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

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Math Expert
Joined: 02 Sep 2009
Posts: 44282
Elliot's allowance was just raised to k dollars per week. He gets a [#permalink]

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01 Mar 2018, 23:27
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Question Stats:

85% (01:17) correct 15% (01:52) wrong based on 19 sessions

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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
[Reveal] Spoiler: OA

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

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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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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

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

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

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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   [#permalink] 03 Mar 2018, 00:50
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