OG Quantitative Review 2020
QUESTION COLLECTION with VIDEO SOLUTION
by
Bhoopendra Singh (Founder: GMATinsight)
Solve them as Quizzes for FREE (Open Access so no Login) CLICK HERE Q-1: Working at a constant rate, a copy machine makes 20 copies of a one-page document per minute. If the machine works at this constant rate, how many hours does it take to make 4,800 copies of a one-page document?
A. 4
B. 5
C. 6
D. 7
E. 8
Q-2: If x + y = 2 and x^2 + y^2 = 2, what is the value of xy ?
A. –2
B. –1
C. 0
D. 1
E. 2
PS11042
Q-3: The sum S of the first n consecutive positive even integers is given by S = n(n + 1). For what value of n is this sum equal to 110 ?
A. 10
B. 11
C. 12
D. 13
E. 14
(PS02978)
Q-4:
A certain harbor has docking stations along its west and south docks, as shown in the figure; any two adjacent docking stations are separated by a uniform distance d. A certain boat left the west dock from docking station #2 and moved in a straight line diagonally until it reached the south dock. If the boat was at one time directly east of docking station #4 and directly north of docking station #7, at which docking station on the south dock did the boat arrive?
A. #7
B. #8
C. #9
D. #10
E. #11
(PS08375)
Q-5: 6(87.30+0.65)−5(87.30)=
A. 3.90
B. 39.00
C. 90.90
D. 91.20
E. 91.85
(PS03887)
Q-6: Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 6 cm, what is CD, in centimeters?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
PS13800
Q-7: What is the value of \(x^2yz − xyz^2\), if x = − 2, y = 1, and z = 3?
(A) 20
(B) 24
(C) 30
(D) 32
(E) 48
PS05292
Q-8: A souvenir vendor purchased 1,000 shirts for a special event at a price of $5 each. The vendor sold 600 of the shirts on the day of the event for $12 each and 300 of the shirts in the week following the event for $4 each. The vendor was unable to sell the remaining shirts. What was the vendor's gross profit on the sale of these shirts?
A. $1,000
B. $2,200
C. $2,700
D. $3,000
E. $3,400
(PS11468)
Q-9: If x > y and y > z, which of the following represents the greatest number?
(A) x − z
(B) x − y
(C) y − x
(D) z − y
(E) z − x
PS06937
Q-10: To order certain plants from a catalog, it costs $3.00 per plant, plus a 5 percent sales tax, plus $6.95 for shipping and handling regardless of the number of plants ordered. If Company C ordered these plants from the catalog at the total cost of $69.95, how many plants did Company C order?
A. 22
B. 21
C. 20
D. 19
E. 18
PS12926
Q-11: A rug manufacturer produces rugs at a cost of $75 per rug. What is the manufacturer's gross profit from the sale of 150 rugs if 2/3 of the rugs are sold for $150 per rug and the rest are sold for $200 per rug?
A. $10,350
B. $11,250
C. $13,750
D. $16,250
E. $17,800
(PS00812)
Q-12: The value of Maureen's investment portfolio has decreased by 5.8 percent since her initial investment in the portfolio. If her initial investment was $16,800, what is the current value of the portfolio?
A. $7,056.00
B. $14,280.00
C. $15,825.60
D. $16,702.56
E. $17,774.40
(PS07793)
Q-13: Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $10.00 each, what was Company C’s gross profit?
(A) $2,250
(B) $2,500
(C) $3,100
(D) $3,250
(E) $3,500
PS03036
Q-14:
The annual profit or loss for the three divisions of Company T for the years 1991 through 1995 are summarized in the table shown, where losses are enclosed in parentheses. For which division and which three consecutive years shown was the division's profit or loss for the three-year period closest to $0 ?
A. Division A for 1991–1993
B. Division A for 1992–1994
C. Division B for 1991–1993
D. Division B for 1993–1995
E. Division C for 1992–1994
(PS02019)
Q-15: Of the following, which is least?
A. \(\frac{0.03}{0.00071}\)
B. \(\frac{0.03}{0.0071}\)
C. \(\frac{0.03}{0.071}\)
D. \(\frac{0.03}{0.71}\)
E. \(\frac{0.03}{7.1}\)
Q-16: If the average (arithmetic mean) of 5 numbers j, j + 5, 2j – 1, 4j – 2, and 5j – 1 is 8, what is the value of j ?
