If x and yare positive, is x/y greater than 1 ?

SOLUTION

If x and yare positive, is x/y greater than 1 ?

Is \(\frac{x}{y}>1\)? --> as given that \(y\) is positive we can safely multiply both parts of the inequality by it --> so the question becomes "is \(x>y\)?" OR: is \(x-y>0\)?

(1) xy > 1 --> product of two numbers is more than one we can't say which one is greater. Not sufficient.

(2) x - y > 0. Directly answers the questions. Sufficient.

Answer: B.
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If x and yare positive, is x/y greater than 1 ?

(1) xy > 1
(2) x - y >O

(1) INFUFF: If x*y is greater than 1, it means that either X or Y is greater than two, the problem is that we do not know which one. X/Y could be 2/1 or 1/2
(2) SUFF (assuming integers) if z-y>0, x>y so necessarily x/y greater than one

IMO B

x > 0; y > 0
x/y > 1?
or x > 1? (safe multiply as both x and y are +ve)

(1)
xy > 1
There can be many values of x and y which can satisfy this equation.
eg. x= 2 and y = 0.75 is OK
x = .75 and y = 2 is also OK
Not sufficient

(2)
x - y > 0
=> x > y
Sufficient

hence B

good thing about this question is we are given that x and y are positive.
is x/y >1 ?
since y is positive ,
we can multiply the inequality both side with y .
now the question changes to
y * x/y > y
=> is x >y ?

from stat 1
xy > 1 , well in this case
x = 2 , y = 2 or x= 2 and y = 1 (both satisfies stat. 1 )
which does not give us x>y
insufficient

from stat 2
x-y >0
ofcourse x > y that is why x-y is greater than 0.
correct option - B.

Solution:

We are asked is x/y > 1?

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. We can eliminate answer choices A and D.

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.

The answer is B.
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(1) is not sufficient, because it is possible that x=1, y=2. So, while xy>1, but x/y <1.

On the other hand, it is possible that x=2, y=1. So, while xy>1, but x/y >1.

(2) is sufficient because it tells that x>y. Since the question mentions that x and y are positive, then it has to be the case that x/y>1.

B is the answer.

(2) x - y > 0

x > y.......... divide by y (No change in sign)

x/y > 1

Sufficient

(1) xy > 1

Let x = 2 & y= 1.......Answer Yes

Let x = 1 & y= 2.......Answer NO

Insufficient

Answer: B

Hello IanStewart
Does the highlighted part make sense?
What if x=5/2 (now it is greater than 2) and y=2/5. May I know your conviction about the highlighted part?
Thanks__
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No, the highlighted part is not correct. It might be true that x = 1.5 and y = 0.8, for example. When x and y are positive, then xy > 1 guarantees that at least one of the two unknowns is greater than 1, but you can't tell if either is greater than 2.
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It seems that the highlighted part is extreme point! Could you explain (with example) a bit the highlighted part, please?
Thanks__
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See my post above:


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Let's analyse what the question needs. for x/y>1, we definitely need the magnitude of x to be larger than y.since the question mentions clearly that both variables are positive, we don't need to worry about negative numbers.

S1: this can be any combination of numbers Lets take 2 examples :
a) x=3, y= 2. x/y=3/2. Nice, x/y>1.
b) x=2, y=3. but x/y= 2/3<1. Oops. Inconclusive, therefore let's strike off A and D.

S2: This has resolved our question in red above. Sufficient.

The final answer therefore, B.

Hope that's helpful.

To determine if x/y is greater than 1, we need to evaluate the given statements.

Statement (1): xy > 1
From this statement, we know that the product of x and y is greater than 1. However, this does not provide enough information to determine the relationship between x and y. For example, x could be greater than y, resulting in x/y being greater than 1. On the other hand, y could be greater than x, resulting in x/y being less than 1. Therefore, statement (1) alone is insufficient to determine if x/y is greater than 1.

Statement (2): x - y > 0
This statement tells us that the difference between x and y is greater than 0. Since both x and y are positive, this implies that x must be greater than y. If x is greater than y, then x/y will be greater than 1. Therefore, statement (2) alone is sufficient to determine that x/y is greater than 1.