1. The Johnsons drove from their home to their cabin in the woods at an average speed of 75 mph. If they returned home later that weekend, what was their average speed for the entire trip to and from the cabin? (1) The trip back home took 30% longer than the trip to the cabin. (2) The distance from the Johnson's home to their cabin is 220 miles. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
Transcript
1. The Johnsons drove from their home to their cabin in thewoods at an average speed of 75 mph. If they returned homelater that weekend, what was their average speed for the entiretrip to and from the cabin?
(1) The trip back home took 30% longer than the trip to thecabin.
(2) The distance from the Johnson's home to their cabin is220 miles.
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
2. What is the remainder when is divided by 10?
(1) x is a multiple of 3.
(2) x is a multiple of 5.
A. Statement (1) by itself is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.
D. Either statement by itself is sufficient to answer thequestion.
E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.
3. A brick road has orange, blue, and purple bricks along itspath. In a single row of orange, blue, and purple bricks, everypurple brick is preceded immediately by an orange brick andevery orange brick is preceded immediately by a blue brick.What color is the 26th brick in the row?
(1) The 24th brick in the row is not orange.
(2) The 25th brick in the row is not blue.
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
4. If WXYZ is a trapezoid and WX is parallel to YZ, what is thearea of WXYZ?
(1) The height of the trapezoid is 7 inches.
(2) (WX) + 2(YZ) = 12
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
5. John has a platinum credit card with a certain spending limitand a special black card with three times the spending limit ofthe platinum card. Currently, he has a balance on his platinum
card that is of its spending limit, and he has a balance on
his special black card that is of its spending limit. If John
transfers the entire balance on his platinum card to his specialblack card, what portion of his limit on the special black card willremain unused?
A.
B.
C.
D.
E.
6. Chris started his trip to work by leaving his house andwalking to the bus stop at a constant rate of x miles per hour.
After reaching the bus stop, which is the total distance to his
work, Chris got on a bus that travels at a constant y miles perhour for the remainder of the trip. If it took Chris t hours to reachhis work, how many miles is Chris's work from where he lives?
A.
B.
C.
D. 3x(y + t) + 2y(x + t)
E.
7. Is x negative?
(1) x 2 is a positive number.
(2) x |y| is not a positive number.
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
8. If the sides of a triangle have lengths x, y, and z, x + y =30, and y + z = 20, then which of the following could be theperimeter of the triangle?
I. 28II. 36III. 42
A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III
9. The ACME company manufactured x brooms per month fromJanuary to April, inclusive. At the beginning of production onJanuary 1, ACME had no brooms in its inventory. On the first ofeach month, during the following May to December, inclusive, it
sold brooms. If storage costs were $1 per month per broom,
approximately how much, in terms of x, did the ACME companypay for storage from May 2 to December 31, inclusive?
A. $x
B. $3x
C. $4x
D. $5x
E. $14x
10. Miguel is baking a cake. The cake mix recipe calls for of
the total weight to be milk, to be butter, and the remainder
to be an even mixture of nuts and spices. If Miguel accidentallydoubles the butter and forgets the mixture of nuts and spicesaltogether, what proportion of the botched cake mix would bemilk?
A.
B.
C.
D.
E.
11. The circular base of a planter sits on a level lawn, and justtouches two straight garden walls at points W and Y. The wallscome together at point X, which is 15 inches from the center ofthe planter. What is the area of the base of the planter?
(1) Both points Y and W are 9 inches from the center of theplanter.
(2) Point W is 12 inches from point X.
A. Statement (1) by itself is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.
D. Either statement by itself is sufficient to answer thequestion.
E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.
12. By approximately what percent is x greater than if
?
A. 34
B. 49
C. 58
D. 66
E. 78
13. If the Board of Selectmen contains 4 positions, and if in thecurrent election two candidates are running for each position,how many different combinations of candidates could beelected to the Board?
A. 6
B. 8
C. 12
D. 16
E. 24
14. A set of numbers contains 7 integers and has an average(arithmetic mean) value as well as a median value of 23. If thelargest value is equal to 15 more than 4 times the smallestnumber, what is the largest possible range for the numbers inthe set?
A. 33
B. 35
C. 38
D. 48
E. 75
15. A summer camp has 25 children enrolled in its golf class,25 children enrolled in its tennis class, and 8 children enrolledin both classes. If all the children in the summer camp areparticipating in at least one of the two classes, how manychildren are enrolled in only one of the two classes?
A. 33
B. 34
C. 38
D. 40
E. 42
16. What is the average of p, q, and r?
(1) p + 3q - 2r = 5
(2) 4p + 2q + 7r = -5
A. Statement (1) by itself is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.
D. Either statement by itself is sufficient to answer thequestion.
E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.