A. \(\frac{1}{3}\)
B. \(\frac{7}{13}\)
C. 1
D. 3
E. 8
Q-17: Guadalupe owns 2 rectangular tracts of land. One is 300 m by 500 m and the other is 250 m by 630 m. The combined area of these 2 tracts is how many square meters?
A. 3,360
B. 307,500
C. 621,500
D. 704,000
E. 2,816,000
PS14037
Q-18: There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
a) Andy
b) Bob
c) Cary
d) Dora
e) Ellen
PS03918
Q-19: In a field day at a school, each child who competed in \(n\) events and scored a total of \(p\) points was given an overall score of \(\frac{p}{n} + n\). Andrew competed in 1 event and scored 9 points. Jason competed in 3 events and scored 5, 6, and 7 points, respectively. What was the ratio of Andrew's overall score to Jason's overall score?
A. \(\frac{10}{23}\)
B. \(\frac{7}{10}\)
C. \(\frac{4}{5}\)
D. \(\frac{10}{9}\)
E. \(\frac{12}{7}\)
PS10862
Q-20: A certain work plan for September requires that a work team, working every day, produce an average of 200 items per day. For the first half of the month, the team produced an average of 150 items per day. How many items per day must the team average during the second half of the month if it is to attain the average daily production rate required by the work plan?
A. 225
B. 250
C. 275
D. 300
E. 350
PS06719
Q-21: A company sells radios for $15.00 each. It costs the company $14.00 per radio to produce 1,000 radios and $13.50 per radio to produce 2,000 radios. How much greater will the company's gross profit be from the production and sale of 2,000 radios than from the production and sale of 1,000 radios?
A. $500
B. $1,000
C. $1,500
D. $2,000
E. $2,500
(PS01949)
Q-22: Which of the following represent positive numbers?
I. −3 − (−5)
II. (− 3)(−5)
III. −5 − (−3)
A. I only
B. II only
C. III only
D. I and II
E. II and III
PS06555
Q-23: Point X lies on side BC of rectangle ABCD, which has length 12 and width 8. What is the area of triangular region AXD ?
A. 96
B. 48
C. 32
D. 24
E. 20
PS09983
Q-24: A grocer has 400 pounds of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer’s stock of coffee is decaffeinated?
A. 28%
B. 30%
C. 32%
D. 34%
E. 40%
PS07659
Q-25: The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 1.50 + 0.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
(A) $ 2.50
(B) $ 3.00
(C) $ 3.50
(D) $ 4.00
(E) $ 5.00
PS05129
Q-26: For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?
(A) − 4
(B) − 2
(C) 0
(D) 2
(E) 4
PS13917
Q-27: If \(x = \frac{-5}{8}\) and \(y = \frac{-1}{2}\),what is the value of the expression \(-2x - y^2\)?
A. \(-\frac{3}{2}\)
B. ‒1
C. 1
D. \(\frac{3}{2}\)
E. \(\frac{7}{4}\)
PS15994
Q-28: If x-y= R and xy=S, then (x-2)(y+2)=
A. R+S-4
B. R+2S -4
C. 2R - S -4
D. 2R + S - 4
E. R + S
PS13686
Q-29: For positive integers a and b, the remainder when a is divided by b is equal to the remainder when b is divided by a. Which of the following could be a value of ab ?
I. 24
II. 30
III. 36
A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III
PS01466
Q-30: List S consists of the positive integers that are multiples of 9 and are less than 100. What is the median of the integers in S ?
A. 36
B. 45
C. 49
D. 54
E. 63
PS01867
Q-31: A rope 20.6 meters long is cut into two pieces. If the length of one piece of rope is 2.8 meters shorter than the length of the other, what is the length, in meters, of the longer piece of rope?
A. 7.5
B. 8.9
C. 9.9
D. 10.3
E. 11.7
PS07380
Q-32: If x and y are integers and x − y is odd, which of the following must be true?
I. xy is even.
II. x^2 + y^2 is odd.
II. (x + y)^2 is even.
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
PS01120
Q-33: On Monday, the opening price of a certain stock was $100 per share and its closing price was $110 per share. On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday, and on Wednesday the closing price of the stock was 4 percent greater than its closing price on Tuesday. What was the approximate percent change in the price of the stock from its opening price on Monday to its closing price on Wednesday?
A. A decrease of 6%
B. A decrease of 4%
C. A decrease of 1%
D. An increase of 3%
E. An increase of 4%
PS00335
Q-34:
In the rectangular coordinate system shown above, points O, P, and Q represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?
