A developer has land that has x feet of lake frontage. The land is to GMAT Problem Solving

Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?

A. 400
B. 3,200
C. 3,700
D. 4,400
E. 4,760

Answer: D

Approach Solution (1):
(8/9)x = 40 * 100 is not correct.
It would be correct if we were 8/9 of the total frontage comes from the 100-feet lots.
Rather:
8/9 (number of lots) = 40 is correct
so (number of lots) = 45
and 1/9 of lots = 5 lots
So we have:
5(80) + 40(100) = 4,400
We can work backwards because we know we have 40 lots with 100 feet of frontage. So we have 4,000 + something.
(A), (B), and (C) are out immediately because they are less than 4000.
To check (D) 4,400:
4,400 - 4000 = 400 which divided by 80 is 5
If 40 is 8/9 then is 1/9 equal to 5? Yes.
Correct option: D

Approach Solution (2):
Let x bet the total length of the lake frontage.
given that, 1/9(x) = 80 and remaining are 40 plots with 100 feet length.
therefore,
1/9(x)+(40*100) = x
now, solve for x,
x+36000=9x
8x=36000
x=4500
the answer nearest to 4500 is D, i.e 4400
Correct option: D

Approach Solution (3):
We are told that 1/9 of the lots have 80 feet of lake frontage, not that 1/9 of the length of the lake frontage is 80 feet.
To solve this question, we have to figure out how many lots have 80 feet of lake frontage, which is 1/9 of the total number of lots. We can use the fact that 40 lots are equal to 8/9 of the lots to determine that there are 45 lots total, 5 of which have 80 feet of lake frontage:
* 5 lots of 80 feet = 400 feet of lake frontage
* 40 lots of 100 feet = 4000 feet of lake frontage
Correct option: D

“A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 40 lots are to have 100 feet of frontage each, what is the value of x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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