Ten people – Chuck, Berry, David, Gilmour, Eric, Clapton, Jimmy, Page, Kirk and Hammett – live in a building that has six floors numbered 1 to 6 (lowest to highest). Each floor is occupied by at least one of the ten people.

If N(x) represents the number of people living on floor x, then N(1) = N(6) ≠ N(3) and N(2) = N(5). Also, N(x) ≠ N(x+1) for x = 1 to 5.

It is also known that:

(i) Both Chuck and Berry live on the floor that is immediately above the floor on which Kirk lives.

(ii) David lives on a higher floor as compared to Clapton, Jimmy and Hammett but on a lower floor as compared to Chuck.

(iii) Gilmour and Page live on the same floor.

(iv) The number of people who live on the floor on which Jimmy lives is equal to that on which Eric lives.

(1) What is the difference between the number of people who live on floor 3 and floor 5?

(a) 0

(b) 1

(c) 3

(d) 2

(2) Who among the following lives on floor 6?

(a) Eric

(b) David

(c) Chuck

(d) Gilmour

(3) How many people live on a floor higher than the one on which Jimmy lives?

(a) 7

(b) 5

(c) 9

(d) 6

**Solutions:**

Let N(1) = N(6) = a, N(2) = N(5) = b, N(3) = c and N(4) = d. Here a, b and c are distinct (as given). Also, b and d cannot be the same. Hence, 2a + 2b + c + d = 10 (the total number of people).

⇒ 2(a + b) + c + d = 10

The least possible value of ‘a + b’ is 3 and it is evident from the above equation that none among a, b, c and d can be greater than or equal to 4. The only possible integer solution to the above equation is when a, b, c and d are equal 1, 2, 3 and 1

respectively.

The following table can thus be concluded:

From statement (ii) and the above table it is evident that Chuck’s floor number is greater than 3 and hence from statement (i) and the above table it can be concluded that Chuck and Berry live on floor 5. Subsequently, Kirk and David live on floor 4 and floor 3 respectively. Clapton, Jimmy and Hammett must occupy

floor 1 and floor 2 (in no particular order), as they live below David. From statement (iii) it can be concluded that Gilmour and Page live on floor 3 with David. Finally, it can be concluded from statement (iv) that Jimmy and Eric live on floor 1 and floor 6 respectively. The table can be completed as given below.

(1) b Difference = 3 – 2 = 1

(2) a Eric lives on floor 6

(3) c Jimmy lives alone on floor 1.

The rest 9 people live on floors higher than his.

**Directions:** Answer the questions on the basis of the information given below.

In a class of 96 students, each student opts for at least one of the three subjects – Physics, Chemistry and Mathematics. It is also known that:

(i) The number of students who opt for Physics only is equal to the number of students who opt for Mathematics only and is also equal to twice the number of students who opt for both Mathematics and Physics but not Chemistry.

(ii) The number of students who opt for exactly two subjects is 25.

(iii) The number of students who opt for Chemistry is 31.

(iv) Among those who opt for Chemistry, 13 students opt for at least two subjects.

(1) If the number of students who opt for Mathematics is the maximum among the three subjects, then what is the maximum possible number of students who opt for both Physics and Chemistry but not Mathematics?

(a) 5

(b) 6

(c) 7

(d) Cannot be determined

(2) Which additional piece of information is required to find the exact number of students who opt for both Chemistry and Mathematics but not Physics?

(a) The number of students who opt for exactly one of the three subjects is 70.

(b) Only one student opts for all the three subjects.

(c) The number of students who opt for Mathematics is 50.

(d) The number of students who opt for Mathematics only is 26.

**Solutions:**

The total number of students in the class is 96 and the number of students who opt for Chemistry is 31; so the number of students who opt for Physics only, Mathematics only and both.

Mathematics and Physics but not Chemistry will be 65.

From the given information, the number of students who opt for: Physics only = 26, Mathematics only = 26, both Mathematics and Physics but not Chemistry = 13.

a + b + 13 = 25

a + b = 12.

