Data Sufficiency

If X is an integer, is X^4 + 4 prime?

1. 2(X+3) < 3X+7

2. X > 1


Source: Original

chieftang wrote:If X^4 + 4 prime?

1. 2(X+3) < 3X+7

2. X > 1


Source: Original

IMO E
we dont know whether x is an integer or not

rijul007 wrote:

chieftang wrote:If X^4 + 4 prime?

1. 2(X+3) < 3X+7

2. X > 1


Source: Original

IMO E
we dont know whether x is an integer or not

That was not intentional. The original question has now been reworded to indicate X is an integer.

The answer would still be E

St(1)
x>-1
Insuff

St(2)
x>1
Insuff

Combinnig the two sts
x>1
Insuff

rijul007 wrote:The answer would still be E

Try again.

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]

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 [/spoiler]

Well, not quite. Do you see it?

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

shucks

rijul007 wrote:shucks

Heheh... don't worry. It may not be GMAT material anyhow.

Good question mate !

chieftang wrote: Heheh... don't worry. It may not be GMAT material anyhow.

I certainly would hope not

very nice question btw

Very good Q. Wicked one

awesome ....thank this is not the actual GMAT question....

What kinda of lateral thinking ability is required for this?

karthikpandian19 wrote:awesome ....thank this is not the actual GMAT question....

What kinda of lateral thinking ability is required for this?

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"

It really gets you to think about concepts differently than when solving questions! Give it a shot.