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Number System

by mallireddy » Tue Mar 22, 2016 9:27 pm
Lata has the same number of sisters as she has brothers but her brother Shyam has twice as many sisters as he has brothers.How many children are there in the family?
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by GMATGuruNY » Tue Mar 22, 2016 9:58 pm
The GMAT would provide answer choices, as follows:
mallireddy wrote:Lata has the same number of sisters as she has brothers but her brother Shyam has twice as many sisters as he has brothers. How many children are there in the family?

3
5
6
7
9
We can PLUG IN THE ANSWERS, which represent the total number of children.
When the correct answer choice is plugged in, Lata will have an equal number of sisters and brothers, while Shyam will have twice as many sisters as brothers.

Let L = Lata and S = Shyam.

Answer choice D: 7
Since Lata must have an equal number of sisters and brothers, the 7 children are as follows:
Girls = L, G, G, G
Boys = S, B, B
In this case:
Lata has 3 sisters G, G, G and 3 brothers S, B, B.
Shyam has 4 sisters L, G, G, G and 2 brothers B, B.
Success!
While Lata has an equal number of sisters and brothers, Shyam has twice as many sisters as brothers.

The correct answer is D.
Last edited by GMATGuruNY on Wed Mar 23, 2016 3:33 am, edited 1 time in total.
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by GMATGuruNY » Tue Mar 22, 2016 10:43 pm
Algebraic solution:

Let T = total children, L = Lata, S = Shyam, B = the additional boys and G = the additional girls.
Thus:
T = L + S + B + G.

Note the following:
Since L and S each constitute ONE CHILD, L=1 and S=1.

Lata's sisters = G.
Lata's brothers = S + B = 1 + B.
Since the number of sisters is equal to the number of brothers, we get:
G = 1+B.

Shyam's sisters = L + G = 1 + G.
Shyam's brothers = B.
Since the number of sisters is twice the number of brothers, we get:
1 + G = 2B
G = 2B-1

Since G=2B-1 and G=1+B, we get:
2B-1 = 1+B
B = 2.

Thus:
G = 1+B = 1+2 = 3.

Substituting L=1, S=1, B=2 and G=3 into T = L + S + B + G, we get:
T = 1 + 1 + 2 + 3 = 7.
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by [email protected] » Wed Mar 23, 2016 9:05 am
Hi mallireddy,

This question can also be solved by 'brute force.'

We're told that:
1) Lata is female; Shyam is male
2) Lata has the SAME number of sisters as brothers
3) Shyam 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:
Shyam 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
Lata and 1 other female
Shyam and 1 other male
But we're told that Lata 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
Lata and 3 other females
Shyam and 2 other males
Here, Lata would have 3 sisters AND 3 brothers, which matches what we were told. This MUST be the answer (7 total children).

Final Answer: D

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