IF x does not equal -1

Question

If X does not equal -1 then 1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) is equal to A) -1 B) 1 C) X D) 1-x E) X-1 Can someone touch on this

mohit_1607 · Answer

IMO D

srcc25anu · Answer

1-x^16 can be broken down using the formula a^2 - b^2 = (a-b)*(a+b)
therefore 1-x^16 = (1+x^8)*(1-x^8)
Now 1-x^8 can be (1+x^4)*(1-x^4)
Now 1-x^4 can be (1+x^2)*(1-x^2)
Now 1-x^2 can be (1+x)*(1-x)

So (1-x^16) = (1+x^8)*(1+x^4)*(1+x^2)*(1+x)*(1-x)
Denominator = (1+x^8)*(1+x^4)*(1+x^2)*(1+x)

Dividing only leaves (1-x)

Hence ans D

GMATGuruNY · Answer

bpolley00 wrote:If X does not equal -1 then 1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) is equal to
A) -1
B) 1
C) X
D) 1-x
E) X-1

Can someone touch on this

Here's another approach.
Plug "nice" values into to the given expression and evaluate.

Try x = 0
1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) = 1-0^16/(1+0)(1+0^2)(1+0^4)(1+0^8)
= 1
So, when x = 0, the expression evaluates to be 1
The correct answer will be an expression that also evaluates to be 1, when x = 0.
When we plug 0 into the 5 answer choices, only B and D evaluate to be 1
So, we can eliminate A, C and E.

Now try another "nice" value for x.
Try x = 1
1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) = 1-1^16/(1+1)(1+1^2)(1+1^4)(1+2^8)
= 0
When we plug 1 into answer choices B and D, only D evaluates to be 0
So, the correct answer is D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Atekihcan · Answer

Note that if we multiply the denominator with (1 - x), it will cause a chain of multiplications and the denominator will become (1 - x¹�) as (1 - x)(1 + x) = (1 - x²) and (1- x²)(1 + x²) = (1 - x�) and so on.

So let us multiply both the numerator and denominator wit (1 - x) and we can safely do that as x ≠ 1.
So, the given expression can be written as (1 - x)(1 - x¹�)/(1 - x¹�) = (1 - x)

Answer : D

Manpreet Singh · Answer

Remember basic algebra rule

(a^2 - b^2)= (a-b)*(a+b)

we are given (1-x^16)it can be written as (1-x^8)(1+x^8)
Further elaborating
(1-x^4)(1+x^4)(1+x^8)
Now
(1-x^2)(1+x^2)(1+x^4)(1+x^8)

Finally (1-x)(1+x)(1+x^2)(1+x^4)(1+x^8)

So (1-x)(1+x)(1+x^2)(1+x^4)(1+x^8)/(1+x)(1+x^2)(1+x^4)(1+x^8)

so we are left with 1-x
Ans is D

Brent@GMATPrepNow · Answer

bpolley00 wrote:If X does not equal -1 then 1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) is equal to
A) -1
B) 1
C) X
D) 1-x
E) X-1

Can someone touch on this

Here's another approach.
Plug "nice" values into to the given expression and evaluate.

Try x = 0
1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) = 1-0^16/(1+0)(1+0^2)(1+0^4)(1+0^8)
= 1
So, when x = 0, the expression evaluates to be 1
The correct answer will be an expression that also evaluates to be 1, when x = 0.
When we plug 0 into the 5 answer choices, only B and D evaluate to be 1
So, we can eliminate A, C and E.

Now try another "nice" value for x.
Try x = 1
1-x^16/(1+X)(1+X^2)(1+X^4)(1+X^8) = 1-1^16/(1+1)(1+1^2)(1+1^4)(1+2^8)
= 0
When we plug 1 into answer choices B and D, only D evaluates to be 0
So, the correct answer is D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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