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Ana is a girl and has the same number of brothers as sisters. Andrew [#permalink]

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06 Jul 2016, 07:02

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Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have?

Re: Ana is a girl and has the same number of brothers as sisters. Andrew [#permalink]

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02 Jun 2017, 04:38

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Another way of solving this. Perhaps the faster way.

Actually, working with the information on ANDREW only tells you that the total number of children is a in the from (3k+1). This comes from (andrew + k brothers + 2k sisters) = Total number of children. Total number of Children can be 1 , 4 , 7 , 10 , 13 , ..... Only Option D is matches.

By The Way: Information on ANA is useless given the answer choices. With different answer choices, we could use this info as follows: Because ANA has n brothers and n sisters, the total number of children is in the from (2n+1), ie ODD. This eliminates option A and E
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Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have?

(A) 2 (B) 3 (C) 5 (D) 7 (E) 8

Source: Nova's Math Prep Course Book

Just use logic:

Ana is a girl and has the same number of brothers as sisters. - this means that number of girls is 1 more than the number of boys (to imagine it, Ana is the extra girl).

Andrew is a boy and has twice as many sisters as brothers. - if that 1 extra sister and 1 fewer brother gave Andrew twice the number of sisters, we are talking about small numbers here such as 3 girls, 2 boys or 4 girls, 3 boys. 4 is twice of 2 so we must have 4 girls and 3 boys.

Re: Ana is a girl and has the same number of brothers as sisters. Andrew [#permalink]

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29 Aug 2017, 03:40

Thought of more as a situation than an equation --> basically it tells us: 1) Ana, apart from herself has equal no of brothers and sisters --> this rules out 2 and 3 as it clearly says brother(s) and sister(s) ('the same number of brothers as sisters') --> she is counting at least 2 of each --> buy beyond this we don't know --> she can have 3 brothers = 3 sisters; 4 brothers = 4 sister 2) Her brother Andrew, has 2x sisters than brothers --> if he had 1 bro, he'd have 2 sisters; but then that way Ana's equality rule doesn't play. So the next number: 2 brothers and 4 sisters: total 4 sisters and 3 brothers; this fits both Ana's and Andrew's rule. 5 and 8 are automatically out; leaving us with 7

Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have?

(A) 2 (B) 3 (C) 5 (D) 7 (E) 8

Let B = number of boys that Emma has Let G = number of girls that Emma has

Ana is a girl and has the same number of brothers as sisters. B = the number of brothers Ana has Since Ana is one of Emma's girls, we know that G-1 = the number of sisters Ana has (we cannot include Ana in this count, since Ana is not her own sister) We can write: B = G-1

Andrew is a boy and has twice as many sisters as brothers. G = the number of sisters Andrew has Since Andrew is one of Emma's boys, we know that B-1 = the number of brothers Andrew has We can write: 2(B-1) = G

We now have the following system: B = G-1 2(B-1) = G

Simplify the bottom equation to get: B = G - 1 2B - 2 = G

Take the blue equation and replace B with G-1 to get: 2(G-1) - 2 = G Expand: 2G - 2 - 2 = G Solve: G = 4

When we plug G = 4 into either equation and solve for B, we get B = 3 So, B+G = 3+4 = 7 So, Emma has 7 children (3 boys and 4 girls)

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