Damian needs 1/4 of the wood in the shed on the first day and 2/9 of

Question

Damian needs 1/4 of the wood in the shed on the first day and 2/9 of the remaining wood on the second day to make a tree-house in his backyard. Given that 2/5 of the wood in the shed is unusable due to fungal damage what fraction of useable wood is left once he has completed the tree-house?

A. 11/36
B. 1/3
C. 13/36
D. 7/18
E. 17/37

A. 11/36
B. 1/3
C. 13/36
D. 7/18
E. 17/37

Hoehenheim · Answer

let the amount of wood be 'w'

amount of wood consumed on first and second day is (1/4)w + 2/9*(3/4)w = (1/4)w + (1/6)w = (5/12)w
it is mentioned that (2/5)w is useless. which means usable wood is (3/5)w

question asks for: what fraction of usable wood remains, i.e-> x / (3/5)w = ? Where x is the remaining usable wood

To find x: we must subtract used usable wood and unused wood from total wood to give remaining usable wood., i.e

x = w - (5/12)w - (2/5)w = (11/60)w

Finally, fraction of usable wood left = 11/60 * 5/3 = 11/36

sarthak1701 · Answer

Solved many times and got 11/60 and got other wrong answers (changing the logic of the question) and then I finally read that it asks for the FRACTION of the usable wood. I keep making such mistakes in Quant, any suggestions? Thanks.

Hoehenheim · Answer

Sarthak, keep practicing HQ questions. Whenever you do make mistakes, evaluate. Then go through your evaluation again. Mostly, mistakes can be conceptual (where you need to go back to source material and clear things up), calculative (you messed up your working and need to be more alert), and the third but the most underrated yet a silent killer is language, as is the one you ended up facing in this particular circumstance. Know what the question asks of you. 
This question right now has a 20% correct rate, which would've easily fallen down much more if it was an OG question and 11/60 was an option.

Anyway, tally your mistakes in the above proposed categories over a week of practicing quant. Find out where you're lacking. If it is 1, go hit theory books. If it is 2 or 3, do what I said in line 1 then repeat.

Not being from a quant background, more so, not even taking math post 10th grade, I struggled to get Q15-16/21 up until a month ago. But now I can confidently get Q20/21. Just follow the above religiously. Best of luck.

sarthak1701 · Answer

Thanks Damian for the detailed reply! It’s definitely the language and silly mistakes. On my most recent mock I got 9 incorrect in Quant, analysing it, I could’ve easily got 7 of those correct but got them wrong due to silly mistakes/language and time pressure. Quant is what preventing me from scoring over 645. Gonna practice religiously now. Thanks again!

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Posted from my mobile device

Hoehenheim · Answer

Unfortunately my lumber skills are not on par with Damian

, but you're welcome nonetheless.

sarthak1701 · Answer

I wood say you can definitely get there!

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zlishz · Answer

chetan2u   Bunuel

Please tell me where am I going wrong.

Total wood is 1.
(2/5) is unusable so (3/5) is useable for building the tree house.
Now, on Day 1, he needs (1/4)th of the wood, so
(1/4)*(3/5) = (3/20)
 Remaining useable wood =(3/5)-(3/20) = (45/100)

On day 2, he needs (2/9)of the remaining wood, so, we have, 
(2/9)* (45/100) = (1/10)
Reaming useable wood = (45/100)-(1/10)= (35/100)

We have been asked what fraction of the useable wood is left once the house is built
(35/100) is left out of (3/5) of useable wood
which is equal to (35/100) * (5/3) = (7/12)

sarthak1701 · Answer

Damn, just realized you are not Damian! Lol! See this is what I mean. Anyway, thanks!

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=82908 Harsha GMAT-Club-Forum-jsrehf2l.png

shivampaul · Answer

I've solved the same way. Waiting on a reply from someone who can explain the issue in this approach.

Bunuel · Answer

That setup mistake is treating 1/4 and 2/9 as fractions of the usable pile. They are fractions of the total pile, and “remaining wood” on day 2 also means total remaining pile. All usage comes out of the usable stock.

Damian needs 1/4 of the wood in the shed on the first day and 2/9 of the remaining wood on the second day to make a tree-house in his backyard. Given that 2/5 of the wood in the shed is unusable due to fungal damage what fraction of useable wood is left once he has completed the tree-house?

A. 11/36
B. 1/3
C. 13/36
D. 7/18
E. 17/37

A. 11/36
B. 1/3
C. 13/36
D. 7/18
E. 17/37

Pick a smart total: 180 units.

Unusable at start: 2/5 of 180 = 72
Usable at start: 180 - 72 =  108

Day 1 uses 1/4 of total: 1/4 of 180 = 45
 Usable left: 108 - 45 = 63
 Total left: 180 - 45 = 135

Day 2 uses 2/9 of remaining total: 2/9 of 135 = 30
 Usable left: 63 - 30 =  33

Fraction of usable wood left = 33/108 = 11/36

Answer: A.

ravi1522 · Answer

Hello 
lets assume total woods as 180 (LCM of 4,9,5)
wood required on 1st day =1/4 *180=45
wood required on 2nd day =2/9 *(180-45)=30
Useable wood =3/5 *180=108
Fraction of usable wood left = (108-75)/108 = 11/36

Hence option A is correct

Damian needs 1/4 of the wood in the shed on the first day and 2/9 of

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