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# Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a

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Joined: 02 Sep 2009
Posts: 52285
Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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15 Feb 2017, 02:22
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Difficulty:

35% (medium)

Question Stats:

58% (01:36) correct 42% (01:43) wrong based on 110 sessions

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Timmy grew by 10% between the ages of 6 and 8 and by 20% between the ages of 6 and 10. Which of the following is closest to the percentage by which Timmy grew between the ages of 8 and 10?

A. 7%
B. 8%
C. 9%
D. 10%
E. 11%

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Re: Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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15 Feb 2017, 04:16
lets say, starting size was 100cm
so by the age of 8 he grew by 10 cm and became 110cm
by the age 10 he grew by 20cm and became 120cm

%increase from 8-10=(120-110)/100*100 thats approximately 9%

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Re: Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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15 Feb 2017, 07:10
1
Bunuel wrote:
Timmy grew by 10% between the ages of 6 and 8 and by 20% between the ages of 6 and 10. Which of the following is closest to the percentage by which Timmy grew between the ages of 8 and 10?

A. 7%
B. 8%
C. 9%
D. 10%
E. 11%

Let, height at age 6 years be 100
Height at age 8 years will be 110
Height at age 10 years will be 120

So, percentage by which Timmy grew between the ages of 8 and 10 will be

$$\frac{10}{110}*100$$ = $$9.09$$%

Thus, answer will be (C) $$9.09$$%
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Re: Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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16 Feb 2017, 11:19
1
Bunuel wrote:
Timmy grew by 10% between the ages of 6 and 8 and by 20% between the ages of 6 and 10. Which of the following is closest to the percentage by which Timmy grew between the ages of 8 and 10?

A. 7%
B. 8%
C. 9%
D. 10%
E. 11%

We can let Timmy’s height at age 6 = x. Thus, by age 8, his height is 1.1x, and by age 10, his height is 1.2x. We need to determine the percentage by which Timmy grew between the ages of 8 and 10, that is, the percent change of his height from age 8 to age 10. We can use the percent change formula:

(1.2x - 1.1x)/(1.1x) * 100

(0.1x)/(1.1x) * 100

1/11 * 100

100/11 ≈ 99/11 = 9 percent

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Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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17 Feb 2017, 00:30
1
Bunuel wrote:
Timmy grew by 10% between the ages of 6 and 8 and by 20% between the ages of 6 and 10. Which of the following is closest to the percentage by which Timmy grew between the ages of 8 and 10?

A. 7%
B. 8%
C. 9%
D. 10%
E. 11%

Let's assume Tommy Height at age of 6 = 10
then Tommy Height at age of 8 = 11
Also, Tommy Height at age of 10 = 12

The growth of Tommy from 8 to 10 is 1 (from 11 to 12)

Hence, Percentage growth = (12-11)*100/11 = 9.09%

A little suggestion to the readers here is that one who remembers the reciprocal of Integers from 1-10 becomes really strong in these percentage calculations and approximation so if it is not much of task for someone then please learn them (with a few tricks

1/1 = 100%
1/2 = 50%
1/3 = 33.33%
1/4 = 25% (half of 1/2)
1/5 = 20%
1/6 = 16.66% (Half of 1/3 i.e. half of 33.33)
1/7 = 14.28% (twice of 7 is 14 and twice of 14 is 28 this is how it becomes 14.28)
1/8 = 12.5% (half of 1/4)
1/9 = 11.11% (Brother of 11)
1/10 = 10%
1/11 = 9.09% (Brother of 9)

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Re: Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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22 Feb 2017, 18:38
Bunuel wrote:
Timmy grew by 10% between the ages of 6 and 8 and by 20% between the ages of 6 and 10. Which of the following is closest to the percentage by which Timmy grew between the ages of 8 and 10?

A. 7%
B. 8%
C. 9%
D. 10%
E. 11%

Official solution from Veritas Prep.
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Re: Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a  [#permalink]

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11 Mar 2017, 13:18
let's try smart numbers, so:
when he is 6 he is 100
8 - 110
10 - 120
120-110/110= cca 9%
Re: Timmy grew by 10% between the ages of 6 and 8 and by 20% between the a &nbs [#permalink] 11 Mar 2017, 13:18
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