If x and y are greater than 0, is x = 1 ?

Question

(1) x/y = 1
(2) xy = 1

I don't understand why it's C.

Shouldn't statement (2) be sufficient?

If xy=1 wouldn't that mean x and y are both "1" b/c given "x and y >0"?

What am I missing?

cellydan · Answer

Why 2 isn't sufficient is that X or Y can also be fractions.

X = 1/2, Y = 2

XY = 1

Sovjet · Answer

Fairly straightforward:

Statement 1:

Both of these are valid:  \frac{x}{y}=\frac{7}{7}=1  and  \frac{x}{y}=\frac{100}{100}=1  -   Insufficient

Statement 2:

Both of these are valid:  x*y=1*1=1  and  x*y=0.2*5=1  -   Insufficient

However, combining both statements, the only valid solution is:  \frac{x}{y}=\frac{1}{1}=1=x*y=1*1  where  x=1  and  y=1 .

Don't forget those pesky real numbers! Nowhere does the stem insist that these be integers.

krishp84 · Answer

You are not wrong, but check there are multiple values that x can take ?
 As per GMAC - All numbers are real numbers if not mentioned.

If X and Y are greater than 0, is x=1?
 Question gives : 
If X and Y are greater than 0.
Question asks : Is X = 1? --> Yes/No 
(1) x/y = 1
 Since y > 0 as per question stem, so x=y 
x > 0 , so x can take any value - 1,2,3,etc
So 1 is not sufficient 
(2) xy = 1
 If x is equal to 1, then y is equal to 1
If x is equal to 2, then y is equal to 1/2
If x is equal to 3, then y is equal to 1/3
All are valid, but there is no unique value of x. 
So (2) is not sufficient

Combining 1 and 2 - xy=1 and x=y
 XY = 1 
=>  x^2 = 1 
=>  x = +1 or -1 
But question tells x is greater than 1
So x = 1 is the only value x can take.

OA is C

Silver89 · Answer

ST 1 
x/y=1 and this means x=y so x and y can be 1 , 2, 3 , 4 , .......
EX : 5/5=1 4/4=1 1000/1000=1
NOT sufficient

ST2 
xy=1 and means x=1/y so x can be 1/5 so y = 5
EX" 1/5 * 5 = 1 
also not sufficient

ST1 & ST2 
x=y and xy=1
you can simply find that xx=1 this means x^2 = 1 so x= +1 or x= -1
and because y and x must be larger than 0 so x must be +1
sufficient

the answer is C

gmati3 · Answer

Nice question. I used to fall in this trap a lot.

S1: x/y = 1 
hence x = y .

Not sufficient

S2: xy =1 
No more info hence not sufficient

Now combining both

X^2 =1 
or x = +1,-1

Here is the trap where i used to miss the question statement all together . Since x is positive. It cannot take the negative value.

Hence x = 1. Sufficient

Answer is D

BrentGMATPrepNow · Answer

Target question :     Is x = 1 ?

Given : x and y are POSITIVE

Statement 1 : x/y = 1  
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two: 
 Case a : x = 1 and y = 1. In this case, the answer to the target question is  YES, x DOES equal 1 
 Case b : x = 2 and y = 2. In this case, the answer to the target question is  NO, x does NOT equal 1 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : xy = 1 
There are several values of x and y that satisfy statement 2. Here are two: 
 Case a : x = 1 and y = 1. In this case, the answer to the target question is  YES, x DOES equal 1 
 Case b : x = 2 and y = 1/2. In this case, the answer to the target question is  NO, x does NOT equal 1 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that x/y = 1
Statement 2 tells us that xy = 1
Take x/y = 1 (statement 1) and multiply both sides by y to get:  x = y 
Now take xy = 1 (statement 2) and replace  y  with  x  to get: (x)( x ) = 1
Simplify: x² = 1
This means EITHER x = 1, OR x = -1
However, since we're told that x is POSITIVE, it must be the case that  x = 1  
So, the answer to the target question is  YES, x DOES equal 1 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

ChiefsFan · Answer

Bunuel   mcelroytutoring   ScottTargetTestPrep

I understand this problem theoretically. Statement one says x and y are the same number. Statement two says that they are reciprocals of each other. Combined, the only number whose reciprocal is itself is one.

However, algebraically, I don't understand something. When I combine the two statements (both are equal to one), I see that "x/y=xy". This equation itself lends itself to multiple values of x; the "x" variables cancel each other out. This would lead me to believe that x can be multiple values (suggesting answer E), but I know that this is incorrect. Where am I going wrong here?

ScottTargetTestPrep · Answer

Setting x/y equal to xy is another way to solve this question. As you mentioned, x variables will cancel each other out (which is possible because we are given that x > 0) and we will be left with 1/y = y, or, equivalently, y^2 = 1. Now, y^2 = 1 implies that y = 1 or y = -1; but the latter is ruled out since we are given that y > 0. Thus, y = 1 and using either equation, we get that x = 1 as well.

Basshead · Answer

(1)  if x = y = 1; yes 
 if x = y = 7; no

INSUFFICIENT

(2)  xy = 1 
if  x = 0.5 y = 2; no 
if  x = y = 1; yes

INSUFFICIENT.

(1&2) Combined, x must be 1. SUFFICIENT.

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If x and y are greater than 0, is x = 1 ?

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