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CIO
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How can we do this quickly? [#permalink] New post 25 Aug 2004, 17:32
Hello everyone.

For years, everyone's been talking about plugging in numbers for algebra problems. You pick a number for the variable, plug it in, get an answer, and then find that answer in the answer choices.

I think this is dangerous, because it only works sometimes, and I think that algebra or some other trick is always important as a backup. Plugging in should be done by people who understand it and when not to use it.

Sorry for waxing on about that, but I ran across a problem today that would be very difficult to plug numbers into, but is also very time consuming using straightforward algebra. You might expect it to work out well with substitution, but you'll see that it doesn't. So I thought I'd post it here and see what everyone thought about it, and if there's some clever thing that I'm not seeing.

--------------
If 2x + 3y = 1, what is (x/2) + (y/3) in terms of y?

A) y/5

B) (1 - 3y)/2

C) (1 - 3y)/4

D) (3y + 4)/15

E) (3 - 5y)/12

Last edited by ian7777 on 25 Aug 2004, 17:56, edited 1 time in total.
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 [#permalink] New post 25 Aug 2004, 17:49
I guess I am losing my mind. But for (x/2) + (y/2), I am getting (1-y)/4. This is not an option listed.
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 [#permalink] New post 25 Aug 2004, 17:51
i'm getting (1-y)/4 as well
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 [#permalink] New post 25 Aug 2004, 17:56
Sorry, my bad completely. The question should read,

"...what is (x/2) + (y/3) in terms of y?"

I'll fix the original post.
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 [#permalink] New post 25 Aug 2004, 18:00
If 2x + 3y = 1, what is (x/2) + (y/3) in terms of y?

---> 2x+3y=1
---> 2x=1-3y
---> x= (1-3y)/2
---> x/2=(1-3y)/4

Add y/3 on both sides.....

(x/2)+(y/3)= (1-3y)/4 + (y/3)

---> u get (3-5y)/12

(Solved less than one minute) :)
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 [#permalink] New post 25 Aug 2004, 18:02
(E). 20 secs. I think good old substitution is still very fast in this case. If you note that you'll end up with 2 and 3 as denominator, you can work two steps ahead while substituting by adjusting the integer value of y as you work throuhg the problem.
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 [#permalink] New post 25 Aug 2004, 18:54
I guess solving might be faster than substituting numbers (I mean, if Ian hadn't given the preface).

Let the value be M

2x + 3y = 1
3x + 2y = 6M

Solving this,
-5y = 12M-1
M = (3-5y)/12
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 [#permalink] New post 26 Aug 2004, 07:41
15 seconds , I got it as E .

divide the existing equation by 4 and move 3y/4 to the right side ,
you know x/2 and then simply add y/3 .

x /2 = (1-3y)/4

x/2 + y/3 = (1-3y)/4 + y/12
= (3-5y)/12
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 [#permalink] New post 26 Aug 2004, 07:43
Infact the moment you see the denominator as 12 , you can choose the choice E , because there is no other choice which has denominator 12 .

My bad , if i had not overlooked the choices , i think this problem can be solved with in 15 seconds .
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 [#permalink] New post 26 Aug 2004, 07:50
hardworker_indian wrote:
I guess solving might be faster than substituting numbers (I mean, if Ian hadn't given the preface).

Let the value be M

2x + 3y = 1
3x + 2y = 6M

Solving this,
-5y = 12M-1
M = (3-5y)/12

This is probably one of the most straightforward way of solving the equation!
  [#permalink] 26 Aug 2004, 07:50
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