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555-605 Level|   Statistics and Sets Problems|                              
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MRVN
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If S is a set of four numbers w, x, y, and z, is the range of the numb 12 Jan 2023, 07:58
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Bunuel
SOLUTION

If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?

(1) w - z > 2. The range of a set is the difference between the largest and the smallest elements of the set, since the difference of some particular two numbers are already more than 2 then the the range must also be more than 2. Sufficient.

(2) z is the least number in S --> just says that from four unknowns z is the smallest one (obviously one of the unknowns would be the smallest one, what difference does it make to know that it's z?). Not sufficient.

Answer: A.
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What if the numbers are negative though?

-> If w = (-2), z = (-4), the statement would remain true [(-2)-(-4)]=6; however, the range would be 2. Therefore, the statement would be insufficient.

I'd appreciate your help 🙏
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If S is a set of four numbers w, x, y, and z, is the range of the numb 12 Jan 2023, 12:27
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MRVN
Bunuel
SOLUTION

If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?

(1) w - z > 2. The range of a set is the difference between the largest and the smallest elements of the set, since the difference of some particular two numbers are already more than 2 then the the range must also be more than 2. Sufficient.

(2) z is the least number in S --> just says that from four unknowns z is the smallest one (obviously one of the unknowns would be the smallest one, what difference does it make to know that it's z?). Not sufficient.

Answer: A.

What if the numbers are negative though?

-> If w = (-2), z = (-4), the statement would remain true [(-2)-(-4)]=6; however, the range would be 2. Therefore, the statement would be insufficient.

I'd appreciate your help 🙏
Show more

-2 - (-4) = -2 + 4 = 2, not 6. So, those values of w and z do not satisfy the first statement.
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MRVN
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If S is a set of four numbers w, x, y, and z, is the range of the numb 12 Jan 2023, 13:33
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Oh, you're right... Thought I was very smart there :D

Thank you! <3

Bunuel
MRVN
Bunuel
SOLUTION

If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?

(1) w - z > 2. The range of a set is the difference between the largest and the smallest elements of the set, since the difference of some particular two numbers are already more than 2 then the the range must also be more than 2. Sufficient.

(2) z is the least number in S --> just says that from four unknowns z is the smallest one (obviously one of the unknowns would be the smallest one, what difference does it make to know that it's z?). Not sufficient.

Answer: A.

What if the numbers are negative though?

-> If w = (-2), z = (-4), the statement would remain true [(-2)-(-4)]=6; however, the range would be 2. Therefore, the statement would be insufficient.

I'd appreciate your help 🙏

-2 - (-4) = -2 + 4 = 2, not 6. So, those values of w and z do not satisfy the first statement.
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If S is a set of four numbers w, x, y, and z, is the range of the numb 25 Feb 2024, 12:42
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Bunuel
If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?

(1) w - z > 2
(2) z is the least number in S.
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­It is not expressly mentioned that the variables representing the numbers are listed in order, therefore I do not agree with the given solution. For example, when the GMAT does not state that the numbers are integers, I do not assume they are. I thought this case was analogous.
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If S is a set of four numbers w, x, y, and z, is the range of the numb 25 Feb 2024, 12:52
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Bunuel
If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?

(1) w - z > 2
(2) z is the least number in S.
­It is not expressly mentioned that the variables representing the numbers are listed in order, therefore I do not agree with the given solution. For example, when the GMAT does not state that the numbers are integers, I do not assume they are. I thought this case was analogous.
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­
Yes, the variables are not necessarily in a specific order. However, this does not matter. The question asks whether the range of the numbers is greater than 2. From (1), since the difference between certain pairs of numbers within the set already exceeds 2, then the range must also be more than 2.
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If S is a set of four numbers w, x, y, and z, is the range of the numb 25 Feb 2024, 13:11
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Bunuel

Steven_Iallonardo

Bunuel
If S is a set of four numbers w, x, y, and z, is the range of the numbers in S greater than 2 ?

(1) w - z > 2
(2) z is the least number in S.
­It is not expressly mentioned that the variables representing the numbers are listed in order, therefore I do not agree with the given solution. For example, when the GMAT does not state that the numbers are integers, I do not assume they are. I thought this case was analogous.
­
Yes, the variables are not necessarily in a specific order. However, this does not matter. The question asks whether the range of the numbers is greater than 2. From (1), since the difference between certain pairs of numbers within the set already exceeds 2, then the range must also be more than 2.
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­I see, thank you very much for clarifying Bunuel!
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If S is a set of four numbers w, x, y, and z, is the range of the numb 29 Jun 2025, 03:24
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