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Elliot's allowance was just raised to k dollars per week. He gets a

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Elliot's allowance was just raised to k dollars per week. He gets a  [#permalink]

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New post 01 Mar 2018, 23:27
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Elliot's allowance was just raised to k dollars per week. He gets a raise of c dollars per week every 2 years. How much will his allowance be per week y years from now? (Assume that y is a positive even integer).

(A) k + cy

(B) k + 2cy

(C) k + cy/2

(D) k + 2c

(E) ky + 2c

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Re: Elliot's allowance was just raised to k dollars per week. He gets a  [#permalink]

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New post 01 Mar 2018, 23:59
Bunuel wrote:
Elliot's allowance was just raised to k dollars per week. He gets a raise of c dollars per week every 2 years. How much will his allowance be per week y years from now?

(A) k + cy

(B) k + 2cy

(C) k + cy/2

(D) k + 2c

(E) ky + 2c


With Elliot's current allowance of k dollars per week, as his allowance was raised
by c dollar per week every 2 years, it must have been raised by \(\frac{c}{2}\) dollars per week every year.

In y years, the allowance would have been raised by \(y * \frac{c}{2}\)

Therefore, Elliot's allowance per week in y years will be \(k + \frac{cy}{2}\) (Option C)
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Elliot's allowance was just raised to k dollars per week. He gets a  [#permalink]

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New post 02 Mar 2018, 20:51
Bunuel wrote:
Elliot's allowance was just raised to k dollars per week. He gets a raise of c dollars per week every 2 years. How much will his allowance be per week y years from now? (Assume that y is a positive even integer).

(A) k + cy

(B) k + 2cy

(C) k + cy/2

(D) k + 2c

(E) ky + 2c

Choose somewhat spread out numbers.

k, allowance now = $4
c, raise every 2 years = $1
y, years =10

A raise every 2 years means 10/2 = 5 raises
5 raises * $1 per raise = $5 total
In 10 years Elliott will get ($4 + $5) = $9 per week

OR:
$4.. +2 years = $5
......+2 years = $6
......+2 years = $7
......+2 years = $8
......+2 years = $9
....= 10 yrs

With k = $4, c = $1, y = 10, look for the answer that gives you $9

(A) k + cy: ($4 + $10) = $14. NO

(B) k + 2cy: REJECT. $14 from A, cy = 10, is too high. This answer is higher.

(C) k + cy/2: ($4 + 10/2) = ($4 + $5) = $9. MATCH

(D) k + 2c: ($4 + $2) = $6. NO

(E) ky + 2c: ($4 * 10) = $40. ...REJECT. $40 alone is too high

ANSWER C
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Re: Elliot's allowance was just raised to k dollars per week. He gets a  [#permalink]

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New post 03 Mar 2018, 00:50
This is a AP problem. the series is as follows:

k, k+c, k+2c......

a1=k
d= c
n=y/2 +1 ( between K and K+3C number of terms = 4 ( k+3c=k+(n-1)c, solving for n, you get n=4)

An =k+(y/2+1-1)c {nth term of an AP}
Therefore, An = K+yc/2 ( option C)

Bunuel wrote:
Elliot's allowance was just raised to k dollars per week. He gets a raise of c dollars per week every 2 years. How much will his allowance be per week y years from now? (Assume that y is a positive even integer).

(A) k + cy

(B) k + 2cy

(C) k + cy/2

(D) k + 2c

(E) ky + 2c
Re: Elliot's allowance was just raised to k dollars per week. He gets a &nbs [#permalink] 03 Mar 2018, 00:50
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