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Manager  Joined: 26 Nov 2014
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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.

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Joined: 02 Aug 2009
Posts: 7960
Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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shyind wrote:
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.

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
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Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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Hi Chetan,

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

Thanks
Math Expert V
Joined: 02 Aug 2009
Posts: 7960
Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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tyagamagus wrote:
Hi Chetan,

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

Thanks

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..
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Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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Thanks a ton for the explanation Chetan. Cheers!
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Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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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).
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Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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shyind wrote:
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.

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
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Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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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 wrote:
shyind wrote:
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.

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
Math Expert V
Joined: 02 Aug 2009
Posts: 7960
Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe  [#permalink]

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ajtmatch wrote:
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 wrote:
shyind wrote:
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.

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

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.
_________________ Re: If Ms. Anna and Mr. Mathew are children of Mrs. Smith, how many brothe   [#permalink] 27 Mar 2019, 05:56
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