2016SHSAT_English

Sample Test – MathematicsExplanations of Correct AnswersBForm90. (H) The left side of the given equation(xy 1 xz 5 100) must be rearranged to look like​x __ ​ (3y 1 3z) 1 10 to get the answer.5First, factor out the x: x (y 1 z) 5 100Next, multiply both sides of the equation by 3:3x (y 1 z) 5 3(100) x (3y 1 3z) 5 300Then, divide both sides by 5:​1 __5 ​ x (3y 1 3z) 5 ​ ____ 3005 ​ ​x __ ​ (3y 1 3z) 5 605Finally, add 10 to both sides:​x __ ​ (3y 1 3z) 1 10 5 705Now that the left side looks like the expressionin the question, the answer is the number onthe right side (70).91. (D) The volume of the container is10 10 10 1,000 cubic feet. Since it isalready half full at 9:00 a.m., it will beginto overflow after 500 cubic feet of water isadded to it.7 cubic feet of water are being added perminute, but 2 cubic feet of water leak out perminute. That means 7 – 2 5 cubic feet ofwater are being added to the tank each minute.500 cubic feet 5 cubic feet per minute 100 minutes100 minutes is equal to 1 hour 40 minutes.1 hour 40 minutes after 9:00 a.m. is 10:40 a.m.92. (G) Angle PQR and the marked 40° angle arevertical angles and thus are congruent, soangle PQR is 40°. Similarly, angle QRP is45° because it is a vertical angle with the onemarked 45°. Given those two angles, calculatethe third angle of triangle PQR (angle RPQ):40 1 45 1 RPQ 5 180RPQ 5 95Angle RPQ and angle x are supplementary,which means they sum to 180, sox 5 180 2 95 5 85.Similarly, angle y and angle QRP aresupplementary, so y 5 180 2 45 5 135.Thus, the value of y 2 x 5 135 2 85 5 5093. (A) Each chair costs Arnold $150 to make, and hesells the chair for $275. His profit is found bysubtracting the cost from the price:$275 $150 $125 per chairIf Arnold makes and sells 25 chairs in a week,his initial profit is 25 • $125 $3,125. However,Arnold has additional fixed expensesof $1,250 per week, so this cost must also besubtracted. Thus, his final profit is:$3,125 $1,250 $1,87594. (H) First, calculate the area of the entire lot:75 3 100 5 7,500 sq ftThere are 12 equal-sized squares, so eachsquare is equal to 7,500 ÷ 12 = 625 sq ft.From the figure, it appears the building(shaded region) covers 1 full square, 1 halfsquare,and 2 quarter-squares, for a total of2 full squares (1 1 ​1__2 ​ 1 2(​ 1__ ​) 5 2). Two full4squares are equal to 625 1 625 5 1,250 sq ft.To find the area that is not shaded, subtractthe area of the building from the area of theentire lot: 7,500 – 1,250 = 6,250 sq ft, whichrounds to 6,000 sq ft.Remember that the question asks you to findout about how many square feet and notexactly how many square feet.95. (B) To find the mean salary for all 12 employees,find the sum for each group. Thus, 4 peopleearned a total of $272,000 and 8 people earneda total of $376,000. Use the mean formula:648,000272,000 376,000 5 ​________​ $54,00012106