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24 Dec 2019, 10:13
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x: 4
Median: 2
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
54% (02:22) correct
46%
(02:20)
wrong
based on 970
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For the three distinct numbers \(1, x\), and \(y,\) the difference \(y − 1\) is one-half of the difference \(x − y.\)
Select a value that represents x and a value that represents the Median of 1, x, and y. The two values must be consistent with each other in the context of the given information. Make only two selections, one in each column.
Select a value that represents x and a value that represents the Median of 1, x, and y. The two values must be consistent with each other in the context of the given information. Make only two selections, one in each column.
| x | Median | Values |
| -3 | ||
| -1 | ||
| 0 | ||
| 1 | ||
| 2 | ||
| 4 |
ShowHide Answer
Official Answer
x: 4
Median: 2
04 Apr 2021, 03:28
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Official Explanation
Analyze the information
You must determine one of the three terms (x) and the three terms' median. Summarize the given text in the form of an equation: \(y−1=\frac{1}{2}(x−y).\) Note that all the answer choices are integers, so the values of x and the median you're seeking must be integers.
Approach strategically
To determine the value of x, simplify your equation to eliminate the y-terms or at least clarify the relationship between x and y.
2(y – 1) = x – y
2y – 2 = x – y
x = 3y – 2
At this point, you cannot eliminate y from the equation, but you have a clear relationship between x and y. Since you have only numbers in the answer choices, back solve to determine x.
If x = –3, then –3 = 3y – 2, and y=−1/3. The median of –3, −1/3, and 1 is a fraction, but no fractions exist in the answer choices. Thus, x cannot equal –3; eliminate this choice from the left column.
If x = –1, then –1 = 3y – 2, so y=1/3. The median of –1, 1/3, and 1 is a non integer, so eliminate x = –1 from the left column.
If x = 0, then 0 = 3y – 2, so y=2/3. The median of 0, 2/3, and 1 is a non integer, so eliminate x = 0 from the left column.
Regarding x = 1, the question stem states that the three terms are distinct from each other, so eliminate this choice from the left column.
If x = 2, then 2 = 3y – 2, so y=4/3. The median of 1, 4/3, and 2 is a non integer, so eliminate x = 2 from the left column.
If x = 4, then 4 = 3y – 2, so y = 2. The median of 1, 2, and 4 is 2, which is an answer choice.
The correct answers are these:
x: 4
Median: 2
TAKEAWAY: As you do on Problem Solving questions in the Quantitative section, look for opportunities to backsolve on math-focused Two-Part Analysis questions. This is an efficient way to find two values listed in the answer choices that work together.
Analyze the information
You must determine one of the three terms (x) and the three terms' median. Summarize the given text in the form of an equation: \(y−1=\frac{1}{2}(x−y).\) Note that all the answer choices are integers, so the values of x and the median you're seeking must be integers.
Approach strategically
To determine the value of x, simplify your equation to eliminate the y-terms or at least clarify the relationship between x and y.
2(y – 1) = x – y
2y – 2 = x – y
x = 3y – 2
At this point, you cannot eliminate y from the equation, but you have a clear relationship between x and y. Since you have only numbers in the answer choices, back solve to determine x.
If x = –3, then –3 = 3y – 2, and y=−1/3. The median of –3, −1/3, and 1 is a fraction, but no fractions exist in the answer choices. Thus, x cannot equal –3; eliminate this choice from the left column.
If x = –1, then –1 = 3y – 2, so y=1/3. The median of –1, 1/3, and 1 is a non integer, so eliminate x = –1 from the left column.
If x = 0, then 0 = 3y – 2, so y=2/3. The median of 0, 2/3, and 1 is a non integer, so eliminate x = 0 from the left column.
Regarding x = 1, the question stem states that the three terms are distinct from each other, so eliminate this choice from the left column.
If x = 2, then 2 = 3y – 2, so y=4/3. The median of 1, 4/3, and 2 is a non integer, so eliminate x = 2 from the left column.
If x = 4, then 4 = 3y – 2, so y = 2. The median of 1, 2, and 4 is 2, which is an answer choice.
The correct answers are these:
x: 4
Median: 2
TAKEAWAY: As you do on Problem Solving questions in the Quantitative section, look for opportunities to backsolve on math-focused Two-Part Analysis questions. This is an efficient way to find two values listed in the answer choices that work together.
General Discussion
25 Dec 2019, 14:08
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y-1=0.5*(x-y) --> 3y-x=2
Three distinct numbers 1,x,y
Choices -3,-1,0,1,2,4
If x=-3, y=-1/3, median=-1/3 (WRONG. No options for median)
If x=-1, y=1/3, median=1/3 (WRONG. No options for median)
If x=0, y=2/3, median=2/3 (WRONG. No option for median)
If x=1, y=1, median=1 (WRONG. Need distinct number)
If x=2, y=4/3, median=1 (WRONG. Need distinct number)
If x=4, y=2, median=2 (CORRECT ANSWER. 1,2,4 with x=4 and median= 2)
Posted from my mobile device
Three distinct numbers 1,x,y
Choices -3,-1,0,1,2,4
If x=-3, y=-1/3, median=-1/3 (WRONG. No options for median)
If x=-1, y=1/3, median=1/3 (WRONG. No options for median)
If x=0, y=2/3, median=2/3 (WRONG. No option for median)
If x=1, y=1, median=1 (WRONG. Need distinct number)
If x=2, y=4/3, median=1 (WRONG. Need distinct number)
If x=4, y=2, median=2 (CORRECT ANSWER. 1,2,4 with x=4 and median= 2)
Posted from my mobile device
