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M18-32

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M18-32  [#permalink]

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New post 16 Sep 2014, 01:04
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A
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C
D
E

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  5% (low)

Question Stats:

92% (00:46) correct 8% (00:50) wrong based on 195 sessions

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Re M18-32  [#permalink]

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New post 16 Sep 2014, 01:04
Official Solution:

If an executive's salary increased by 20% from 1995 to 1996 but decreased by 25% from 1996 to 1997, what percent lower was the executive's salary in 1997 than in 1995?

A. 5
B. 8
C. 10
D. 12
E. 15

Denote \(x\) as the executive's salary in 1995. Then the executive's salary in 1996 was \(1.2x\) while in 1997 it was \(1.2*0.75*x = 0.9x\). Thus, in 1997 the executive's salary was \(\frac{x - 0.9x}{x}*100\% = 10\%\) lower than in 1995.

Answer: C
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Re: M18-32  [#permalink]

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New post 27 Jun 2016, 16:56
Bunuel wrote:
Official Solution:

If an executive's salary increased by 20% from 1995 to 1996 but decreased by 25% from 1996 to 1997, what percent lower was the executive's salary in 1997 than in 1995?

A. 5
B. 8
C. 10
D. 12
E. 15

Denote \(x\) as the executive's salary in 1995. Then the executive's salary in 1996 was \(1.2x\) while in 1997 it was \(1.2*0.75*x = 0.9x\). Thus, in 1997 the executive's salary was \(\frac{x - 0.9x}{x}*100\% = 10\%\) lower than in 1995.

Answer: C



Instead of x if I use a number for eg 10 then 1995 -->10, 1996--.1.2x10=12 and 1997 is 9 so when I do the next step to find percent lower (10-9)/9x100=11.11 I am not getting 12 exactly .Can you please explain where am I going wrong?
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Re: M18-32  [#permalink]

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New post 28 Jun 2016, 05:34
89renegade wrote:
Bunuel wrote:
Official Solution:

If an executive's salary increased by 20% from 1995 to 1996 but decreased by 25% from 1996 to 1997, what percent lower was the executive's salary in 1997 than in 1995?

A. 5
B. 8
C. 10
D. 12
E. 15

Denote \(x\) as the executive's salary in 1995. Then the executive's salary in 1996 was \(1.2x\) while in 1997 it was \(1.2*0.75*x = 0.9x\). Thus, in 1997 the executive's salary was \(\frac{x - 0.9x}{x}*100\% = 10\%\) lower than in 1995.

Answer: C



Instead of x if I use a number for eg 10 then 1995 -->10, 1996--.1.2x10=12 and 1997 is 9 so when I do the next step to find percent lower (10-9)/9x100=11.11 I am not getting 12 exactly .Can you please explain where am I going wrong?


1995 - 10
1996 - 12
1997 - 9

(10 - 9)/10 = 1/10.
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M18-32  [#permalink]

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New post 14 Jul 2017, 06:07
89renegade wrote:
Instead of x if I use a number for eg 10 then 1995 -->10, 1996--.1.2x10=12 and 1997 is 9 so when I do the next step to find percent lower (10-9)/9x100=11.11 I am not getting 12 exactly .Can you please explain where am I going wrong?



Question Stem wrote:
what percent lower was the executive's salary in 1997 than in 1995

The bold part is what we should treat as denominator.
The value based on which percentage is to be calculated should be used as denominator.
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Re: M18-32  [#permalink]

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New post 14 Jul 2017, 08:48
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Bunuel wrote:
If an executive's salary increased by 20% from 1995 to 1996 but decreased by 25% from 1996 to 1997, what percent lower was the executive's salary in 1997 than in 1995?

A. 5
B. 8
C. 10
D. 12
E. 15


Let the initial salary be \(= 100\)

Salary increased by \(20\)% from 1995 to 1996 \(= 120\)% of \(100 = \frac{120}{100} * 100 = 120\)

Salary decreased by \(25\)% from 1996 to 1997 \(= 75\)% of \(120 = \frac{75}{100} * 120 = 90\)

Difference between initial salary and final salary \(= 100 - 90 = 10\)

Percent Change \(= \frac{10}{100} * 100 = 10\)%

Answer (C)...
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Re: M18-32  [#permalink]

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New post 14 Jul 2017, 09:28
+20-25+(-25*20)/100 = -10


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New post 14 Jul 2017, 09:36
Let's consider the salary in 1995 as 100

Salary increased by 20% (120% \(=\frac{6}{5}\)) from 1995 to 1996 and decreased by 25% (75% \(=\frac{3}{4}\)) from 1996 to 1997

The total salary at the in 1997 \(= \frac{6}{5} * \frac{3}{4} * 100=90\)

Difference in the salaries is 100-90=10

Percent Change \(= \frac{10}{100} * 100 = 10\)

Answer (C)
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M18-32  [#permalink]

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New post 16 Jul 2017, 11:08
we can apply successive percentage formula
total discount=20+(-25)+(20*(-25))/100
=20-25-500/100
=-5-5=-10
hence salary decreased by 10%
Answer C
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M18-32   [#permalink] 16 Jul 2017, 11:08
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