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The number of bananas harvested in 2000 was the integer x. I

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The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 08 Apr 2014, 20:00
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The number of bananas harvested in 2000 was the integer x. In 2001, the number of bananas harvested grew by 150% from the year 2000. In 2002, the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?

(A) 100%
(B) 167%
(C) 200%
(D) 250%
(E) 500%
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 09 Apr 2014, 00:23
1
Hi ,

This is how i approached the solution :

Bananas harvested in 2001 = 1.5 X
Bananas harvested in 2002 = 4X

Percentage growth = ((4X - 1.5X)/1.5X) * 100 = 166.67% = 167% (B)

Hope this helps.
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 09 Apr 2014, 18:29
Thats the second way I did it but how did you find it so accurately without using a calculator?

So this is the way I did it. The least complicated way like yours but slightly different. Please let me know if this is wrong.

2000 = X
2001 = 1.5 x
2002 = 4x

SO New value - Old value / old value =

4x - 1.5x / 1.5x = 2.5x / 1.5x = 5/3 (in fraction form) reduced from 25/15

1/3 = 0.33333

so 5 * 0.3333 = 0.16665 * 100 = 166.65 = 167% :)

or if you know 3/3 is a whole 100 % then 2/3 = .666666 continuous * 100 = 66.66

and added together 166.67 --> 167%
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 10 Apr 2014, 06:04
If bananas harvested in 2000 was X (100) then surely a 150% growth of X (100) would mean bananas harvested in 2001 of 2.5X (250)

Going from 1X to 1.5X would be equivalent of 50% growth (as opposed to 150)?

I think the answer is A
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 10 Apr 2014, 07:07
jasdhanda wrote:
Thats the second way I did it but how did you find it so accurately without using a calculator?

So this is the way I did it. The least complicated way like yours but slightly different. Please let me know if this is wrong.

2000 = X
2001 = 1.5 x
2002 = 4x

SO New value - Old value / old value =

4x - 1.5x / 1.5x = 2.5x / 1.5x = 5/3 (in fraction form) reduced from 25/15

1/3 = 0.33333

so 5 * 0.3333 = 0.16665 * 100 = 166.65 = 167% :)

or if you know 3/3 is a whole 100 % then 2/3 = .666666 continuous * 100 = 66.66

and added together 166.67 --> 167%


Hi ,

You were correct till this step : 4x - 1.5x / 1.5x = 2.5x / 1.5x = 5/3 (in fraction form) reduced from 25/15

But then to find 5/3, you do not need to do 1/3 * 5 . Just simply do a long division of 5 by 3. You will get 1.66666..... Now to convert this decimal to percent, shift the decimal 2 places to the right and you get 166.66.. The closest option in the answers is 167%.
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 10 Apr 2014, 07:12
phferr1984 wrote:
If bananas harvested in 2000 was X (100) then surely a 150% growth of X (100) would mean bananas harvested in 2001 of 2.5X (250)

Going from 1X to 1.5X would be equivalent of 50% growth (as opposed to 150)?

I think the answer is A



Hi,

A growth of 150 % means 1.5 * X and not 2.5 * X.

For e.g : Lets say the number of bananas in 2000 = 100
Then number of bananas in 2001 = 150 % of 100 ; which means add 50 % of 100 to itself = 100 + 50 = 150.
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 10 Apr 2014, 08:59
[quote="saket2160"


Hi,

A growth of 150 % means 1.5 * X and not 2.5 * X.

For e.g : Lets say the number of bananas in 2000 = 100
Then number of bananas in 2001 = 150 % of 100 ; which means add 50 % of 100 to itself = 100 + 50 = 150.[/quote]

So if there were 100 bananas harvested in 2001 and the harvest grew BY 50% - how many bananas would be harvested? How can 50% growth be the same as 150% growth?

If I have a stock portfolio (100) and it grew by 9% in one year - it would be worth 109 at the end of the year?

I'm struggling with this one...
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 10 Apr 2014, 10:37
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phferr1984 wrote:
[quote="saket2160"


Hi,

A growth of 150 % means 1.5 * X and not 2.5 * X.

For e.g : Lets say the number of bananas in 2000 = 100
Then number of bananas in 2001 = 150 % of 100 ; which means add 50 % of 100 to itself = 100 + 50 = 150.


So if there were 100 bananas harvested in 2001 and the harvest grew BY 50% - how many bananas would be harvested? How can 50% growth be the same as 150% growth?

