Source: Revised GRE PDF 1st Ed. Section 6: Math; #23 (p. 90)

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# A developer has land that has x feet

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 ? 400; 3,200; 3,700; 4,400; 4,760

### 7 Explanations

4

Kat Hidalgo

i try to eliminate choices as fast as possible, so knowing from the start that 40 lots are 100ft means that the total size of the lake, x, is at least 40 x 100 = 4,000 ft. this eliminates the first three choices immediately.

that leaves us with options D. 4,400 and E. 4,760. or as we can also think of it as, 400ft and 760ft to be split into the remaining lots of 80ft. so we have 400/80 = 5 lots and 760/80 = 9.5 lots. first off, i'm already doubtful about the possibility of half of a lot so i'm leaning towards 5 lots (option D) already.

to check, if E is correct and 1/9 of the lots = 9.5 lots, then that should mean the remaining 8/9 lots would be 76 lots (9.5 x 8 = 76). but the problem explicitly tells us that the remaining number of lots is 40, not 76. (check the math using chris' method!)

so answer D. 4,400ft is what we go with.

Sep 25, 2019 • Comment

That's excellent logic! Thinking like this is a good way to ace the GRE :) Keep it up!

2

to find the number of lots for 80 feet we can use
(40+x)/9 = x
=>40+x=9x
=>8x=40
=>x=5

May 11, 2019 • Comment

That could definitely work!

Thanks and even
40+X/9 = X
(360+X)/9=X
360=8x
X=45
Would work I guess

Sam Kinsman, Magoosh Tutor

Yes, that works! That will give us the total number of lots, which is 45.

1

Anna Roberts

Can we solve by
8/9 x = 40*100?
I solved for x and got 4500 so picked 4400 the correct answer.

Also I am having doubts how to check backwards from answer like Chris mentioned.
For D should I check if 4000/4400 is roughly 8/9 and 400/4400 is roughly 1/9?
And For E should I check if 760/4760 is close to 1/9?
Btw neither of them is exact 1/9.

Nov 23, 2017 • Comment

Jonathan , Magoosh Tutor

(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.

So, (D) is correct.

4

Phanindra Chandraprakash

I had solved this problem in this way:

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.

Hence, D is the correct answer.

Sep 14, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Phanindra :)

It looks like there's a slight conceptual mistake: (1/9)x = 80 is not actually true.

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

I hope this helps!

Cheers,
Cydney :)

Mayank Chandok

Wow, I just loved your explanation.

3 Jonathan , Magoosh Tutor

Hi Thomas,
Kevin mean 40 total of the REMAINING lots.

40 remaining lots is 8/9 of the total. 40 represents 8 of the 9 parts, so there are 5 lots per part.

And yes, that means the original number of lots is 45.

I hope that clarifies.

Apr 14, 2015 • Comment

3

Gabriella Gonzalez

where did you get 5 from???

Oct 2, 2014 • Comment

, Magoosh Tutor

Hi Gabriella,

Happy to help! :) The 5 lots comes from seeing that there are 40 lots total. Then we can see that the difference between 1/9 and 8/9 is 8 times. Thus if we want to find the total lots that have 80 ft of frontage, we can set up this equation:

40 / 8 = 5

In this way, we can work backwards from what we know, determine the multiples, and figure out how many lots have 80 feet of frontage.

Then we move forward to solve the problem. :D

I hope that this helps!

Cheers,

Kevin

Thomas Robinson

Do you mean 45 lots? Doesn't 8/9x=40 mean there are 45 total lots: 5 at 80ft, 40 at 100ft?

10 Chris Lele, Magoosh Tutor

Sep 26, 2012 • Comment