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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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30 Nov 2015, 08:45
The answer is a. (i) Given, x>0 Since x is positive, we can rewrite the inequality as 3x >4y 3x > 4y x > (4/3) y x > 1.something*y Clearly we can conclude that x>y. Hence sufficient. (ii) y>0 Given y is positive and hence the inequality becomes 3x> 4y x> (4/3)*y x> 1.something*y This can be true for a negative value of x, where x<y and also for a positive value of x where x>y. Hence insufficient.
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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30 Nov 2015, 10:46
3x>4y So, to make this true, it has to be x>y
Now st1: x>0, as 3 is multiplied with x, and 4 is with y, x has to be bigger than y. even x will be > y.
For St 2: y>0, lets say y is 6(and positive)... so 4y is 24... to satisfy initial condition, x has to be > 8, so, x can be 9 or +9(etc)... So, insufficient.
Thus A



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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30 Nov 2015, 18:43
Ans:A Since the question has mod    it is obvious that the actual value of x will always be greater than y for the inequality to work. The trick is to figure out the sign.
1. if x>0  Sufficient x=1, 3x = 3. For the inequality to work  y has to be 0. any other value for y will make 4y > 3.
2. y>0. Not sufficient. for y=5, x can be 7 or 7. in both cases 3x > 20. Hence not sufficient.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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01 Dec 2015, 10:06
Statement 1 If x>0, 3x is positive. y could be either positive or negative. If y is positive, since 3x>4y, x>y. If y is negative, anyways x>y. Sufficient.
Statement 2 If y>0, 4y is positive. x could be either positive or negative. If x is positive, since 3x>4y, x>y. If x is negative, it is possible that 3x>4y but not necessarily x>y. Not sufficient.
Answer A.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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01 Dec 2015, 23:55
If 3x > 4y, is x > y?
(1) x > 0
(2) y > 0
Stmt 1:
X>0 We have 2 scenarios for y i) y>0 > 3x>4y > x/y > 3/4 if x/y = 4/5 => x<y if x/y = 2 => x>y ii)if y<0 => x>y
Since we cannot say for sure => insuff
Stmt 2:
Y>0 We have 2 scenarios for x i) x>0 > 3x>4y > x/y > 3/4 if x/y = 4/5 => x<y if x/y = 2 => x>y ii)if x<0 => x<y
Since we cannot say for sure => insuff
Stmt 1 & 2: Still we have x/y>3/4 => Still we cannot say if x>y. Hence Insuff
Ans: E



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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Updated on: 04 Dec 2015, 07:55
3X >4y
1) X>0
3X = 3X ..
X= 1.33 Y
SO, X IS ALWAYS GREATER IRRESPECTIVE OF Y SIGN
2) y>0 NO INFO ABT X NS
1+2 X>0,Y>0
SO, 3X>4Y X>(4/3)Y.. S
A
Originally posted by mango aadmi on 02 Dec 2015, 08:21.
Last edited by mango aadmi on 04 Dec 2015, 07:55, edited 1 time in total.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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02 Dec 2015, 22:24
If 3x > 4y, is x > y?
(1) x > 0
(2) y > 0
1)x > 0
==> X is not a negative number. ==> x > (4/3) y and x > (4/3)y (Assuming we don't know if y>0) The factor 4/3 is greater than 1 Test cases 1)Assuming integers if y = 1; x > 1.33 ==> x >y 2)Assuming them to be decimals
if y = 0.5; x >0.66 ==>x >y
Hence sufficient.
2) y > 0
==> y is not a negative number. y < (3/4)x .Since y > 0, y cannot be less than (3/4)x.
Test cases 1)Assuming integers if x = 1; y < 0.75 ==> x >y
2)Assuming them to be decimals if x = 0.2; y < 0.15 ==>x >y
Hence sufficient.
Hence (D)Both alone are sufficient.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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03 Dec 2015, 12:44
QUESTION #1:
If 3x > 4y, is x > y?
(1) x > 0
(2) y > 0
Soln: 3x > 4y, or 3*x > 4*y (since A*B=A*B; 3=3, and 4=4) or \(\frac{3}{4}\)x > y, or x > y (if 3/4th of a is greater than b; a must also be greater than b, when a & b both +ve).
1. x>0. suppose x = 5. So, y < 5, or 5 < y < 5. So, we see all the value of y must be less than x=5. or x>y. SUFFICIENT.
2. y>0. Suppose y = 5. So, x > 5. The range of x is thus: x > 5, or x < 5. In other words, x > y or x < y. NOT SUFFICIENT. Answer: A.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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03 Dec 2015, 14:11
If 3x > 4y, is x > y?
(1) x > 0 (2) y > 0
Solution : Statement (1) : x > 0 suppose x = 0.1, given 3x > 4y 0.3 > 4y y < 0.075 so x > y (Sufficient)
Statement (2) : y > 0 suppose y = 1, given 3x > 4y 3x > 4 x > 4/3 ......... x > y or x < 4/3 ....... x < y we have two answers .. so Not Sufficient
Answer (A)



