Please help me with this question.
If I plug in 2 for both x and y then A and E yield the same result. I cannot think of any other number that fits the criteria (x+y = xy). Is there a way to solve it with plugging in numbers?
Thanks
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Strategy:melguy wrote:Please help me with this question.
If I plug in 2 for both x and y then A and E yield the same result. I cannot think of any other number that fits the criteria (x+y = xy). Is there a way to solve it with plugging in numbers?
Thanks
PLUG IN for x and solve for y.
Case 1: x=2
If we plug x=2 into (x+y)/(xy), we get:
(2+y)/(2y) = 1
2+y = 2y
y = 2.
Since the question stem asks for the value of y, the value in blue is our target.
Now we plug x=2 into the answer choices to see which yields our target of 2.
In this case, two answer choices work:
A: x/(x-1) = 2/(2-1) = 2.
E: x = 2.
To determine whether the correct answer is A or E, TEST A SECOND CASE.
Case 2: x=3
If we plug x=3 into (x+y)/(xy), we get:
(3+y)/(3y) = 1
3+y = 3y
3 = 2y
y = 3/2.
Since the question stem asks for the value of y, the value in blue is our target.
Now we plug x=3 into A and E to see which yields our target of 3/2.
A: x/(x-1) = 3/(3-1) = 3/2.
E: x = 3.
Only A works.
The correct answer is A.
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If (x+y)/xy = 1, then y = 1
A) x/(x-1)
B) x/(x+1)
C) (x-1)/x
D) (x+1)/x
E) x
Another approach is to take (x+y)/xy = 1 and multiply both sides by xy to get: x+y = xy
Subtract y from both sides: x = xy - y
Factor: x = y(x - 1)
Divide both sides by (x-1) to get: x/(x-1) = y
Answer: A
Cheers,
Brent
A) x/(x-1)
B) x/(x+1)
C) (x-1)/x
D) (x+1)/x
E) x
Another approach is to take (x+y)/xy = 1 and multiply both sides by xy to get: x+y = xy
Subtract y from both sides: x = xy - y
Factor: x = y(x - 1)
Divide both sides by (x-1) to get: x/(x-1) = y
Answer: A
Cheers,
Brent
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Jay@ManhattanReview
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Hi Melguy,melguy wrote:Please help me with this question.
If I plug in 2 for both x and y then A and E yield the same result. I cannot think of any other number that fits the criteria (x+y = xy). Is there a way to solve it with plugging in numbers?
Thanks
Plug-in test values such as 0, +/-1, and +/-2 are very common; test-makers design questions in such a way that if you test only one or sometimes two test values, two or more options qualify. Sometimes, these common numbers do not save time.
With regard to the question, we can try with relative not-very-common yet a convenient number to deal with, say, x = 4.
@x = 4, (x+y)/(xy) = 1 => (4+y)/(4y) = 1 => 4+y = 4y => y = 4/3.
Now, you find that only option A fits: correct answer.
Hope this helps.
-Jay
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