Are you sure you transcribed the question correctly?sanjoy18 wrote:If (ax+b)+3/(ax+b)=2 then value of [(ax+b)^3-(ax+b)]is
a)-2
b)-3
c)-6
d)-4
e)none of these
Cheers,
Brent
Algebra
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Cheers,
Brent
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sanjoy18
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Hi Brent.
Actually i tried the question yesterday almost 2 hours but could not get correct result. so I posted in this forum..But Today morning I have tried again and get the solution..Here It is..
lets ax+b=p
then it is given that
p+3/p=2 then p^3-p???
now p+3/p=2
>>p^2=2p-3..............(A)
>> p^3=2p^2-3p
>>p^3=2(2p-3)-3p..using (A) again
>> p^3=4p-6-3p
>> p^3=p-6
>> p^3-p= -6
therefore Ans is -6
hence C
Let me know if you have issues to my approach
Regards,
Sanjoy
Actually i tried the question yesterday almost 2 hours but could not get correct result. so I posted in this forum..But Today morning I have tried again and get the solution..Here It is..
lets ax+b=p
then it is given that
p+3/p=2 then p^3-p???
now p+3/p=2
>>p^2=2p-3..............(A)
>> p^3=2p^2-3p
>>p^3=2(2p-3)-3p..using (A) again
>> p^3=4p-6-3p
>> p^3=p-6
>> p^3-p= -6
therefore Ans is -6
hence C
Let me know if you have issues to my approach
Regards,
Sanjoy
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Brent@GMATPrepNow
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That's a very elaborate/tricky solution. Unless there's a different (nicer) solution here, this one might be past the 800+ range.sanjoy18 wrote:Hi Brent.
Actually i tried the question yesterday almost 2 hours but could not get correct result. so I posted in this forum..But Today morning I have tried again and get the solution..Here It is..
lets ax+b=p
then it is given that
p+3/p=2 then p^3-p???
now p+3/p=2
>>p^2=2p-3..............(A)
>> p^3=2p^2-3p
>>p^3=2(2p-3)-3p..using (A) again
>> p^3=4p-6-3p
>> p^3=p-6
>> p^3-p= -6
therefore Ans is -6
hence C
Let me know if you have issues to my approach
Regards,
Sanjoy
Now there is another solution, but this solution highlights the larger issue with this question. This question goes beyond the realm of real numbers, and GMAT questions stay within the realm of real numbers.
Here's what I mean:
As you noted, if we let ax + b = p, then we get the equation p + 3/p = 2
Multiply both sides by p to get: p² + 3 = 2p
Rearrange to get: p² - 2p + 3 = 0
Since we can't factor this quadratic equation, we can apply the quadratic formula.
When we do so, we get p = 1 + √(-2) or p = 1 - √(-2)
Since √(-2) is not a real number, p is not a real number, which means a, b and x are not real numbers.
Once we know that p = 1 + √(-2) or p = 1 - √(-2), we can plug these values into the expression p^3 - p and then evaluate.
Doing so, however, would require us to know how to deal with non-real (complex/imaginary) numbers, and this goes beyond the scope of the GMAT.
It's certainly a clever question, but I don't think it's something that anyone would see on test day.
Cheers,
Brent
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cd86
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this might be a really silly way to guess the answer without solving for the whole thing :
q : If (ax+b)+3/(ax+b)=2 then value of [(ax+b)^3-(ax+b)]is
I first took (ax+b)=m
so the equation becomes m+ 3/m =2
=> m^2 -2m+3= 0 ,realised that this cannot be solved quickly..so looked at what is being asked i.e (m^3-m) = ?
m^3-m => m( m^2-1) = (m-1)m (m+1)
now amongst the answer choices only -6 can be split into a multiplication of 3 consecuitve numbers..so i chose -6
q : If (ax+b)+3/(ax+b)=2 then value of [(ax+b)^3-(ax+b)]is
I first took (ax+b)=m
so the equation becomes m+ 3/m =2
=> m^2 -2m+3= 0 ,realised that this cannot be solved quickly..so looked at what is being asked i.e (m^3-m) = ?
m^3-m => m( m^2-1) = (m-1)m (m+1)
now amongst the answer choices only -6 can be split into a multiplication of 3 consecuitve numbers..so i chose -6
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Brent@GMATPrepNow
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This approach is a great idea. However, it might not apply here.cd86 wrote:
m^3-m => m( m^2-1) = (m-1)m (m+1)
now amongst the answer choices only -6 can be split into a multiplication of 3 consecutive numbers..so i chose -6
(m-1), m, and (m+1) aren't 3 consecutive integers. In fact, they aren't even real numbers. As such, we can't make many conclusions about their product.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
