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3x + 6y = 27 x + 2y + z = 11

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3x + 6y = 27 x + 2y + z = 11 [#permalink] New post 20 May 2018, 16:51
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Question Stats:

64% (00:48) correct 35% (00:53) wrong based on 34 sessions
3x + 6y = 27
x + 2y + z = 11

Quantity A
Quantity B
z + 5
x + 2y - 2


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.
[Reveal] Spoiler: OA

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Re: 3x + 6y = 27 x + 2y + z = 11 [#permalink] New post 18 Sep 2018, 06:15
\(3(x +2y)= 27\)
or, \(x+2y = 9\)

Qyt B = \(x+2y - 2\)
or, Qty B = \(9-2 = 7\)

Qty A = \(z + 5\)
we have, \(x+2y + z = 11\)
or, \(9 +z = 11\)
therefore \(z = 2\)
Hence Qty A = \(2 + 5 = 7\)
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Re: 3x + 6y = 27 x + 2y + z = 11 [#permalink] New post 03 Oct 2020, 07:18
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Expert's post
sandy wrote:
3x + 6y = 27
x + 2y + z = 11

Quantity A
Quantity B
z + 5
x + 2y - 2


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.


Notice that we can simplify of the first given equation, 3x + 6y = 27, by dividing both sides by 3 to get: x + 2y = 9

So are two different equations now look like this:
x + 2y + z = 11
x + 2y = 9

Subtract the bottom equation from the top equation to get: (x + 2y + z) - (x + 2y) = 11 - 9
Simplify: z = 2

Now we can take the given equation x + 2y + z = 11 and replace z to get: x + 2y + 2 = 11
Subtract 2 from both sides of the equation to get: x + 2y = 9

We now have:
QUANTITY A: z + 5 = 2 + 5 = 7
QUANTITY B: x + 2y - 2 = (x + 2y) - 2 = 9 - 2 = 7

Answer: C

Cheers,
Brent
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Re: 3x + 6y = 27 x + 2y + z = 11   [#permalink] 03 Oct 2020, 07:18
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