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If x, y, and z are positive numbers such that 3x < 2y < 4z , which of

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If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 20 May 2019, 03:56
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 20 May 2019, 04:35
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III



Let us take each option..

I. y=z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes...let y=z=2 and x=1...3*1<2*2<4*2...3<4<8...

II. y>z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes, y can be between z and 2z..let y=3, z=2 and x=1...3*1<2*3<4*2...3<6<8...

III. x>z....
Let us compare x and z in the inequality 3x<2y<4z, so 3x<4z or x<4z/3..
So yes, x can be between z and 4z/3...let z=30 and x=31, and y=...3*31<2*50<4*30...91<100<120.

All three possible

E
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 20 May 2019, 08:24
chetan2u
thanks for the solution , I had a doubt that since the question has given that x,y,z are +ve numbers so shouldnt we check the given relations with a fraction value as well?


chetan2u wrote:
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III



Let us take each option..

I. y=z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes...let y=z=2 and x=1...3*1<2*2<4*2...3<4<8...

II. y>z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes, y can be between z and 2z..let y=3, z=2 and x=1...3*1<2*3<4*2...3<6<8...

III. x>z....
Let us compare x and z in the inequality 3x<2y<4z, so 3x<4z or x<4z/3..
So yes, x can be between z and 4z/3...let z=30 and x=31, and y=...3*31<2*50<4*30...91<100<120.

All three possible

E
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 08 Oct 2019, 02:18
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


Asked: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
2y<4z
If y=z
2y<4y; Take y=1; 2<4
COULD BE TRUE

II. y > z
2y<4z
Take y = 1.5; z =1
2*1.5=3<4*1=4
COULD BE TRUE

III. x > z
3x<4z
Take x = 1.1
z = 1
3.3 < 4
COULD BE TRUE

IMO E
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If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 14 Oct 2019, 03:39
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


Hello Bunuel,

For II condition y>z
if I take Y=3, Z=2 and X=1
Then,
3*1 < 2*3 < 4*2
3 < 6 < 8 ..........Correct
But if I choose values as below: -
X=1 Y=10 & Z=3
Then,
3*1 < 2*10 < 4*3
3 < 20 < 12 .......... Its wrong 20 > 12. So II. Y>Z is may be or may not be condition.

Similar for III. X>Z. It is also may be or may not be condition.

So don't you think that only I Y=Z i.e. Option A should be the answer.

Regards
Chetak
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 14 Oct 2019, 03:57
chetaksatav wrote:
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


Hello Bunuel,

For II condition y>z
if I take Y=3, Z=2 and X=1
Then,
3*1 < 2*3 < 4*2
3 < 6 < 8 ..........Correct
But if I choose values as below: -
X=1 Y=10 & Z=3
Then,
3*1 < 2*10 < 4*3
3 < 20 < 12 .......... Its wrong 20 > 12. So II. Y>Z is may be or may not be condition.

Similar for III. X>Z. It is also may be or may not be condition.

So don't you think that only I Y=Z i.e. Option A should be the answer.

Regards
Chetak


Notice that the question asks: "which of the following statements COULD be true?" NOT "which of the following statements MUST be true?"
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 14 Oct 2019, 04:14
Bunuel wrote:
chetaksatav wrote:
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III


Hello Bunuel,

For II condition y>z
if I take Y=3, Z=2 and X=1
Then,
3*1 < 2*3 < 4*2
3 < 6 < 8 ..........Correct
But if I choose values as below: -
X=1 Y=10 & Z=3
Then,
3*1 < 2*10 < 4*3
3 < 20 < 12 .......... Its wrong 20 > 12. So II. Y>Z is may be or may not be condition.

Similar for III. X>Z. It is also may be or may not be condition.

So don't you think that only I Y=Z i.e. Option A should be the answer.

Regards
Chetak


Notice that the question asks: "which of the following statements COULD be true?" NOT "which of the following statements MUST be true?"


Thanks Bunuel for clarifying.
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If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 14 Oct 2019, 22:39
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

3x<2y<4z
3/2x<y<2z=1.5x<y<2z
Since all are positive numbers
x=1/2, y =1, z=1 then 0.75<1<2
x=0.61, y=0.99, z=0.6 then 0.91<0.99<1.2
E:)
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If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 01 Jul 2020, 08:28
chetan2u wrote:
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III



Let us take each option..

I. y=z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes...let y=z=2 and x=1...3*1<2*2<4*2...3<4<8...

II. y>z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes, y can be between z and 2z..let y=3, z=2 and x=1...3*1<2*3<4*2...3<6<8...

III. x>z....
Let us compare x and z in the inequality 3x<2y<4z, so 3x<4z or x<4z/3..
So yes, x can be between z and 4z/3...let z=30 and x=31, and y=...3*31<2*50<4*30...91<100<120.

All three possible

E


VeritasKarishma

In this ques, since we have to just tell whether a situation involving 2 variables is possible, do we also need to consider what value the 3rd variable can take? (Just want to confirm if doing so would add something)

Like for statement 3, I just considered x<4z/3. So take z=3/4=.75 ---> 1>x>.75 take x=.76 (Now do we need to see for what value of y the inequation 3x < 2y < 4z is true?)


Thanks in advance!
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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New post 05 Jul 2020, 02:48
1
GDT wrote:
chetan2u wrote:
Bunuel wrote:

FRESH GMAT CLUB TESTS QUESTION



If x, y, and z are positive numbers such that 3x < 2y < 4z , which of the following statements could be true?

I. y = z
II. y > z
III. x > z

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III



Let us take each option..

I. y=z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes...let y=z=2 and x=1...3*1<2*2<4*2...3<4<8...

II. y>z....
Let us compare y and z in the inequality 3x<2y<4z, so 2y<4z or y<2z..
So yes, y can be between z and 2z..let y=3, z=2 and x=1...3*1<2*3<4*2...3<6<8...

III. x>z....
Let us compare x and z in the inequality 3x<2y<4z, so 3x<4z or x<4z/3..
So yes, x can be between z and 4z/3...let z=30 and x=31, and y=...3*31<2*50<4*30...91<100<120.

All three possible

E


VeritasKarishma

In this ques, since we have to just tell whether a situation involving 2 variables is possible, do we also need to consider what value the 3rd variable can take? (Just want to confirm if doing so would add something)

Like for statement 3, I just considered x<4z/3. So take z=3/4=.75 ---> 1>x>.75 take x=.76 (Now do we need to see for what value of y the inequation 3x < 2y < 4z is true?)


Thanks in advance!


No, you do not need to worry about the third variable here.
Note that in stmnts I and II, I can just say x = 1/1000 and focus my energies on y and z.
Again, in statement III, for all values such that 3x < 4z, there will certainly be some values in between these two so it will work for some values of y for sure.
Note that we might want to be more careful if we were given that x, y and z are positive integers.
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Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of   [#permalink] 05 Jul 2020, 02:48

If x, y, and z are positive numbers such that 3x < 2y < 4z , which of

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