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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. 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]

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New post 03 Aug 2013, 01:57
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]

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New post 29 Oct 2013, 20:10
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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 29 Jan 2015, 00:07, edited 1 time in total.

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New post 04 Dec 2013, 21:11
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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]

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New post 28 Jan 2015, 15:36
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]

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New post 28 Jan 2015, 23:07
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]

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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.

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Re: John's front lawn is 1/3 the size of his back lawn. [#permalink]

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New post 25 Sep 2017, 09:56
why couldn't it be in this way?

let back = B
front = 1/3B

done for front = 1/2*1/3B = 1/6B
done for back = 2/3B

combining workdone for front and back = 1/6 + 4/6 = 5/6B
what left to be done = (front + back) - (work done for front and back) = (1/3B + B) - 5/6B = 4/3B - 5/6B = 1/2B

ans. D?

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John's front lawn is 1/3 the size of his back lawn. [#permalink]

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New post 25 Sep 2017, 12:48
Quote:
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

pannathat wrote:
why couldn't it be in this way?

let back = B
front = 1/3B

done for front = 1/2*1/3B = 1/6B
done for back = 2/3B

combining workdone for front and back = 1/6 + 4/6 = 5/6B
what left to be done = (front + back) - (work done for front and back) = (1/3B + B) - 5/6B = 4/3B - 5/6B = 1/2B

ans. D?

pannathat , it looks as if it should work. I had to stare at it for a minute. But the question asks for the fraction left unmowed.

Thus your remaining amount, \(\frac{1}{2}B\), is the part. \(\frac{4}{3}B\) is the whole.

\(\frac{(\frac{1}{2})B}{(\frac{4}{3})B}\)= \(\frac{3}{8}\)

I think choosing numbers is easier on this question. Or, if algebra is preferred, maybe use whole numbers? Seems easier to see or remember the "fraction" part.

That is, maybe try front = F, back = 3F, whole = 4F

F(1/2 unmowed) = 1/2F left
3F(1/3 unmowed) = 1F left
Total left: \(\frac{3}{2}\)F
What remains as fraction of whole?
Whole = 4F

\(\frac{(\frac{3}{2})F}{4F}\)= \(\frac{3}{8}\)

Answer C

Hope it helps. :-)

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Re: John's front lawn is 1/3 the size of his back lawn. [#permalink]

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New post 25 Sep 2017, 12:57
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 Back lawn = 6 ....then Front lawn = 2....total = 8 units

mowed = (1/2) (2) + ( 2/3) ( 6) = 1 + 4 = 5 units

unwoed = 8 - 5 =3 units

Fraction land unmowed = 3/8

Answer: C

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Re: John's front lawn is 1/3 the size of his back lawn.   [#permalink] 25 Sep 2017, 12:57
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