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Bunuel
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John's daughter, Alice, has twice as many sisters as brothers, whereas 20 Sep 2023, 08:00
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69% (02:31) correct 31% (02:26) wrong based on 127 sessions

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John's daughter, Alice, has twice as many sisters as brothers, whereas her brother, Bob, has thrice as many sisters as brothers. How many children does John have?

A. 8
B. 9
C. 11
D. 13
E. 14

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D
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ankitgoswami
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John's daughter, Alice, has twice as many sisters as brothers, whereas 20 Sep 2023, 10:09
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Without Alice, the number of siblings should be divisible by 3
Without Bob, the number of siblings should be divisible by 4

So, we can say that number of siblings = (Number divisible by 4 & 3) + 1

Only '13' fulfills the condition.

Ans D
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John's daughter, Alice, has twice as many sisters as brothers, whereas 20 Sep 2023, 11:08
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Bunuel
John's daughter, Alice, has twice as many sisters as brothers, whereas her brother, Bob, has thrice as many sisters as brothers. How many children does John have?

A. 8
B. 9
C. 11
D. 13
E. 14
Show more

Solution:

  • Assuming Alice has \(x\) brother and \(2x\) sisters, John has \(x+2x+1=3x+1\) children
  • Assuming Bob has \(y\) brother and \(3y\) sisters, John has \(y+3y+1=4y+1\) children

  • This means John has \(LCM(3, 4)+1=12+1=13\) children

Hence the right answer is Option D
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John's daughter, Alice, has twice as many sisters as brothers, whereas 20 Sep 2023, 13:42
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Bunuel
John's daughter, Alice, has twice as many sisters as brothers, whereas her brother, Bob, has thrice as many sisters as brothers. How many children does John have?

A. 8
B. 9
C. 11
D. 13
E. 14
Show more

Let's assume that

  • the number of boys that John has = \(b\)
  • the number of girls that John has = \(g\)

John's daughter, Alice, has twice as many sisters as brothers,

From the point of view of John's daughter, Alice

  • the number of boys (her brothers) = \(b\)
  • the number of girls (her sisters) = \(g - 1\)
    \(g - 1\) because Alice is also one of the girls
  • Given : \(g - 1 = 2b \) ------------ (1)

...her brother, Bob, has thrice as many sisters as brothers...

From the point of view of John's son, Bob

  • the number of boys (his brothers) = \(b-1\)
    \(b - 1\) because Bob is also one of the boys
  • the number of girls (his sisters) = \(g \)
  • Given : \(3(b-1) = g \) ------------ (2)

From (1)

\(g = 2b + 1\)

From (2)

\(g = 3b - 3\)

Equating both

\(2b + 1 = 3b - 3\)

\(b = 4\)

\(g = 2*4 + 1 = 9\)

Total children = \(b + g = 9 + 4 = 13\)

Option D
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John's daughter, Alice, has twice as many sisters as brothers, whereas 23 Sep 2023, 06:56
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Alice is a sister and Bob is a brother, so the information they give is always for the whole family, minus themselve:
Let S be the # of sisters and B the # of brothers

"Alice, has twice as many sisters as brothers":
S - 1 = 2B

"Her brother, Bob, has thrice as many sisters as brothers":
S = 3(B-1)

Simplifying and setting these two equations equal, we find that:
B=4

which means that:
S -1 = 2*4
S = 8+1 = 9

Total Number of Children = S + B = 9 + 4 = 13

Option D
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John's daughter, Alice, has twice as many sisters as brothers, whereas 07 Oct 2024, 01:01
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