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A list contains 11 consecutive integers. Whats is the

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A list contains 11 consecutive integers. Whats is the [#permalink] New post   08 Apr 2005, 10:17
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A list contains 11 consecutive integers. Whats is the greatest integer on the list?

1) If X is the smallest integer on the list, then (x+72)^(1/3)=4
2) If X is the smallest integer on the list, and Y is the greatest integer on the list, then 16 x^(-2)=y^(-2)



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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   08 Apr 2005, 11:51
I hope your X and x are referring to the same integers and the variation isn't intentional. In GMAT I'd consider them different.

(1) Specifies x+72 = 64 =>x = smallest integer in the list = -8.
This gives the largest integer as +2.

(2) Here y = x+10
Therefore, 16x^(-2) = (x+10)^(-2)
16 x^2 + 1600 + 320x = x^2
15x^2 + 320x + 1600 = 0
3x^2 + 64x + 340 = 0
3x^2 + 34x + 30x + 340 = 0
x(3x + 34) + 10(3x+34) = 0
x = -10, x=34/3.
Since x is an integer, 34/3 is inadmissible, and so we get a unique value of x here too.

Hence solution possible by either statement independently.

(D).
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   09 Apr 2005, 05:26
D)...

1) (x+72)^(1/3)=4 => sqrt(x+72)=4 => x+72=64 => x=-8 => suff

2) 16 x^(-2)=y^(-2) => 16/(x^2)=1/(y^2) => 16y^2=x^2 => 4y=x and y=x+10 => solve for x and y => suff
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 04:44
christoph wrote:
D)...

1) (x+72)^(1/3)=4 => sqrt(x+72)=4 => x+72=64 => x=-8 => suff

2) 16 x^(-2)=y^(-2) => 16/(x^2)=1/(y^2) => 16y^2=x^2 => 4y=x and y=x+10 => solve for x and y => suff


Does 16y^2=x^2 truly simplify to 4y=x? Methinks that at best 16y^2=x^2 should give y/x= +1/4. In anycase, assuming Christoph, is right solving 4y=x and y=x+10 does not give any any integer values for x and y.

I'll stick by Kapslock's solution for now ....
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 04:59
kapslock wrote:
I hope your X and x are referring to the same integers and the variation isn't intentional. In GMAT I'd consider them different.

(1) Specifies x+72 = 64 =>x = smallest integer in the list = -8.
This gives the largest integer as +2.

(2) Here y = x+10
Therefore, 16x^(-2) = (x+10)^(-2)
16 x^2 + 1600 + 320x = x^2
15x^2 + 320x + 1600 = 0
3x^2 + 64x + 340 = 0
3x^2 + 34x + 30x + 340 = 0
x(3x + 34) + 10(3x+34) = 0
x = -10, x=34/3.
Since x is an integer, 34/3 is inadmissible, and so we get a unique value of x here too.

Hence solution possible by either statement independently.

(D).


How did you get greatest number as 2 from stmt 1?
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 05:07
the integers are consecutive and are 11 in total.
If the smallest is -8, you need to add 10 (not 11! because 11 is the number of integers, so their difference is not 11 but 10, or (n-1)
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 06:43
Pardon me if I am slow in this case, but where did you guys get y= x + 10?
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 06:47
Folaa3 wrote:
Pardon me if I am slow in this case, but where did you guys get y= x + 10?


2) states "If X is the smallest integer on the list, and Y is the greatest integer on the list" => means the difference between Y and X is 11 => y=x+10
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 06:51
Folaa3 wrote:
Pardon me if I am slow in this case, but where did you guys get y= x + 10?


Ooops I got it folks.

y-x = 10 since consecutive integers and we have 11 integers in total….yeah got it
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Re: A list contains 11 consecutive integers. Whats is the [#permalink] New post   14 Apr 2005, 06:51
christoph wrote:
Folaa3 wrote:
Pardon me if I am slow in this case, but where did you guys get y= x + 10?


2) states "If X is the smallest integer on the list, and Y is the greatest integer on the list" => means the difference between Y and X is 11 => y=x+10


see my post below...but thanks though :lol:



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Re: A list contains 11 consecutive integers. Whats is the [#permalink]
14 Apr 2005, 06:51
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