Is Z between Z & Y?
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Target question: Is z between x and y?If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y
Statement 1: x < 2z < y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 3, y = 10, and z = 2, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2x < z < 2y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 1, y = 2, and z = 3, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: x < 2z < y
Statement 2: 2x < z < 2y
Since the two inequalities are facing the same direction, we can add them to get:
3x < 3z < 3y
Divide all three parts by 3 to get: x < z < y
As we can see, z IS definitely between x and y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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There is no need to even put values for the First and Second Statement alone.
I) x < 2z < y => x/2 < z < y/2
Now, y/2 may be bigger than x and in that case x < z < y, else not. So, no unique solution.
II) 2x < z < 2y Now, 2x may be lesser than y and in that case x < z < y, else not. So, no unique solution.
Just visualize the 4 variables mentioned above on Number line and it becomes easy.
Combining I and II : 3x < 3z < 3y => x < z < y. Hence both statements are required.
I) x < 2z < y => x/2 < z < y/2
Now, y/2 may be bigger than x and in that case x < z < y, else not. So, no unique solution.
II) 2x < z < 2y Now, 2x may be lesser than y and in that case x < z < y, else not. So, no unique solution.
Just visualize the 4 variables mentioned above on Number line and it becomes easy.
Combining I and II : 3x < 3z < 3y => x < z < y. Hence both statements are required.
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Brent@GMATPrepNow wrote:Target question: Is z between x and y?If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y
Statement 1: x < 2z < y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 3, y = 10, and z = 2, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 2x < z < 2y
There are several set values of x, y and z that satisfy this condition. Here are two:
Case a: x = 1, y = 2, and z = 3, in which case z is NOT between x and y
Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: x < 2z < y
Statement 2: 2x < z < 2y
Since the two inequalities are facing the same direction, we can add them to get:
3x < 3z < 3y
Divide all three parts by 3 to get: x < z < y
As we can see, z IS definitely between x and y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Dear Brent,
What if we are unable to think of the values of x, y and z under exam pressure.
Any other way to tackle this question.
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When statements are not sufficient, it can often be difficult to show that they are not sufficient using means other than PLUGGING IN.a_new_start wrote:
Dear Brent,
What if we are unable to think of the values of x, y and z under exam pressure.
Any other way to tackle this question.
Here, each statement contains very little information, so I can't see any options other than plugging in.
Fortunately, with the statements combined, we have something to work with.
Cheers,
Brent
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Yeah. True.Brent@GMATPrepNow wrote:When statements are not sufficient, it can often be difficult to show that they are not sufficient using means other than PLUGGING IN.a_new_start wrote:
Dear Brent,
What if we are unable to think of the values of x, y and z under exam pressure.
Any other way to tackle this question.
Here, each statement contains very little information, so I can't see any options other than plugging in.
Fortunately, with the statements combined, we have something to work with.
Cheers,
Brent
I agree with you.
Thank You
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One suggestion:a_new_start wrote:What if we are unable to think of the values of x, y and z under exam pressure.If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y
Any other way to tackle this question.
Since the question stem asks whether z is between x and y, test values for x and y that are SPREAD OUT.
Let x=10 and y=100.
Statement 1: x < 2z < y
Substituting x=10 and y=100, we get:
10 < 2z < 100
5 < z < 50.
If z=20, then z is between x and y.
If z=6, then z is NOT between x and y.
INSUFFICIENT.
Statement 2: 2x < z < 2y
Substituting x=10 and y=100, we get:
2*10 < z < 2*100
20 < z < 200.
If z=30, then z is between x and y.
If z=150, then z is NOT between x and y.
INSUFFICIENT.
Statements combined:
Adding together x < 2z < y and 2x < z < 2y, we get:
x+2x < 2z+z < y+2y
3x < 3z < 3y
x < z < y.
SUFFICIENT.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Mitch,GMATGuruNY wrote:One suggestion:a_new_start wrote:What if we are unable to think of the values of x, y and z under exam pressure.If x, y and z are positive numbers, is z between x and y?
(1) x < 2z < y
(2) 2x < z < 2y
Any other way to tackle this question.
Since the question stem asks whether z is between x and y, test values for x and y that are SPREAD OUT.
Let x=10 and y=100.
Statement 1: x < 2z < y
Substituting x=10 and y=100, we get:
10 < 2z < 100
5 < z < 50.
If z=20, then z is between x and y.
If z=6, then z is NOT between x and y.
INSUFFICIENT.
Statement 2: 2x < z < 2y
Substituting x=10 and y=100, we get:
2*10 < z < 2*100
20 < z < 200.
If z=30, then z is between x and y.
If z=150, then z is NOT between x and y.
INSUFFICIENT.
Statements combined:
Adding together x < 2z < y and 2x < z < 2y, we get:
x+2x < 2z+z < y+2y
3x < 3z < 3y
x < z < y.
SUFFICIENT.
The correct answer is C.
You have really made it easy.
Kudos!
I'm satisfied now.
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Note that summing inequalities is often helpful in data sufficiency questions when you're testing the statements together. Another good thread here:
https://www.beatthegmat.com/is-m-z-0-t13539.html
https://www.beatthegmat.com/is-m-z-0-t13539.html