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?

Sovjet · Accepted 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

cellydan · Answer

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

X = 1/2, Y = 2

XY = 1

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards