2016SHSAT_English

​Sample Test – MathematicsExplanations of Correct AnswersBForm72. (K) Since 714 is even, factor out a 2:77. (B) The formula for the circumference of a circle714 2 • 357. The sum of the digits of 357 isis C = 2rπ. Let f be the radius of the front tire15, so we know 357 is a multiple of 3:and b equal the radius of the back tire. Then714 2 • 3 • 119the circumference of the front tire would beFinally, 119 is divisible by 7, so2fπ and the circumference of the back tire714 2 • 3 • 7 • 17would be 2bπ.Since it takes the front tire 3 revolutions forevery 1 revolution of the back tire, the circumferenceof the back tire must be three times73. (A) Since R S is odd, then one of the two variables(R or S) must be odd and the other mustthe circumference of the front tire:be even. Similarly, since T – S is odd, one ofthe two variables must be odd and the other2bπ = 3(2fπ)must be even. Since S is common to bothb = 3fexpressions, if S is odd, then R and T are bothThus, the radius of the back tire (b) is 3 timeseven; and if S is even, both R and T are odd. Itlarger than the radius of the front tire (f).is not possible to determine which of the twopossibilities is true, so Options C, D, and E canbe eliminated as the correct answer.78. (G) First, calculate the three possible values of q:Option B (S T) can be eliminated because ifT – S is odd, then S T is also odd.If n 5 1, then q 5 ​ ___ 1​5 ​ 1__3 1 3 ​.Option A (R T) is the only possible answer.If R and T are both odd, then R T is even. IfIf n 5 2, then q 5 ​ ___ 1​ 5 ​ 1__3 2 9 ​.R and T are both even, then R T is even.If n 5 3, then q 5 ​ ___ 1​5 ​ ___ 13 3 27 ​.74. (J) Calculate the locations of points E and F onThe least value of r will occur when q is thethe number line using the midpoint formula:smallest (q 5 ___ 1 ​). So, the least possible value27Point E (point A point C) 2 ​ _______ 4 6​ 12of r is: r 5 3(​ ___ 127 ​) 1 2 5 ​ 1__9 ​ 1 2 5 2​ 1__9 ​Point F (point B point D) 2 ​ ________ 2 10​ 42Now calculate the length of ___79. (B) |(​ EF​: 4 – 1 3 units 6) – ( 5) 4| – |3 – 11| 5|3| – | 8 | 5 3 – 8 5 575. (C) Lily has a coupon for 30% off, which meansshe will pay 70% of the regular price80. (G) Create a proportion to calculate the total(100% 30% 70%). Lily will paynumber of gallons of paint used:$2.90 • 70% $2.03 for this bag of candy._______________Gallons of blueTo calculate the price per ounce, divide thetotal gallons ​ 5 ​ ______ 88 3 ​ 5 ​ __ 6x ​final price Lily pays by the number of ouncesin the bag:8x 6(11)$2.03 12 $0.16917, which rounds to $0.17x 8​1__4 ​ gallons76. (K) z – ​ __ 13 ​ z 5 1281. (D) Of the fractions listed in the options​2__3 ​ z 5 12__​ 1 2 ​, ​ 1__3 ​, ​ 1__4 ​, ​ 1__5 ​, and ​ 1__6 ​ , ​1__3 ​ and ​ 1__ ​are the only fractionsthat can be written as repeating deci-6z 5 ​ ___ 362 ​ 5 18 mals. Adding a non-repeating decimalto a repeating decimal will result in a104