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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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New post 06 Jul 2016, 06:02
2
9
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (02:12) correct 39% (02:01) wrong based on 259 sessions

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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
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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, 07:18
1
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, 05:35
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, 01:02
1
1
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, 06:30
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, 03:38
1
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, 08:00
1
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, 02:40
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, 15:23
1
Top Contributor
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:

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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, 23:49
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, 01:11
=> 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]

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New post 06 Dec 2017, 13:50
Hi All,

This question can also be solved by 'brute force.'

We're told that:
1) Ana is female; Andrew is male
2) Ana has the SAME number of sisters as brothers
3) Andrew has TWICE as many sisters as brothers

We're asked for the total number of children in the family.

Let's start with the 3rd fact first:
Andrew COULD have
2 sisters and 1 brother
4 sisters and 2 brothers
6 sisters and 3 brothers
etc.

IF... it's 2 sisters and 1 brother, then we have
Ana and 1 other female
Andrew and 1 other male
But we're told that Ana has the SAME number of sisters as brothers (here though, she has 1 sister and 2 brothers), so this is NOT the correct answer.

IF... it's 4 sisters and 2 brothers, then we have
Ana and 3 other females
Andrew and 2 other males
Here, Ana would have 3 sisters AND 3 brothers, which matches what we were told. This MUST be the answer (7 total children).

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Re: Ana is a girl and has the same number of brothers as sisters. Andrew &nbs [#permalink] 06 Dec 2017, 13:50
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