Does xy = 1? (1) x > y (2) x = 1/y

Solution

Step 1: Analyse Question Stem

We need to find if \(x*y = 1\).

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: \(x > y\)

• We don’t know what type of numbers are x and y. Hence based on this statement only, we cannot determine if xy =1.
• For example, let us take two simple cases:

o Case1: If \(x = 2 \) and \(y = \frac{1}{2}\)

 \(xy = 2*\frac{1}{2 }= 1\)
o Case 2: \(x = 2\) and \(y = 1\)

 \(xy = 2*1 =2 ≠1\)

Results of the above two cases are not same.Hence, statement 1 is not sufficient and we can eliminate answer options A and D
Statement 2: \(x = 1/y\)

• From statement 2: \(x = \frac{1}{y}\)

o Multiplying both side of the above equation by y, we get:

 \(x*y = y*\frac{1}{y} = 1\)

Hence, statement 2 is sufficient.
Thus, the correct answer is Option B.
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Does xy = 1?

Starting from statement (2)

(2) x = 1/y
Multiplying y on both the sides
xy = 1
Sufficient

(1) x > y
Product xy is unknown
Insufficient

IMO B

Target question: Does xy = 1?

Statement 1: x > y
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 0.5. In this case, xy = (2)(0.5) = 1. So, the answer to the target question is YES, xy equals 1
Case b: x = 2 and y = 1. In this case, xy = (2)(1) = 2. So, the answer to the target question is NO, xy does NOT equal 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: x = 1/y
Multiply both sides of the equation by y to get: xy = 1
So, the answer to the target question is YES, xy equals 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

ASIDE: Some students may be concerned that I just multiplied both sides of the equation by a variable (y), which opens up the potential of inadvertently multiplying by zero.
However, the equation x = 1/y implies that why cannot equal zero, because 1/0 is undefined (i.e., it cannot be evaluated to be a real number).
So, if 1/0 it's not a real number, then we cannot say that x = 1/0, since that would mean that X is also not a real number

Answer: B

Cheers,
Brent

Asked: Does xy = 1?

(1) x > y
There are many possibilities e.g.
1. x= 2 & y=1; xy=2
2. x=2 & y=1/2; xy=1
NOT SUFFICIENT

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

IMO B

Posted from my mobile device

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The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
The question \(xy = 1\) is equivalent to \(x = \frac{1}{y}\).

Then, condition 2) is sufficient obviously.

Condition 1)

If \(x = 2, y = \frac{1}{2}\), then we have \(xy = 1\) and the answer is 'yes'.
If \(x = 4, y = \frac{1}{2}\), then we have \(xy = 2\) and the answer is 'no'.

Since condition 1) does not yield a unique solution, it is not sufficient.

Therefore, B is the answer.

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