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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04 Dec 2015, 05:43
Answer : A Explanation : given = 3x>4y
S1 : X>0, we know multiple of x is 3 and multiple of y is 4. So in order to have 3x more than 4y , y has to be less than x i.e. if x=3, then 3x=9 so 9>4y. Therefore y shall be less than 2.25. Which is x>y. So S1 is sufficient.
S2 : y>0, we know 3x>4y. x could be negative and still value of 3x could be more than 4y i.e. x=3, 3x =9, y=2, 4y = 8 or x=3, 3x =9, y=2, 4y = 8 So S2 is not sufficient.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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04 Dec 2015, 23:21
If 3x > 4y, is x > y?
(1) x > 0
If x>0 then x= x So, 3x >4y y can be positive or negative. If y is positive, 3x > 4y and x>4y/3 . Therefore x>y If y is negative, since x is positive, x >y. Therefore x is always greater than y, when x is positive. Choice A is sufficient.
(2) y > 0 If y is positive, then 3x > 4y Here x can be either positive or negative. When x is positive, 3x > 4y and x>4y/3. Therefore x>y When x is negative, 3x >4y and x<4y/3. Therefore x<y. This choice leads to one yes and one no answer. Hence not sufficient.
Therefore answer is choice A.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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06 Dec 2015, 09:26
(1) x > 0 => 3x > 4y => x > 4y/3 > y => x > y : Sufficient (2) y > 0 is insufficient because if x > 0 then x > y, if x < 0 then x < y. Answer A
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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06 Dec 2015, 09:57
since 3x>4y we can take out 3 and 4 outside mode as both are positive (Absolute number). now we have x>4/3y. It imply absolute value of x is greater than 1.33times absolute value of Y. Now look at options 1. x>0 >> If X is positive , then y can be positive or negative provided absolute value of y is less than . If Y >0, it has to be less than X, if Y <0, then x is always greater than y. In either case X>Y. Sufficient 2. Y>0 > X can be > or <0. If X>0, then X>Y, if X<0( absolute value of X is greater than Y), then X <Y. Not Sufficient.
Ans :A



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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14 Dec 2015, 08:58
Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #1:If 3x > 4y, is x > y? (1) x > 0 (2) y > 0 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you! MATH REVOLUTION OFFICIAL SOLUTION:This type of question appears within a score range of 45 to 48. Under the original condition, there are 2 variables (x and y) and 1 equation (3x>4y). In order to have the same number of equations, we need 1 more equation. In that sense, D seems highly correct answer because there is 1 equation each for both 1) and 2). In case of 1), if x>0, then 3x>4y→ 3x>4y≥3y≥3y→ 3x>3y → x>y, which means yes, this is sufficient. In case of 2), if y>0, then 3x>4y=4y, if x=2 and y=1, which means yes. However, if x=2 and y=1, which means no. Because both yes and no are there, this is not sufficient. Therefore, the correct answer is A.You can solve this question in less than 2 minutes while conventional way of solving takes 45 minutes. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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16 Jun 2017, 17:20
If 3x > 4y, is x > y?
(1) x > 0
Let x = 2 & y= 1.......Answer to question is yes
Let x = 1/3 & y=1/6..Answer to question is yes
Let x =1 & y =0.........Answer to question is yes
As x =0, y =any negative value...Answer to question is yes
Sufficient
(2) y > 0
Let x = 2 & y= 1.......Answer to question is yes
Let x = 2 & y= 1.......Answer to question is No
Insufficient
Answer: A



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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16 Jun 2017, 18:02
A From initial expression you know that the absolute value of X is greater than that of Y. From that we can derive that if X is positive number, than X is greater than Y. If X is a negative number, than X is smaller than Y irrespective of the sign of Y.
Statement 1: Now we now that X is positive, hence X is greater than Y irrespective of the the sign of Y
Statement 2: Not sufficient. We cannot make implication. Two possible scenarios: X is negative > smaller, X is positive > larger
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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