If x and y are greater than 0, is x = 1 ?
(1) x/y = 1
(2) xy = 1
OA C
Source: GMAT Prep
If x and y are greater than 0, is x = 1 ?
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BTGmoderatorDC wrote: ↑Thu Feb 16, 2023 10:02 pmIf x and y are greater than 0, is x = 1 ?
(1) x/y = 1
(2) xy = 1
OA C
Source: GMAT Prep
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
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Brent

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If x and y are greater than 0, is x = 1 ?
(1) x/y = 1
This means x=y.
All values will satisfy the equation.
Insufficient
(2) xy = 1
x=1/y.
Thus, x and y are reciprocal, and all values will again satisfy the equation.
Insufficient
Combined.
x=y=1/y
So, y=1/y will give us y^2=1 or y = 1 or 1.
But y>0, so y=1.
Also x=y=1.
Sufficient
C
(1) x/y = 1
This means x=y.
All values will satisfy the equation.
Insufficient
(2) xy = 1
x=1/y.
Thus, x and y are reciprocal, and all values will again satisfy the equation.
Insufficient
Combined.
x=y=1/y
So, y=1/y will give us y^2=1 or y = 1 or 1.
But y>0, so y=1.
Also x=y=1.
Sufficient
C

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If x and y are greater than 0, is x = 1 ?
(1) x/y = 1
This means x=y.
All values will satisfy the equation.
Insufficient
(2) xy = 1
x=1/y.
Thus, x and y are reciprocal, and all values will again satisfy the equation.
Insufficient
Combined.
x=y=1/y
So, y=1/y will give us y^2=1 or y = 1 or 1.
But y>0, so y=1.
Also x=y=1.
Sufficient
C
(1) x/y = 1
This means x=y.
All values will satisfy the equation.
Insufficient
(2) xy = 1
x=1/y.
Thus, x and y are reciprocal, and all values will again satisfy the equation.
Insufficient
Combined.
x=y=1/y
So, y=1/y will give us y^2=1 or y = 1 or 1.
But y>0, so y=1.
Also x=y=1.
Sufficient
C