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Math Expert V
Joined: 02 Sep 2009
Posts: 65765
If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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12 00:00

Difficulty:   75% (hard)

Question Stats: 57% (02:02) correct 43% (02:12) wrong based on 201 sessions

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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

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8792
Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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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Posts: 6504
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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
CEO  V
Joined: 03 Jun 2019
Posts: 3339
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
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Joined: 28 Jun 2019
Posts: 8
Location: India
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If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 65765
Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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?"
_________________
Intern  B
Joined: 28 Jun 2019
Posts: 8
Location: India
GPA: 3.43
WE: Engineering (Transportation)
Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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.
Senior Manager  P
Joined: 10 Dec 2017
Posts: 282
Location: India
If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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:)
Senior Manager  G
Joined: 02 Jan 2020
Posts: 257
If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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

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?)

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Joined: 16 Oct 2010
Posts: 10780
Location: Pune, India
Re: If x, y, and z are positive numbers such that 3x < 2y < 4z , which of  [#permalink]

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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

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?)

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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Karishma
Veritas Prep GMAT Instructor 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  