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Ana is a girl and has the same number of brothers as sisters. Andrew

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

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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
[Reveal] Spoiler: OA

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

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New post 06 Jul 2016, 08:18
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no of girls X
no of boys Y
x-1 = y
y-1 = 2x

multiple first with 2
2x-2= 2y
y-1 -2 = 2y => y=3 ignore sign
put in 1 x= 4
total 7

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

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New post 28 Jul 2016, 06:35
mbaprep2016 wrote:
no of girls X
no of boys Y
x-1 = y
y-1 = 2x

multiple first with 2
2x-2= 2y
y-1 -2 = 2y => y=3 ignore sign
put in 1 x= 4
total 7


I got the reasoning but is there a way to equate the system without having to "ignore" the sign ?

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

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New post 21 Apr 2017, 02:02
Excellent Question.
Here is what i did in this one =>


Number of children =>

X + X + Ana=> 2X+1



Brothers in the family => X
Sisters in the family => X+1


After removing andrew =>
Brothers => X-1
Sisters => X+1

As per the question =>2(X-1)=X+1
2X-2=X+1
X=3

Hence number of children for Emma => 2X+1 => 7


SMASH THAT D.


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

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New post 14 May 2017, 07:30
mbaprep2016 wrote:
no of girls X
no of boys Y
x-1 = y
y-1 = 2x

multiple first with 2
2x-2= 2y
y-1 -2 = 2y => y=3 ignore sign
put in 1 x= 4
total 7


Actually, your second stated equation "y-1 = 2x" has a little typo.

It should be: y-1 = x/2.

Thus, you don't need to ignore the sign to achieve the solution.

(I) x-1 = y
(II) y-1 = x/2

Replacing (I) in (II):

(x-1)-1 = x/2

2(x-2) = x

2x-4 = x

x = 4

So, y = 3 and total = 7.

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

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

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New post 02 Jun 2017, 09:00
DensetsuNo wrote:
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.

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

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New post 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

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

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New post 14 Sep 2017, 16:23
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DensetsuNo wrote:
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)

Answer:
[Reveal] Spoiler:
D


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

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New post 15 Sep 2017, 00:49
7
Ana -3 brothers (boys)
-3 sisters (girls)
total 3 boys 4 girls.
Andrew: 2 brothers (boys), 4 sisters. Ana and other 3
Total 3 boys 4 girls.
Total=7


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

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New post 27 Sep 2017, 02:11
=> Equal number of girls and boys + Ana so 2B + Ana OR 2G + Ana
=> Girls twice the boys + Andrew so 3G + Andrew

The correct answer would be a multiple of both 2 and 3 after subtracting 1.

Option D: 7 - 1 = 6 and 6 is a multiple of both 2 and 3. So D is the right answer.

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Re: Ana is a girl and has the same number of brothers as sisters. Andrew   [#permalink] 27 Sep 2017, 02:11
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