17. Jill jogs the 4 miles from her house to the park in 40 minutesand then she sprints back to her house along the same route at8 miles per hour. Jon also makes the same trip from Jill's houseto the park and back to her house, but he does so at half of Jill'saverage speed. How many hours does Jon spend on his totaltrip?
A. 2
B.
C.
D. 3
E. 4
Explanation:
18. In the figure above, points A, B, C, and D are evenly
spaced. If point A equals 217
and point C equals 49, what is the
value of point D?
A. 219
B. 217
C. 5(216
)
D. 3(216
)
E. 216
19. Which of the following must be true if the square root of X isa positive integer?
I. X has an even number of distinct factors.
II. X has an odd number of distinct factors.
III. The sum of X's distinct factors is odd.
A. I only
B. II only
C. I and III
D. II and III
E. I, II, and III
20. If two sides of a triangle are 12 and 8, which of the followingcould be the area of the triangle?
I. 35II. 48III. 56
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
21. What is the ratio of r to s?
(1) 2s =14
(2)
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
22. Is x 0?
(1) x - y -8
(2) x + y = -8
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though neitherstatement by itself is sufficient.
D. Either statement BY ITSELF is sufficient to answer thequestion.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
23. A certain property spent 3 years on the market. The priceof the property increased by 25% in the first year, decreased by50% in the second year, and then increased by 40% in the thirdyear. By how many dollars did the property's price decreaseduring the second year?
(1) The total decrease in the property's price over the first 2years was $10,000 more than the increase in the property'sprice during the third year.
(2) The price of the property at the end of the third year was$70,000.
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
24. If x and y are positive integers, which of the following must
be a factor of x if ?
A. 3
B. 6
C. 10
D. 11
E. 24
Explanation:
25. A fruit drink advertises that it has 5 percent apple juice.
Children pour themselves cup of this fruit drink and then add
another cup of fruit drink that has 50 percent apple juice.
Which is most nearly the percent of apple juice in the children'smixed drink?
A. 12.5%
B. 16.3%
C. 17.5%
D. 55.0%
E. 65.0%
26. If m = z5, is m 1?
(1) 3 - (y- x) x- (y- 3z)
(2) z 3
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
27. If , is z 8?
(1) x 4
(2) |y| 4
A. Statement (1) by itself is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) by itself is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) taken together are sufficient toanswer the question, even though neither statement byitself is sufficient.
D. Either statement by itself is sufficient to answer thequestion.
E. Statements (1) and (2) taken together are not sufficientto answer the question, requiring more data pertaining tothe problem.
28. If A is the average of B numbers, what is B?
(1) The sum of the B numbers is 211.5.
(2) A = 23.5
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
32. All but 50 of the 1,000 plants at the annual flower showwere sold. Of the plants sold, 30 percent were sold at adiscount of 25 percent off the full price, and the remainingplants were sold at the full price of $12. What was the totalrevenue from the plant sales?
A. $8,550
B. $8,835
C. $10,545
D. $11,100
E. $12,000
30. In the cube shown, the straight-line difference in lengthbetween points B and C, and points A and B is approximatelywhat fraction of the distance from A to C ?
A.
B.
C.
D.
E.
31. How many consecutive zeros will appear at the end of 43! ifthat number is expanded out to its final result?
A. 12
B. 11
C. 10
D. 9
E. 8
32. All but 50 of the 1,000 plants at the annual flower showwere sold. Of the plants sold, 30 percent were sold at adiscount of 25 percent off the full price, and the remainingplants were sold at the full price of $12. What was the totalrevenue from the plant sales?
A. $8,550
B. $8,835
C. $10,545
D. $11,100
E. $12,000
33. What is the ratio of s to t?
(1) 2s + t = 4
(2)
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
34. If it is true that -6 n 10, which of the following must betrue?
A. n 8
B. n = -6
C. n -8
D. -10 n 7
E. none of the above
35. Which of the following equations does not have at least onesolution?
A. (-3)-x = -3-x
B. (-3)x = (-3)-x
C. (-3)- x = -3x
D. 3-x = (-3)x
E. 3x = (-3)-x
36. Jason is doing his weekend chores so he can collect hisallowance. He needs to clean his room, mow the lawn, and puthis clothes in the dryer after the washer finishes. If the washeris currently running and has 30 minutes remaining in its cycle,can Jason complete all the tasks before his mom comes homein exactly one hour?
(1) Putting away the dishes will take Jason 33 minutes.
(2) Cleaning his room and mowing the lawn will take Jason20 minutes.
A. Statement (1) BY ITSELF is sufficient to answer thequestion, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer thequestion, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER aresufficient to answer the question, even though NEITHERstatement BY ITSELF is sufficient.
D. EITHER statement BY ITSELF is sufficient to answerthe question.
E. Statements (1) and (2) TAKEN TOGETHER are NOTsufficient to answer the question, requiring more datapertaining to the problem.
