This Much Then That Much Again
Mathematics:
Answers and Explanations
This page includes VERY detailed explanations of the math practice problems. If you had trouble answering some of the questions, take the time to review my explanations very advisedly. If you lot have answered any questions incorrectly, I recommend that you lot go back and make another attempt and so turn to this page again. You should do this until you can confidently complete all of the problems correctly.
Number Sense
1. A nswer C � 25%
Explanation � The first footstep in solving this problem is to subtract the old toll from the new toll,
which is $five.00 - $four.00 = $1.00. This means that the ticket price increased by $one.00. The next
step in solving this problem is to separate the price increment by the original price, so $one.00 should
be divided by $4.00, which equals 0.25. To find out what percentage this is, you must multiply
by 100%. The final respond is 0.25 X 100% = 25%.
2. Answer C � $48.00
Explanation � First, recollect to read the question carefully. The question asks for the interest
earned in three years. In order to solve this trouble you start past multiplying $200 by 8%. In guild
t o practise this you need to change 8% into a decimal number. This is found past dividing 8 past 100,
which gives you 0.08. Next, to discover 8% of $200, you multiply $200 X 0.08 = $16.00. Remember
the question asks for the interest gained in three years, so you need to multiply $16.00 X 3 = $48.00.
Statistics, Data Analysis, and Probability
1. Answer D � ane/2
Caption � Remember that each fourth dimension y'all flip the coin the result is independent any time you
flipped the coin before. Then the result of flipping a coin is Not dependent upon the previous flip.
If the chances of getting a tails is 50% the FIRST time that you flipped a coin, then the chances of
getting a tails is 50% EVERY time that you lot flipped the coin. Since 50% is the same as ane/2, the
right respond is D.
�
2. Respond C � How many male members of the order attended the coming together?
Explanation � Remember to read the question thoroughly and underline exactly what information technology is asking.
All the question tells u.s. is that out of 36 total members, 27 attended a meeting, and ten of those
were female. This question gives information about but those members of a club that attended a specific meeting, NOT all members of the gild. In order to answer questions A, B, and D, we
would need to know how many of the total members were male or how many were female person. In other words, we can only answer these questions if we know More than information than what was given.
This leaves simply answer C equally the right answer.
Measurement & Geometry
1. Answer D � 6 ft. half-dozen in. �
Explanation � This question tests your knowledge of conversion factors.� First you lot must figure out
how many inches are in 2 meters. In order to practice this you must multiply 39 inches by 2 which = 78 in.� Next yous detect out how many anxiety are in 78 inches. Given that in that location are 12 inches in 1 ft, you lot demand to divide 78 inches by 12 feet = half dozen.5, which is translated into 6 feet and five inches, but you do non have an respond that says six ft. v in.� The question asks about how alpine, which ways that this does not need
to be an exact reply, only a close approximation.� Answer D, 6 ft. half dozen in. is therefore the all-time answer. �
2. Answer D � 54 cm
Explanation � This is a proportion problem. The question is request for y'all to determine what the
length of an actual rectangle would exist if the width was 18 cm. A calibration drawing is representative of
the bodily rectangle, and then you can compare the proportions and observe the right reply. The width of
the scale cartoon is i.2 cm. The length of the scale drawing is 3.6 cm. The ratio of width to length
in the scale rectangle is 1.2 cm divided by 3.half dozen cm. Since the proportion of the scale drawing is the same as the proportion of the actual rectangle you tin compare the ratios directly using a variable
as a placeholder (let'due south call it X). That� means that 1.ii cm / three.6 cm = 18 cm / X (the placeholder). To
get the final pace completed, you can cross multiply, which gives you one.2X cm = �64.8 cm, and and so divide 64.8 cm by ane.two cm (to get the X by itself), which leaves you with 54 cm. Answer D is right.
