Inequalities (Pos/Neg): Is x less than y ?

II wrote:Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.

(1) 2x < 3y

Let's pick numbers to see if we can get a yes and a no:

x = 1 y=20 (2 < 60)
Is 1 < 20? YES

x=2.5 y=2 (5 < 6)
Is 2.5 < 2? NO

YES and NO: insufficient.

(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).

Thanks Stuart. This was also the approach I used.
Is there another approach to solve this, apart from plugging-in numbers ?

Thanks.

II wrote: Is there another approach to solve this, apart from plugging-in numbers ?

Here is the another solution:-

Statement 1: 2X < 3Y

Now analyze this above statement....

X/Y <3/2

X/Y < 1.5

It means that X/Y could be greater than 1 also but always less than 1.5

To make X/Y >= 1, the Y should either be equal to X or less than X.

In other words, X could be less Y only in case X/Y < 1.

So statement 1 would be insufficient.

For statement 2 and combined, its simple as explained by Stuart.

Stuart wrote:(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).

Hope it makes sense

Stuart Kovinsky wrote:

II wrote:Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.

(1) 2x < 3y

Let's pick numbers to see if we can get a yes and a no:

x = 1 y=20 (2 < 60)
Is 1 < 20? YES

x=2.5 y=2 (5 < 6)
Is 2.5 < 2? NO

YES and NO: insufficient.

(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).

FOR STATEMENT 1 HOW DO YOU KNOW YOU IF YOU CAN ONLY PICK POSITIVE NUMBERS? HOW DO YOU DETERMINE THAT?

We can pick any number with any sign we want to as long as the stem condition and condition in statement (1) are satisfied.

x < y : YES

x > y : NO


2x < 3y

2*1/2 < 3*1 (Considering x = 1/2 and y = 1 : YES)

2*1 < 3*1 (Considering x = 1 and y = 1 : NO)

KICKGMATASS123 wrote:

Stuart Kovinsky wrote:

II wrote:Is x less than y ?

(1) 2x is less than 3y

(2) xy is greater than 0.

Interested in your logic in solving this question.

Thanks in advance.

(1) 2x < 3y

Let's pick numbers to see if we can get a yes and a no:

x = 1 y=20 (2 < 60)
Is 1 < 20? YES

x=2.5 y=2 (5 < 6)
Is 2.5 < 2? NO

YES and NO: insufficient.

(2) xy > 0

i.e. x and y are either both negative or both positive.
No info about values: insufficient.

Combined:

The numbers we chose for (1) are all positive, so they also follow (2). Therefore, we can pick the same numbers and still get a YES and a NO: not enough information, choose (E).

FOR STATEMENT 1 HOW DO YOU KNOW YOU IF YOU CAN ONLY PICK POSITIVE NUMBERS? HOW DO YOU DETERMINE THAT?