Several lecturers from four disciplines, viz. physics, chemistry, mathematics and biology were selected. They were to attend a recently organized faculty conclave. All applicants were classified into five age groups, namely: Young : Age less than 50; Middle aged : 50 Age < 60 ; Senior : 60 Age < 70 Stalwart : 70 Age < 80; Retired : Age 80 and above For the conclave, not more than two lecturers of a particular age group were short-listed for representing a discipline. Initially, the maximum possible lecturers were short-listed. However, only five more than half of them got selected and they finally sat for the conclave. The following observations about the selected lecturers were recorded. I. If two lecturers were excluded from the retired lecturers, then the number of seniors and stalwarts, each is one less than the number in each of the other three age groups. II. Total number of lecturers in physics, chemistry and biology put together is the square of an integer. III. There is no biology lecturer who is middle aged or stalwart and there is no physics lecturer who is a senior. Every other discipline is represented by at least one lecturer from each age group. IV. Rocky and Platy are Young physics lecturers.
Transcript
Several lecturers from four disciplines, viz. physics, chemistry, mathematics and biology were selected. They were to attend a recently organized faculty conclave. All applicants were classified into five age groups, namely:Young : Age less than 50; Middle aged : 50 Age < 60 ; Senior : 60 Age < 70 Stalwart : 70 Age < 80; Retired : Age 80 and above
For the conclave, not more than two lecturers of a particular age group were short-listed for representing a discipline. Initially, the maximum possible lecturers were short-listed. However, only five more than half of them got selected and they finally sat for the conclave. The following observations about the selected lecturers were recorded.
I. If two lecturers were excluded from the retired lecturers, then the number of seniors and stalwarts, each is one less than the number in each of the other three age groups.
II. Total number of lecturers in physics, chemistry and biology put together is the square of an integer.
III. There is no biology lecturer who is middle aged or stalwart and there is no physics lecturer who is a senior. Every other discipline is represented by at least one lecturer from each age group.
IV. Rocky and Platy are Young physics lecturers.
Now the following questions pertain to those selected lecturers.
Q.1 If the number of physics lecturers is greater than the number of chemistry lecturers, then which of the following is NOT possible to determine?
a Number of middle aged physics lecturers. b Number of retired physics lecturers. c Number of middle-aged chemistry lecturers. d Number of retired chemistry lecturers. e All of these
Q.2 What can be said about the total number of physics and chemistry lecturers put together?I. It is less than or equal to 12.II. It is more than or equal to 12.
a Only I b Only II c Both I and II d Neither I nor II e Cannot be determined
Q.3 If Kandy is the lone retired chemistry lecturer, then which of the following is certain?
A There is one middle aged physics lecturer. B There are two middle-aged physics lecturers. C There is one retired biology lecturer. D There are two retired biology lecturers. E All of these
Q.4 Which of the combinations is NOT possible?
A Two retired physics lecturers and two retired chemistry lecturers were selected for the conclave. B One retired physics lecturer and two retired chemistry lecturers were selected for the conclave. C One retired physics lecturer and one retired chemistry lecturer
were selected for the conclave. D Two retired physics lecturers and one retired chemistry lecturer were selected for the conclave. E All of these
• For the conclave, not more than two lecturers of a particular age group were short-listed for representing a discipline.
• 2x(5 age groups)x(4 disciplines) = 40
• Initially, the maximum possible lecturers were short-listed.
• Shortlisted = 40
• However, only five more than half of them got selected and they finally sat for the conclave.