Algebra and Functions
one. Answer D � 10-15+2y
Explanation � This question is request you understand how to translate a discussion problem into a mathematical expression.� When reading a word problem like this you have to be careful to include
all of the data given. The original weight of tea that the shopkeeper has in stock is denoted
past the letter x. Since the shopkeeper then sells some of the tea, y'all would then decrease the sold
weight (15 kg) from the original weight (x kg), which gives the states x - fifteen. Then the shopkeeper receives
a shipment from his supplier, which will add an amount to his stock. In this case the added weight
is denoted by the term 2y kg. So if we integrate all of this information into the mathematical
expression we get x kg (the original weight) minus 15 kg (the corporeality sold) plus 2y kg
(the amount received). This means that 10 - 15 + 2y = the weight of tea the shopkeeper now has
in stock, which is answer D. �
ii. Answer A � 12
Due east xplanation � With the data given in the problem, you can determine how many pages she
can read each day, this is chosen the charge per unit. The rate is 168 pages divided by 7 days = 24 pages per 24-hour interval. Using this rate you can observe out how long it volition accept her to read the unabridged 456 page book. This is 456 divided past 24 pages per twenty-four hours = 19 days total. The question asks "how many more days will it take her to terminate reading the volume?" At beginning it seems similar the answer is xix days, merely you must remember that she has already read for seven days, so xix - vii = 12 days, and the correct answer is A.
Math Reasoning
one. Reply B � It is an even number
Explanation � in lodge to answer this question correctly, yous demand some understanding of odd
and even numbers.� Recall that 1,3,5 etc. are odd numbers and 2,iv,vi etc. are even numbers.�
In gild to respond this question you demand to plug in an odd number for n and add 1 to information technology, as the expression n+one asks. For example, 1+ 1= two, 3 + 1 = 4, 5 + 1 = six, etc. Observe that each fourth dimension you lot
add together ane to an odd number, the sum is an fifty-fifty number. This means the right answer is B. You
can likewise figure out this problem through the process of elimination. Answer A is incorrect because,
every bit yous saw above, whatever odd number plus i equals an even number. Respond C is wrong because
in can be any number and therefore it is incommunicable to tell whether or non due north+ane would exist a prime. Answer D is wrong considering a number plus one cannot yield the same reply as that number minus ane (it defies the laws of add-on and subtraction).
2. Answer A � Dissever 100 by 2.5
Explanation � This question checks your agreement of two major mathematical concepts. The showtime is existence able to grasp the idea of rate. A rate is a measurement of an action done per unit time. For example, driving 60 miles per 60 minutes means that for every hour of driving, yous will have traveled 60 miles. The second concept is an understanding of fourth dimension segments. For example, 15 minutes is the aforementioned every bit 0.25 hours is the same every bit ane/iv 60 minutes; all of these terms are equal to each other. In this trouble you are expected to understand that xxx minutes is the aforementioned as 0.5 hours. The trouble explains that Chris drove 100 km in ii hours and 30 minutes. An understanding of rate tells you lot that the activity (driving 100 km) has the charge per unit of 100 km / ii hours and thirty minutes. The problem is simplified if you know that 2 hours and thirty minutes is equal to 2.5 hours. The correct reply then, is A, or 100 km / two.5 hours.
Algebra 1
1. Answer A � (0,4)
Explanation � Nosotros can test each pair of coordinates in the equation of 4x + 5y = 20 and encounter which set works the all-time.� Permit�due south showtime with answer D (5, 4) which indicates x is equal to 5 and Y is equal
to 4. Substituting those two numbers into the formula gives us: 4(5) + 5(four)= twenty + xx = 40, which
is not the correct respond. If nosotros try the fix from respond C (4,5), we get iv(iv) + 5(v)= sixteen + 25 = 41, which is also incorrect. The coordinates from set B are (0,5) give usa: 4(0) + 5 (5) = 25, which is as well incorrect. Fix A is the pair (0,4), which gives u.s.a. the correct answer when substituting into the formula like as follows: 4(0) + v(4) = twenty, correct!
2. Answer A � 4x+xx-3x-6=14
Explanation �The question is asking you lot to write out the expression 4(x+ 5) � iii(x+ 2)= fourteen in a different fashion. In order to exercise this you commencement need to multiply the 4 past (x + 5) using the distributive dominion of algebra, which gives y'all 4x + twenty.� Side by side you multiply �3 past (x + 2), once more using the distributive rule, which gives yous -3x -6. Y'all then put these terms together and grade the new equation, every bit shown in answer A: 4x+20-3x-6 = 14.
Source: https://www.sjsu.edu/faculty/chang/servlearn/vivtestpage/Answers%20to%20Math%20Problems.htm
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