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

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Harold and Millicent are getting married and need to combine their alr  [#permalink]

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New post 06 Oct 2014, 14:00
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A
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E

Difficulty:

  25% (medium)

Question Stats:

81% (01:47) correct 19% (02:10) wrong based on 263 sessions

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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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Harold and Millicent are getting married and need to combine their alr  [#permalink]

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New post 06 Oct 2014, 17:58
5
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]

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New post 07 Oct 2014, 01:38
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1
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]

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New post 07 Oct 2014, 02:06
3
1
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]

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New post 09 Oct 2014, 03:12
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]

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New post 26 Feb 2018, 09:59
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 &nbs [#permalink] 26 Feb 2018, 09:59
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