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

Question

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

BrentGMATPrepNow · Accepted Answer

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:  D

Cheers,
Brent

mbaprep2016 · Answer

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

matsuda · Answer

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

stonecold · Answer

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.

kdgodoy · Answer

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.

guialain · Answer

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

KarishmaB · Answer

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)

Madhavi1990 · Answer

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

scofield1521 · Answer

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

kaleem765 · Answer

=> 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.

EMPOWERgmatRichC · 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:  D

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

mimajit · Answer

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.

ScottTargetTestPrep · Answer

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

Regor60 · Answer

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

atharvadixit · Answer

Bunuel  - is this approach right?
x and x assigned to bros and sisof Anna and y and 2y assigned to bros and sis of Andrew.
Now total would be -

x + x + y + 2y + 2 (Anna and Andrew) = plugging in answer choices
therefore 2x + 3y + 2 = 7
2x + 3y = 5 x and y have to be 1 and 1 respectively.

Only answer choice D fits the equation

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

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