If I have a stock portfolio (100) and it grew by 9% in one year - it would be worth 109 at the end of the year?

I'm struggling with this one...[/quote]

The question says grew by 150%, i think it means x+1.5x = 2.5x
if it would have said grew to 150% of the harvest in 2000, it meant 1.5x

For 2001 harvest = x+1.5x = 2.5x
For 2002 harvest = x+4x = 5x

hence % growth from 2001 to 2002 = (5x-2.5x)/2.5x = 100%

Answer is A

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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 10 Apr 2014, 18:54
I agree A.

2000: x
2001: 2.5x
2002: 5x

(5x/2.5x) - 1 = Y%/100
Y%=100
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 11 Apr 2014, 03:29
jasdhanda wrote:
The number of bananas harvested in 2000 was the integer x. In 2001, the number of bananas harvested grew by 150% from the year 2000. In 2002, the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?

(A) 100%
(B) 167%
(C) 200%
(D) 250%
(E) 500%



Year 2000 = x

Year 2001 \(= x + \frac{150x}{100}= \frac{250x}{100}\)

Year 2002 \(= x +\frac{400x}{100}= \frac{500x}{100}\)

Percentage growth from the year 2001 to the year 2002

\(= \frac{\frac{500x}{100} - \frac{250x}{100}}{\frac{250x}{100}} * 100\)

= 100

Answer = A = 100%

Bunuel, can you kindly confirm the answer ?
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 11 Apr 2014, 05:35
jasdhanda,phferr1984,

Apologies from my end. I made a mistake in considering the increase in the percentages as they were above 100%. Option A would be the correct answer.
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 11 Apr 2014, 11:53
saket2160 wrote:
jasdhanda,phferr1984,

Apologies from my end. I made a mistake in considering the increase in the percentages as they were above 100%. Option A would be the correct answer.


After going through the thread it feels like the real confusion was that did the harvest increased by the given % or became equal to.

I believe the question means increased by the given %.

Hence, the answer is A

2001 = x+1.5X
2002 = x+4X

so the % increase is 2.5x/2.5x *100 = 100%

-------------------
Kudos if the answer helped :)
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 11 Apr 2014, 22:19
We get x, 2.5x, 5x. So, 5x/2.5x=2 times means 100%
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 11 Apr 2014, 22:22
We get x, 2.5x, 5x. So, 5x/2.5x=2 times means 100%. Picking gives 100, 250, 500, and 500/250=2 times (100%)
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New post 09 Jun 2016, 10:46
The number of bananas harvested in 2000 was the integer x. In 2001 the number of bananas harvested grew by 150% from the year 2000. In 2002 the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?

a) 100%
b) 167%
c) 200%
d) 250%
e) 500%
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 09 Jun 2016, 10:51
sabrina3509 wrote:
The number of bananas harvested in 2000 was the integer x. In 2001 the number of bananas harvested grew by 150% from the year 2000. In 2002 the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?

a) 100%
b) 167%
c) 200%
d) 250%
e) 500%


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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 09 Jun 2016, 11:00
jasdhanda wrote:
The number of bananas harvested in 2000 was the integer x. In 2001, the number of bananas harvested grew by 150% from the year 2000. In 2002, the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?

(A) 100%
(B) 167%
(C) 200%
(D) 250%
(E) 500%


The question says the harvest grew by 150% and 400% in the years 2001 and 2002 respectively. So the harvest grew by 1.5x and 4x in the years 2001 and 2002. so the total harvest in the 3 years are:

2000 - x
2001 - x+1.5x=2.5x
2002 - x+4x=5x

So the harvest grew from 2.5x (in 2001) to 5x (in 2002), which is a 100% increment.
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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New post 09 Jun 2016, 11:02
sabrina3509 wrote:
The number of bananas harvested in 2000 was the integer x. In 2001 the number of bananas harvested grew by 150% from the year 2000. In 2002 the number of bananas harvested grew by 400% from the year 2000. What was the percentage growth in the number of bananas harvested from the year 2001 to the year 2002?

a) 100%
b) 167%
c) 200%
d) 250%
e) 500%


Year - Bananas
2000 - x
2001 - x + 1.5x = 2.5x
2002 - x + 4x = 5x

Percentage growth from 2001 to 2002 = (5 - 2.5) / 2.5*100 = 100%

Correct Option: A
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Re: The number of bananas harvested in 2000 was the integer x. I  [#permalink]

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Re: The number of bananas harvested in 2000 was the integer x. I &nbs [#permalink] 10 Jun 2018, 06:59
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