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# In 1980 the Immigration and Naturalization Service (INS) granted 1024

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
In 1980 the Immigration and Naturalization Service (INS) granted 1024  [#permalink]

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14 Jan 2018, 06:49
00:00

Difficulty:

55% (hard)

Question Stats:

69% (03:32) correct 31% (02:43) wrong based on 21 sessions

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In 1980 the Immigration and Naturalization Service (INS) granted 1024 refugee status visas, and R of these visas were granted to people from Eastern Europe. In 1990 the total number of such visas granted by the INS was 1468, and r of these were granted to people from Eastern Europe. If the number of refugee status visas to people from Eastern Europe increased from 1980 to 1990, was the increase greater than 20%?

(1) r = R + 33
(2) 1/6 < r/1468 < 1/5

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Re: In 1980 the Immigration and Naturalization Service (INS) granted 1024  [#permalink]

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14 Jan 2018, 14:22
Bunuel wrote:
In 1980 the Immigration and Naturalization Service (INS) granted 1024 refugee status visas, and R of these visas were granted to people from Eastern Europe. In 1990 the total number of such visas granted by the INS was 1468, and r of these were granted to people from Eastern Europe. If the number of refugee status visas to people from Eastern Europe increased from 1980 to 1990, was the increase greater than 20%?

(1) r = R + 33
(2) 1/6 < r/1468 < 1/5

As this is a very wordy question, to avoid confusion we'll translate it into equations before trying to solve.
This is a Precise approach.

Our data is:
1980: 1024 visas granted, R of these to Eastern Europe
1990: 1468 visas granted, r of these to Eastern Europe
Our question is: is r - R greater than 20% of R?

It is now easy to write our question as an expression: r - R > 0.2R (?)

(1) gives us one equation with two variables - insufficient!
(2) gives no additional information on R - insufficient!

Combined:
As (2) gives a range of values we have no choice but to estimate the extremes:
We'll start with the larger value: 1468/5 = about 1470/5 = (1500 - 30)/5 = (300 - 6)/5 = about 59.
Then r < 59 and R < 26. In this case r - R is more than a 20% increase over R.
Since the smaller value will only make R smaller without changing r - R it must make r - R/r larger.
Meaning that it will be larger than 20% for sure.

(C) is our answer.
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Re: In 1980 the Immigration and Naturalization Service (INS) granted 1024   [#permalink] 14 Jan 2018, 14:22
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# In 1980 the Immigration and Naturalization Service (INS) granted 1024

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