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John's front lawn is 1/3 the size of his back lawn.

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John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 03 Aug 2013, 00:53
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John's front lawn is 1/3 the size of his back lawn. If John mows 1/2 of his front lawn and 2/3 of his back lawn, what fraction of his lawn is left unmowed?

1. 1/6
2. 1/3
3. 3/8
4 1/2
5.5/8
[Reveal] Spoiler: OA
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Re: John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 03 Aug 2013, 00:57
genuinebot85 wrote:
John's front lawn is 1/3 the size of his back lawn. If John mows 1/2 of his front lawn and 2/3 of his back lawn, what fraction of his lawn is left unmowed?

1. 1/6
2. 1/3
3. 3/8
4 1/2
5.5/8


let say back lawn = 6
therefore front lawn = 1/3 * 6 =2
total = 6+2 = 8
now moved lawn= 1/2)*2 + 2/3)*6 = 5
therefore unmoved lawn = total - moved = 8 - 5 =3
fraction = unmoved / total = 3/8

hence C
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John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 29 Oct 2013, 19:10
Say back lawn = x, so front lawn \(= \frac{x}{3}\)

Total lawn \(= x + \frac{x}{3} = \frac{4x}{3}\) ................ (i)

back lawn mowed\(= \frac{2x}{3}\) & front lawn mowed \(= \frac{x}{6}\)

Total mowed \(= \frac{2x}{3} + \frac{x}{6} = \frac{5x}{6}\) .......... (ii)

Total Unmowed = (i) - (ii)

\(= \frac{4x}{3} - \frac{5x}{6} = \frac{x}{2}\) ................... (iii)

Unmowed Fraction = (iii) / (i)

\(\frac{x}{2} * \frac{3}{4x} = \frac{3}{8}\) (Answer = C)
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Last edited by PareshGmat on 28 Jan 2015, 23:07, edited 1 time in total.
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Re: John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 04 Dec 2013, 20:11
Fraction of unmoved lawn = Total un mowed lawn / Total Area
F - Front Lawn
B - Back Lawn

F = 1/3(B)

Total Area = F+B = 4F (or 4/3 B; lets keep it as 4F for simplicity)

Total un mowed = Remaining of Front + Remaining of Back;
"John mows 1/2 of his front lawn": so 1/2F remaining
"and mows 2/3 of his back lawn,": so 1/3 of B remaining; which is 1/3(3F) = F
Total un mowed = 3/2(F)

Fraction = \(\frac{3}{2}*F/4F\) = 3/8.

Ans: C
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Re: John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 28 Jan 2015, 14:36
Hi
I tried this task too, but my result is wrong. I dont know why because our solution path seems similar.

5/6 of the back lawn is mowed. Means 1 /6B is not mowed.
The total lawn is 4 /3 lawn.

(1/6 B) / (4/3B) = 1/8 which is incorrect.

Why ?

Thanks in advance for your help.
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Re: John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 28 Jan 2015, 22:07
Here we go:

Let the size of back lawn - 3
Then front lawn - 1
Total Lawn area = 4 ---- (1)

John mows 1/2 of his front lawn and 2/3 of his back lawn


Total lawn area left unmowed = 1/2 + 1 = 3/2 ---- (2)
Fraction = (2) / (1) = 3/8

Option C
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John's front lawn is 1/3 the size of his back lawn. [#permalink] New post 28 Jan 2015, 22:20
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gmatstrong wrote:
Hi
I tried this task too, but my result is wrong. I dont know why because our solution path seems similar.

5/6 of the back lawn is mowed. Means 1 /6B is not mowed.
The total lawn is 4 /3 lawn.

(1/6 B) / (4/3B) = 1/8 which is incorrect.

Why ?

Thanks in advance for your help.


According to me.....
5/6 of the total lawn is mowed as per your solution
and the total lawn is 4/3 (as per your solution)

So the lawn left unmowed will be given by (Total - Lawn mowed) ----> 4/3 - 5/6 = 1/2

and then (1/2) / (4/3) = 3/8

I hope that is clear now.
John's front lawn is 1/3 the size of his back lawn.   [#permalink] 28 Jan 2015, 22:20
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