Visa

[manik11]

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

OA : C

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Hi manik11,

While this DS question is 'wordy', it can be answered by TESTing VALUES and thinking logically about how the two variables relate to one another.

We're given a series of facts to start:
1) in 1980, R of 1024 visas were granted to people from E.E.
2) In 1990, r of 1468 visas were granted to people from E.E.
3) r > R

We're asked if r is greater than R by MORE than 20%. This is a YES/NO question.

1) r = R + 33

IF...
R = 1
r = 34
(34-1)/1 = 33 = 3300% greater
Then the answer to the question is YES.

IF...
R = 1000
r = 1034
(1034-1000)/1000 = 34/1000 = 0.34% greater
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT.

From this information, you should note that as R gets bigger, the percentage increase from R to r gets SMALLER.

2) 1/6 < r/1468 < 1/5

This Fact tells us NOTHING about the value of R, so we cannot determine the relationship between those two values.
Fact 2 is INSUFFICIENT.

Combined, we know....
r = R + 33
1/6 < r/1468 < 1/5

From the second fact, we can do a quick approximation. 1/6 of 1468 is about 244 and 1/5 of 1468 is about 294, so...
244 < r < 294

IF....
r = 245
R = 212
(245-212)/212 = 33/212 = about 15% greater
Then the answer to the question is NO.

As r and R get increase, the percentage increase will DECREASE, so that increase will ALWAYS be LESS than 20% and the answer to the question is ALWAYS NO.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

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

Question stem:
Is r more than 120% of R?

Translated into math:
r > (120/100)R ?
r > (6/5)R ?

Statement 1:
Substituting R = r-33 into the resulting inequality above, we get:
r > (6/5)(r - 33) ?
5r > 6r - 198 ?
198 > r ?
r < 198 ?

No way to determine whether r < 198.
INSUFFICIENT.

Statement 2:
No information about R.
INSUFFICIENT.

Statements combined:
Rephrased question stem yielded by Statement 1:
Is r < 198 ?

Test r=198 in 1/6 < r/1468:

1/6 < 198/1468
1468*1 < 6*198
1468 < integer less than 1200.
Doesn't work:
The right-hand side is too small.

To increase the value of the right-hand side, r must increase to a value GREATER THAN 198.
Thus, the answer to the rephrased question stem is NO.
SUFFICIENT.

The correct answer is C.

[Matt@VeritasPrep]

S1::

Try some extreme values. We could have r = 34, R = 1, in which case the increase is huge. We could also have r = 1057, R = 1024, in which case the increase is very small. NOT SUFFICIENT

S2::

1468/5 > r > 1468/6

293.6 > r > 244.66...

But this doesn't tell us about R; NOT SUFFICIENT.

S1+S2::

We could have anything from r = 245, R = 212 to r = 293, R = 260. The smaller value gives us the bigger increase, so consider 20% greater than 212. This would be

212 * 1.2

or

≈254

So we can't have an increase of at least 20%, and we're set!

A lot of arithmetic in this problem!