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655-705 (Hard)|   Algebra|      
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nick1816
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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 20 Jul 2019, 18:39
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65% (hard)

Question Stats:

60% (02:23) correct 40% (02:33) wrong based on 144 sessions

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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – y)(n – z) = 4. Which of the following can't be the value of difference between w and z?

A. -1
B. 1
C. 3
D. 4
E. 5
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E
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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 20 Jul 2019, 21:19
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nick1816
If n, w, x, y and z are different integers such that (n– w)(n – x)(n – y)(n – z) = 4. Which of the following can't be the value of difference between w and z?

A. -1
B. 1
C. 3
D. 4
E. 5
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The only possible way of getting product 4 = -2 x -1 x 1 x 2
--> Possible arrangements of given integers can be as shown with the difference between successive integers = 1 unit on a number line with 'n' always at the center
Case 1: "w -- x -- n -- z -- y" Difference b/w "w & z" = 3 units
Case 2: "w -- x -- n -- y -- z" Difference b/w "w & z" = 4 units
Case 3: "x -- w -- n -- z -- y" Difference b/w "w & z" = 2 units
Case 4: "z -- w -- n -- x -- y" Difference b/w "w & z" = 1 units
Case 5: "w -- z -- n -- x -- y" Value of "w - z" = -1 units

So, the difference can never be 5 units between w & z

IMO Option E

However, Difference can never be negative also!!
So, Option 1 can also be the answer?

Pls Hit Kudos if you like the solution
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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 20 Jul 2019, 21:22
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Dillesh4096
nick1816
If n, w, x, y and z are different integers such that (n– w)(n – x)(n – y)(n – z) = 4. Which of the following can't be the value of difference between w and z?

A. -1
B. 1
C. 3
D. 4
E. 5

The only possible way of getting product 4 = -2 x -1 x 1 x 2
--> Possible arrangements of given integers can be as shown with the difference between successive integers = 1 unit on a number line with 'n' always at the center
Case 1: "w -- x -- n -- z -- y" Difference b/w "w & z" = 3 units
Case 2: "w -- x -- n -- y -- z" Difference b/w "w & z" = 4 units
Case 3: "x -- w -- n -- z -- y" Difference b/w "w & z" = 2 units
Case 4: "z -- w -- n -- x -- y" Difference b/w "w & z" = 1 units
Case 5: "w -- z -- n -- x -- y" Value of "w - z" = -1 units

So, the difference can never be 5 units between w & z

IMO Option E

However, Difference can never be negative also!!
So, Option 1 can also be the answer?

Pls Hit Kudos if you like the solution
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Dillesh4096 the difference can be -1; if n-z = 1 and n-w = 2, then (n-z) - (n-w) = w-z = 1-2 = -1
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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 20 Jul 2019, 21:48
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RJ7X0DefiningMyX
Dillesh4096
nick1816
If n, w, x, y and z are different integers such that (n– w)(n – x)(n – y)(n – z) = 4. Which of the following can't be the value of difference between w and z?

A. -1
B. 1
C. 3
D. 4
E. 5

The only possible way of getting product 4 = -2 x -1 x 1 x 2
--> Possible arrangements of given integers can be as shown with the difference between successive integers = 1 unit on a number line with 'n' always at the center
Case 1: "w -- x -- n -- z -- y" Difference b/w "w & z" = 3 units
Case 2: "w -- x -- n -- y -- z" Difference b/w "w & z" = 4 units
Case 3: "x -- w -- n -- z -- y" Difference b/w "w & z" = 2 units
Case 4: "z -- w -- n -- x -- y" Difference b/w "w & z" = 1 units
Case 5: "w -- z -- n -- x -- y" Value of "w - z" = -1 units

So, the difference can never be 5 units between w & z

IMO Option E

However, Difference can never be negative also!!
So, Option 1 can also be the answer?

Pls Hit Kudos if you like the solution

Dillesh4096[/url] the difference can be -1; if n-z = 1 and n-w = 2, then (n-z) - (n-w) = w-z = 1-2 = -1
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RJ7X0DefiningMyX
Difference between any 2 values on a number line can never be negative. That’s the definition of the word Difference.

Yes a “-1” VALUE is possible (Not difference) as I have mentioned in the highlighted part!

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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 20 Jul 2019, 22:59
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In this case are we assuming n =0?
What if n is some other integer?

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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 20 Jul 2019, 23:04
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kitipriyanka
In this case are we assuming n =0?
What if n is some other integer?

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kitipriyanka

No, we are not assuming n as 0.
In fact, n can be any value, its the difference between the integers which is taken a 1 unit on a number line

Eg: Take
Case 1: "w -- x -- n -- z -- y" Difference b/w "w & z" = 3 units
It can be (-2) -- (-1) -- 0 -- 1 -- 2 --> Difference = 1 -(-2) = 3 units
or
5 -- 6 -- 7 -- 8 -- 9 --> Difference = 8 - 5 = 3 units

Hope it's clear!
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If n, w, x, y and z are different integers such that (n– w)(n – x)(n – 23 Jan 2025, 07:36
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