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

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3x + 6y = 27 x + 2y + z = 11 [#permalink]  20 May 2018, 16:51
Expert's post
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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]  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]  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

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