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If (1+x)y=y, which of the following must be true?

This topic has 5 expert replies and 3 member replies

If (1+x)y=y, which of the following must be true?

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If (1+x)y=y, which of the following must be true?
A. x=-1 or y=0
B. x=0 or y=0
C. x=1 or y=1
D. x=-1 or y=-1
E. x=0 or y=1

OA is B

How to approach this question ?
My working:-
y + xy - y = 0
xy = 0
Now, here I am little confused. While taking answer choices should I put both values of x and y or should I work with the values of x and y independently or one at a time i.e
For (A) case 1 : x = -1 --> -1 * y = 0 (might be true)
case 2: y = 0 --> x * 0 = 0 (TRUE)
So, A is not the answer

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Hi vinni.k,

We're told that (1+X)(Y) = (Y). We're asked which of the following MUST be true - meaning that one of these answers is ALWAYS true no matter how many different examples we come up with. The answer choices provide us with a limited number of possibilities, so we can use them 'against' the prompt and TEST THE ANSWERS.

Mathematically-speaking, it would likely be easiest to TEST one of the '0' values first, so let's see what happens IF Y = 0....
(1+X)(Y) = (Y)
(1+X)(0) = (0)
0 = 0
This is clearly a possible solution to the given equation. If Y=0, then X could be any value. Thus, we need an answer that includes Y=0 and we need an "or" (since the value of X doesn't matter in this scenario). Eliminate Answers C, D and E.

Of the remaining 2 Answers, let's TEST X = 0 next...
(1+X)(Y) = (Y)
(1+0)(Y) = (Y)
(1)(Y) = Y
Y = Y
This is also clearly a possible solution to the given equation. If X=0, then Y could be any value. We now have the answer to the question.

Final Answer: B

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

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vinni.k wrote:
If (1+x)y=y, which of the following must be true?
A. x=-1 or y=0
B. x=0 or y=0
C. x=1 or y=1
D. x=-1 or y=-1
E. x=0 or y=1

OA is B

How to approach this question ?
My working:-
y + xy - y = 0
xy = 0
Now, here I am little confused. While taking answer choices should I put both values of x and y or should I work with the values of x and y independently or one at a time i.e
For (A) case 1 : x = -1 --> -1 * y = 0 (might be true)
case 2: y = 0 --> x * 0 = 0 (TRUE)
So, A is not the answer
Once you have determined that xy=0, consider each solution separately.

One solution for xy=0 is x=0.

A: x=-1 or y=0
If x=0, then it does not have to be true that x=-1 or y=0.
Eliminate A.

C: x=1 or y=1
If x=0, then it does not have to be true that x=1 or y=1.
Eliminate C.

D: x=-1 or y=-1
If x=0, then it does not have to be true that x=-1 or y=-1.
Eliminate D.

Another solution for xy=0 is y=0.

E: x=0 or y=1
If y=0, then it does not have to be true that x=0 or y=1.
Eliminate E.

The correct answer is B.

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Last edited by GMATGuruNY on Tue Feb 06, 2018 11:11 am; edited 1 time in total

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Quote:
If (1+x)y=y, which of the following must be true?
A. x=-1 or y=0
B. x=0 or y=0
C. x=1 or y=1
D. x=-1 or y=-1
E. x=0 or y=1

OA is B

How to approach this question ?
My working:-
y + xy - y = 0
xy = 0
Now, here I am little confused. While taking answer choices should I put both values of x and y or should I work with the values of x and y independently or one at a time i.e
For (A) case 1 : x = -1 --> -1 * y = 0 (might be true)
case 2: y = 0 --> x * 0 = 0 (TRUE)
So, A is not the answer
Hi vinni.k,
Let's take a look at your question.
$$\left(1+x\right)y=y$$
$$\left(1+x\right)=\frac{y}{y}$$
$$\left(1+x\right)=1$$
$$x=1-1=0$$

To find y let's evaluate the equation:
$$\left(1+x\right)y=y$$
$$y+xy=y$$
$$xy=y-y$$
$$xy=0$$
$$y=0$$

Therefore, Option B is correct.

I hope it helps.
I am available if you'd like any follow up.

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Thanks Economist for your explanation.

I understood your explanation, but i can still stuck when i am putting value of x = 0 back to the equation while evaluating for y. I can plug in x = 0 here (1+x)y=y
(1 + 0)y = y
(1)y = y
y = y
Now, it can create a problem, but after understanding your approach, i think if i play around with the equation, then i can land with y = 0. However, i still want to understand how can i use the answer choices as i have explained my doubt in the first post.

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Hi,

Can anyone please let me know how to approach this question through answer options. I have explained my doubt in the first post.
Though i have understood what Economist has explained, but i still think that i can get stuck somewhere.

Thanks

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vinni.k wrote:
If (1+x)y=y, which of the following must be true?
A. x=-1 or y=0
B. x=0 or y=0
C. x=1 or y=1
D. x=-1 or y=-1
E. x=0 or y=1
Let’s simplify the given equation:

(1 + x)y = y

y + xy = y

xy = 0

We see that either x or y must be zero.

Answer: B

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Master | Next Rank: 500 Posts
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Thanks for your different approaches on this question. Finally doubt cleared.
Really appreciate it

Regards

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vinni.k wrote:
Thanks Economist for your explanation.

I understood your explanation, but i can still stuck when i am putting value of x = 0 back to the equation while evaluating for y. I can plug in x = 0 here (1+x)y=y
(1 + 0)y = y
(1)y = y
y = y
Now, it can create a problem, but after understanding your approach, i think if i play around with the equation, then i can land with y = 0. However, i still want to understand how can i use the answer choices as i have explained my doubt in the first post.
Hi vinni.k,
xy=0 itself indicates that one of the variables either x or y or both should be zero, only then this equation will be true.
So we can say that
either x = 0 or y = 0.

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