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

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

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)

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

We see that Ana and Andrew are sister and brother. Let’s test various case scenarios.

Let’s say Andrew has one brother and two sisters (one of whom is Ana). Then Ana would have one sister and two brothers (one of whom is Andrew). However, since we are given that Ana has the same number of brothers as sisters, Andrew can’t have only one brother and two sisters.

Let’s say Andrew has two brothers and four sisters (one of whom is Ana). Then Ana would have three sisters and three brothers (one of whom is Andrew). We see that Ana does have the same number of brothers as sisters, so Emma has 3 sons and 4 daughters, for a total of 7 children.

Answer: D

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

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.

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

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


Sent from my iPhone using GMAT Club Forum

=> 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.

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).

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Dear Brent,

Can u clarify one small doubt? Below is what you mentioned for statement 2.

"If 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 "

My doubt here is if Andrew is a boy and has twice as many sisters as brothers
Then the second equation should be (B-1)= 2G ie if Andrew has B-1 no of brothers excluding himself and he has twice the no of Sisters compared to brothers = 2G

Please guide me where am I going wrong with my interpretation of the statement.

Let G = number of girls, B = number of boys.

Ana having the same number of brothers as sisters means the number of girls is 1 more than the number of boys because the statement excludes Ana, so

G = B + 1

Andrew having twice as many sisters as brothers means, since the number of brothers is one less than the number of boys (Andrew not being his own brother)

G = 2(B-1)

Equating the above:

B+1 = 2(B-1) = 2B-2, therefore

B = 3, and therefore

G=B+1 = 4, for a total of 7 children

Posted from my mobile device

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.