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Re: From January 1, 1991, to January 1, 1993, the number of peop [#permalink]
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jlgdr wrote:
From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?

(A) 38
(B) 39
(C) 40
(D) 41
(E) 42


From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent.
Let x = the number of enrolled people on January 1, 1991
So, 1.15x = the number of enrolled people on January 1, 1993

The enrollment on January 1, 1993, was 45 million.
We can write: 1.15x = 45 (million)
Solve: x = 45/1.15 ≈ 39.1

Answer: B

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Re: From January 1, 1991, to January 1, 1993, the number of peop [#permalink]
jlgdr wrote:
From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 15 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?

(A) 38
(B) 39
(C) 40
(D) 41
(E) 42

\(\frac{45}{115}*100\) ~ \(39\), Answer must be (B)
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Re: From January 1, 1991, to January 1, 1993, the number of peop [#permalink]
Instead of calculating 45/1.15, we can use answer choices to arrive at answer.

Let's pick easy no. - Option C
15% of 40 = 10% of 40 + 5% of 40 (whenever number like 15% or 5% are given, break down because calculating 10% is easy)
= 4 + 4/2
= 6
40+6 = 46 mil, so answer must be little less than 40, select B or do a quick approx. for 39 with the above approach
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Re: From January 1, 1991, to January 1, 1993, the number of peop [#permalink]
To find the number of million people enrolled in health maintenance organizations on January 1, 1991, we need to determine the enrollment before the 15 percent increase.

Let's assume the enrollment on January 1, 1991, was x million.

The enrollment on January 1, 1993, increased by 15 percent, so we have:

x + 0.15x = 45

Combining like terms:

1.15x = 45

Dividing both sides by 1.15:

x = 45 / 1.15

Using a calculator, we find:

x ≈ 39.1304

Rounding to the nearest million, we get:

x ≈ 39 million

Therefore, approximately 39 million people were enrolled in health maintenance organizations on January 1, 1991.

The closest option to this value is (B) 39.
Re: From January 1, 1991, to January 1, 1993, the number of peop [#permalink]
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