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OG17 OG18 OG19 OG20 OG2022
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A certain experimental mathematics program was tried out in 2 classes in each of 32 elementary schools and involved 37 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
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OG17
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 In the fugure above, what is the value of z ?(1) x = y = 1(2) w = 2
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PREP07 Test 1
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Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z ?(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.(2) More than half of the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.
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PREP07 Test 1
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Is x > y ? (1) x + y < 0(2) x - y > 0
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PREP07 Test 1
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Is m + z > 0 ? (1) m - 3z > 0(2) 4z - m > 0
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PREP07 Test 1
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This morning, a certain sugar container was full. Since then some of the sugar from this container was used to make cookies. If no other sugar was removed from or added to the container, by what percent did the amount of sugar in the container decrease?(1) The amount of sugar in the container after making the cookies would need to be increased by 30 percent to fill the container.(2) Six cups of sugar from the container were used to make the cookies.
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PREP07 Test 1
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If a and b are positive numbers, what are the coordinates of the midpoint of line segment CD in the xy-plane?(1) The coordinates of C are (a, 1 - b).(2) The coordinates of D are (1 - a, b).
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PREP07 Test 1
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If the sum of three different numbers is 54, what is the largest number?(1) The largest number is twice the smallest number.(2) The sum of the two smaller numbers is 30.
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PREP07 Test 2
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If x, y, and z are integers, is x + y + 2z even?(1) x + z is even.(2) y + z is even.
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PREP07 Test 2
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Each of the 105 students in a certain club is either a freshman, a sophomore, or a junior. How many of the students in the club are sophomores?(1) The ratio of the number of freshmen to the number of sophomores is 1 to 2.
(2) The ratio of the number of freshmen to the number of juniors is 1 to 4.
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PREP07 Test 2
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What is the value of the positive integer m ?(1) When m is divided by 6, the remainder is 3. (2) When 15 is divided by m, the remainder is 6.
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PREP07 Test 2
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Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday? (1) Last week Store S sold 8 copies of the book on Thursday. (2) Last week Store S sold 38 copies of the book on Saturday.
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PREP07 Test 2
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Are the two nonzero integers x and y on opposite sides of 0 on the number line?(1) The sum of x and y is 0.
(2) The product of x and y is less than 0.
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PREP07 Test 2
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One member of a committee of 5 men and 8 women resigned and was not replaced. What fraction of the remaining members were men? (1) 7 of the 12 remaining members were women. (2) The member who resigned was a woman.
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PREP07 Test 2
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Is the positive integer n odd?(1) n = 2k + 1, where k is a positive integer.(2) 2n + 1 is an odd integer.
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PREP07 Test 2
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If a wire 27 meters long is cut into three pieces of three different lengths, what is the length of the longest piece? (1) The length of the longest piece is twice the length of the shortest piece. (2) The sum of the lengths of the two shorter pieces is 15 meters.
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PREP07 Test 2
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If ax + b = 0, is x > 0 ? (1) a + b > 0 (2) a - b > 0
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PREP07 Test 2
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Are the integers z and f to the right of 0 on the number line? (1) The product of z and f is positive. (2) The sum of z and f is positive.
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PREP07 Test 2
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If c and d are integers, is c even? (1) c(d + 1) is even. (2) (c + 2)(d + 4) is even.
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PREP07 Test 2
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There are two types of rolls on a counter, plain rolls and seeded rolls. What is the total number of rolls on the counter? (1) The ratio of the number of seeded rolls on the counter to the number of plain rolls on the counter is 1 to 5. (2) There are 16 more plain rolls than seeded rolls on the counter.
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