If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe

Question

If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothers and sisters are there in Mrs. Smith’s family?

(1) Ms. Anna has the same number of brothers and sisters.

(2) Mr. Mathew has twice as many sisters as brothers.

chetan2u · Accepted Answer

1) It gives us the number of brothers and sisters of Anna same or say b=s.. nothing on number..insuff
2) it gives us mathews brothers and sis ratio.. insuff
but lets see the eq in terms of b and s..
mathews bro=b-1; sis=s+1...
s+1=2(b-1)

combined we have two eq and two variable so suff..
s+1=2(b-1)...
b=s..
so b+1=2(b-1)
b+1=2b-2... or b=3...
s=3..
therefore there are 4 sisters and 3 brothers..
C

tyagamagus · Answer

Hi Chetan,

Can you explain how you arrived at the equation for mathews bros and siss' as s+1 = 2(b-1).

Thanks

chetan2u · Answer

Hi,
The first sentence says Anna has same number of sis and bro, so the boys are one less than girls, as girls increase by one when Anna is also counted.
So s=b+1
So if we convert this info in terms of Mathews bro and sis...
Mathews brother are b-1, as Mathew himself is part of total b..
And sister is s..
As per statement ll, s=2(b-1)..... s=2b-2
Substitute s=b+1 in it..
b+1=2b-2...or b=3 And s =3+1=4..

tyagamagus · Answer

Thanks a ton for the explanation Chetan. Cheers!

guptarahul · Answer

From Statement (1) alone, we have that Ms. Anna has the same number of brothers as sisters. If m is the number of male children Mrs. Smith has (so Anna has this many brothers), then she must have m sisters also. Hence, including Ms. Anna, Mrs. Smith must have m + 1 female children. Now, the number of children Mrs. Smith has equals m + (m + 1) = 2m + 1. But, we still do not know the value of m. Hence, Statement (1) alone is not sufficient.
From Statement (2) alone, we have that Mr. Mathew has twice as many sisters as brothers. Hence, if Mathew has, say, m – 1 brothers, then he must have 2(m – 1) sisters. Hence, the total number of children of Mrs. Smith equals m – 1 brothers of Mathew + 1 (Mathew himself) + 2(m – 1) sisters = m + 2(m – 1) = 3m – 2. Since we do not know the value m, Statement (2) alone is not sufficient.
Equating the number of children from both statements yields 2m + 1 = 3m – 2. Solving this equation for m yields m = 3. Hence, the number of children of Mrs. Smith is 2m + 1 = 2  3 + 1 = 7. Hence, the statements together answer the question.
The answer is (C).

guenthermat · Answer

My following approach is obviously incorrect - I am very happy to get your thoughts:

(1) Mr. Mathew is Anna's brother. If Anna has the same number of brothers and sisters, she has one more sister. Thus, 3 children all in all. SUFF

ajtmatch · Answer

Hi  chetan2u ,

If in this calculation :

combined we have two eq and two variable so suff..
s+1=2(b-1)...
b=s..
so b+1=2(b-1)
b+1=2b-2... or b=3...
s=3..
therefore there are 4 sisters and 3 brothers.

from this we get s=3 and b=3. so shouldnt the total be 6 siblings?

chetan2u · Answer

HI,

We have taken  the sisters of Ms Anna to be s , and we get s=b=3. Now, this  s does not consider Ms Anna  as a part of it.
But  we are looking for total sisters  and brother in the family, so now  we have to include Ms Anna., so 3+1 sisters.

crampipan · Answer

They both could have siblings on their respective father's side, so neither is sufficient. We only know they have the same mom.

bumpbot · Answer

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If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe

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