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Manager  G
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If S is a set of four numbers x, y, z and w, is the range of the numbe  [#permalink]

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Question Stats: 49% (02:13) correct 51% (02:22) wrong based on 103 sessions

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If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?

(1) x > y + z + 6
(2) y > w – z – 1

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Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe  [#permalink]

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duahsolo wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?

(1) x > y + z + 6
(2) y > w – z – 1

Similar question: https://gmatclub.com/forum/if-s-is-a-se ... 66184.html
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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe  [#permalink]

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duahsolo wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?

(1) x > y + z + 6
(2) y > w – z – 1

Range = Highest value - Lowest value of the set

Statement 1: x > y + z + 6
This statement doesn't give us the range of the values between any two numbers of set hence
NOT SUFFICIENT

Statement 2: y > w – z – 1
This statement doesn't give us the range of the values between any two numbers of set hence
NOT SUFFICIENT

Combining the two statements

Add the two inequalities
x+y > (y + z + 6)+(w – z – 1)

i.e. x-w > 5

Since the difference of the two numbers of the set is greater than 5 hence the Range of the set is bound to be greater than 5, Hence
SUFFICIENT

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Re: If S is a set of four numbers x, y, z and w, is the range of the numbe  [#permalink]

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duahsolo wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?

(1) x > y + z + 6
(2) y > w – z – 1

1) x-6>y+z
if x=-6, y=-7, z=-6, range could be 5<= or greater depending on w. Not suff.

2) y+1>w-z
if y=3, w=4,z=2, range could be 5<= or greater depending on x. Not suff.

1)&2)

x > y + z + 6
y > w – z – 1

x+y>y+z+6+w-z-1
x>6+w-1
x-w>5 and therefore range must be greater than 5 if 2 elements in the set are greater than 5.

Agree?
Intern  S
Joined: 02 Jan 2017
Posts: 35
Location: India
WE: Engineering (Telecommunications)
Re: If S is a set of four numbers x, y, z and w, is the range of the numbe  [#permalink]

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Cez005 wrote:
duahsolo wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?

(1) x > y + z + 6
(2) y > w – z – 1

1) x-6>y+z
if x=-6, y=-7, z=-6, range could be 5<= or greater depending on w. Not suff.

2) y+1>w-z
if y=3, w=4,z=2, range could be 5<= or greater depending on x. Not suff.

1)&2)

x > y + z + 6
y > w – z – 1

x+y>y+z+6+w-z-1
x>6+w-1
x-w>5 and therefore range must be greater than 5 if 2 elements in the set are greater than 5.

Agree?

Hi

For x>6+w-1
x-w>5

How can we take w from RHS to LHS. without knowing the sign???
and nowhere it is mentioned that w is + or _ve..
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Manager  G
Joined: 07 Aug 2018
Posts: 108
Location: United States (MA)
GMAT 1: 560 Q39 V28 GMAT 2: 670 Q48 V34 Re: If S is a set of four numbers x, y, z and w, is the range of the numbe  [#permalink]

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er.arun88 wrote:
Cez005 wrote:
duahsolo wrote:
If S is a set of four numbers x, y, z and w, is the range of the numbers in S greater than 5?

(1) x > y + z + 6
(2) y > w – z – 1

1) x-6>y+z
if x=-6, y=-7, z=-6, range could be 5<= or greater depending on w. Not suff.

2) y+1>w-z
if y=3, w=4,z=2, range could be 5<= or greater depending on x. Not suff.

1)&2)

x > y + z + 6
y > w – z – 1

x+y>y+z+6+w-z-1
x>6+w-1
x-w>5 and therefore range must be greater than 5 if 2 elements in the set are greater than 5.

Agree?

Hi

For x>6+w-1
x-w>5

How can we take w from RHS to LHS. without knowing the sign???
and nowhere it is mentioned that w is + or _ve..

We do not need to know!
We can subtract or add variables with inequalities regardless of their signs! The sign is only important when multiplying or dividing by a variable!
_________________ Re: If S is a set of four numbers x, y, z and w, is the range of the numbe   [#permalink] 18 Sep 2018, 07:33
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