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GMAT Exam  >  GMAT Questions  >  In the x-y plane, the area of the region boun... Start Learning for Free
In the x-y plane, the area of the region bounded by |x + y| < 20 and 0 < y < 20.
  • a)
    900
  • b)
    800
  • c)
    700
  • d)
    600
  • e)
    500
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In the x-y plane, the area of the region bounded by |x + y| < 20 an...
The condition |x + y| < 20 represents the region between two parallel lines that are symmetric about the x-axis. The inequality can be rewritten as -20 < x + y < 20.
We can break down this inequality into two separate inequalities:
x + y < 20
-(x + y) < 20
For the first inequality, x + y < 20, the region is below the line y = -x + 20.
For the second inequality, -(x + y) < 20, we multiply both sides by -1 to change the direction of the inequality, which gives us x + y > -20. The region for this inequality is above the line y = -x - 20.
Combining these two regions, we have a trapezoidal shape with two parallel sides: y = -x + 20 and y = -x - 20.
Now, we need to find the intersection points of these lines with the line y = 20 (0 < y < 20) to determine the boundaries of our trapezoid.
For y = 20:
-20 = -x + 20 => x = 0
-20 = -x - 20 => x = 0
So, the trapezoid is symmetric about the y-axis and its base has a length of 2x, where x = 20.
The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
In this case, a = b = 2x = 40 and h = 20. Plugging in these values, we get:
Area = (40 + 40) * 20 / 2
= 80 * 20 / 2
= 1600 / 2
= 800
Therefore, the area of the region bounded by |x + y| < 20 and 0 < y < 20 is 800. So the answer is B.
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Most Upvoted Answer
In the x-y plane, the area of the region bounded by |x + y| < 20 an...
The condition |x + y| < 20 represents the region between two parallel lines that are symmetric about the x-axis. The inequality can be rewritten as -20 < x + y < 20.
We can break down this inequality into two separate inequalities:
x + y < 20
-(x + y) < 20
For the first inequality, x + y < 20, the region is below the line y = -x + 20.
For the second inequality, -(x + y) < 20, we multiply both sides by -1 to change the direction of the inequality, which gives us x + y > -20. The region for this inequality is above the line y = -x - 20.
Combining these two regions, we have a trapezoidal shape with two parallel sides: y = -x + 20 and y = -x - 20.
Now, we need to find the intersection points of these lines with the line y = 20 (0 < y < 20) to determine the boundaries of our trapezoid.
For y = 20:
-20 = -x + 20 => x = 0
-20 = -x - 20 => x = 0
So, the trapezoid is symmetric about the y-axis and its base has a length of 2x, where x = 20.
The formula for the area of a trapezoid is:
Area = (a + b) * h / 2
In this case, a = b = 2x = 40 and h = 20. Plugging in these values, we get:
Area = (40 + 40) * 20 / 2
= 80 * 20 / 2
= 1600 / 2
= 800
Therefore, the area of the region bounded by |x + y| < 20 and 0 < y < 20 is 800. So the answer is B.
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MEMORANDUMTo: Regional Office ManagersFrom: Chief Operations OfficerRE: Travel planningOnce again, our annual management retreat will be held in Bloomsbury. In preparation for this year’s retreat, all Regional Office Managers (ROMs) will be responsible for arranging the travel reservations for all Level 2 managers within his or her Region. You may delegate that task should you wish.ROMs will receive a research memorandum from the Logistics Division providing the average airfare from the 6 Regions to Bloomsbury. While ROMs should use that average airfare as a guide, we anticipate that there may be some variation in ticket prices based upon the specifics of travel arrangements. As such, Regional offices will be reimbursed for the full cost of any plane ticket priced within 1 (on e) standard deviation of the average airfare from its region to Bloomsbury, inclusive. For any ticket priced more than 1 (one) standard deviation above the mean, regional offices will be reimbursed up to the average airfare from your region to Bloomsbury. For any ticket priced more than 1 (one) standard deviation below the average, in addition to full reimbursement of the ticket cost, regional offices will receive a “Budget Bonus” of 50% of the difference between the ticket price and the average airfare from your region to Bloomsbury.MEMORANDUMTo: Regional Office ManagersFrom: Logistics DivisionRE: Airfare ResearchThe attached chart lists the average (arithmetic mean) airfare from the listed Regions to Bloomsbury. The mean airfare was calculated based upon takinga normally distributed sample of airfares. The standard deviation and size of each sample is also listed in the chart.Email from Marco Roland, Human Resources Manager, West Region to MarisaCortland, Regional Office Manager, West RegionDear Marisa,Tickets have been purchased for all of the Level 2 Managers in the WestRegion. Below is a summaryBest,MarcoQ. Consider each of the following statements. Based upon the information contained in the two memoranda and the email, determine whether each statement is true or false as stated.In the Mid-Atlantic sample, more than 20 tickets werepriced over $450.

MEMORANDUMTo: Regional Office ManagersFrom: Chief Operations OfficerRE: Travel planningOnce again, our annual management retreat will be held in Bloomsbury. In preparation for this year’s retreat, all Regional Office Managers (ROMs) will be responsible for arranging the travel reservations for all Level 2 managers within his or her Region. You may delegate that task should you wish.ROMs will receive a research memorandum from the Logistics Division providing the average airfare from the 6 Regions to Bloomsbury. While ROMs should use that average airfare as a guide, we anticipate that there may be some variation in ticket prices based upon the specifics of travel arrangements. As such, Regional offices will be reimbursed for the full cost of any plane ticket priced within 1 (on e) standard deviation of the average airfare from its region to Bloomsbury, inclusive. For any ticket priced more than 1 (one) standard deviation above the mean, regional offices will be reimbursed up to the average airfare from your region to Bloomsbury. For any ticket priced more than 1 (one) standard deviation below the average, in addition to full reimbursement of the ticket cost, regional offices will receive a “Budget Bonus” of 50% of the difference between the ticket price and the average airfare from your region to Bloomsbury.MEMORANDUMTo: Regional Office ManagersFrom: Logistics DivisionRE: Airfare ResearchThe attached chart lists the average (arithmetic mean) airfare from the listed Regions to Bloomsbury. The mean airfare was calculated based upon takinga normally distributed sample of airfares. The standard deviation and size of each sample is also listed in the chart.Email from Marco Roland, Human Resources Manager, West Region to MarisaCortland, Regional Office Manager, West RegionDear Marisa,Tickets have been purchased for all of the Level 2 Managers in the WestRegion. Below is a summaryBest,MarcoQ. Consider each of the following statements. Based upon the information contained in the two memoranda and the email, determine whether each statement is true or false as stated.In the Northeast sample, more than 50 tickets were pricedunder $250.

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In the x-y plane, the area of the region bounded by |x + y| < 20 and 0 < y < 20.a)900b)800c)700d)600e)500Correct answer is option 'B'. Can you explain this answer?
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