Data Sufficiency  Vikas Saini  Part 1

Q. Ram distributes 40 chocolates among 5 children in such a way that each child gets at least one chocolate and no two children get the same number of chocolates.
What is the number of chocolates received by the child who gets the maximum number of chocolates among the 5 children ?
A. Each child gets more than 4 chocolates.
B. The sum of number of chocolates received by the child who gets the maximum and the child who gets the minimum number of chocolates among the five children is 29.
Solution :
By using statement A
(a+4 )+(b+4)+(c+4)+(d+4)+(e+4) = 40.
a+b+c+d+e = 20.
Many possibilities.
By using statement B
possibilites
i) 1,2,4,5,28.
ii)1,2,3,6,28.
So maximum chocolates received = 28.
Result : Question can be answered by using statement B.
Q. Some students are standing in a row facing the west direction.14 students are standing to the left of Mukesh and 22 students are standing right of Rakesh.
How many students are there in hall ?
A. Exactly 5 students are standing between Mukesh and Rakesh.
B. The total number of students is a prime number less than 37.
solution :
By using statement A
We can't determine Mukesh is at right of Rakesh or at left.
By using statement B
Prime number less than 37 are 31 and many other.
So there is also not any possibility to determine the position.
Result : Both statements are not sufficient.
Q. If f(x) is linear function, then what is the value of f(5) ?
A. f(1) > = f(2), f(3) > = f(2), f(0) = 5.
B. f(1) = 3, f(1) < = f(2), f(2) < = f(3)
Solution :
A linear function can be strictly increasing or strictly decreasing or constant.
By using statement A
f(0) = 5 and f(1)=f(2)=f(3).
It means coefficient of x = 0.
f(5) = 5.
By using statement B
f(1) = 3, f(1)=f(2)=f(3).
We can say function is increasing but can't determine f(5).
Result : Statement A only.
Q. N is a natural number. How many factors of N are perfect squares ?
A. N has only two distinct prime factors.
B. N has 9 distinct composite factors, including itself.
Solution :
From statement A
N = x^{a }. y^{b }
we can't say anything about here about a & b.
From statement B
From here also we can' t find any conclusion.
Result : Neither A nor B Sufficient to answer this.
Q. If x, y, z are positive integers, then 11x+7y+8z divisible by 5 ?
A. 6x+y+3z is divisible by 5.
B. x+2y+3z is divisible by 10.
Solution :
From statement A
6x+y+3z = 5k.
then 11x+7y+8z = 5k + (5x+6y+5z).
no conclusion from this statement.
From satement B
x+2y+3z = 10k.
11x+7y+8z = 10k + (10x+5y+5z)
= 10k + 5(2x+y+z)
It is divisible by 5.
Result : Statement B alone sufficient.
Q. In a class of 200 students, the highest and the lowest scores in a test are 98 and 18 respectively. Is 50 the average score of the class in the test ?
A. 100 students score above 50 and the remaining 100 students score below 50 in the test.
B. If the highest score and the lowest score in the test are excluded, the sum of the top 99 scores is exactly double of the sum of the bottom 99 scores.
Solution :
Statement A can't assure us about total score of students and average scores also.
Statement B is also insufficient to calculate the exact average score.
Q. When three times of the unit's digit of a number is subtracted from the number,28 is obtained.
What is the number ?
A. The digit at the ten's place is greater than the digit at the unit's place.
B. The digit at the ten's place is less than the digit at the unit's place.
Solution :
(10b+c)  3c = 28.
10b  2c = 28.
5b  c = 14.
possibilities
(i) b=3, c = 1.
(ii)b = 4, c =6.
number is either 31 or 46.
From statement A
number = 31.
From statement B
number = 46.
Result : Either statement A or statement B alone sufficient.
Q. Six tennis players Abhas, Golu, Nagendra , Puneet , Saral and Vikas are ranked 1 to 6 in the same order. Each player plays one match against one of the five other players. Neither Saral nor Nagendra plays against Puneet. All the three matches are won by the better ranked player. At least one among Abhas, Golu and Nagendra does not win his match.
Who plays against whom ?
A. Golu does not win his match.
B. Golu and Saral don't play against each other. Only one of them win his match.
Solution :
Using Statement A
Abhas  Golu
Nagendra  Saral
Vikas  Puneet
Statement A sufficient.
Using Statement B
Abhas  Saral
Puneet  Vikas
Statement B alone sufficient.
Result : Either A or B alone sufficient.
Q. Three leading strikers  Messi , Neymar , Ronaldo make some interesting statement on their goals.
I. Neymar : If I score 7 goals in world cup, my total goals would be equal to Ronaldo's present goal.
II. Ronaldo : If I score 8 goals in world cup, my total goals would be double of Messi's present goal.
What is the number of goals scored by each of them before the world cup.
A. Neymar and Messi together have 21 goals before the world cup.
B. The absolute difference between the total goals scored by Neymar and Messi before the world cup is 3.
Solution :
Before the world cup no of goals.
Messi  M
Neymar = N
Ronaldo  R
N + 7 = R = > N = R  7.
R + 8 = 2M = > M = (R + 8 ) / 2.
From statement A
N + M = 21.
(R  7) + (R + 8 ) / 2 = 21.
2R  14 + R + 8 = 42.
3R  6 = 42.
3R = 48.
R = 16.
N= 9.
M = 12.
Statemnt A alone sufficient.
From statement B
N  M = +4 , 4.
We will not get any unique value.
Result : Statement A alone sufficient.

@vikas_saini a few doubts, please clarify them 
In cases where using either of the two given statements, we don't get a unique answer, shouldn't we mark the answer as 'can't be solved using either of the two statements' ?
For example, take the question 
When three times of the unit's digit of a number is subtracted from the number,28 is obtained.
What is the number ?
A. The digit at the ten's place is greater than the digit at the unit's place.
B. The digit at the ten's place is less than the digit at the unit's place.from statement A, we got answer as 31, from statement B it is 46, so isn't this conflicting?
Second Doubt
In a class of 200 students, the highest and the lowest scores in a test are 98 and 18 respectively. Is 50 the average score of the class in the test ?
A. 100 students score above 50 and the remaining 100 students score below 50 in the test.
B. If the highest score and the lowest score in the test are excluded, the sum of the top 99 scores is exactly double of the sum of the bottom 99 scores.here we are to only ascertain if 50 is class average or not? So, doesn't statement B lead to a conclusion that the average is beyond 50?