A. (3,1)
B. (1,3)
C. (3,2)
D. (2,2)
E. (2,3)
PS05109
Q-35: What is the perimeter, in meters, of a rectangular garden 6 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
(A) 48
(B) 56
(C) 60
(D) 76
(E) 192
PS05008
Q-36: 1 − 0.000001 =
A. (1.01)(0.99)
B. (1.11)(0.99)
C. (1.001)(0.999)
D. (1.111)(0.999)
E. (1.0101)(0.0909)
PS00918
Q-37: \(|−4|(|−20| − |5|) =\)
A. −100
B. −60
C. 60
D. 75
E. 100
PS04362
Q-38: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
A. 2.8%
B. 3.6%
C. 4.4%
D. 5.2%
E. 6.0%
PS12934
Q-39: How many integers x satisfy both \(2 < x \leq 4\) and \(0 \leq x \leq 3\) ?
A. 5
B. 4
C. 3
D. 2
E. 1
PS15469
Q-40: At the opening of a trading day at a certain stock exchange, the price per share of stock ABC was $120. If the price per share of stock ABC was $125 at the closing of the day, what was the approximate percent increase in the price per share of stock ABC for that day?
A. 10%
B. 4%
C. 2%
D. 1%
E. -2%
PS09322
Q-41:
As shown in the diagram above, a lever resting on a fulcrum has weights of w1 pounds and w2 pounds, located d1 feet and d2 feet from the fulcrum. The lever is balanced and \(w_1d_1=w_2d_2\). Suppose w1 is 50 pounds and w2 is 30 pounds. If d1 is 4 feet less than d2, what is d2, in feet?
A. 1.5
B. 2.5
C. 6
D. 10
E. 20
PS14237
Q-42: If r and s are positive integers such that (2^r)(4^s) = 16, then 2r + s =
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
PS01650
Q-43: Three people each contributed x dollars toward the purchase of a car. They then bought the car for y dollars, an amount less than the total number of dollars contributed. If the excess amount is to be refunded to the three people in equal amounts, each person should receive a refund of how many dollars?
A. \(\frac{3x-y}{3}\)
B.\(\frac{x-y}{3}\)
C.\(\frac{x-3y}{3}\)
D.\(\frac{y-3x}{3}\)
E. 3(x-y)
PS06726
Q-44: Last week Jack worked 70 hours and earned $ 1,260. If he earned his regular hourly wage for the first 40 hours worked, 3/2 times his regular hourly wage for the next 20 hours worked, and 2 times his regular hourly wage for the remaining 10 hours worked, what was his regular hourly wage?
A. $ 7.00
B. $ 14.00
C. $ 18.00
D. $ 22.00
E. $ 31.50
PS07080
Q-45: If a and b are positive integers and \((2^a)^b = 2^3\), what is the value of \(2^a*2^b\)?
A) 6
B) 8
C) 16
D) 32
E) 64
PS13426
Q-46: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
(A) 3
(B) 5
(C) 6
(D) 16
(E) 24
PS01099
Q-47: A certain toll station on a highway has 7 tollbooths, and each tollbooth collects $0.75 from each vehicle that passes it. From 6 o'clock yesterday morning to 12 o'clock midnight, vehicles passed each of the tollbooths at the average rate of 4 vehicles per minute. Approximately how much money did the toll station collect during that time period?
A. $1,500
B. $3,000
C. $11,500
D. $23,000
E. $30,000
PS01443
Q-48: How many integers between 1 and 16, inclusive, have exactly 3 different positive integer factors? (Note: 6 is NOT such an integer because 6 has 4 different positive integer factors: 1, 2, 3, and 6.)
A. 1
B. 2
C. 3
D. 4
E. 5
PS13829
Q-49: Stephanie has 9/4 cups of milk on hand and makes 2 batches of cookies, using 2/3 cup of milk for each batch of cookies. Which of the following describes the amount of milk remaining after she makes the cookies?
A. Less then \(\frac{1}{2}\) cup
B. Between\(\frac{1}{2}\)cup and \(\frac{3}{4}\)cup
C. Between \(\frac{3}{4}\)cup and 1 cup
D. Between 1 cup and\(\frac{3}{2}\) cups
E. More than \(\frac{3}{2}\) cups
PS14063
Q-50: The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?
A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!
PS01656