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Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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28 Nov 2015, 09:54
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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.
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 09:13
If 3x > 4y, is x > y?
Statement 1  x > 0 Statement 2  y > 0
Answer  Option A
1. x>0 implies 3x >4y or 3x >4y , As coefficient of x is smaller than coefficient of y. We can conclude if x>y 2. y>0 implies 3x > 4y but nothing can be concluded about the relation b/w 3x ?? 4y
Thus answer choice A




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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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28 Nov 2015, 10:14
If 3x > 4y, is x > y?
the question tells us that 3x>4y this is true only when x>y
how can we find out if x>y? well, if x is positive, then y definitely can't be greater than x, since the y would have to be x<y<x if y is smaller than x, then the absolute value of y is greater than the absolute value of x, and this is not possible, since we are already given that x>y
(1) x > 0 ok, now we know that x is positive, we know for sure that y should be x<y<x, which only means that y is smaller than x, and the answer to our main question is YES, x>y.
we can cross B,C, and E.
and we're left with A and D.  if we don't know how to solve if further, at least we try to make a strategic guess 50% of getting the correct answer is better than 20%.
(2) y > 0 this doesn't help us much. let's take two examples: x=3 and y = 2. x>y and x>y > satisfies the condition, and the answer is yes
now, let's say x = 7 and y=2 x<y but x>y > satisfies the condition, but the answer is no.
we can cross D, and select A as the correct answer!



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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28 Nov 2015, 12:16
1)Using this info , the stated equation becomes. 3x > 4y Now if y is negative then x > y If y is positive , then 3x > 4y so still>y
Hence statement one is sufficient .
2)  3x > 4y
If x is positive then x > y But if negative , then x < y So two. Answers are possible . not sufficient
So Correct Answer is A



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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28 Nov 2015, 12:47
The answer is We can simplify the Given statement as follows x >y*4/3 (we can take 4 & 3 out of the modulus). In other words, x will be slightly (1.33 times) greater than y. Since Mod X is greater Mod Y, we cannot say for sure whether x or y is positive or negative. 1) x>0, applying a +ve number to x in the equation x > y *4/3, we cannot determine y, it can be both +ve or ve. For instance if x is 1.33, y can be both +1 or 1 > in both cases x will still be 1.33. NOT Sufficient 2) y>0, applying a +ve number to y in the equation x > y *4/3, we cannot determine x, it can be both +ve or ve. For instance if y is 1, x can be both +1.33 or 1.33 > in both cases y will still be 1. NOT Sufficient But combining, both we can easily say x > y, since x = y*4/3.
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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28 Nov 2015, 21:31
We put in values of x & y to check if 3x>4y We get conditioned fulfilled for 3 cases Eg: x= 2,y=1 X=2, y=1 X=2, y=1 I.e in all cases where x>y But if x=2 and y=1 we don't get x>y Option A: x>0 Sufficient as yes x>y Option B : y>0 Sufficient as yes x>y Thus ans is D



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 00:28
1. X>0 Let x=1, 3*1 > 4y, this is only possible for y=0, x > y for x=2, 3*2 > 4y, this is only possinle for y=1,0, 1, again x>y Sufficient
2. y>0 For y=1, 3x > 4*1, x could be 2 or 2.. Insufficient.
Ans: A



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 06:34
If 3x > 4y, is x > y? To check whether x > y or not, accept values of x & y for which 3x > 4y holds true . To check whether x > y or not, discard values of x & y for which 3x > 4y does not hold true.(1) x > 0 Case1: x > 0, y >= 0 x > y, x = 2, y = 1 then 3x > 4y holds true as 3*2 > 4 *1 i.e. 6 > 4. Accepted. x > y, x = 2, y = 0 then 3x > 4y holds true as 3*2 > 4 *0 i.e. 6 > 0. Accepted. x < y, x = 1, y = 2 then 3x > 4y does not hold true as 3*1 > 4*1 i.e. 3 > 4 is wrong. Discarded. Hence, Answer to the question "is x > y?" is YES! case2: x > 0, y < 0 x > y, x = 2, y = 1 then 3x > 4y holds true as 3*2 > 4 * (1) = 6 > 4 = 6 > 4. Accepted. x > y, x = 2, y = 2 then 3x > 4y does not hold true as 3*2 > 4 *(2) = 6 > 8 = 6 > 8 is wrong. Discarded. Hence, Answer to the question "is x > y?" is YES! In Both case1 & 2 We get definite answer "Yes". Statement1 Sufficient!(2) y > 0 Case1: y > 0, x >= 0 x > y, x = 2, y = 1 then 3x > 4y holds true as 3*2 > 4*1 i.e. 6 > 4. Accepted. x < y, x = 1, y = 2 then 3x > 4y does not hold true as 3*1 > 4*2 i.e. 3 > 8 is wrong. Discarded. x < y, x = 0, y = 2 then 3x > 4y does not hold true as 3*0 > 4*2 i.e. 0 > 8 is wrong. Discarded. Hence, Answer to the question "is x > y?" is YES! case2: y > 0, x < 0 x < y, x = 2, y = 1 then 3x > 4y holds true as 3*(2) > 4*1 = 6 > 4 = 6 > 4. Accepted. Hence, Answer to the question "is x > y?" is NO! From Case1 we get "Yes" and from case2 we get "NO". Answer is not definite. Statement2 Insufficient!Hence "A" is the final answer!
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 06:38
A OPTION A IS SUFFICIENT TO ANSWER THE QUESTION



