For which of the following functions is g(c-d) = g(c) - g(d)

Question

For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = 3x−−√3x
D g(x) = 5x
E g(x) 15/x

well its jus asking if they are the same or not, for that just substitute the value and we can find out.
Option D is the corect answer.

EMPOWERgmatRichC · Accepted Answer

Hi All,

In these types of "function" questions, you can TEST VALUES (especially really simple ones) to find the correct answer.

Let's TEST...
C = 2
D = 1

The question asks us to find the equation that gives us the same result when...

g(2-1) = g(1) is calculated

and when

g(2) - g(1) is calculated

Answer A: g(X) = X^3
g(1) = 1^3 = 1
g(2) - g(1) = 2^3 - 1^3 = 8 - 1 = 7
1 does NOT = 7

Answer B: g(X) = X+5
g(1) = 1+5 = 6
g(2) - g(1) = (2+5) - (1+5) = 7 - 6 = 1
6 does NOT = 1

Answer C: g(X) = \sqrt{3X}
g(1) = \sqrt{3}
g(2) - g(1) = \sqrt{6} - \sqrt{3} = \sqrt{3}(\sqrt{2} - 1)
\sqrt{3} does NOT = \sqrt{3}(\sqrt{2} - 1)

Answer D: g(X) = 5X
g(1) = 5(1) = 5
g(2) - g(1) = 5(2) - 5(1) = 10 - 5 = 5
5 DOES = 5

Answer E: g(X) = 15/X
g(1) = 15/1 = 15
g(2) - g(1) = 15/2 - 15/1 = -15/2
15 does NOT = -15/2

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

emmak · Answer

This problem arises because in such type of questions the original function is not given. Instead, we have to find a function which can satisfy the constraint mentioned in the question.
Constraint--> g(c-d) = g(c) - g(d)--->(1), where (c-d), c, d are the values of x. 
I am directly putting the value in the answer. You can verify the incorrect option by yourself.

Function as per option D is --->g(x) = 5x
Put the value of x = (c-d), we get --->g(c-d) = 5 (c-d) = 5c - 5d----(LHS)
Put the value of x = c, we get --->g(c) = 5 (c) = 5c ----(RHS)
Put the value of x = d, we get --->g(d) = 5 (d) = 5d----(RHS)

Equate RHS & LHS we get--> 5c - 5d = 5c - 5d
Thus equal.

So the answer is D.

Emma

Kris01 · Answer

In such questions these are the steps I find useful!!

1) The first step is to check whether you could solve the expression stated in the question( in case the expression is too long) or substitute the expression into the solutions in some manner so as to solve it quickly. If so, this is the quickest way out and usually with a little bit of practice, you can start judging whether this step would work or not before you place your pen on the paper to solve the question.

2) The next method is to find whether the solutions can be substituted into the original expression in some way that is fast and quick. This usually takes some time and hence, mostly does not work. However, if the answer options involve numbers instead of expressions, this might work better.

This method is only for those questions in which the answer options and the questions both contain expressions.

3) You could try substitution of base values to confirm.

.

Rajkiranmareedu · Answer

Why is option C Wrong
\sqrt{3(c-d)} = \sqrt{(3c)}-\sqrt{(3d)}

doe007 · Answer

Option C says g(x) =  \sqrt{3x}

So, g(c-d) =  \sqrt{c-d} 
g(c) =  \sqrt{c} 
g(d) =  \sqrt{d}

We cannot say that  \sqrt{c-d}  =  \sqrt{c}  -  \sqrt{d}  for all values of c and d
So we cannot say that g(c-d) = g(c) - g(d) for all values of c and d.

Thus, option c is wrong.

krrish · Answer

put c = 3 and d = 2 or directly substitute c and d we get option D,

PareshGmat · Answer

A g(x) = x^3

Power of "x" is changed, so IGNORE

B g(x) = x+5

"x" is added by constant, so IGNORE

C g(x) = \sqrt{3x}

Power of "x" is changed, so IGNORE

D g(x) = 5x

"x" is multiplied by constant 5, so required result is true

E g(x) 15/x

\frac{15}{x} = 15 * x^{-1}

Again power of "x" is changed, so IGNORE

Answer = D

FB2017 · Answer

Plug in values as c=4 and d=2
which will bring down the funtion in problem statement to g(2)=g(4)-g(2).
Now substituting the values in the option available as per the above equation LHS=RHS is option D.

abhishekdadarwal2009 · Answer

For which of the following functions is g(c-d) = g(c) - g(d) for all positive numbers c and d?

A g(x) = x^3
B g(x) = x+5
C g(x) = 3x−−√3x
D g(x) = 5x
E g(x) 15/x

well its jus asking if they are the same or not, for that just substitute the value and we can find out.
Option D is the corect answer.

ScottTargetTestPrep · Answer

We can let c = 2 and d = 1, and thus we are solving for both sides being equal when:

g(1) = g(2) - g(1)

Starting with answer choice E, we have 15/x:

g(1) = 15/1 = 15

g(2) = 15/2 = 7.5

g(2) - F(1) = 7.5 - 15 = -7.5

Since 15 does not equal -7.5, E is not correct.

Moving to D, we have 5x:

g(1) = 5 x 1 = 5

g(2) = 5 x 2 = 10

g(2) - g(1) = 10 - 5 = 5

Since 5 does equal 10 - 5, D might be correct.

For answer choice C, we have √3x:

g(1) = √(3*1) = √3

g(2) = √(3*2) = √6

Since √3 does not equal √6 - √3 = √3(√2 - 1), C is not correct.

For answer choice B, we have x + 5:

g(1) = 1 + 5 = 6

g(2) = 2 + 5 = 7

Since 6 does not equal 7 - 6 = 1, B is not correct.

For answer choice A, we have x^3:

g(1) = 1

g(2) = 8

Since 1 does not equal 8 - 1 = 7, A is not correct.

Since the only answer choice that is definitely not incorrect is D, it must be the correct answer.

Answer: D

achloes · Answer

ScottTargetTestPrep   EMPOWERgmatRichC

Would you mind explaining your reasoning behind picking the numbers you picked for c and d?

Does one need to be strategic with the number-picking or will any small integers work for such questions?

Thanks in advance!

EMPOWERgmatRichC · Answer

Hi achloes, In most situations in which you can TEST VALUES to get to the correct answer, you can use whichever value(s) you like (as long as the values fit whatever 'restrictions' the prompt defines). There are absolutely situations in which choosing specific numbers can make the work easier; in this prompt, we are told that the values of C and D and POSITIVE numbers - so selecting a couple of small positive integers (for example, 2 and 1, respectively) makes working through the five answer choices really easy. GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

ScottTargetTestPrep · Answer

Just pick numbers that are easy to work with. For example, here, 2 and 1 seemed like they would not make the math too difficult.

bumpbot · Answer

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For which of the following functions is g(c-d) = g(c) - g(d)

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