Ana is a girl and has the same. . .

Vincen 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)

Cheers,
Brent

Hi Vincen,

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

Vincen wrote: ↑

Thu Sep 14, 2017 2:38 pm

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

The OA is D.

Uff. I am confuse. Do I have to set any equation?

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