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

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Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 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


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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 29 Nov 2015, 09:13
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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?  [#permalink]

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New post 28 Nov 2015, 10:14
1
1
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?  [#permalink]

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New post 28 Nov 2015, 12:16
3
2
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?  [#permalink]

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New post 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?  [#permalink]

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New post 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?  [#permalink]

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New post 29 Nov 2015, 00:28
1
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?  [#permalink]

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New post 29 Nov 2015, 06:34
1
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

Case-1: 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!

case-2: 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 case-1 & 2 We get definite answer "Yes". Statement-1 Sufficient!

(2) y > 0
Case-1: 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!

case-2: 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 Case-1 we get "Yes" and from case-2 we get "NO". Answer is not definite. Statement-2 Insufficient!

Hence "A" is the final answer!
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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 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?  [#permalink]

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New post 29 Nov 2015, 08:54
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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?  [#permalink]

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New post 29 Nov 2015, 10:14
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QUESTION #1:

If |3x| > |4y|, is x > y?

(1) x > 0

(2) y > 0

Solution

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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 29 Nov 2015, 10:21
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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
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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 29 Nov 2015, 11:30
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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?  [#permalink]

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New post 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?  [#permalink]

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New post 29 Nov 2015, 11:35
1
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. Insufficient

Solution - A

Alternatively same can be shown on the number line
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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 29 Nov 2015, 12:50
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(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?  [#permalink]

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New post 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?  [#permalink]

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New post 29 Nov 2015, 23:48
|3x| > |4y|
3|x| > 4|y|
|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?  [#permalink]

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New post 30 Nov 2015, 00:51
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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.

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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y?  [#permalink]

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New post 30 Nov 2015, 07:00
1
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
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Re: Math Revolution and GMAT Club Contest! If |3x| > |4y|, is x > y? &nbs [#permalink] 30 Nov 2015, 07:00

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