GWD31MATH[1].6

gmat Math Section ------------------------------------------------------------------------------------------------------------ Q1: A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995? A.​ 5% B.​ 18% C.​ 33% D.​ 35% E.​ 38% Answer: ------------------------------------------------------------------------------------------------------------ Q2: If every car sold last week at a certain used-car dealership was either a coupe or a sedan, what was the average (arithmetic mean) sale price for all the cars that were sold at the dealership last week? (1) The average sale price for the sedans that were sold at the dealership last week was $10,600. (2) The average sale price for the coupes that were sold at the dealership last week was $8,400. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q3: Pat, Kate, and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate? A.​ 18 B.​ 36 C.​ 72 D.​ 90 E.​ 108 Answer: ------------------------------------------------------------------------------------------------------------ Q4: What is the greatest prime factor of 2100 - 296? A.​ 2 B.​ 3 C.​ 5 D.​ 7 E.​ 11 Answer: ------------------------------------------------------------------------------------------------------------ Q5: If b, c, and d are constants and x2 + bx + c = (x + d)2 for all values of x, what is the value of c? (1) d = 3 (2) b = 6 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q6: If a, b, k, and m are positive integers, is ak a factor of bm? (1) a is a factor of b. (2) k ≤ m A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q7: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions? A.​ 42 B.​ 70 C.​ 140 D.​ 165 E.​ 315 Answer: ------------------------------------------------------------------------------------------------------------ Q8: R S T Q U P V W Note: Figure not drawn to scale. In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS? A.​ 5 B.​ 5.5 C.​ 6 D.​ 6.5 E.​ 7 Answer: ------------------------------------------------------------------------------------------------------------ Q9: If the average (arithmetic mean) of four different numbers is 30, how many of the numbers are greater than 30? (1) None of the four numbers is greater than 60. (2) Two of the four numbers are 9 and 10, respectively. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q10: If each of the students in a certain mathematics class is either a junior or a senior, how many students are in the class? (1) If one student is to be chosen at random from the class to attend a conference, the probability that the student chosen will be a senior is 4/7. (2) There are 5 more seniors in the class than juniors. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q11: Note: Not drawn to scale. A rectangular picture is surrounded by a boarder, as shown in the figure above. Without the boarder the length of the picture is twice its width. If the area of the boarder is 196 square inches, what is the length, in inches, of the picture, excluding the boarder? A.​ 10 B.​ 15 C.​ 30 D.​ 40 E.​ 60 Answer: ------------------------------------------------------------------------------------------------------------ Q12: Each week Connie receives a base salary of $500, plus a 20 percent commission on the total amount of her sales that week in excess of $1,500. What was the total amount of Connie’s sales last week? (1) Last week Connie’s base salary and commission totaled $1,200. (2) Last week Connie’s commission was $700. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q13: If n is the greatest positive integer for which 2n is a factor of 10!, then n = A.​ 2 B.​ 4 C.​ 6 D.​ 8 E.​ 10 Answer: ------------------------------------------------------------------------------------------------------------ Q14: A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)] A.​ 1/4 B.​ 7/12 C.​ 2/3 D.​ 7/8 E.​ 8/7 Answer: ------------------------------------------------------------------------------------------------------------ Q15: Of the following, which is greatest? A.​ (1/5)-2 B.​ (1/3)-2 C.​ 3-2 D.​ 5-2 E.​ 23 Answer: ------------------------------------------------------------------------------------------------------------ Q16: Is │x - y│>│x - z│? (1) │y│>│z│ (2) x < 0 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q17: Raymond purchased a package of ground beef at a cost of $1.98 per pound. If, for the same amount of money, Raymond could have purchased a piece of steak that weighed 40 percent less than the package of ground beef, what was the cost per pound of the steak? A.​ $4.95 B.​ $4.20 C.​ $3.60 D.​ $3.30 E.​ $3.10 Answer: ------------------------------------------------------------------------------------------------------------ Q18: A rectangular region has a fence along three sides and a wall along the fourth side. The fenced side opposite the wall is twice the length of each of the other two fenced sides. If the area of the rectangular region is 128 square feet, what is the total length of the fence, in feet? A.​ 4 B.​ 8 C.​ 16 D.​ 32 E.