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# question from MGMAT test -

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Joined: 29 Jul 2009
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question from MGMAT test - [#permalink]

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18 Apr 2010, 08:30
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If #p# = ap3+ bp – 1 where a and b are constants, and #-5# = 3, what is the value of #5#?

The answer I found was (5) and here is how I solved the question.
for #-5# = 3, here is the equation -125a – 5b – 1 = 3
For #5#, the equation is 125a + 5b – 1 = X

then to find X, I substract the first equation from the second one

-125a – 5b – 1 = 3
-
125a + 5b – 1 = X

that gives -2 = 3-x, so x = 5

However, the correct answer is (-5) and here is how MGMAT solved it. I got their explanation, but I'm curious to know why my way didn't work!

Since we know the value of #-5# = 3, we can plug p = -5 into our formula:

(-5)3a + (-5)b – 1 = 3
-125a – 5b – 1 = 3
-125a – 5b = 4

We are asked to solve for #5#. If we plug 5 into our formula, we get:
(5)3a + (5)b – 1 = ?
125a + (5)b – 1 = ?

To figure this out, we would need to know the value of 125a + 5b.

From the first equation we know that -125a – 5b = 4. By multiplying both sides by negative one, we see that 125a + 5b = -4.

125a + 5b – 1 = ?
–4 – 1 = -5

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Re: question from MGMAT test - [#permalink]

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18 Apr 2010, 08:46
Expert's post
If #p# = ap3+ bp – 1 where a and b are constants, and #-5# = 3, what is the value of #5#?

The answer I found was (5) and here is how I solved the question.
for #-5# = 3, here is the equation -125a – 5b – 1 = 3
For #5#, the equation is 125a + 5b – 1 = X

then to find X, I substract the first equation from the second one

-125a – 5b – 1 = 3
-
125a + 5b – 1 = X

that gives -2 = 3-x, so x = 5

Your approach is much better than that of MGMAT's. Though there are two problems:

When you subtract equations you'll get: $$-250a-10b=3-x$$ (so you subtracted incorrectly) and this doesn't work.

What you should have done is to add equations instead of subtracting: $$-125a-5b-1+125a+5b-1=3+x$$ --> $$-2=3+x$$ --> $$x=-5$$.

Hope it helps.
_________________
Re: question from MGMAT test -   [#permalink] 18 Apr 2010, 08:46
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