MGMAT- VICS problem

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Wed May 11, 2011 10:27 pm

Jake was 4.5 feet tall on his 12th birthday, when he began to have a growth
spurt. Between his 12th and 15th birthdays, he grew at a constant rate. If Jake
was 20% taller on his 15th birthday than on his 13th birthday, how many inches
per year did Jake grow during his growth spurt? (12 inches = 1 foot)

[spoiler]ans-6inches/year.[/spoiler]

I made a mistake in this question that I started this way.
12th birthday - P0 * k
13th birthday - P0 * k^2
14th birthday - P0 * k^3
15th birthday - P0 * k^4

given 15th-13th = 20%.

But obviously this question aint saying that the height increased by the same factor everyyear? how do i identify that this is a linear growth problem ? just because height cant grow exponentially ?

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Source: Beat The GMAT — Problem Solving | Wed May 11, 2011 10:27 pm

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Wed May 11, 2011 10:46 pm

If the height grows exponentially, the question would mention it explicitly.

he grew at a constant rate: This directly means his growth was linear.

Last edited by vineeshp on Wed May 11, 2011 10:55 pm, edited 1 time in total.

Vineesh,
Just telling you what I know and think. I am not the expert.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed May 11, 2011 10:51 pm

bblast wrote:Jake was 4.5 feet tall on his 12th birthday, when he began to have a growth
spurt. Between his 12th and 15th birthdays, he grew at a constant rate. If Jake
was 20% taller on his 15th birthday than on his 13th birthday, how many inches
per year did Jake grow during his growth spurt? (12 inches = 1 foot)

[spoiler]ans-6inches/year.[/spoiler]

I made a mistake in this question that I started this way.
12th birthday - P0 * k
13th birthday - P0 * k^2
14th birthday - P0 * k^3
15th birthday - P0 * k^4

given 15th-13th = 20%.

But obviously this question aint saying that the height increased by the same factor everyyear? how do i identify that this is a linear growth problem ? just because height cant grow exponentially ?

experts...

Solution:
A constant rate of change is anything that increases or decreases by the same amount for every trial. The question says that "Between his 12th and 15th birthdays, he grew at a constant rate". That means the increase is same every year.
Let the increase every year be 'i' feet.
So, on 13th birthday he is 4.5 + i feet.
On fourteenth birthday he is 4.5 + 2i feet and on 15th birthday he is 4.5 + 3i feet.
Now 1.2*(4.5 + i) = 4.5 + 3i.
Or 5.4 + 1.2i = 4.5 + 3i.
Or .9 = 1.8i
Or i = 0.5 feet = 6 inches.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed May 11, 2011 11:29 pm

bblast wrote:Jake was 4.5 feet tall on his 12th birthday, when he began to have a growth
spurt. Between his 12th and 15th birthdays, he grew at a constant rate. If Jake
was 20% taller on his 15th birthday than on his 13th birthday, how many inches
per year did Jake grow during his growth spurt? (12 inches = 1 foot)

[spoiler]ans-6inches/year.[/spoiler]

I made a mistake in this question that I started this way.
12th birthday - P0 * k
13th birthday - P0 * k^2
14th birthday - P0 * k^3
15th birthday - P0 * k^4

given 15th-13th = 20%.

But obviously this question aint saying that the height increased by the same factor everyyear? how do i identify that this is a linear growth problem ? just because height cant grow exponentially ?

experts...

Initial height = 4.5* 12 = 54 inches.

On the GMAT we could plug in the answers, which would represent the growth per year.

Answer choice: 6 inches per year
At 13, Jake would be 54+6 = 60 inches.
At 15, Jake would be 60 + 2*6 = 72 inches.
72-60=12.
Since 12 =.2*60, success!

The correct answer is 6 inches per year.

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