Are x and y both positive?

[arielle.bertman]

Are x and y both positive?

(1) 2x - 2y = 1
(2) x/y > 1

I quickly eliminated A and B since neither statement alone is sufficient but I am having a hard time setting up a methodical way to prove that together they are sufficient (the correct answer).

Thanks!

Arielle

[furtadovinod]

Are x and y both positive?

(1) 2x - 2y = 1
(2) x/y > 1

I quickly eliminated A and B since neither statement alone is sufficient but I am having a hard time setting up a methodical way to prove that together they are sufficient (the correct answer).

Thanks!

Arielle

Hi Areille,

I hope this can help.

Let's look at Statement (2) first

(2) x/y > 1
This statement tells me one of two things
(i) x & y are positive and x > y, OR
(ii) x & y are negative and x < y
By itself, as you have noted, its insufficient.

Statement (1) now
(1) 2x-2y=1
i.e. x - y = 0.5
i.e x = 0.5 + y
This tells me that x > y because I need to add 0.5(a positive value) to y to get x.
Again by itself insufficient.

For this statement, if you want to be sure just consider cases for variable y.
(i) y is positive: Then x is definitely a positive number greater than 1.
(ii) y is negative and greater than 0.5: Then x > y and x is also negative.
(iii) y is negative and lesser than 0.5: Then x > y and x is positive.

As you can see all the above cases show that x > y.

Taking (1) and (2) together, because (1) tells me that x > y it follows from (2) that x & y are positive.

Therefore, the answer is C.

[furtadovinod]

Are x and y both positive?

(1) 2x - 2y = 1
(2) x/y > 1

I quickly eliminated A and B since neither statement alone is sufficient but I am having a hard time setting up a methodical way to prove that together they are sufficient (the correct answer).

Thanks!

Arielle

Hi Areille,

I hope this can help.

Let's look at Statement (2) first

(2) x/y > 1
This statement tells me one of two things
(i) x & y are positive and x > y, OR
(ii) x & y are negative and x < y
By itself, as you have noted, its insufficient.

Statement (1) now
(1) 2x-2y=1
i.e. x - y = 0.5
i.e x = 0.5 + y
This tells me that x > y because I need to add 0.5(a positive value) to y to get x.
Again by itself insufficient.

For this statement, if you want to be sure just consider cases for variable y.
(i) y is positive: Then x is definitely a positive number greater than 1.
(ii) y is negative and greater than 0.5: Then x > y and x is also negative.
(iii) y is negative and lesser than 0.5: Then x > y and x is positive.

As you can see all the above cases show that x > y.

Taking (1) and (2) together, because (1) tells me that x > y it follows from (2) that x & y are positive.

Therefore, the answer is C.

(i) y is positive: Then x is definitely a positive number greater than 1.
should read as
(i) y is positive: Then x is definitely a positive number greater than y.

[dsprashanth]

Remember to not cross multiply without knowing the sign of the X and Y.

[Ben Ku]

Are x and y both positive?

(1) 2x - 2y = 1
(2) x/y > 1

Statement (1) can be rephrased: x - y = 0.5. We only know that x > y, since the difference is positive. (1) alone is insufficient.

Statement (2) has two options.
If x and y are both positive, then x must be larger than y, so x > y > 0.
If x and y are both negative, then x is more negative than y, so x < y < 0.
Because we don't know whether they are both positive or both negative, (2) alone is insufficient.

From (1), we know that x >y. The only option in (2) for this to be true is if they are both positive. (1) and (2) together are sufficient. (C) is the answer.

Hope that helps.

[lalitkc]

Hi Ben,
If x= - 9.5 and y = -10 ,
x-y= 0.5 and
x/y > 1 should be equivalent to saying x > y
However, x and y are negative .
So answer should be E

[anoo.anand]

answer chus be E for this.

x/y gives >> x and y either both +ve or both -ve

combining bith th options.

take x = 4 , Y = 3.5

2X-2Y = 1 ... thus both positive.

take X = -3.5 , Y = -4
2(-3.5)-2(-4) = 1 ...thus bith negative ...thus option E..

[kunalv3]

Hi,

can this be solved like this (is there anything wrong with this method,because this came instinctively to me)

to check for AC C: solving for 1 and 2

2x-2y=1
x=1/2+y
x/y=y/2+1

from2:x/y>1 this implies: y/2+1>1,this implies y>0

now that we know y>0,then from 2 (x/y>1)we can conclude x>0.
hence x>0 and y>0

IMO C

[Ben Ku]

lalitkc and anoo.anand:
Your examples don't hold for statement (2):

Hi Ben,
If x= - 9.5 and y = -10 ,
x-y= 0.5 and
x/y > 1 should be equivalent to saying x > y
However, x and y are negative .
So answer should be E

In this example, x/y = (-9.5)/(-10) which is less than 1. This example doesn't work for statement (2).

take X = -3.5 , Y = -4
2(-3.5)-2(-4) = 1 ...thus bith negative ...thus option E..

Here, x/y = (-3.4)/(-4), which is less than 1. This example doesn't work for statement (2) either.

kunalv3:

can this be solved like this (is there anything wrong with this method,because this came instinctively to me)

to check for AC C: solving for 1 and 2

2x-2y=1
x=1/2+y
x/y=y/2+1 [this line isn't quite right]

from2:x/y>1 this implies: y/2+1>1,this implies y>0

now that we know y>0,then from 2 (x/y>1)we can conclude x>0.
hence x>0 and y>0

You approach is fine except for a small error in algebra:
2x - 2y = 1
x = (2y + 1)/2 or x = y + 1/2
x/y = (y + 1/2) / y = 1 + 1/(2y)

Since x/y > 1
1 + 1/(2y) > 1
1/(2y) > 0
y > 0

Because x/y > 1, and y > 0, therefore x > 0.