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31 May 2026, 05:16
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X: 6
Y: 10
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Company T projected the number of international students studying in the United States (US) for three consecutive school years from 2014–2015 through 2016–2017. The projected numbers for the 2014–2015 school year and during the 2016–2017 school year would be 880,000 and 1,026,080, respectively. Let X % and Y % denote the company’s predicted percentage increase in the number of international students studying in the US from school year 2014–2015 to school year 2015–2016, and from school year 2015–2016 to school year 2016–2017, respectively. Both X and Y are positive integers, and X is less than Y.
In the table, identify the value of X and the value of Y. Make only two selections, one in each column.
In the table, identify the value of X and the value of Y. Make only two selections, one in each column.
| X | Y | |
| 2 | ||
| 6 | ||
| 10 | ||
| 15 | ||
| 20 |
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X: 6
Y: 10
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31 May 2026, 05:21
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Official Answer :
Let A, B, and C be the projected numbers of international students for school years 2014–2015, 2015–2016, and 2016–2017, respectively.
Since A equals 880,000 and C equals 1,026,080, C divided by A equals 1,026,080 divided by 880,000 equals 1.166. So the percent increase from A to C is (C / A - 1) * 100% = 0.166 * 100% = 16.6%.
We now want to find percent increases from A to B and from B to C that yield this 16.6% increase from A to C.
To do this, first note that since C / A = (B / A) * (C / B), it follows that 1.166 = (B / A) * (C / B).
Also note that X is the percent increase from A to B, which is (B / A - 1) * 100%, and that Y is the percent increase from B to C, which is (C / B - 1) * 100%.
Finally, note that we’ve been told that X < Y.
The five answer options 2, 6, 10, 15, and 20 given in the first column, for X, stand for percentage increases of 2%, 6%, 10%, 15%, and 20% from A to B, so these answer options yield the five possible values for B / A of 1.02, 1.06, 1.1, 1.15, and 1.2, respectively.
Likewise, the same five answer options given in the second column, for Y, stand for the same five percentage increases from B to C, so they yield the same five possible values of 1.02, 1.06, 1.1, 1.15, and 1.2 for C / B.
Therefore, since 1.166 = 1.06 * 1.1, the two correct answer options must be 6 and 10.
Since we know X < Y, this gives us answers of X = 6 (corresponding to B / A = 1.06) for the first column and Y = 10 (corresponding to C / B = 1.1) for the second column.
X: The correct answer is 6.
Y: The correct answer is 10.
Let A, B, and C be the projected numbers of international students for school years 2014–2015, 2015–2016, and 2016–2017, respectively.
Since A equals 880,000 and C equals 1,026,080, C divided by A equals 1,026,080 divided by 880,000 equals 1.166. So the percent increase from A to C is (C / A - 1) * 100% = 0.166 * 100% = 16.6%.
We now want to find percent increases from A to B and from B to C that yield this 16.6% increase from A to C.
To do this, first note that since C / A = (B / A) * (C / B), it follows that 1.166 = (B / A) * (C / B).
Also note that X is the percent increase from A to B, which is (B / A - 1) * 100%, and that Y is the percent increase from B to C, which is (C / B - 1) * 100%.
Finally, note that we’ve been told that X < Y.
The five answer options 2, 6, 10, 15, and 20 given in the first column, for X, stand for percentage increases of 2%, 6%, 10%, 15%, and 20% from A to B, so these answer options yield the five possible values for B / A of 1.02, 1.06, 1.1, 1.15, and 1.2, respectively.
Likewise, the same five answer options given in the second column, for Y, stand for the same five percentage increases from B to C, so they yield the same five possible values of 1.02, 1.06, 1.1, 1.15, and 1.2 for C / B.
Therefore, since 1.166 = 1.06 * 1.1, the two correct answer options must be 6 and 10.
Since we know X < Y, this gives us answers of X = 6 (corresponding to B / A = 1.06) for the first column and Y = 10 (corresponding to C / B = 1.1) for the second column.
X: The correct answer is 6.
Y: The correct answer is 10.
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