SSAT : Quantitative Section
Test 6
Following each problem in this section, there are five suggested answers. Work each problem in your head or in the blank space provided at the right of the page. Then look at the five suggested answers and decide which one is best.
Note: Figures that accompany problems in this section are drawn as accurately as possible EXCEPT when it is stated in a specific problem that its figure is not drawn to scale.
[start-test type=10 col=1 line-height=3]
[question text="An arithmetic sequence begins as follows: −128, −124.7, ... Which of the following terms is the first positive term in the sequence? " answers="*The fortieth term#The thirty-eighth term#The sequence has no positive terms#The thirty-seventh term#The thirty-ninth term "]
[question text="Three consecutive integers have a sum of 312. What is their product? " answers="1,190,910#1,092,624#*1,124,760#No three consecutive integers have sum 312#1,157,520 "]
[question text="Simplify: $\frac{\frac23+\frac15}{\frac45}$ " answers="*$\frac{13}{12}$#$\frac15$#$\frac3{10}$#$\frac{52}{75}$#$\frac37$ "]
[question text="Simplify and express as a decimal: $\frac{4\frac23}{5\frac35}$ " answers="*$0.8\overline{3}$#$0.875$#$0.9$#$0.8$#$0.\overline{8}$ "]
[question text="In a small school, ninth grade comprises 50 students, including 18 boys. Each student is assigned to one of two home rooms - those of Mr. Jones and Mrs. Wilson. The boys and the girls are both divided evenly between the home rooms. According to the charter, two of the student council representatives from the ninth grade will be selected by choosing one at random from each home room. What are the odds of one boy and one girl being selected? " answers="481 to 144 against#481 to 144 in favor#*337 to 288 against#Even#337 to 288 in favor "]
[question text="Three fair six-sided dice are rolled, and the numbers are added. What is the probability that the sum will be 16 or greater? " answers="$\frac{11}{216}$#*$\frac5{108}$#$\frac9{216}$#$\frac1{18}$#$\frac1{27}$ "]
[question text="Estimate the result $8.19×4.87+3.27×7.42$ by first rounding each number to the nearest unit. " answers="$64$#$53$#$56$#*$61$#$77$ "]
[question text="K and L are prime integers. $35<K<45$ and $85<L<95$. What is the greatest possible value of $K+L$ ? " answers="$136$#*$132$#$128$#$134$#$130$ "]
[question text="Simplify by rationalizing the denominator: $\frac{16}{4-\sqrt{6}}$ " answers="$\frac{32-8\sqrt{6}}{5}$#$\frac{32-8\sqrt{6}}{11}$#$\frac{32+8\sqrt{6}}{11}$#$-32-8\sqrt{6}$#*$\frac{32+8\sqrt{6}}{5}$ "]
[question text="Candidate A gets $\frac27$ of the votes in an election. Candidate B gets $35%$ of the votes. If $2.8$ million people votes, how many more votes than Candidate A did Candidate B receive? " answers="$150,000$#$225,000$#*$180,000$#$120,000$#$360,000$ "]
[question text="Joe drove an average of 45 miles per hour along a 60-mile stretch of highway, then an average of 60 miles per hour along a 30-mile stretch of highway. What was his average speed, to the nearest mile per hour? " answers="$53$mph#*$49$mph#$55$mph#$52$mph#$46$mph "]
[question text="Melissa is trying to come up with a reasonable estimate of the amount she spent on groceries over the last six months. She notices that the six checks she wrote out to the local grocery store are in the following amounts: €187.54, €218.89, €174.74, €104.76, €189.75, and €228.64. By estimating each of the amounts of the checks to the nearest ten dollars, come up with a reasonable estimate for Melissa's total expenditure for groceries. " answers="€$1,120$#*€$1,100$#€$1,130$#€$1,110$#€$1,090$"]
[question text="Which of the following is one more than $\frac{34}7$ ? " answers="*$5\frac67$#$5\frac47$#$6\frac17$#$5\frac27$#$5$ "]
[question text="A right cone has a volume of 8π, a height of 3t and a radius of the circular base of 2t. Find t. " answers="$2\sqrt[3&rb{2}$#$\sqrt[3&rb{3}$#*$\sqrt{2}$#$\sqrt[3&rb{2}$#$2$ "]
[question text="What is the volume of a cube with surface area N? " answers="$6N\sqrt{N}$#*$\frac{N\sqrt{6N}}{36}$#$6\sqrt[3&rb{N^2}$#$\frac{N^3}{216}$#$\frac{N^3}{36}$ "]
[question text='What is the perimeter of the above parallelogram if BD=24? 
' answers="$24 + 24\sqrt{3}$#*$48\sqrt{3}$#$48\sqrt{2}$#$32 + 16\sqrt{3}$#$24 + 24\sqrt{2}$ "]
[question text='Refer to the diagram. $45°≤m∠1≤50°$, $60°≤m∠2≤70°$ . Which of the following could be a measure of $∠3$ ? 
