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In a psychology school the grade of the students is determin

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In a psychology school the grade of the students is determin [#permalink] New post 05 Mar 2010, 23:20
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In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 40, what will be his grade at the end of the third year?

A. 44
B. 56
C. 62
D. 75
E. 80
[Reveal] Spoiler: OA

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Re: In a psychology school the grade of the students is determin [#permalink] New post 05 Mar 2010, 23:27
Cool question!

There's a lot of information given here, so let's eat slow here.

Joey scores a 40 at the end of his first year. That means that he's currently 20 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).

Now, come next year, or his second year at this psychology school, he's technically 21 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.

Well, his second year is then going to be 21(2) + 20 = 62.

Now let's tackle the main question: what's his grade going to be the third year?

Well, he will be at an age of 22 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (22x2), plus half of his previous year's grade (as calculated for his second year, his grade is 62; therefore, 62/2)

Having said that, the final answer would be 22(2) + 62/2 = 44 + 31 = 75 --> (D)
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Re: In a psychology school the grade of the students is determin [#permalink] New post 05 Mar 2010, 23:38
bakfed wrote:
Cool question!

There's a lot of information given here, so let's eat slow here.

Joey scores a 40 at the end of his first year. That means that he's currently 20 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).

Now, come next year, or his second year at this psychology school, he's technically 21 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.

Well, his second year is then going to be 21(2) + 20 = 62.

Now let's tackle the main question: what's his grade going to be the third year?

Well, he will be at an age of 22 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (22x2), plus half of his previous year's grade (as calculated for his second year, his grade is 62; therefore, 62/2)

Having said that, the final answer would be 22(2) + 62/2 = 44 + 31 = 75 --> (D)


Thanks man! nice explanation gonna note that explanation into my collection.
Actually I am collecting questions posted here with 1 or 2 best explanations of them by members so that I can review them when practicing and also will share here as there is too much data but not compiled or organized. just my 2 cents. I am sure, others will compile too & then share them for community.
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Re: In a psychology school the grade of the students is determin [#permalink] New post 08 Jul 2014, 04:22
Can we not do it by : Age at the end of the third year : 2(x+2) +1/2(2(x+1)+20) = 3x +15 = therefore a multiple of three
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Re: In a psychology school the grade of the students is determin [#permalink] New post 08 Jul 2014, 07:23
Expert's post
adeel2000 wrote:
Can we not do it by : Age at the end of the third year : 2(x+2) +1/2(2(x+1)+20) = 3x +15 = therefore a multiple of three


If you already calculated that x=20, why do you need to use x further?
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Re: In a psychology school the grade of the students is determin [#permalink] New post 08 Jul 2014, 20:23
Age ............. Grade ..............

20 .................. 40 ..........
(Age is 1/2 the grade)

Next Year

21 ................... 2(21) + \frac{40}{2} = 62 (Twice age + 1/2 of earlier grade)

Next Year

22 .................... 2(22) + \frac{62}{2} = 75

Answer = D
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Re: In a psychology school the grade of the students is determin   [#permalink] 08 Jul 2014, 20:23
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