IMO Echieftang wrote:If X^4 + 4 prime?
1. 2(X+3) < 3X+7
2. X > 1
Source: Original
we dont know whether x is an integer or not
Is an expression prime (750+ level question?)
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chieftang
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That was not intentional. The original question has now been reworded to indicate X is an integer.rijul007 wrote:IMO Echieftang wrote:If X^4 + 4 prime?
1. 2(X+3) < 3X+7
2. X > 1
Source: Original
we dont know whether x is an integer or not
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rijul007
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oki got it
x^4+4
=> (x^2)^2 + 2^2 + 2(2)(x^2) - 2(2)(x^2)
=> (x^2 + 2)^2 - 4x^2
=> (x^2 + 2 - 2x)(x^2 + 2 +2x)
Not a prime no
Nice question..
this was one nasty trap
Option [spoiler]F- The ques itself is suff[/spoiler]
x^4+4
=> (x^2)^2 + 2^2 + 2(2)(x^2) - 2(2)(x^2)
=> (x^2 + 2)^2 - 4x^2
=> (x^2 + 2 - 2x)(x^2 + 2 +2x)
Not a prime no
Nice question..
this was one nasty trap
Option [spoiler]F- The ques itself is suff
[/spoiler]-
chieftang
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Well, not quite. Do you see it?rijul007 wrote:oki got it
x^4+4
=> (x^2)^2 + 2^2 + 2(2)(x^2) - 2(2)(x^2)
=> (x^2 + 2)^2 - 4x^2
=> (x^2 + 2 - 2x)(x^2 + 2 +2x)
Not a prime no
Nice question..
this was one nasty trap
Option [spoiler]F- The ques itself is suff
1. X > -1
Let X=0, then X^4+4 = 4, non-prime
Let X=1, then X^4+4 = 5, prime
INSUFFICIENT
2. X > 1
OK, what do we know about prime numbers? Well a prime number is the product of 1 and itself. Let's see if we can restate X^4 + 4 as a product of two numbers via factoring...
This is a little tricky.
Let A=X^2 just to make things look a little more sane:
A^2 + 4
(A^2 + 4A + 4) - 4A (add and subtract 4A to the above eqn)
(A+2)(A+2) - 4A (factored the parenthetical part of the previous eqn)
Now let's substitute X^2 back in for A and simplify:
(X^2+2)^2 - (2X)^2 (now we have the difference of two squares)
We know how to factor the difference of two squares:
(X^2 + 2 + 2X)(X^2 + 2 - 2X)
There. Now we have a product of two expressions which we know are integers.
So, given X > 1, let's look at the product of (X^2 + 2X + 2) * (X^2 - 2X + 2)
By testing values:
X=2:
10*2 Non-prime
X=3:
17*5 Non-prime
Clearly we can now see, when X > 1, neither term of the product (X^2 + 2X + 2)(X^2 - 2X + 2) will ever be 1.
Therefore, the product is never prime. If the product is never prime, then X^4+4 is never prime.
SUFFICIENT
Answer B
Last edited by chieftang on Sun Jan 08, 2012 5:23 pm, edited 2 times in total.
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neelgandham
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Good question mate !
Anil Gandham
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Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
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santhoshsram
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karthikpandian19
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awesome ....thank this is not the actual GMAT question....
What kinda of lateral thinking ability is required for this?
What kinda of lateral thinking ability is required for this?
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chieftang
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Thanks guys. I gotta say, one piece of advice over at gmathacks that I'm both having a lot of fun with and learning from is this: "Trying writing your own questions"karthikpandian19 wrote:awesome ....thank this is not the actual GMAT question....
What kinda of lateral thinking ability is required for this?
It really gets you to think about concepts differently than when solving questions! Give it a shot.