(1) a As the number of students who opt for Mathematics is the maximum among the three subjects, b > a. As we have to maximise ‘a’, we get a = 5 and b = 7.

(2) c If the exact number of students who opt for Mathematics is known, a and b can be calculated. The rest three statements don’t give any new information

**Directions** : Answer the questions on the basis of the information given below.

Four people – Alfred, Buckley, Cherry and Dirk – went to a museum on a Sunday. No two of them reached the museum at the same time. They were wearing shirts of different colours among Purple, Red, White and Yellow, in no particular order.

It is also known that:

(i) Cherry was not the first one to reach the museum and he was wearing the Red shirt.

(ii) The person wearing the Yellow shirt reached the museum earlier than Buckley.

(iii) The person wearing the White shirt was not the last one to reach the museum.

(iv) Alfred was not wearing the Yellow shirt.

(v) The person wearing the Purple shirt reached the museum earlier than the person wearing the White shirt.

(vi) Alfred reached the museum before Dirk.

(1) Who among the four was wearing the White shirt?

(a) Alfred

(b) Buckley

(c) Cherry

(d) Dirk

(2) Who among the four was the last to reach the museum?

(a) Alfred

(b) Buckley

(c) Cherry

(d) Dirk

(3) Which of the following statement(s) is/are correct?

I. Dirk was wearing the Yellow shirt and he reached the museum before Cherry.

II. Alfred was wearing the White shirt and he reached the museum before Cherry.

(a) Only I

(b) Only II

(c) Neither I nor II

(d) Both I and II

**Solutions:**

From statements (i), (ii) and (vi), it can be concluded that Alfred was the first person to reach the museum.

From statements (i), (ii) and (iv), it can be concluded that Dirk was wearing the Yellow shirt.

Hence, either Alfred or Buckley was wearing the Purple shirt and the other one was wearing the White shirt.

From statement (v), it can be concluded that Alfred was wearing the Purple shirt while Buckley was wearing the White shirt.

Further analysis leads to the following table:

(1) b Buckley

(2) c Cherry

(3) a Only statement I is correct.

Ten people – Chuck, Berry, David, Gilmour, Eric, Clapton, Jimmy, Page, Kirk and Hammett – live in a building that has six floors numbered 1 to 6 (lowest to highest). Each floor is occupied by at least one of the ten people.

If N(x) represents the number of people living on floor x, then N(1) = N(6) ≠ N(3) and N(2) = N(5). Also, N(x) ≠ N(x+1) for x = 1 to 5.

It is also known that:

(i) Both Chuck and Berry live on the floor that is immediately above the floor on which Kirk lives.

(ii) David lives on a higher floor as compared to Clapton, Jimmy and Hammett but on a lower floor as compared to Chuck.

(iii) Gilmour and Page live on the same floor.

(iv) The number of people who live on the floor on which Jimmy lives is equal to that on which Eric lives.

(1) What is the difference between the number of people who live on floor 3 and floor 5?

(a) 0

(b) 1

(c) 3

(d) 2

(2) Who among the following lives on floor 6?

(a) Eric

(b) David

(c) Chuck

(d) Gilmour

(3) How many people live on a floor higher than the one on which Jimmy lives?

(a) 7

(b) 5

(c) 9

(d) 6

**Solutions:**

Let N(1) = N(6) = a, N(2) = N(5) = b, N(3) = c and N(4) = d. Here a, b and c are distinct (as given). Also, b and d cannot be the same. Hence, 2a + 2b + c + d = 10 (the total number of people).

⇒ 2(a + b) + c + d = 10

The least possible value of ‘a + b’ is 3 and it is evident from the above equation that none among a, b, c and d can be greater than or equal to 4. The only possible integer solution to the above equation is when a, b, c and d are equal 1, 2, 3 and 1

respectively.

The following table can thus be concluded:

From statement (ii) and the above table it is evident that Chuck’s floor number is greater than 3 and hence from statement (i) and the above table it can be concluded that Chuck and Berry live on floor 5. Subsequently, Kirk and David live on floor 4 and floor 3 respectively. Clapton, Jimmy and Hammett must occupy

floor 1 and floor 2 (in no particular order), as they live below David. From statement (iii) it can be concluded that Gilmour and Page live on floor 3 with David. Finally, it can be concluded from statement (iv) that Jimmy and Eric live on floor 1 and floor 6 respectively. The table can be completed as given below.

