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

Question

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

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

Bunuel · Answer

Given: x>0 and y>0 . Question: is 4x>3y ? (1) x>y-x --> 2x>y --> 4x>2y , not sufficient to say whether 4x is more than 3y . (2) \frac{x}{y}<1 --> as y>0 we can cross multiply --> x 4x<4y , not sufficient to say whether 4x is more than 3y . (1)+(2) We know that 4x is more than 2y but less than 4y --> 2y<4x<4y , but from this we can not find the relationship between 4x and 3y (we have 2y---3y---4y , 4x is somewhere between endpoints but we can not say whether it's between 2y and 3y , equal to 3y or between 3y and 4y ). Not sufficient. Answer: E.

Eden · Answer

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

ajit257 · Answer

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

KarishmaB · Answer

Since x and y are positive, you can multiply/divide the inequality by them. Now, another thing is that it is hard to wrap your head around a question if it has more than one variables. So try to get the variables together so that you can consider them a single variable.
is 4x > 3y ?
I can change this to: is x/y > 3/4?

Stmnt 1: x > y - x
2x > y
x/y > 1/2
So we know that x/y is greater than 1/2 but we do not know whether it is greater than 3/4. Not sufficient.

Stmnt 2: x/y < 1
So we know that x/y is less than 1 but we still do not know whether x/y is greater than or less than 3/4. Not sufficient.

Using both statements, we know x/y is greater than 1/2 and less than 1 but we still do not know whether it is greater than or less than 3/4. Not sufficient.

Answer (E).

tfincham86 · Answer

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

ajit257 · Answer

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.

KarishmaB · Answer

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....

animeshsen · Answer

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

Thanks
Animesh

KarishmaB · Answer

Look at the diagrams below. Ques5.jpg 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).

animeshsen · Answer

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

KarishmaB · Answer

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 https://gmatclub.com/forum/ps-triple-mod ... ml#p807380 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..

KarishmaB · Answer

DavidTutorexamPAL · Answer

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.

GMATGuruNY · Answer

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.

E .

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

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