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31 Dec 2022, 04:33
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B
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Difficulty:
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Question Stats:
87% (01:07) correct
13%
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If xy = 4 and x/y = 36, for positive numbers x and y, what is the value of y ?
A. 1/6
B. 1/3
C. 1/2
D. 2
E. 3
A. 1/6
B. 1/3
C. 1/2
D. 2
E. 3
31 Dec 2022, 08:35
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Bunuel
If \(xy = 4\) and \(\frac{x}{y} = 36\), for positive numbers x and y, what is the value of y ?
A. 1/6
B. 1/3
C. 1/2
D. 2
E. 3
A. 1/6
B. 1/3
C. 1/2
D. 2
E. 3
If \(\frac{x}{y} = 36\), then \(\frac{y}{x} = \frac{1}{36}\) (equation 1)
Also: \(xy = 4\) (equation 2)
Multiply equations 1 and 2 to get: \((\frac{y}{x})(xy) = (\frac{1}{36})(4)\)
Simplify: \(y^2 = \frac{4}{36}\), which means EITHER \(y = \frac{2}{6}\) OR \(y = -\frac{2}{6}\).
Since we're told y is POSITIVE, we know that \(y = \frac{2}{6} = \frac{1}{3} \)
Answer: B
31 Dec 2022, 09:31
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Hi !
Here is an alternate approach-
Use the answer choices to your advantage.
GMAT Track of thought
All answer choices report values of y
Operation
Let me pick C.
If y= 1/2 then from xy= 4,substituting y= 1/2 , we have x*1/2=4 or x=8
With y=1/2 and x=8 x/y = 16 and is NOT equal to 36. Eliminate.
You can eliminate D and E also since they would provide values smaller than 36 as values of y keeps increasing.
For D,
If y=2, then with xy=4, x*2=4 =>x=2
With x=2,y=2, x/y = 1 and is NOT equal to 36
For E,
If y=3, then with xy=4, x*3=4=>x=4/3
With x=4/3, y= 3, x/y =(4/3)/3 =4/9 and is NOT equal to 36
For A,
If y=1/6 then with xy =4, x*1/6=4=>x=24
With x=24, y=1/6 , x/y = 24/(1/6) = 144 and is NOT equal to 36
Option B is the correct choice,
For B,
If y = 1/3, then with xy=4, x*1/3 =4 =>x=12
With x=12,y=1/3 => x/y = 12/(1/3)=36
GMAT Tip:Testing values is a good strategy on GMAT, specially when the answer choices all carry variables.
Let me know if this makes sense.
Devmitra Sen
GMAT Mentor
Here is an alternate approach-
Use the answer choices to your advantage.
GMAT Track of thoughtAll answer choices report values of y
Operation
Let me pick C.
If y= 1/2 then from xy= 4,substituting y= 1/2 , we have x*1/2=4 or x=8
With y=1/2 and x=8 x/y = 16 and is NOT equal to 36. Eliminate.
You can eliminate D and E also since they would provide values smaller than 36 as values of y keeps increasing.
For D,
If y=2, then with xy=4, x*2=4 =>x=2
With x=2,y=2, x/y = 1 and is NOT equal to 36
For E,
If y=3, then with xy=4, x*3=4=>x=4/3
With x=4/3, y= 3, x/y =(4/3)/3 =4/9 and is NOT equal to 36
For A,
If y=1/6 then with xy =4, x*1/6=4=>x=24
With x=24, y=1/6 , x/y = 24/(1/6) = 144 and is NOT equal to 36
Option B is the correct choice,
For B,
If y = 1/3, then with xy=4, x*1/3 =4 =>x=12
With x=12,y=1/3 => x/y = 12/(1/3)=36
GMAT Tip:Testing values is a good strategy on GMAT, specially when the answer choices all carry variables.Let me know if this makes sense.
Devmitra Sen
GMAT Mentor
