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Bunuel
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The first term of a sequence of consecutive positive even integers is 16 Nov 2021, 08:15
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35% (medium)

Question Stats:

80% (02:56) correct 20% (02:35) wrong based on 105 sessions

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The first term of a sequence of consecutive positive even integers is equal to half the range. If the difference between the squares of the first and last terms is 512, what is the sum of the first and last terms?

A. 24
B. 28
C. 32
D. 40
E. 44
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C
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The first term of a sequence of consecutive positive even integers is 16 Nov 2021, 08:42
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My approach:

Set X to be the first even integer - because the X is half the range, the range = 2x:

First value = X
Range = 2X
Last Value = 3X

(3x)^2 - x^2 = 9x^2 - x^2 = 8x^2 ----> from the stem this equals 512

8x^2 = 512
x^2 = 64
x= 8 (from the stem pos even int)

First value = 8
Range = 16
Last value = 24

24 + 8 = 32
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The first term of a sequence of consecutive positive even integers is 21 Nov 2021, 06:20
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samc88
My approach:

Set X to be the first even integer - because the X is half the range, the range = 2x:

First value = X
Range = 2X
Last Value = 3X

(3x)^2 - x^2 = 9x^2 - x^2 = 8x^2 ----> from the stem this equals 512

8x^2 = 512
x^2 = 64
x= 8 (from the stem pos even int)

First value = 8
Range = 16
Last value = 24

24 + 8 = 32
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Hi! Could you please explain the logic behind setting the last value as "3X"? Thanks!
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The first term of a sequence of consecutive positive even integers is 21 Nov 2021, 06:35
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vansh789
samc88
My approach:

Set X to be the first even integer - because the X is half the range, the range = 2x:

First value = X
Range = 2X
Last Value = 3X

(3x)^2 - x^2 = 9x^2 - x^2 = 8x^2 ----> from the stem this equals 512

8x^2 = 512
x^2 = 64
x= 8 (from the stem pos even int)

First value = 8
Range = 16
Last value = 24

24 + 8 = 32

Hi! Could you please explain the logic behind setting the last value as "3X"? Thanks!
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Range = Last term - First term
Last term = First term + Range
= x + 2x = 3x

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The first term of a sequence of consecutive positive even integers is 21 Nov 2021, 06:37
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So if the first value, is X, and the range is 2X... then the last value will be X + 2X = 3X.

Alternatively, think of this:
Range = last value - first value
2X = Last Value - X
3X = Last Value
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The first term of a sequence of consecutive positive even integers is 18 Mar 2025, 16:03
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