CAT 2008: Quantitative Questions a Day 101-133 - The discussions

theinquizitive

Quote:

A gathering of a certain number of families consists of people belonging to two generations only. It is known that the number of families is less than the number of girls, the number of girls is less than the number of boys and that the
number of boys is less than the number of parents. If the minimum number of single parent families is two, then what is the minimum number of families, given that no family has more than 3 children?

(1) 3 (2) 4 (3) 5 (4) 7 (5) none of these

Ans : Problem broken down to following:

1. Single parents : 2
2. Max kids in family =< 3.

So if :

f = no. of families
g = no. of girls
b = no. of boys
p = no. of parents

answer :

f<g<b<p

5<6<7<8

Also since only 2 generations are present the problem means that the kids of the parents of first generation cannot also be parents to the kids of next generation.

So answer is (3).

PS : Remember no data is unimportant!!

**genius_yogi**

F<G<B<P

now if no. of families is F then no. of parents will be max 2F - 2 (minimum 2 families having single parents)
now
F<G<B<(2F-2)
now going by the options
option 1
F=3
P can be <= 4
B+G(max) can be 9
so no possibilities
so ruled out

option 2
F=4
P can be <= 6
B+G(max) can be 12
so possibilities are 4 5 6 6(not possible since B<P)
so ruled out

option
F=5
P can be <= 8
B+G(max) can be 15
so possibilities are 5 6 7 8 in the order F G B P
Hence minimum no. of families is 5
ans. (3)

v-factor

families<girls<boys<parents

For 3 families including 2 single parents
3<g<b<4
So values for g and b not possible

For 4 families including 2 single parents
4<g<b<6
So values for g and b not possible

For 5 families including 2 single parents
5<g<b<8
So values for g and b are 6 and 7
5<6<7<8
Answer option 3)5

gir

Families = F
Girls = G
Boys = B
Parents = P

With Min(F) with single parent = 2
max children 3 per family

F < G < B < P
2 3 4 5 (2*3 = 6 doesn't satify 3+4)
3 < 4 < 5 < 6 this case parents condn not satisfies
4 < 5 < 6 < 7 parents condn not satisified
5 < 6 < 7 < 8 all condn satified 2 single parents + 3*2=6 total parents = 8, children can be accordingly
distributed.

option (3)

sanyo

A gathering of a certain number of families consists of people belonging to two generations only. It is known that the number of families is less than the number of girls, the number of girls is less than the number of boys and that the
number of boys is less than the number of parents. If the minimum number of single parent families is two, then what is the minimum number of families, given that no family has more than 3 children?

(1) 3 (2) 4 (3) 5 (4) 7 (5) none of these

Answer option (3)5

let the number of family, girls, boys anfd parents be f, g, b, p.
Now f< g<b<p.
Take the case when single parent family = 2, and 2 parent family = 0, not possible.

Now if single parent family = 2, and 2 parent family = 1.
=> f = 3
=> p = 4,
3< _ <_<4 , again not possible.

Now if single parent family = 2, and 2 parent family = 2.
f = 4, p=6
4 < _ < _ <6, again not possible.

Now if single parent family = 2, and 2 parent family = 3.
f = 5, p=8.
5 < 6< 7< 8... is possible , hence min no. of families = 5..

kamalesh123

Here's my attempt:
number of parents > number of boys > number of girls > number of families
Let there be x single parent families (x>2) and y two parent families
=>
Total families = x + y and
Total parents = x + 2y
Let no. of boys be b and girls be g

=>
g > x + y
b > g
x + 2y > b

=>
x + 2y > b > g > x + y

Minimising =>
g = x + y + 1
b = x + y + 2
then x + 2y = x + y + 3
=> y = 3 and x = 2

Families H H H+W H+W H+W
D D S S S
D D S S
D D S S
Min. No. of families = 5
So answer option (3)

Aarav

Quote:

Originally Posted by gripened

We have
F : No. of families
G : No. of girls
B : No. of boys
P : No. of Parents

Answer Option (3) 5 Families minimum

Did you attempt Practice Test 3?

prade

Quote:

Originally Posted by gripened

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Quantitative Question # 101
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A gathering of a certain number of families consists of people belonging to two generations only. It is known that the number of families is less than the number of girls, the number of girls is less than the number of boys and that the
number of boys is less than the number of parents. If the minimum number of single parent families is two, then what is the minimum number of families, given that no family has more than 3 children?

(1) 3 (2) 4 (3) 5 (4) 7 (5) none of these

families =f
parents = ps(single) + pd (double)
girls = g
and boys = b

Considering the fact that none of the girls and boys are parents.

f<g<b<ps+pd
min(ps) = 2
min(f) = 2
=> g>2 and b>3 hence ps+pd > 4. now ps+pd is even
if ps+pd = 6 => f = 4 we cant get satisfying values of g and b
if ps+pd = 8 => f = 5 => g = 6 and b = 7

hence min number of families = 5 option - 3.

Now if we consider girls and boys to be parents as well then

f >= (g,b)

Fuzon

All We have to care care is Number of Families)F<(number of Girls)G ,G<B
(Number of Boys )B<(Number of Parents)P

1) F = 2 , G = 3 , B = 3 , P= 2 : G<B not satisfied
2) F=3 , G=4 , B = 5 , P= 4 : B<P not satisfied
3) F= 4 , G= 5 , B=6 , P = 6 : B<P not satisfied
4) F=5 , G= 6 , B=7 , P = 10 : All conditions satisfied

Thus Number of families is 5 ... Option 3 is the right answer

milindagrawal

min no. of single parent families=x
b0ye=b
girls=g
families=f
f>b>g>x
checking with options, 5 satisfies all the conditions..
with single parent fam=2
so, 8>b>g>5
where b/g can take values 6/7... 6+7=13<=15
So min. no of families=5