Percent Problem

[talaangoshtari]

In a certain community, 39,285 more apartments were converted to condominiums and sold in 1981 than in 1980. If this was a 30 percent increase, how many apartments were converted and sold in 1981?

(A) 11,786
(B) 51,070
(C) 91,665
(D) 130,950
(E) 170,235

[[email protected]]

Hi talaangoshtari,

Since the answer choices to this question are numbers (and they're rather "spread out"), you can use them to your advantage, do some estimation and TEST THE ANSWERS.

The prompt tells us that a 39,285 apartment INCREASE in sales in 1981 represents a 30% increase in sales over 1980. We're asked how many apartments were sold in 1981.

IF...the sales in 1980 had been 100,000, then a 30% increase would be 30,000....

Since 39,285 is MORE than 30,000, the sales in 1980 MUST have been GREATER than 100,000....

Thus, to get the number in 1981, we have to add 39,285 to a number that is GREATER than 100,000 and end up with one of the answer choices. Since, 139,285+ is greater than 4 of the answers, there's only one possible answer that fits...

Final Answer: E

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

[GMATGuruNY]

In a certain community, 39,285 more apartments were converted to condominiums and sold in 1981 than in 1980. If this was a 30 percent increase, how many apartments were converted and sold in 1981?

(A) 11,786
(B) 51,070
(C) 91,665
(D) 130,950
(E) 170,235

Alternate approach:

Let x = the number sold in 1980 and y = the number sold in 1981.

Since the number sold in 1981 is 30% greater than the number sold in 1980, we get:
x/y = 100/130
x/y = 10/13
x = (10/13)y.

In other words, x is 3/13 less than y.
Implication:
The difference between the two years -- 39285 apartments -- must be equal to 3/13 the value of y:
(3/13)y = 39285
y = (13/3)(39285) ≈ (13/3)(39000) = (13)(13000) = 169000.

The correct answer is E.