UC MATH 1A - Sample Section 2: Answers and Explanations

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Sample Section 2 Answers and Explanations 1 2 3 4 5 6 7 A A B C C C D equal If the average of 3 things is 7 the total is 3 7 21 21 a 2a 9 3a 9 and a 4 Therefore Quantity A is greater Divide both sides of the inequality by 3 to get 4 x 3y Quantity B must be less than 4 and thus less than Quantity A Follow the dotted lines r corresponds to the x coordinate 5 and s corresponds to the y coordinate 3 5 Quantity B is greater than Quantity A Try rearranging the problem If then Hence AB A 78 7 and A B 15 The quantities are For Quantity A substitute the numbers provided in the question for the variables in the function 10 7 3 3 Quantity B is 3 The quantities are equal The company sold 300 2 150 of Product B The remainder A C 150 Since Quantity B is a number try plugging it in to the problem for Product A If A 100 then C 50 the quantities are equal Plug in 1 for z Quantity A is and Quantity B is Quantity B is greater so eliminate A and C Plug in 1 for z Quantity A is and Quantity B is Quantity A is closer to 0 and thus is greater Eliminate B and select D since different numbers gave different answers 8 B 9 B The probability that the flower is red is so the probability that it is not red is 1 Quantity A is The probability that the flower is not yellow equals the probability that it is red the probability that it is blue 40 Quantity B is and is greater Start by assuming that arc AB is equal to arc BD even though the problem states that they cannot be equal It s often helpful to evaluate a limiting case when solving a math question That s particularly true with Quantitative Comparison questions Because arc BD is equal to arc AC all three arcs are equal AB AC BD Next draw lines AO and BO These lines which are radii of the semicircle create three central angles AOC AOB and BOD Because AB AB BD the three central angles have equal degree measures AOC AOB BOD 60 Consider triangle AOB which was created by drawing the two radii This triangle is an equilateral triangle because OA OB and hence the remaining 120 must be split equally between angles OAB and OBA Because triangle AOB is equilateral OA OB AB r where r is the radius of the semicircle Then because CD is the diameter of the semicircle CD 2r So Quantity A is Now consider the restriction stipulated in the problem that AB BD For that to be true the degree measure of central angle AOB 60 When AOB 60 the length of AB r For example AB could be r Then Quantity A is Quantity B is greater whenever AB BD The correct answer is B 10 11 E D 12 A and D 13 D 14 B You are given a value for each of the variables If you put these values directly into 4 a 4 b you get 4 4 4 4 8 4 4 8 8 64 If the average of 2 numbers is 35 the total is 2 35 70 Plug In for k and let k 20 You get 70 20 50 the other number and the target answer Go to the answer choices and Plug In 20 for k Only D matches your target of 50 If x is 100 then Alejandro found 25 of 100 25 instead of increasing 100 by 25 to 125 The question asks what Alejandro could do to turn 25 into 125 If he adds x this will work because 25 100 125 or in math terms 0 25x 1x 1 25x Multiplying by x will not work because 25 100 2 500 not 125 Dividing by 0 25 will not work because 25 0 25 100 not 125 Multiplying by 5 works because 25 5 125 Use the Ratio Box Fill in that the ratio of x to y is 6 to 7 Fill in that the actual value of x is 15 The multiplier is Use this multiplier to find y 7 17 5 Plug In If b 2 c 3 and a 4 then x 20 The question asks for the value of b so the target answer is 2 Plug c 3 a 4 and x 20 into all the answers to find the answer that yields 2 Choice A yields a fraction not 2 Choice B yields 3 2 so keep this answer Estimate that C and D are larger than 2 Choice E yields 8 not 2 Choice B is the only choice that yields the target answer Notice that the exact same numbers appear in the numerator and denominator of the fraction Since it doesn t matter in what order you add quantities the numerator and denominator of the fraction are the same You don t even have to add it up The answer is 1 because a nonzero number divided by itself is 1 You could multiply 6 by 17 and start dividing the answer choices by the result but there s an easier way Because 6 3 2 the correct answer must be a multiple of 2 Eliminate C because it s odd Next the correct answer is a multiple of 3 To check to see which numbers are multiples of 3 add their digits and check to see if the sum is a multiple of 3 For example A is 6 8 14 which is not a multiple of 3 Eliminate A You can also eliminate D this way Try dividing B by 17 Since you don t get an integer that leaves only E There are 180 in a triangle so you know that 2x 3x 4x 180 Solve for x 9x 180 and x 20 The smallest angle is 40 the middle angle is 60 and the largest angle is 80 The sum of the smallest and largest angles is 120 or D You know only the sum of the two prices 8a b 8b a 135 cents or 9a 9b 135 You could simplify this by dividing by 9 to get a b 15 However you cannot determine the values of a and b individually nor their values relative to each other For example try a 5 and b 10 and then try a 10 and b 5 Different outcomes are possible so the answer is D Work with numerical portion of the square root first Eliminate A B and C Next work with the variable If you are struggling with exponent rules you can expand it out x4 So y 0 6 x4 Notice that x2 2xy y2 25 is a quadratic equation The question asks for x y 3 The first step is to factor x2 2xy y2 25 It becomes x y x y 25 Therefore x y 5 Since you know that x y could …


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