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30 May 2024, 15:12
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X: 910
Z: 1,350
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
87% (02:18) correct
13%
(02:42)
wrong
based on 1502
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Let X, Y, and Z denote the number of international students, in thousands, that Company U predicted would be studying in the United States (US) during the school years 2014–2015, 2019–2020, and 2024–2025, respectively. The average (arithmetic mean) of X, Y, and Z is 1,128, and Y = 1,124. Company U predicted that there would be more international students studying in the US during the 2024–2025 school year than during the 2014–2015 school year.
In the table, identify a value of X and a value of Z that are jointly consistent with the information provided. Make only two selections, one in each column.
In the table, identify a value of X and a value of Z that are jointly consistent with the information provided. Make only two selections, one in each column.
ID: 100364
| X | Z | |
| 910 | ||
| 995 | ||
| 1,1175 | ||
| 1,350 | ||
| 1,435 |
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Official Answer
X: 910
Z: 1,350
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30 May 2024, 23:38
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guddo
It is not important that you just correctly answer an easy question, but that you answer it correctly in the least time frame.
The information that can be drawn is
- Z>X
- Y =1124
- X+Y+Z = 3*1128
Look for options that add up to 2260 = > 910 + 1350 = 2260
As Z>X, Z=1350 and X = 910
General Discussion
18 Sep 2024, 08:54
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1. Let's draw a diagram of the values on a number line.
2. Because the average of X, Y, Z is 1128, then their (signed) distances to the average sum up to 0. We also know that Y = 1124.
3. We can write the following equation:
a + b + c = 0 \(\rightarrow\) (X - 1128) + (Y - 1128) + (Z - 1128) = 0 \(\rightarrow\) -1128 - 1128 + (X + Z) - 4 = 0 \(\rightarrow\) X + Z = 2260.
4. The only other information we have is that X < Z.
5. Now consider the possible answers: 910, 995, 1,175, 1350, 1435. Estimating them will make summation faster: 900, 1000, 1200, 1350, 1400. The closest sum to 2260 is 900 + 1350. The original sum would be 910 + 1350 = 2260, which works.
6. Our answer is X = 910 and Z = 1350.
Image_AverageDiagram.jpg [ 8.36 KiB | Viewed 8719 times ]
2. Because the average of X, Y, Z is 1128, then their (signed) distances to the average sum up to 0. We also know that Y = 1124.
3. We can write the following equation:
a + b + c = 0 \(\rightarrow\) (X - 1128) + (Y - 1128) + (Z - 1128) = 0 \(\rightarrow\) -1128 - 1128 + (X + Z) - 4 = 0 \(\rightarrow\) X + Z = 2260.
4. The only other information we have is that X < Z.
5. Now consider the possible answers: 910, 995, 1,175, 1350, 1435. Estimating them will make summation faster: 900, 1000, 1200, 1350, 1400. The closest sum to 2260 is 900 + 1350. The original sum would be 910 + 1350 = 2260, which works.
6. Our answer is X = 910 and Z = 1350.
Attachment:
Image_AverageDiagram.jpg [ 8.36 KiB | Viewed 8719 times ]
