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.

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:

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.