' answers="$130°$#$100°$#$125°$#*$110°$#All of the other choices give a possible measure of $∠3$ "]
[question text="Which of the following lines is perpendicular to the line $3x−5y=11$ ?" answers="*$9y+15x−54=0$#$3y−5x=−3$#$3x+5y=−11$#$10y−6x+5=0$#$5y+3x=2$ "]
[question text="Line A has equation $5x−7y=20$. Line B has equation $7x−5y=32$. Which statement is true of the two lines? " answers="*The lines are different but neither parallel nor perpendicular#None of the other four statements are true#The lines are identical#The lines are parallel#The lines are perpendicular "]
[question text="Which of the following points is on both the line $y=3x−2$ and the line $\frac{1}{2}{y}+3x=17$ " answers="$(6, 16)$#$(1, 1)$#*$(4, 10)$#$(6, -2)$#$(3, 16)$ "]
[question text="On the coordinate plane, $M$ is the midpoint of $\overline{AB}$ and $N$ is the midpoint of $\overline{AM}$. A has coordinates $(288, 108)$ and $N$ has coordinates $(176, 300)$. What is the x-coordinate of $B$. " answers="$736$#$204$#$116$#*$-160$#684 "]
[question text="The length and width of a rectangle are $x+16$ and $2x−7$. What is its perimeter in terms of $x$? " answers="$6x+46$#*$6x+18$#$2{x}^2+25x−112$#$2{x}^2−25x−112$#$3x+9$ "]
[question text="A rectangle has the width of $t−1$ and the diagonal length of $t+1$. What is the area of the rectangle in terms of $t$? " answers="$\sqrt{t}(t+1)$#$4\sqrt{t}(t-1)$#$\sqrt{t}(t-1)$#$2\sqrt{t}(t+1)$#*$2\sqrt{t}(t-1)$ "]
[question text='What is the area of the figure in the diagram? 
' answers="$12π$#*$24π$#$16π$#$8π$#$6π$ "]
[question text="What is the area of a circle that circumscribes a $30−60−90$ triangle whose longer leg has length $11$? " answers="*$\frac{121π}{3}$#$242π$#$121π$#$\frac{484π}{3}$#$\frac{121π}{2}$" ]
[question text='Examine the Venn diagram on the right. The universal set $U$ is defined to be {$1,2,3,4...16$}, with each element placed in its correct region in the diagram. What is $\overline{A}$ $∪$ $\overline{B}$?
' answers="*{1,2,4,6,7,8,9,10,11,12,15,16}#{3,5,13,14}#{6,7,8,16}#{1,2,3,4,5,9,10,11,12,13,14,15}#{1,2,4,9,10,11,12,15} "]
[question text='
The Venn diagram on the right represents all of this years graduating seniors at Rockwell High School, the universal set U. A represents all of the students who are in the National Honor Society. B represents all of the students who became old enough to vote in the November 5 election during their senior year. C represents all of the students who enrolled in a French course during senior year. Cathy was inducted into the National Honor Society in her junior year, and is still a member. She turned 18 on January 4 during her senior year, and she is carrying a respectable B average in her schools third-year French course. If her name were to be written in the above diagram in the correct place, in which of the five numbered regions would her name fall? 
'answers="$4$#$3$#$5$#*$2$#$1$ "]
[question text='In the Venn diagram to the right, the universal set U is the set of Presidents of the United States. A represents the set of Presidents who were born after 1850. B represents the set of Presidents who were born in a state completely west of the Mississippi River. C represents the set of Presidents who served eight years or more. Which of the following Presidents would fall in the pink region? 
' answers="Richard M. Nixon, who was born on January 9, 1913 in California and resigned during his seventh year in office#Woodrow Wilson, who was born on December 28, 1856 in New Jersey and served eight years in office#Abraham Lincoln, who was born on February 12, 1809 in Kentucky and was shot to death during his fifth year in office#*Warren G. Harding, who was born on November 2, 1865 in Ohio and died during his third year in office#Ronald Reagan, who was born on February 6, 1911 in Illinois and served eight years in office "]
[question text='The table illustrates an annual income tax amount for single persons in a given state. Grant earned 4,389 dollars per month over a one-year period in his regular job. He also claimed 1,736 dollars in interest income and 3,781 dollars in stock dividends. Based on the above table, how much income tax will he pay (nearest dollar)? 
