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# A certain college's enrollment at the beginning of 1992

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A certain college's enrollment at the beginning of 1992  [#permalink]

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26 Jul 2016, 06:32
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Difficulty:

5% (low)

Question Stats:

90% (01:26) correct 10% (02:09) wrong based on 120 sessions

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A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?

A) 17.5%
B) 24%
C) 30%
D) 35%
E) 38%

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Re: A certain college's enrollment at the beginning of 1992  [#permalink]

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26 Jul 2016, 23:17
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NandishSS wrote:
A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?

A) 17.5%
B) 24%
C) 30%
D) 35%
E) 38%

Suppose enrollment in 1991 was 100

Then enrollment in 1992 will be 120

And enrollment in 1993 will be 120*1.15=138

Increase in 1993 from 1991 = 138-100= 38

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Re: A certain college's enrollment at the beginning of 1992  [#permalink]

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27 Jul 2016, 13:00
NandishSS wrote:
A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?

A) 17.5%
B) 24%
C) 30%
D) 35%
E) 38%

Let's suppose enrollment for 1991= x

Enrollment in 1992= 1.2x (20% greater that previous year)

Enrollment in 1993= 1.15*1.2x (15% greater than previous year)= 1.38x = 38% greater than it was in 1991

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Re: A certain college's enrollment at the beginning of 1992  [#permalink]

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27 Jul 2016, 22:57
value in 91 is 100
value in 92 becomes 120
values in 93 would be 115*120 = 13800/100= 138 , which is 38 % greater. E
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A certain college's enrollment at the beginning of 1992  [#permalink]

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08 Sep 2017, 14:49
NandishSS wrote:
A certain college's enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991, and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992. The college's enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?

A) 17.5%
B) 24%
C) 30%
D) 35%
E) 38%

Shortcut Formula

When there are only two successive percent changes, A and B, and the numbers are reasonable, there is a simple formula* to calculate the total percent change, in this case, percent increase:

A + B + $$\frac{A*B}{100}$$ = total percent change

A here is 20
B here is 15

20 + 15 + $$\frac{20*15}{100}$$ =

20 + 15 + $$\frac{300}{100}$$ =

20 + 15 + 3 = 38 percent increase

*"Successive Percentage Changes," in Percentages, Interest, and More, from GMAT Club, here: https://gmatclub.com/forum/percentages-interest-and-more-208098.html#p1596558
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Joined: 20 Sep 2016
Posts: 24
Re: A certain college's enrollment at the beginning of 1992  [#permalink]

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07 Oct 2017, 22:16
use the concept of percent of percent:
(1.2*1.15*x)/ x

solve it to find an increase of 38 %
Re: A certain college's enrollment at the beginning of 1992 &nbs [#permalink] 07 Oct 2017, 22:16
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