• Selected = (40/2) + 5 = 25
Young Middle Aged Senior Stalwart Retired
Physics
Chemistry
Math
Biology
a a a-1 a-1 a+2
I. If two lecturers were excluded from the retired lecturers, then the number of seniors and stalwarts, each is one less than the number in each of the other three age groups.
a+a+a-1+a-1+a+2 = total selected = 25-> a = 5
Young Middle Aged
Senior Stalwart Retired Total
Physics
Chemistry
Math 9
Biology
A=5 A=5 a-1=4 a-1=4 a+2=7
II. Total number of lecturers in physics, chemistry and biology put together is the square of an integer.
As each subject can have a min of 4 lecturers and a max of 10, the sum of P+C+B should be greater than 4+4+4 but less than 10+10+10, but total no. of lecturers is 25
So, the only perfect square between 12 and 25 is 16. Therefore, the number of lecturers in math is 25-16 = 9.
III. There is no biology lecturer who is middle aged or stalwart and there is no physics lecturer who is a senior. Every other discipline is represented by at least one lecturer from each age group.
IV. Rocky and Platy are Young physics lecturers.
Young Middle Aged Senior Stalwart Retired Total
Physics 2 0
Chemistry
Math 9
Biology 0 0
A=5 A=5 a-1=4 a-1=4 a+2=7
Young Middle Aged Senior Stalwart Retired Total
Physics 2 0
Chemistry 1Math 1 9
Biology 1 0 0
Total -> 5 5 4 4 7
Filling in the rest accordingly
Young Middle Aged Senior Stalwart Retired Total
Physics 2 0
Chemistry 1
Math 1 2 2 2 2 9
Biology 1 0 0
Total -> 5 5 4 4 7
Filling in the rest accordingly
Young Middle Aged Senior Stalwart Retired Total
Physics 2 0
Chemistry 1 1
Math 1 2 2 2 2 9
Biology 1 0 1 0
Total -> 5 5 4 4 7
Filling in the rest accordingly
Young Middle Aged Senior Stalwart Retired Total
Physics 2 0 1Chemistry 1 1 1Math 1 2 2 2 2 9
Biology 1 0 1 0
Total -> 5 5 4 4 7
Filling in the rest accordingly
Young Middle Aged Senior Stalwart Retired Total
Physics 2 1/2 0 1 1 2 2
Chemistry 1 2/1 1 1 2 2 1
Math 1 2 2 2 9
Biology 1 0 1 0 2 1 2
Total -> 5 5 4 4 7
Filling in the rest accordingly
For Middle Aged Lecturers to be 5, Middle aged physics lecturers + MA Chemistry Lecturers should be 2+1 or 1+2
Questions• Q.1
If the number of physics lecturers is greater than the number of chemistry lecturers, then which of the following is NOT possible to determine?
a Number of middle aged physics lecturers. b Number of retired physics lecturers. c Number of middle-aged chemistry lecturers. d Number of retired chemistry lecturers. e All of these
Young Middle Aged Senior Stalwart Retired Total
Physics 2 2 0 1 2
Chemistry 1 1 1 1 2 / 1
Math 1 2 2 2 2 9
Biology 1 0 1 0 1 / 2
Total -> 5 5 4 4 7
Questions• Q.2
What can be said about the total number of physics and chemistry lecturers put together?I. It is less than or equal to 12.II. It is more than or equal to 12.
a Only I b Only II c Both I and II d Neither I nor II e Cannot be determined
If Kandy is the lone retired chemistry lecturer, then which of the following is certain?
A There is one middle aged physics lecturer. B There are two middle-aged physics lecturers. C There is one retired biology lecturer. D There are two retired biology lecturers. E All of these
Young Middle Aged Senior Stalwart Retired Total
Physics 2 1/2 0 1 2
Chemistry 1 2/1 1 1 1
Math 1 2 2 2 2 9
Biology 1 0 1 0 2
Total -> 5 5 4 4 7
QuestionsQ.4 Which of the combinations is NOT possible?
A Two retired physics lecturers and two retired chemistry lecturers were selected for the conclave. B One retired physics lecturer and two retired chemistry lecturers were selected for the conclave. C One retired physics lecturer and one retired chemistry lecturer were selected for the conclave. D Two retired physics lecturers and one retired chemistry lecturer were selected for the conclave. E All of these