​ 64 Answer: ------------------------------------------------------------------------------------------------------------ Q19: At a certain company, 25 percent of the employees are male and 50 percent of the employees are sales staff. What is the number of employees at this company? (1) Exactly 7 of the employees at the company are males who are sales staff. (2) There are 16 more female employees than male employees at the company. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q20: If 2x + 2x + 2x + 2x = 2n, what is x in terms of n? A.​ n/4 B.​ 4n C.​ 2n D.​ n - 2 E.​ n + 2 Answer: ------------------------------------------------------------------------------------------------------------ Q21: ׀ ׀ ׀ ׀ ׀ 2 p s 6 If m lies between the integers p and s on the number line shown, which of the following is a possible value for m? A.​ √17 B.​ √4 C.​ 2.9 D.​ 20/4 E.​ 10/3 Answer: ------------------------------------------------------------------------------------------------------------ Q22: Q yº xº xº P R In ΔPQR above, what is the value of y? (1) (3/2)x = 120 (2) x + y = 100 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q23: If –4 < x < 7 and –6 < y < 3, which of the following specifies all the possible values of xy? A.​ –42 < xy < 21 B.​ –42 < xy < 24 C.​ –28 < xy < 18 D.​ –24 < xy < 21 E.​ –24 < xy < 24 Answer: ------------------------------------------------------------------------------------------------------------ Q24: A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? A.​ 8 B.​ 12 C.​ 15 D.​ 21 E.​ 27 Answer: ------------------------------------------------------------------------------------------------------------ Q25: Company K has an annual budget for a certain project, and 1/5 of this budget was spent during the first quarter of the year. If 1/8 of the remainder of the budget was spent during the second quarter, what fraction of the budget was left at the end of the second quarter? A.​ 7/10 B.​ 31/40 C.​ 27/40 D.​ 3/10 E.​ 9/40 Answer: ------------------------------------------------------------------------------------------------------------ Q26: K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K? (1) 50 is in K. (2) 150 is in K. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q27: The sum of positive integers x and y is 77. What is the value of xy? (1) x = y + 1 (2) x and y have the same tens digit. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q28: A total of n trucks and cars are parked in a slot. If the number of cars is 1/4 the number of trucks, and 2/3 of the trucks are pickups, how many pickups, in terms of n, are parked in the slot? A.​ 1/6 n B.​ 5/12 n C.​ 1/2 n D.​ 8/15 n E.​ 11/12 n Answer: ------------------------------------------------------------------------------------------------------------ Q29: From 1985 to 1994, what was the percent increase in total United States trade? (1) Total United States trade in 1985 was 17 percent of gross domestic product in 1985. (2) Total United States trade in 1994 was 23 percent of gross domestic product in 1994. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q30: T ● ● U ● S The circle shown has center R. If arc UST has length 48π, what is the radius of the circle? A.​ 18 B.​ 24 C.​ 32 D.​ 48 E.​ 64 Answer: ------------------------------------------------------------------------------------------------------------ Q31: If (2 -√5)x = -1, then x = A.​ 2 + √5 B.​ 1 + (√5)/2 C.​ 1 – (√5)/2 D.​ 2 - √5 E.​ -2 - √5 Answer: ------------------------------------------------------------------------------------------------------------ Q32: If x is a positive integer, is the remainder 0 when (3x + 1)/10? (1) x = 3n + 2, where n is a positive integer. (2) x > 4 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q33: A salesperson received a 6-percent commission on the amount of total sales up to and including $10,000, and an r-percent commission on the amount of total sales over $10,000. If the salesperson received a total commission of $920 on total sales of $14,000, what was the value of r? A.​ 3.2 B.​ 4.3 C.​ 6.6 D.​ 8.0 E.​ 9.2 Answer: ------------------------------------------------------------------------------------------------------------ Q34: A clothing store acquired an item at a cost of x dollars and sold the item for y dollars. The store’s gross profit from the item was what percent of its cost for the item? (1) y – x = 20 (2) y/x = 5/4 A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q35: In the xy-plane, what is the x-intercept of the line whose equation is 3y – 4x = 15? A.​ – 15/4 B.​ – 4/3 C.​ 4/3 D.​ 15/4 E.​ 5 Answer: ------------------------------------------------------------------------------------------------------------ Q36: If four of the five integers in a list are 10, 2, 8, and 5, what is the fifth integer? (1) The product of the five integers is 0. (2) The sum of the five integers is 25. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient. Answer: ------------------------------------------------------------------------------------------------------------ Q37: A certain state has a sales tax of 5 percent on the portion of a purchase price that is greater than $100. If a customer paid a sales tax of $4 on a particular item, what was the purchase price of the item? A.​ $120 B.​ $124 C.​ $180 D.​ $184 E.​ $220 Answer: ------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------ Answers: EEDCD, CECCC, CDDBA, EDDBD, EDBEA, ADDEC, AEDBA, DC