1. If z = 25x125y, what is the value of z ? (1) y = 2 (2) 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. If z = 25x125y, what is the value of z ?
(1) y = 2
(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.
2. If n is an integer and , which of the
following could be the value of (n + 3)2?
A. -2
B. 1
C. 4
D. 11
E. 64
3. Is the positive integer z a prime number?
(1) z and the square root of integer y have the same numberof unique prime factors.
(2) z and the perfect square y have the same number ofunique factors.
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 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
5. On the Lamville Llamas baseball team last year, what wasthe average (arithmetic mean) number of home runs hit perplayer?
(1) Last July, home runs from the top 4 players accounted for80% of the team's homeruns, and the number of home runsfor these players was 48 per person.
(2) Last year, the Lamville Llamas had 20 players and hit atotal of 240 home runs.
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.
6.
Does line P (not pictured) intersect line segment QR in thecoordinate plane shown above?
(1) The slope of line P is -1.
(2) The equation of line P is y = -x + 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 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.
7. All but 50 of the 1,000 plants at the annual flower show weresold. Of the plants sold, 30 percent were sold at a discount of25 percent off the full price, and the remaining plants were soldat the full price of $12. What was the total revenue from theplant sales?
A. $8,550
B. $8,835
C. $10,545
D. $11,100
E. $12,000
8. During winter break, Johnny sells 3 types of waffles at the skiresort: plain, strawberry, and banana. Last week, the ratio ofplain to strawberry to banana waffles Johnny sold was 24:6:5.How many waffles did Johnny sell last week?
(1) Johnny sold 624 strawberry waffles.
(2) Johnny sold 4 times as many plain waffles as strawberrywaffles.
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.
9. Is a% of a% of b equal to a% less than b?
(1) b(b + 1) = 1
(2) a(a + 100) = 10,000
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.
10. The ACME company manufactured x brooms per monthfrom January to April, inclusive. At the beginning of productionon January 1, ACME had no brooms in its inventory. On thefirst of each 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 theACME company pay for storage from May 2 to December 31,inclusive?
A. $x
B. $3x
C. $4x
D. $5x
E. $14x
11. 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
12. Which of the following, when squared, will yield a value
greater than ?
A.
B. (.75)
2
C.
D.
E.
13. At the Butterfly Scout Cookie Chow Down, each girl wasgiven equal time to decorate as many cookies as possible. Ifthe winner took an average of 20 seconds to decorate eachcookie, how many cookies did the second-place finisherdecorate?
(1) The second-place finisher was only able to decorate athalf the rate of the winner.
(2) The winner decorated 15 more cookies than the second-place finisher.
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.
14. Bill owns a large collection of fishing lures consisting oftiny, small, medium, and large lures that weigh 1, 3, w, and 5grams each, respectively. The medium lures weigh more thanthe small lures but less than the large lures. If the product of thelure weights that Bill sold to his friend is 216,000 grams, howmany medium lures did he sell?
A. 6
B. 5
C. 4
D. 3
E. 2
15. Bobby walks 4 miles to school and then walks back homeagain along the same route every day at a constant rate of3 miles per hour. However, on the last day of school, Bobbywalks to school at his usual rate but then sprints back home ata constant rate of 6 miles per hour. On his last day of school,what is Bobby's average speed for the entire trip in miles perminute?
A.
B.
C.
D.
E.
16. 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.
17. Jim has arrived late for his golf tee time with his friends.When he arrives at the course, he discovers that his friendshave already walked 180 yards ahead on the course andthat they are continuing to walk forward at a rate of 1.5 yardsper second. A bystander with a golf cart takes pity on Jimand drives him to meet his friends at the rate of 4 yards persecond. Once Jim meets his friends, he exits the cart and walkswith them at their rate for the next 120 yards. What is Jim'sapproximate average speed for his total trip?
A. 1.8 yards per second
B. 2.0 yards per second
C. 2.4 yards per second
D. 2.7 yards per second
E. 3.0 yards per second
18. 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.
19. What is the units digit of z if (385a)(225b) = z, where a andb are positive integers?
(1) a = 3
(2) a + b = 11
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.
20. 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
21. 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
22. All the paralegals at the Zindler law firm support eitherthe family law attorneys, the estate planning attorneys, orboth the family law and estate planning attorneys. Seventypercent of the paralegals work in only one area of practice,and 121 paralegals work in family law only. If 55 percent ofthe paralegals are in family law only, how many work in estateplanning only?
A. 26
B. 30
C. 33
D. 55
E. 79
23. 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.
24. Dan and Craig stand back-to-back at point X. Dan beginsto rollerblade in a straight line away from Craig at a rate of 4miles per hour. Thirty minutes later, Craig begins to bicycle in astraight line in the exact opposite direction at a rate of 12 milesper hour. What is the positive difference, in hours, between theamount of time it takes Craig to cover the exact distance thatDan has covered and the amount of time it would take Craig tocover 50% more distance than Dan has covered? Round youranswer to the nearest hundredth.
A. .08
B. .16
C. .25
D. .50
E. .75
3 1
a 4
+ 1 b
9 0
25. In the correctly solved problem above, a and b are digitsof their respective numbers. What is the value of the two-digitinteger ba, where b is the tens digit and a is the units digit?
A. 20
B. 45
C. 54
D. 64
E. 71
26. Let a represent the average of b consecutive integers and
c represent the sum of d consecutive integers. If , then
each of the following could be true EXCEPT
A. a c.
B. a c.
C. is an integer.
D. c is an integer.
E. a is an integer.
27. 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
28. What was the total distance that Bill drove from MountPleasant to Springfield through Hollyberry?
(1) The entire trip took Bill exactly four hours.
(2) The segment from Mount Pleasant to Hollyberry took Billtwo hours to complete at an average speed of 50 miles perhour.
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.
29. A certain language club has an equal number of native
English and Spanish speakers. On a certain day, of the
members were absent from the club meeting. Of the members
there that day, were native Spanish speakers. What is the
ratio of the number of native English speakers who were notat the meeting to the number of native Spanish speakers whowere not at the meeting?
A.
B.
C.
D.
E.
30. 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%
31. If x- 1 is a positive integer, is x- 1 divisible by 3?
(1) (x2 + x)(x + 1) is divisible by 3.
(2) x(x2-x) is divisible by 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.
32. 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.
33. Several students are studying together for an exam. 60%of the students who studied less than 10 hours a week feelunprepared. 80% of students who studied 10 hours or moreeach week feel prepared. If 75% of the students studied lessthan 10 hours per week, what percent of the students feelprepared for the exam?
A. 20
B. 25
C. 30
D. 35
E. 65
34. For all positive integers s and t, s @ t represents theremainder when s is divided by t. What is the sum of all thepossible values of t for which 18 @ t = 2?
A. 38
B. 28
C. 16
D. 12
E. 10
35. If x and y are integers, is ?
(1) x - y 2 0
(2) x 2 y 0
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.
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.
