Does x + y = xy ? (1) The product of x and a positive integer, z, is

Question

Does x + y = xy ?

(1) The product of x and a positive integer, z, is not equal to x.

(2) y is neither positive nor negative.

sumitkrocks · Answer

statement (1) The product of x and a positive integer, z, is not equal to x.

This tells us 
x is not equal to 0 and 
z is not equal to 1

Not sufficient

Statement (2) y is neither positive nor negative.
This tells us 
y = 0
Not sufficient

Combined 
 x + y = xy
LHS = x as y is 0 and x is not 0 ( some poitive or negative value)
But RHS = 0 as y = 0

Sufficient 
Answer is NO

C is the answer IMO

QuantMadeEasy · Answer

Step 1: Understanding the question 
Rephrasing the question as:
"Does y = xy - x ?"
"Does y = x(y - 1) ?"
"Does x = y /(y - 1) ?"

Step 2: Understanding statement 1 alone 
x*z ≠ x
x ≠0
As y is unknown, Insufficient

Step 3: Understanding statement 2 alone 
y=0
As x is unknown, Insufficient

(1)+(2),  
x ≠0 and y =0
Sufficient

C is correct

kantapong · Answer

Q: Does x + y = xy? (Nothing can be done about it)
1) If z is positive integer, xz != x -> (z-1)x != 0
This means both x != 0 and z-1 != 0 (still tell nothing)
2) y = 0 -> x = 0? (still tell nothing)
Combine both 1 and 2, 1 implies x != 0 and 2 implies y = 0, so x = 0 is false.
Answer = C

ReedArnoldMPREP · Answer

The question is interesting. Sums and products are usually different. 2+3 ≠ 2*3, 4*15 ≠ 4+15....

When would these be equal? Well, 0 + 0 = 0*0, so if they were both zero... 2+2 = 2*2...

I don't think there are any other possibilities! (in general, if math looks 'weird' at all, check the numbers -1, 0, 1, and 2. They are relatively weird numbers).

Statement 1 says xz≠x, so x is not zero. Because if x = 0, 0z=0.

So I know I'm not in the '0 + 0' category.

Statement 2 says y is neither positive nor negative, so the only thing left is that y is 0. But with st 2 alone, I have to pretend to forget that x≠0 from statement 1. So statement 2 alone is NS.

But together, y = 0, x≠0, so x+y ≠ xy because xy=0 and x+y ≠ 0.

TAKEAWAYS: 
--Some investigation upfront is a good idea. 
--Math that looks 'weird' often involves -1, 0, 1, or 2.
--When you move to statement 2, remember to 'forget' the information in statement 1, for a moment.

harshtandel838 · Answer

This is a YES/NO question
 x + y = xy ?

Let’s dig down the statements

STATEMENT 1:
 xz is not equal to x  and z is a positive integer. Not possible situations  x = 0   OR  x and y both equals ‘1’ 
So,  x is not equal to 0 or 1 
What about  y..?  we need to answer the stimulus.. No idea!
 Insufficient

STATEMENT 2:
From the set of number system, if  y  is not  positive  OR  negative,   the.  y is ‘0’ 
Okay! What about x?
 INSUFFICIENT

CONSIDERING BOTH STATEMENTS:
Clearly,  y  is  ‘0’  we don’t need to worry about value of  x,  because the answer will always be  ‘0’ 
 SUFFICIENT

Hence, answer is  C

Posted from my mobile device

Archit3110 · Answer

target find whether x+y=xy
#1
The product of x and a positive integer, z, is not equal to x.
this means that value of x is not 0 and z can be any value
insufficient as y is not known
#2
 y is neither positive nor negative.
y is 0 ; but x is not known
from 1 &2
x is not 0 and y is 0 
so x + y = xy is not possible
sufficient
option C

HarshaBujji · Answer

As there is no info in the question, Let's dive into statements.

Statement 1: 
So x cannot be 0 from this statement.

Statement 2: 
So y=0;

x+y=xy;
If y=0;
x=0 which may or may not be possible.

Hence if x not equal to 0, x+y=xy, Always false.

So  IMO C

IanStewart · Answer

There are infinitely many possibilities:

x + y = xy
xy - y = x
y(x - 1) = x
y = x/(x - 1)

so any time y = x/(x-1), it will be true that x + y = xy, e.g. x = 3 and y = 3/2 is another solution.

It's true that x = 0, y = 0, and x = 2, y = 2, are the only two integer solutions. If x is negative, y is between 0 and 1. When x is positive, since x and x-1 are consecutive, their GCD is 1, so the fraction x/(x-1) will never cancel down at all, and will only equal a whole number when x - 1 = 1, or x = 2.

Does x + y = xy ? (1) The product of x and a positive integer, z, is

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