(1) b Difference = 3 – 2 = 1

(2) a Eric lives on floor 6

(3) c Jimmy lives alone on floor 1.

The rest 9 people live on floors higher than his.

**Directions:** Answer the questions on the basis of the information given below.

In a class of 96 students, each student opts for at least one of the three subjects – Physics, Chemistry and Mathematics. It is also known that:

(i) The number of students who opt for Physics only is equal to the number of students who opt for Mathematics only and is also equal to twice the number of students who opt for both Mathematics and Physics but not Chemistry.

(ii) The number of students who opt for exactly two subjects is 25.

(iii) The number of students who opt for Chemistry is 31.

(iv) Among those who opt for Chemistry, 13 students opt for at least two subjects.

(1) If the number of students who opt for Mathematics is the maximum among the three subjects, then what is the maximum possible number of students who opt for both Physics and Chemistry but not Mathematics?

(a) 5

(b) 6

(c) 7

(d) Cannot be determined

(2) Which additional piece of information is required to find the exact number of students who opt for both Chemistry and Mathematics but not Physics?

(a) The number of students who opt for exactly one of the three subjects is 70.

(b) Only one student opts for all the three subjects.

(c) The number of students who opt for Mathematics is 50.

(d) The number of students who opt for Mathematics only is 26.

**Solutions:**

The total number of students in the class is 96 and the number of students who opt for Chemistry is 31; so the number of students who opt for Physics only, Mathematics only and both.

Mathematics and Physics but not Chemistry will be 65.

From the given information, the number of students who opt for: Physics only = 26, Mathematics only = 26, both Mathematics and Physics but not Chemistry = 13.

a + b + 13 = 25

a + b = 12.

(1) a As the number of students who opt for Mathematics is the maximum among the three subjects, b > a. As we have to maximise ‘a’, we get a = 5 and b = 7.

(2) c If the exact number of students who opt for Mathematics is known, a and b can be calculated. The rest three statements don’t give any new information

**Directions** : Answer the questions on the basis of the information given below.

Four people – Alfred, Buckley, Cherry and Dirk – went to a museum on a Sunday. No two of them reached the museum at the same time. They were wearing shirts of different colours among Purple, Red, White and Yellow, in no particular order.

It is also known that:

(i) Cherry was not the first one to reach the museum and he was wearing the Red shirt.

(ii) The person wearing the Yellow shirt reached the museum earlier than Buckley.

(iii) The person wearing the White shirt was not the last one to reach the museum.

(iv) Alfred was not wearing the Yellow shirt.

(v) The person wearing the Purple shirt reached the museum earlier than the person wearing the White shirt.

(vi) Alfred reached the museum before Dirk.

(1) Who among the four was wearing the White shirt?

(a) Alfred

(b) Buckley

(c) Cherry

(d) Dirk

(2) Who among the four was the last to reach the museum?

(a) Alfred

(b) Buckley

(c) Cherry

(d) Dirk

(3) Which of the following statement(s) is/are correct?

I. Dirk was wearing the Yellow shirt and he reached the museum before Cherry.

II. Alfred was wearing the White shirt and he reached the museum before Cherry.

(a) Only I

(b) Only II

(c) Neither I nor II

(d) Both I and II

**Solutions:**

From statements (i), (ii) and (vi), it can be concluded that Alfred was the first person to reach the museum.

From statements (i), (ii) and (iv), it can be concluded that Dirk was wearing the Yellow shirt.

Hence, either Alfred or Buckley was wearing the Purple shirt and the other one was wearing the White shirt.

From statement (v), it can be concluded that Alfred was wearing the Purple shirt while Buckley was wearing the White shirt.

Further analysis leads to the following table:

(1) b Buckley

(2) c Cherry

(3) a Only statement I is correct.