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Which is greater x+y-1 or x-y+1
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27 Jan 2020, 09:25
27 Jan 2020, 09:25
Expert Reply
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Question Stats:
92% (00:42) correct
7% (00:17) wrong based on 27 sessions
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Quantity A |
Quantity B |
\(x+y-1 \) |
\(x-y+1\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
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Which is greater x+y-1 or x-y+1
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27 Jan 2020, 10:17
27 Jan 2020, 10:17
1
Carcass wrote:
Quantity A |
Quantity B |
\(x+y-1 \) |
\(x-y+1\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
We can solve this question using matching operations
Given:
Quantity A: \(x+y-1 \)
Quantity B: \(x-y+1\)
Subtract \(x\) from both quantities to get:
Quantity A: \(y-1 \)
Quantity B: \(-y+1\)
Add \(y\) to both quantities to get:
Quantity A: \(2y-1 \)
Quantity B: \(1\)
Add \(1\) to both quantities to get:
Quantity A: \(2y \)
Quantity B: \(2\)
Divide both quantities by \(2\) to get:
Quantity A: \(y \)
Quantity B: \(1\)
Since there is no information about the value of \(y\), \(y\) COULD be greater than 1, less than 1, or equal to 1
Answer: D
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Re: Which is greater x+y-1 or x-y+1
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28 Jan 2020, 05:36
28 Jan 2020, 05:36
1
Carcass wrote:
Quantity A |
Quantity B |
\(x+y-1 \) |
\(x-y+1\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
We have:
Quantity A: \(x + y - 1 = x + (y - 1) \)
Quantity B: \(x - y + 1 = x - (y + 1) \)
Assume \(y - 1 = z\)
Thus, we have:
Quantity A: \(x + y - 1 = x + z \)
Quantity B: \(x - y + 1 = x - z \)
The sum of 2 numbers x and z is greater than the difference between x and z if both z (= y - 1) is positive
The sum of 2 numbers x and z is less than the difference between x and z if z (= y - 1) is negative
Since nothing is mentioned about the value of y, we cannot compare the quantities
Answer D
Alternate approach:
We need to compare:
\(x + y - 1\) VS \(x - y + 1\)
Adding \((y - x)\) to both sides:
\(2y - 1\) VS \( 1 \)
Adding 1 to both sides:
\(2y\) VS \( 2 \)
\(=> y\) VS \( 1 \)
However, there is no information about \(y\)
Answer D
