If x and y are positive, is 4x > 3y?

from the stem: \(x/y>3/4\)?
1) \(2x>y\)
\(x/y > 1/2\)
not sufficient as \(x/y\) could be greater or smaller than \(3/4\)
2) \(x/y < 1\)
not sufficient for the same reason
both:
\(1/2 < x/y < 1\)
still not sufficient for the same reason

If x and y are positive is 4x > 3y ?

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

Can someone provide good pointers into handling such question. I also have a doubt about the ans. thanks

This is how I would have done it:

Question: is 4x>3y
Or is (x/y)>(3/4)?

Stmt1 -- Given x>y-x
Hence, 2x>y or (x/y)>(1/2) --INSUFF

Stmt 2 -- Given (x/y)<1 --INSUFF

Together 1/2<x/y<1 INSUFF

My answer would be E

Karishma,
Thanks! I do have a small doubt though...when should you solve such questions using algebraic approach and when should you take the intuitive approach. I always get caught up in this dilemma.

First of all, one method is not better than the other. They both have their pros and cons. I like logical approach for most questions since it helps in finding the answer very quickly. On the other hand, using the algebraic approach, you don't need to think very much. Just make equations and solve. Also the probability that you will overlook something is less using algebraic approach. Ideally, you need to be comfortable with both. Different questions demand a different approach but during the exam, pick the one which comes first to mind and with which you are comfortable. For inequality questions, I prefer to use algebra since using logic too takes time.. It isn't as intuitive as in the case of arithmetic... Numbers between 0 and 1 behave in a different manner and those between 1 and infinity behave in a different manner. Similarly negative number follow their own rules too.... So if I can see simple straight forward algebra, I use it for inequalities. Else you have to use logic, plug in number etc....

Hi,
Can anyone plz explain the above question using graphical method.

Thanks
Animesh

Look at the diagrams below.


The first one shows the region asked in the question stem: is 4x > 3y? or is 4x - 3y > 0? (The Green region in the first diagram.)
The second and third show the statements 1 and 2 respectively
1. x > y - x or 2x - y > 0 (shown by the Red region)
2. x/y < 1 or x - y < 0 (shown by the Blue region)
Since Red and Blue regions have points that are not in Green region, a point satisfying 2x - y > 0 or x - y < 0 doesn't necessarily satisfy 4x - 3y > 0. So each alone is not sufficient.
Look at the last diagram now. Using both 1 and 2 together, we get the points that satisfy both inequalities: 2x - y > 0 and x - y < 0. (Region where Red and Blue overlap) Even here, some points will lie in Green region, some will not. Hence, even together, the statements are not enough. Answer (E).

Thanks Karishma,
The explanation is really nice and what exactly I wanted.... Can you please tell me more about solving inequalities using graphs(some links..etc)

thanks
Animesh

Check out a couple of questions on gmat club where I have given graphical solutions:
https://gmatclub.com/forum/is-the-line-s-intercept-with-axis-x-greater-than-r-94505.html#p810874
https://gmatclub.com/forum/2-sums-with-modulus-and-inequality-both-103746.html#p808305
[url]
https://gmatclub.com/forum/ps-triple-mod ... ml#p807380[/url]
though the mod questions are higher level...

In addition, try solving questions using graphs and if you get stuck, pm me... Also, I think shrouded1 here uses graphs frequently too so you can check some of his/her solutions as well..

1) x>y-x ==> 2x>y ==> 4x > 2y. We have no way of comparing 4x to 3y, however. Insufficient!
2) x/y < 1 ==> x<y ==> 4x < 4y. We have no way of comparing 4x to 3y, however. Insufficient!

Combined: 4y<4x<2y. This still gives us no way to compare 4x and 3y. Insufficient!
Answer E.

Since y is POSITIVE, the inequalities can safely be divided by y.

4x > 3y
x > (3/4)y
x/y > 3/4
Question stem, rephrased:
Is x/y > 3/4?

Statement 1:
x > y-x
2x > y
2(x/y) > 1
x/y > 1/2

Case 1: x/y = 2/3
In this case, x/y < 3/4, so the answer to the rephrased question stem is NO.
Case 2: x/y = 9/10
In this case, x/y > 3/4, so the answer to the rephrased question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT.

Cases 1 and 2 satisfy BOTH statements.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

.

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