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

[Manu Gupta]

Hai..My answer for QQAD 101..

Let F be the no of families.B boys,G girls, P parents.
From given single parent families is 2.So the solution cant be achieved if total no of Families is 2.
If F is 5, then P is 2*1 + 3*2 =8
Each family doesnt have more than 3 children.
Hence F=5 and P=8 obviously B and G must be 7 and 6 resp. inorder to satisfy the condition.

Cheers!!
Satya

[prashy_tr]

My solution to QQAD 101,

Given conditions:
F<G<B<P ------> (1)
Single parent = minimum 2 -----> (2)
only 2 generations ------> (3)

Let F=3
So P= 1+1+2 = 5.=> B,G do not get natural numbers.
Let F=4
So P= 1+1+2+2 = 6 =>B,G do not get natural numbers.
Let F=5
So P = 1+1+2+2+2 =8 =>B,G can get 6,7.

Arranging suitably,we can get as below
M1 M2 M3W3 M4W4 M5W5
b b g g g
Hence option (3)

[Catalyst2008]

need a help...can someone gimme the link where I can find previous years' CAT papers? or the papers itself
Thanks in advance!

[soumya_withu]

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

Number of families = F
Number of single parents = S
Number of Double Parents = D
Number of Boys = B
Number of Girls = G
Number of Parents = P = S + D

Important Info : None among B or G can double up as D or S.

P >= D+2
F= D/2 + S
=>F >= D/2 + 2

Now F <G<B<P
Putting minimum value of F and P
D/2+ 2 <G < B< D + 2
=>D/2 < G-2 < B-2 < D
Now we need two distinct integers between D and D/2
Least possible value for D = 6.
In that case minimum value for F = D/2 + 2 = 5

Answer : 5

[prvineeth]

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Quantitative Question # 101
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Ans:
Let B=Number of boys
G=Number of girls
x=Number of families with both the parents


x+2 < G < B < 2X+2


When x=1 3<G<B<4 , G &B not possible
x=2 4<G<B<6 , Either of G or B not possible
x=3 5<G<B<8, G=6 ,B=7


So minimum number of families= 5


Answer option (3) 5

[WannaBThere]

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

As we have to get the minimum number, so I'll be as conservative as possible in allocating numbers.

Let x be the number of families.
number of girls = x+1 (just more than number of families)
Likewise,
number of boys = x+2
number of parents = x+3 = (x+1) + 2 (since, minimum number of single parent families is two)
Therefore, number of families (x)= 1/2(x+1)+2
So, number of families (x)=5
Hence the answer is (3) 5
Did I fell in some trap while solving this?

[jayaram85]

hi puys

let the number of single family parent be f1, 2 family be f2
number of girls as g, number of boys as b
from the conditions in the question

(f1+f2)<g<b<(f1+2f2)

since its given that number of single parent family is at least 2 we can take f1 as 2
now
given that no family has more than 3 children the total number of girls plus boys is less than or equal to 3(f1+f2)

so we have the eqs as

(f1+f2)<g<b<(f1+2f2)
g+b<3(f1+f2)

substituting f1 as 2and taking each option we get

f2 as 1,2,3,5

now we have to find g and b such that they lie between f1+f2 and f1+2f2

only when number of families is 5 we get

f1+f2 as 5
f1+2f2 as 8

thus g=6 b=7 and g+b=13<3(f1+f2)

thus option 3)

[ankit_aspire]

(3) 5 families

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

as minimum value of f that satisfies condition --- f<g<b<p
can be obtained from p= f+3 = b+1 = g+2 and single parent families are at least 2 . so after that we need to maximize number of 2 parents family least value that satisfies this is 5 .
so f=5, g=6, b=7 , p=8 . the two single parents family has a boy each as parent, 3-two parents families contribute 3 boys & 3 girls and 3 girls and 2 boys in 2nd generation as children .

[hismajesty143]

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

My take on this:

We can express the situation by the relation:
families<girls<boys<parents

Evaluating the options:

(1) In this case, using the relation above we get:
at least 3<4<5<6 which means 6 parents from 3 families which is impossible as there are at least 2 single parent families.

(2) 4<5<6<7. Here too, 7 parents from 4 families is impossible using similar argument as in (1)

(3) 5<6<7<8. Here the number of parents criteria is JUST met. Also, the total number of children is 13<15, which means the other criteria (not more than 3 children per family) is also met.

HENCE THE CORRECT OPTION IS (3).
NO NEED TO EVALUATE (4), AS WE ARE REQUIRED TO FIND THE MINIMUM NUMBER OF FAMILIES.
THE ANSWER CANNOT BE (5) BECAUSE THE PARENTS CRITERIA IS JUST MET IN (3)

[fiction]

with no. of family = 3. min no. parents = 6, which is not possible since atleast two single parent families are present.
For the same reason no. of family cant be 4.

Now for family = 5,
F1 = mother + father + daughter
F2 = m + f + son
F3 = m + f + s
F4 = m + s
F5 = m + s

family = 5
girls = 6
boys = 7
no. parents = 8

so answer option c.