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andrewjohn8
GMAT Focus 1: 645 Q80 V88 DI78 
Posts: 34
13 Jul 2024, 13:51
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The rug with the greatest KPSI has more than 5,500,000 knots.: T
The median KPSI of the 4 newest rugs is 162.: F
The median length of Kashan rugs is equal to the median length of Kashmar rugs.: F
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
74% (03:04) correct
26%
(03:03)
wrong
based on 1986
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The table provides data about 12 different Persian rugs currently available for sale by a rug dealer. For each rug, the data includes the number of knots per square inch (KPSI) in the yarn, which can be assumed consistent throughout the rug. There are 12 inches in a foot, so a rug having a width of x feet and a length of y feet has an area equal to (12^2)xy square inches.
For each of the following statements, select T if it is true based on the information provided; otherwise select F.
Screenshot 2024-07-13 164746.png [ 18.6 KiB | Viewed 13434 times ]
| Type | Age | Width (ft) | Lenghth (ft) | KPSI | Price |
|---|---|---|---|---|---|
| Kashan | 20 | 10 | 14 | 212 | $3,950 |
| Kashan | 20 | 10 | 12 | 162 | $3,852 |
| Kashmar | 20 | 8 | 9 | 162 | $3,920 |
| Kerman | 20 | 10 | 14 | 280 | $3,530 |
| Isfahan | 25 | 10 | 15 | 158 | $3,930 |
| Kashan | 25 | 9 | 15 | 158 | $3,762 |
| Kashmar | 25 | 10 | 13 | 158 | $3,763 |
| Kashmar | 25 | 10 | 12 | 158 | $3,762 |
| Mashad | 25 | 10 | 12 | 158 | $3,762 |
| Isfahan | 35 | 10 | 14 | 158 | $3,470 |
| Isfahan | 35 | 10 | 14 | 158 | $3,470 |
| Ardabil | 45 | 9 | 13 | 112 | $3,952 |
For each of the following statements, select T if it is true based on the information provided; otherwise select F.
Attachment:
Screenshot 2024-07-13 164746.png [ 18.6 KiB | Viewed 13434 times ]
| T | F | |
| The rug with the greatest KPSI has more than 5,500,000 knots. | ||
| The median KPSI of the 4 newest rugs is 162. | ||
| The median length of Kashan rugs is equal to the median length of Kashmar rugs. |
ShowHide Answer
Official Answer
The rug with the greatest KPSI has more than 5,500,000 knots.: T
The median KPSI of the 4 newest rugs is 162.: F
The median length of Kashan rugs is equal to the median length of Kashmar rugs.: F
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04 Nov 2025, 05:12
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The table provides data about 12 different Persian rugs currently available for sale by a rug dealer. For each rug, the data includes the number of knots per square inch (KPSI) in the yarn, which can be assumed consistent throughout the rug. There are 12 inches in a foot, so a rug having a width of x feet and a length of y feet has an area equal to (12^2)xy square inches.
For each of the following statements, select T if it is true based on the information provided; otherwise select F.
• The rug with the greatest KPSI has more than 5,500,000 knots.
The total number of knots in a rug equals its total area in square inches multiplied by the number of knots per square inch (KPSI). Since the width and length of the rugs are given in feet, and each square foot has 12^2 square inches, total knots = 12^2 * width * length * KPSI.
Sorting by KPSI, the rug with the highest KPSI is the Kerman rug (KPSI 280, width 10 ft, length 14 ft). Its total knots = 12^2 * 10 * 14 * 280 = 5,644,800, which is greater than 5,500,000.
Therefore, the statement is true.
• The median KPSI of the 4 newest rugs is 162.
Sort by age. The four newest rugs are all 20 years old, with KPSI values, in ascending order, of 162, 162, 212, and 280. The median is the average of the two middle values, 162 and 212, which is clearly greater than 162.
Therefore, the statement is false.
• The median length of Kashan rugs is equal to the median length of Kashmar rugs.
Sort by type and use lengths. Kashan lengths, in ascending order, are 12, 14, and 15, which give a median of 14. Kashmar lengths, in ascending order, are 9, 12, and 13, which give a median of 12. These are not equal.
Therefore, the statement is false.
As seen above, the only exact arithmetic needed is for statement 1.
GMAT-Club-Forum-qha3737w.png [ 19.71 KiB | Viewed 5213 times ]
| Type | Age | Width (ft) | Lenghth (ft) | KPSI | Price |
|---|---|---|---|---|---|
| Kashan | 20 | 10 | 14 | 212 | $3,950 |
| Kashan | 20 | 10 | 12 | 162 | $3,852 |
| Kashmar | 20 | 8 | 9 | 162 | $3,920 |
| Kerman | 20 | 10 | 14 | 280 | $3,530 |
| Isfahan | 25 | 10 | 15 | 158 | $3,930 |
| Kashan | 25 | 9 | 15 | 158 | $3,762 |
| Kashmar | 25 | 10 | 13 | 158 | $3,763 |
| Kashmar | 25 | 10 | 12 | 158 | $3,762 |
| Mashad | 25 | 10 | 12 | 158 | $3,762 |
| Isfahan | 35 | 10 | 14 | 158 | $3,470 |
| Isfahan | 35 | 10 | 14 | 158 | $3,470 |
| Ardabil | 45 | 9 | 13 | 112 | $3,952 |
For each of the following statements, select T if it is true based on the information provided; otherwise select F.
• The rug with the greatest KPSI has more than 5,500,000 knots.
The total number of knots in a rug equals its total area in square inches multiplied by the number of knots per square inch (KPSI). Since the width and length of the rugs are given in feet, and each square foot has 12^2 square inches, total knots = 12^2 * width * length * KPSI.
Sorting by KPSI, the rug with the highest KPSI is the Kerman rug (KPSI 280, width 10 ft, length 14 ft). Its total knots = 12^2 * 10 * 14 * 280 = 5,644,800, which is greater than 5,500,000.
Therefore, the statement is true.
• The median KPSI of the 4 newest rugs is 162.
Sort by age. The four newest rugs are all 20 years old, with KPSI values, in ascending order, of 162, 162, 212, and 280. The median is the average of the two middle values, 162 and 212, which is clearly greater than 162.
Therefore, the statement is false.
• The median length of Kashan rugs is equal to the median length of Kashmar rugs.
Sort by type and use lengths. Kashan lengths, in ascending order, are 12, 14, and 15, which give a median of 14. Kashmar lengths, in ascending order, are 9, 12, and 13, which give a median of 12. These are not equal.
Therefore, the statement is false.
As seen above, the only exact arithmetic needed is for statement 1.
Attachment:
GMAT-Club-Forum-qha3737w.png [ 19.71 KiB | Viewed 5213 times ]
General Discussion
13 Jul 2024, 23:26
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First find the area of rugs in square inches using formula given in question hikamikubo
10 *14 *144
Multiply that with KPSI to get the number of Knots 10*14*144*280 = 5644800 > 5500000
10 *14 *144
Multiply that with KPSI to get the number of Knots 10*14*144*280 = 5644800 > 5500000
