I'm not sure but the question was written exactly like what i post[email protected] wrote:Hi kellymichaelsohhh,
Are there any typos in this prompt? Is the "extra X" in the phrase "xf(1-x)" supposed to be there?
GMAT assassins aren't born, they're made,
Rich
let's start with x = 0kellymichaelsohhh wrote:Given that the equation f(x) + xf(1-x) = x holds for every real number x. The value of f(-1) + f(1) is ....
(A) -1
(B) 0
(C) 1/3
(D) 1
(E) 4/3
Wowww its so wonderful! Thanks a lot haha. Can I ask you another question? Do you know how to calculate log without using calculator? For example: log(0.025)Brent@GMATPrepNow wrote:let's start with x = 0kellymichaelsohhh wrote:Given that the equation f(x) + xf(1-x) = x holds for every real number x. The value of f(-1) + f(1) is ....
(A) -1
(B) 0
(C) 1/3
(D) 1
(E) 4/3
The given info tells us that f(x) + xf(1-x) = x
So, f(0) + 0f(1-0) = 0
Simplify to get: f(0) + 0 = 0
This means that f(0) = 0
Now try x = 1
The given info tells us that f(x) + xf(1-x) = x
So, f(1) + 1f(1-1) = 1
Simplify to get: f(1) + 1f(0) = 1
We already determined that f(0) = 0, so when we plug in that value, we get:
f(1) + 1(0) = 1
Simplify to get: f(1) + 0 = 1
This means that f(1) = 1
Now try x = 2
So, f(2) + 2f(1-2) = 2
Simplify to get: f(2) + 2f(-1) = 2
Now try x = -1
So, f(-1) + (-1)f(1-(-1)) = -1
Simplify to get: f(-1) - f(2) = -1
Rearrange to get: -f(2) + f(-1) = -1
We now have two similar equations:
f(2) + 2f(-1) = 2
-f(2) + f(-1) = -1
If we ADD them, we get:
3f(-1) = 1
Divide both sides by 3 to get: f(-1) = 1/3
So, f(-1) + f(1) = 1/3 + 1
= [spoiler]4/3[/spoiler]
Answer: E
Cheers,
Brent
Wowww its so wonderful! Thanks a lot haha. Can I ask you another question? Do you know how to calculate log without using calculator? For example: log(0.025)Brent@GMATPrepNow wrote:let's start with x = 0kellymichaelsohhh wrote:Given that the equation f(x) + xf(1-x) = x holds for every real number x. The value of f(-1) + f(1) is ....
(A) -1
(B) 0
(C) 1/3
(D) 1
(E) 4/3
The given info tells us that f(x) + xf(1-x) = x
So, f(0) + 0f(1-0) = 0
Simplify to get: f(0) + 0 = 0
This means that f(0) = 0
Now try x = 1
The given info tells us that f(x) + xf(1-x) = x
So, f(1) + 1f(1-1) = 1
Simplify to get: f(1) + 1f(0) = 1
We already determined that f(0) = 0, so when we plug in that value, we get:
f(1) + 1(0) = 1
Simplify to get: f(1) + 0 = 1
This means that f(1) = 1
Now try x = 2
So, f(2) + 2f(1-2) = 2
Simplify to get: f(2) + 2f(-1) = 2
Now try x = -1
So, f(-1) + (-1)f(1-(-1)) = -1
Simplify to get: f(-1) - f(2) = -1
Rearrange to get: -f(2) + f(-1) = -1
We now have two similar equations:
f(2) + 2f(-1) = 2
-f(2) + f(-1) = -1
If we ADD them, we get:
3f(-1) = 1
Divide both sides by 3 to get: f(-1) = 1/3
So, f(-1) + f(1) = 1/3 + 1
= [spoiler]4/3[/spoiler]
Answer: E
Cheers,
Brent
You won't be required to perform any log calculations on the GMAT. The closest to this would be a question that required us to find some approximate exponent.kellymichaelsohhh wrote: Can I ask you another question? Do you know how to calculate log without using calculator? For example: log(0.025)
First recognize that 10^(-1) = 0.1If 10^x = 0.025, then what is the value of x?
A) -5.something
B) -4.something
C) -3.something
D) -2.something
E) -1.something
Oh thank you!😃Brent@GMATPrepNow wrote:You won't be required to perform any log calculations on the GMAT. The closest to this would be a question that required us to find some approximate exponent.kellymichaelsohhh wrote: Can I ask you another question? Do you know how to calculate log without using calculator? For example: log(0.025)
For example:
First recognize that 10^(-1) = 0.1If 10^x = 0.025, then what is the value of x?
A) -5.something
B) -4.something
C) -3.something
D) -2.something
E) -1.something
And 10^(-2) = 0.01
Since 0.025 is BETWEEN 0.1 and 0.01, x must be BETWEEN -1 and -2
Answer: E
Cheers,
Brent
