four combinations satisfy the conditions that the coin lands heads at least once.
The probability is 3/4 = .75.
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