' answers="$756#$519#$355#*$446#$236 "]
[question text="Ten balls - five green, three blue, two yellow - are placed in a hat. Two balls are drawn, one after the other, without replacement. What is the probability that at least one will be green? " answers="$\frac{2}{3}$#$\frac{1}{2}$#$1$#*$\frac{7}{9}$#$\frac{3}{4}$ "]
[question text="Two fair dice are rolled. What is the probability that at least one will show a 5 or a 6? " answers="$\frac{2}{3}$#$\frac{4}{9}$#$\frac{1}{3}$#*$\frac{5}{9}$#$\frac{1}{2}$ "]
[question text="The tens from one standard deck of playing cards are added to another deck, and a card is drawn at random from that second, modified deck. What is the probability that that card will be an ace, a two, or a three? " answers="$\frac{1}{4}$#$\frac{2}{7}$#$\frac{3}{13}$#*$\frac{3}{14}$#$\frac{4}{13}$ "]
[question text="John participates in a charity fundraiser in which he pays €1 to draw a card from a standard 52-card deck. If he draws the ace of spades, he wins €25; if he draws any other ace, he wins €5; if he draws any other card, he does not win. To the nearest cent, what is the expected value of the game to John? " answers="−€0.46#*−€0.23#€0#−€0.77#−€0.69 "]
[question text="A card is drawn at random from a standard 52-card deck. The person drawing wins if the card he draws is a two, a three, or a black four. What are the odds against drawing a winning card? " answers="43 to 9#10 to 3#23 to 3#*21 to 5#11 to 2 "]
[question text="Evaluate for $x=0.6$ : $|4x−1.4|+|{x}^2−1|$? " answers="*$1.64$#$0.64$#$0.36$#$2.36$#$1.36$ "]
[question text="Define an operation $▹$ as follows: For all real numbers a,b, $a▹b=∣a−\frac{1}{2}b∣+∣\frac{1}{2}a+b∣$. Evaluate $\frac{1}{3}▹4$. " answers="*$5\frac{5}{6}$#$1\frac{1}{2}$#None of the other responses are correct#$6\frac{1}{2}$#$2\frac{1}{2}$ "]
[question text="Barbara went to the store and bought a shirt for 88 dollars. It had been discounted by 20%. What is the original price of the shirt? " answers="$88#$70.40#$108#$17.60#*$110 "]
[question text='Examine the diagram on the right. What is $x+y$ ? 
' answers="*$125$#$145$#$99$#$135$#$89$ "]
[question text="What number replaces the circle? 1, 1, 2, 4, 6, 18, 21, 84, 88, ?, Ⓞ, ... " answers="440#465#357#*445#352 "]
[question text="Anya, Brian, Clark, and Donna represented Central High in a math contest. The team score is the sum of the three highest scores; Anya outscored Clark, Brian outscored Donna; Donna outscored Clark. Whose scores were added to determine the team score? " answers="*Anya, Brian, Donna#Brian, Donna, Clark#Anya, Brian, Clark#Anya, Clark, Donna#Insufficient information is given to answer the question "]
[question text="In the following number sequence, what number goes in place of the circle? 1, 9, 25, 49, 81, 121, ◯..." answers="144#196#*169#141#161 "]
[question text="${(0.75)}^2$ = " answers="*$\frac{9}{16}$#$5.85$#$58.5$#$49.5$##59.5$ "]
[question text="Express the result in scientific notation $(3\times10^{4})^{3}$ : " answers="$27\times10^{12}$#$9\times10^{7}$#*$2.7\times10^{13}$#$9\times10^{12}$#$2.7\times10^{8}$ "]
[question text="Express the result in scientific notation $\frac{1}{2.5\times10^{5}}$ : " answers="$-2.5\times10^{-5}$#$4\times10^{-4}$#*$4\times10^{-6}$#$2.5\times10^{-5}$#$4\times10^{-5}$ "]
[question text="Assume all variables to be nonzero. Simplify: $6(xyz)^0+4(xyz)^0$ " answers="$10xyz$#$24xyz$#$0$#*$10$#$2$ "]
[question text="Define an operation ? as follows : for all real numbers a,b $a ? b = \frac{a+1}{|a| +|b|}$. Evaluate: $\frac45 ? (-\frac45)$ " answers="The expression is undefined#None of the other responses is correct#*$1\frac18$#$\frac58$#$0$ "]
[question text="Define $f(x)=|3x−|x^2−7||$. Evaluate $f(2)$ " answers="$9$#*$3$#None of the other responses is correct#$5$#$17$ "]
[question text="Simplify : $(8-3i)^2$ " answers="$55$#$73$#$73−48i$#*$55−48i$#$55+48i$ "]
[question text='The picture represents a Venn diagram. The universal set U is the set of all positive integers. Let A represent the set of multiples of 7; let B represent all of the multiples of 11; let C represent all of the multiples of 13. As you can see, the three sets divide the universal set into eight regions. Suppose each positive integer was placed in the correct region. Which of the following numbers would be in the same region as 2,431? 
' answers="2,772#*2,145#3,081#2,409#2,184 "]
[question text='Refer to the graph. Which of the following comes closest to the percent of increase in population enjoyed by Jones City between 1900 and 1950? 
' answers="80% increase#40% increase#100% increase#*60% increase#20% increase "]
[end-test]