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# Abigail used to save 40% of her salary in 2013. Her salary increased

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Abigail used to save 40% of her salary in 2013. Her salary increased [#permalink]

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10 Nov 2017, 03:19
00:00

Difficulty:

65% (hard)

Question Stats:

54% (00:54) correct 46% (01:42) wrong based on 67 sessions

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Abigail used to save 40% of her salary in 2013. Her salary increased by 100% in 2014 and by 50% in 2015, but her expenses remained the same throughout. What was the percentage increase in her annual savings over the two years?

A. 200%
B. 240%
C. 300%
D. 500%
E. 600%
[Reveal] Spoiler: OA

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Re: Abigail used to save 40% of her salary in 2013. Her salary increased [#permalink]

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10 Nov 2017, 04:03
nkmungila wrote:
Abigail used to save 40% of her salary in 2013. Her salary increased by 100% in 2014 and by 50% in 2015, but her expenses
remained the same throughout. What was the percentage increase in her annual savings over the two years?

A. 200%
B. 240%
C. 300%
D. 500%
E. 600%

As the Q asks numeric value, take value of first year and work forward..
Salary be 100, so the savings are 40 and expenses 60
The salary next year = 100*200/100=200
And the next year =200*150/100=300
savings = 300-60=240
Increase in savings=240-40=200

% increase = 200/40 * 100 =500%

D
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Re: Abigail used to save 40% of her salary in 2013. Her salary increased [#permalink]

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10 Nov 2017, 04:27
Salary = x
Savings = 0,4*x
Expenditures = 0,6*x (constant)
After salary increase, new salary becomes x*(1+1)*(1+0,5) = 3*x
New savings = 3*x - 0,6*x = 2,4*x
% increase is (New savings - Old savings)*100 / Old savings = (2,4*x - 0,4*x)*100/0,4*x = 500%

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Re: Abigail used to save 40% of her salary in 2013. Her salary increased [#permalink]

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14 Nov 2017, 06:05
nkmungila wrote:
Abigail used to save 40% of her salary in 2013. Her salary increased by 100% in 2014 and by 50% in 2015, but her expenses remained the same throughout. What was the percentage increase in her annual savings over the two years?

A. 200%
B. 240%
C. 300%
D. 500%
E. 600%

We can let Abigail's salary in 2013 = n, and thus her savings = 0.4n and her expenses = 0.6n in that year.

In 2014, her salary has increased by 100%, which means that it has doubled. Her salary, therefore, is 2n.

In 2015, her salary has increased by 50%, so we increase 2n by 50%, which is the same as multiplying it by 1.5:

2n x1.5 = 3n

Since her expenses are the same throughout the years, her expenses are 0.6n in 2015. Thus, she saves 3n - 0.6n = 2.4n in 2015.

We use the percent increase formula: (New - Old)/Old x 100. Thus, the percentage increase from 2013 to 2015 is (2.4n - 0.4n)/0.4n x 100 = 2.0n/0.4n x 100= 20/4 x 100 = 5 x 100 = 500%.

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Re: Abigail used to save 40% of her salary in 2013. Her salary increased [#permalink]

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14 Nov 2017, 08:55
nkmungila wrote:
Abigail used to save 40% of her salary in 2013. Her salary increased by 100% in 2014 and by 50% in 2015, but her expenses remained the same throughout. What was the percentage increase in her annual savings over the two years?

A. 200%
B. 240%
C. 300%
D. 500%
E. 600%

Plug in a value and check
Attachment:

Capture.PNG [ 2.97 KiB | Viewed 304 times ]

Percentage increase in her annual savings is $$\frac{(240-40)}{40}*100$$ = 500%

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Re: Abigail used to save 40% of her salary in 2013. Her salary increased   [#permalink] 14 Nov 2017, 08:55
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