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# M18-32

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Math Expert
Joined: 02 Sep 2009
Posts: 54495

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16 Sep 2014, 01:04
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Difficulty:

5% (low)

Question Stats:

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

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 54495

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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.

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Joined: 01 Oct 2014
Posts: 39
Schools: DeGroote'21 (A)

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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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 54495

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28 Jun 2016, 05:34
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.

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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Joined: 02 May 2016
Posts: 77
Location: India
Concentration: Entrepreneurship
GRE 1: Q163 V154
WE: Information Technology (Computer Software)

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14 Jul 2017, 06:07
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.
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)

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14 Jul 2017, 08:48
1
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 $$= \frac{10}{100} * 100 = 10$$%

Current Student
Joined: 18 Aug 2016
Posts: 619
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38

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

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Luckisnoexcuse
Intern
Joined: 07 Jan 2017
Posts: 19
Location: India
Concentration: Other, Other
Schools: UConn"19
WE: Medicine and Health (Pharmaceuticals and Biotech)

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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 $$= \frac{10}{100} * 100 = 10$$

Manager
Joined: 27 Mar 2016
Posts: 64

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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%
M18-32   [#permalink] 16 Jul 2017, 11:08
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# M18-32

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