If x and y are positive, is x/y greater than 1 ?
(1) xy > 1
(2) x - y > 0
OA: B
Anyone, please what's the solution to the problem. Bunch of thanks!
OG2015 DS If x and y
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- lionsshare
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Target question: Is x/y > 1?lionsshare wrote:If x and y are positive, is x/y greater than 1 ?
(1) xy > 1
(2) x - y > 0
Given: x and y are positive
Statement 1: xy > 1
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 = 1 and y = 2. Here, x/y = 1/2, which means x/y < 1
Case b: x = 2 and y = 1. Here, x/y = 2/1 = 2, which means x/y > 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x-y > 1
With this statement, it might be useful to consider rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Since x and y are positive, we can take the inequality x/y > 1 and multiply both sides by y to get: x > y.
Now let's subtract both sides by y to get: x - y > 0
So, let's REPHRASE the target question...
REPHRASED target question: Is x-y > 0?
Statement 2 tells us that x - y > 1
Since 1 > 0, we can say that x - y > 1 > 0
So, we can conclude that x - y > 0
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer = B
Cheers,
Brent
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- ceilidh.erickson
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Slight variation on Brent's explanation...lionsshare wrote:If x and y are positive, is x/y greater than 1 ?
(1) xy > 1
(2) x - y > 0
OA: B
Anyone, please what's the solution to the problem. Bunch of thanks!
We rephrase the target question from the beginning as:
is x/y > 1 --> is x > y ?
(Because we know that both x and y are positive, we can multiply both sides by y). We are looking for a RELATIVE relationship between x and y.
(1) xy > 1
Knowing something about the product of the two tells us nothing about the RELATIVE sizes of x and y. We can have a product greater than 1 with a larger x or with a larger y.
Insufficient.
(2) x - y > 0
Add y to both sides: x > y
Since this gives us exactly our target question, it's sufficient.
The answer is B.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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- Jeff@TargetTestPrep
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We are asked is x/y > 1?lionsshare wrote:If x and y are positive, is x/y greater than 1 ?
(1) xy > 1
(2) x - y > 0
Since x and y are positive we can multiply both sides of our inequality by y to obtain:
Is x > y?
Statement One Alone:
xy > 1
Knowing that the product of xy is greater than 1 does not allow us to determine whether x is greater than y.
For example, if x = 2 and y = 1, then x > y, but if x = 1 and y = 2, then x < y.
Statement one alone is not sufficient to answer the question.
Statement Two Alone:
x - y > 0
We can add y to both sides of the inequality to obtain:
x > y
Statement two is sufficient to answer the question.
Answer: B
Jeffrey Miller
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