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 08:54
My answer to this question is A. If 3x > 4y, is x > y? (1) x > 0 (2) y > 0 Given : 3x > 4y Looking at this inequality, we can say that since 3>4, x > y for the given statement to hold. If we can prove that x > y, i.e x is greater than the magnitude of y, we should be good to say "Yes" to the question at hand. 1) x > 0 implies 3x > 4y Hence, x > 4/3 y or x > y. Sufficient!2. y > 0 Considering 3x > 4y, if y>0, x will be greater than y, only if its positive, i.e if x>0 3x > 4y => x > 4y/3. We cannot comment on the sign of X. Insufficient!
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 10:14
QUESTION #1: If 3x > 4y, is x > y? (1) x > 0 (2) y > 0 Solution Attachment:
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 10:21
If 3x > 4y, is x > y? (1) x > 0 (2) y > 0 Pick numbers:  Both positive: if x = 3 and y =2 ==> x> y : ok Negative/Positive: x=3 and y =2, then x< y  Positive/Negative: x= 3 and y= 2 then x > y : ok Negative: x=3 and y =2, then x < y So for x to be greather than y, x must be positive while y can be either positive or negative. Statement 1 alone is sufficient A
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 11:30
Answer : (A). Solution: (I) is sufficient to solve x>y (II) is not sufficient to solve x>y. Hereby,answer choices B, C, D, E can be eliminated easily. (A) is the correct choice.
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 11:32
The answer is A according to me.
x>0, gives us the necessary condition for x>y



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 11:35
The equation 3x>4y the possibilities for [x:y] are [+:+]/[:] or [+:]/[:+] Condition 1 says  x is +ve this implies 4y can be = +ve or ve ; x > y shall always be true. Sufficient Condition 2 says  y is +ve this implies 3x can be = +ve or ve ; x > y or x < y both are possible. InsufficientSolution  A Alternatively same can be shown on the number line  You know the importance of kudos, be generous.
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 12:50
(1) x>0
Case i. \(y\geq{0}\), x>0 3x > 4y => 3x > 4y => x>y
Case ii. y<0, x>0 => x>y
So (1) is sufficient.
(2) y>0
Case i. \(x\geq{0}\), y>0 3x > 4y => 3x > 4y => x>y
Case ii. x<0, y>0 => x<y
So, (2) is not sufficient.
Hence, A.



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 21:48
Given: 3x > 4y, is x > y?
Squaring both sides: 9(x^2) > 16(y^2) > 3x > 4y or 3x < 4y Plug few values of x and y, we get to know that 3x > 4y satisfies 3x > 4y only when x > 0 > In this case, x is always greater than y 3x < 4y satisfies 3x > 4y only when y < 0 > In this case, x is always lesser than y
St1: x > 0 > x > y > Sufficient St2: y > 0 > x > y > Sufficient
Answer: D



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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29 Nov 2015, 23:48
3x > 4y 3x > 4y x > (4/3)y
(1) x > 0 x > (4/3)y x > y > sufficient!
(2) y > 0 x > (4/3)y > can be right with both positive and negative value > not sufficient
So, for me the answer is B!



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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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30 Nov 2015, 00:51
My take is A (1) x>0 ; Say x = 5, then 3x = 15, given condition 3x>4y, that means y could lie between 3 to 3. In any condition x>y. Hence sufficient. (2) y>0; Say y =5, then 4y = 20, given condition 3x>4y, then say x= 7, then it satisfies and x>y but if x=7, then it satisfies given condition but x<y. Hence not sufficient. Hope it helps!!!
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Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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30 Nov 2015, 07:00
Answer is A
If x > 0, then regardless of the value or sign of y , x > y
If y > 0 , then x can either be positive or negative




Re: Math Revolution and GMAT Club Contest! If 3x > 4y, is x > y?
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