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A gnome who was 16 Inches tall swallowed a pill that caused film to g

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A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 10 Nov 2018, 10:03
2
2
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (02:51) correct 47% (02:53) wrong based on 65 sessions

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GMATbuster's Weekly Quant Quiz#8 Ques #2


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A gnome who was 16 Inches tall swallowed a pill that caused film to grow by a certain factor x every minute. After 6 minutes, the gnome was 1,024 Inches tall. He then took another pill that reduced his height by a certain factor y every minute. If this reduced the gnome's height by twice as much as factor x increased his height, now many minutes did it take the gnome to grow to the maximum height and then shrink to a height less than his original height of 16 Inches?
A) 7
B) 8
C) 9
D) 10
E) 11

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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 10 Nov 2018, 10:09
1
Initially, 16 inches, becomes 1024 after 6 minutes.
Then growth by a factor by 2. x = 2.

Now this height reduces by a factor twice that of x. means 4 factor.

Now after 1024/4 = 256----1st minutes
256/4 = 64---2nd minutes
64/4 = 16---3rd minute
16/4 = 4---4th minute

So 6+4 = 10 minutes

D is the answer.
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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 10 Nov 2018, 10:14
1
A gnome who was 16 Inches tall swallowed a pill that caused film to grow by a certain factor x every minute. After 6 minutes, the gnome was 1,024 Inches tall. He then took another pill that reduced his height by a certain factor y every minute. If this reduced the gnome's height by twice as much as factor x increased his height, now many minutes did it take the gnome to grow to the maximum height and then shrink to a height less than his original height of 16 Inches?


If A=16
After 6 minutes it is 1024
Hence the degree of growth = 1024(2^10)/16=2^6

So every minute it grew 2 times.

Now it decreased by twice i.e 4
minutes to make it less than the original height= 1024/4^n=16
Here n =3

So total time taken= 6+3+1(1 added since less )

So Answer 10 minutes from start to finish
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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 10 Nov 2018, 10:23
16 = 2^4

1024=2^10

every minute the height grows by a factor of 2(become 2 times)

When it reduces, it will reduce by a factor of 4 (2^-2)

At 6th minute the height is 2^10=1024
At 7th minute the height is 2^8
At 8th minute the height is 2^6
At 9th minute the height is 2^4=16 (same as original)
At 10th minute the height is 2^2 =8 (less than original)

Hence answer is 10 i.e. D
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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 10 Nov 2018, 10:26
1
Growth= x inch per min
16+6x=1024
so, x=168
Shrink rate= Y inch per min
Y=2X
Y=336
Let Number of minutes to shrink below its height=k
1024-336k<16
k>3
k=4
total time = 6 min (Maximum height) + 4(shrink)
=10minutes

option : D
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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 10 Nov 2018, 11:00
10?

increment in height after 1 min : 16x
after 2 mins : 16x^2.....
16 x^6= 1024 so x=2
y = 2x=4

now reduction after 1 min = 1024/y=1024/4=256....
height after 3 min= 16

so time for total inc + total dec= 6+4=10
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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g  [#permalink]

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New post 12 Nov 2018, 14:46
Hi,

I would like to know why 1024 -16 is not considered by anyone in determining the rate of initial growth x?

/muus
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Re: A gnome who was 16 Inches tall swallowed a pill that caused film to g   [#permalink] 12 Nov 2018, 14:46
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