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Harold and Millicent are getting married and need to combine their alr

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Bunuel
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Harold and Millicent are getting married and need to combine their alr [#permalink] New post   06 Oct 2014, 15:00
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Tough and Tricky questions: Ratios



Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6
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B
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PareshGmat
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Harold and Millicent are getting married and need to combine their alr [#permalink] New post   06 Oct 2014, 18:58
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Harold ............ ......Millicent ............. Total

\(\frac{x}{2}\) ...................... x (Assume)

Books brought in new home

\(\frac{x}{2} * \frac{1}{3} = \frac{x}{6}\) .......... \(\frac{x}{2}\) .............................\(\frac{x}{6} + \frac{x}{2} = \frac{2x}{3}\)

Required \(fraction = \frac{\frac{2x}{3}}{x} = \frac{2}{3}\)

Answer = B
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Re: Harold and Millicent are getting married and need to combine their alr [#permalink] New post   07 Oct 2014, 02:38
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Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

Books with Millicent = M
Books with Harold = M/2
Har. brings 1/3 of books = M/6
Mill. can now bring M/2 books to fill the library completly

Capacity of new library = M/2 + M/6 = 4M/6 = 2M/3

Fraction of old lib = (2M/3) / M = 2 / 3
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Harold and Millicent are getting married and need to combine their alr [#permalink] New post   07 Oct 2014, 03:06
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My approach: plug in numbers.
Because we see H will bring 1/3 of his books to the new home --> try to pick a number that is divisible by 3.

Before:
Assume H = 30 books
H = 1/2 M --> M = 60 books

After:
H' = 1/3H = 10 books
M' = 1/2M = 30 books
Total = 40 books

M' = 40 = 2/3*60
Ratio: 2/3

Ans: B
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Re: Harold and Millicent are getting married and need to combine their alr [#permalink] New post   09 Oct 2014, 04:12
Bunuel wrote:

Tough and Tricky questions: Ratios



Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6


Let,
Mich has m books, she takes m/2 books
Har has m/2 books, he takes m/6 books
Total m/2 + m/6 = 2/3 m
so 2/3 is ans.
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Re: Harold and Millicent are getting married and need to combine their alr [#permalink] New post   26 Feb 2018, 10:59
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Bunuel wrote:

Tough and Tricky questions: Ratios



Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6


We can let the number of books Harold has in his old library be 30 and thus Millicent has 60 books in her old library. We see that Harold will bring 10 of his books and Millicent will bring 30 of her books to the new library, making their new library a capacity of 40. Since 40/60 = ⅔, their new library capacity is ⅔ of Millicent’s old library capacity.

Answer: B
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Re: Harold and Millicent are getting married and need to combine their alr [#permalink] New post   13 Feb 2022, 17:34
Hi, can someone please help translate "What fraction of Millicent's old library capacity is the new home's library capacity?" in math terms? I got it wrong cause I read it as Millicent's old library capacity / the new total capacity. I get the reasoning now but want to ensure that I won't make this simple error again.
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Harold and Millicent are getting married and need to combine their alr [#permalink] New post   13 Feb 2022, 20:03
Bunuel wrote:

Tough and Tricky questions: Ratios



Harold and Millicent are getting married and need to combine their already-full libraries. If Harold, who has 1/2 as many books as Millicent, brings 1/3 of his books to their new home, then Millicent will have enough room to bring 1/2 of her books to their new home. What fraction of Millicent's old library capacity is the new home's library capacity?

A. 1/2
B. 2/3
C. 3/4
D. 4/5
E. 5/6


Let \(h=x\) then \(m=2x\)
From question
Total number of books in new library = \(\frac{x}{3}+x\)
= \(\frac{4x}{3}\)

Required ratio = \(\frac{4x}{3}\)*\(\frac{1}{2x}\)
=\(\frac{2}{3}\)

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Harold and Millicent are getting married and need to combine their alr [#permalink]
13 Feb 2022, 20:03
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