Practice Exercise 1: In a queue, Mr. X is fourteenth from the front and Mr. Y is seventeenth from the end, while Mr. Z is exactly between Mr. X and Mr. Y. If Mr. X is ahead of Mr. Y and there are 48 persons in the queue, how many persons are there between Mr. X and Mr. Z?

A. 6

B. 7

C. 8

D. 9

X’s position from the front = 14th

Y’s position from the front = (Total number of persons in the queue) – (Y’s position from the end) + 1 = 48 –  17 + 1 = 32nd

Z’s position from the front = (X’s position from the front + Y’s position from the front)/2

= (14 + 32)/2 = 23rd

Therefore, Number of persons between X and Z = |Z’s position from the front – X’s position from the front – 1| = 8

Hence, C is the correct option.

Practice Exercise 2: In a row of children, Bhushan is seventh from the left and Motilal is fourth from the right. When Bhushan and Motilal exchange positions, Bhushan will be fifteenth from the left. What will be Motilal’s position from the right?

A. Eighth

B. Fourth

C. Eleventh

D. Twelfth

After exchanging positions, Bhushan’s position would be fifteenth from the left and fourth from the right.

Total number of children in the row = (Bhushan’s position from the left) + (Bhushan’s position from the end) – 1

= 15 + 4 – 1 = 18

After exchanging positions, Motilal would be seventh from the left.

Therefore, Motilal’s position from the right after exchanging = (Total number of children in the row) – (Motilal’s position from the left after exchanging) + 1

= 18 – 7 + 1 = 12th

Hence, D is the correct option.

Practice Exercise 3: Study the information given below and answer the questions based on it.

Seven students – F, G, H, I, J, K, and L are being considered for a university fellowship. In evaluating these students, the dean has received from the registrar’s office their official transcripts, including their cumulative grade point averages (GPAs). In analyzing this information, the dean has made the following observations:

> None of the students has exactly the same GPA as any other student.

> K’s GPA is higher than L’s but lower than H’s.

> I has a higher GPA than J.

> Both F and G have higher GPA’s than  H.

1. Each of the following could be true except

A. F has the highest GPA.

B. G has the highest GPA.

C. I has the highest GPA

D. More than three students have lower GPA’s than K

2. Which of the following, if true, would be sufficient to determine who has the lowest GPA?

A. I has the highest GPA.

B. I has a lower GPA than K.

C. K has a higher GPA than J.

D. J has a higher GPA than K.

3. If J has a higher GPA than F, how many different rankings, by GPA, of the students are possible?

A. 1

B. 2

C. 4

D. 6

4. If H has a higher GPA than I, which of the following cannot be true?

A. I’s GPA is equal to the average of F’s and G’s

B. I’s GPA is equal to the average of K’s and L’s

C. J’s GPA is equal to the average of K’s and L’s

D. J has the second lowest GPA

> K’s GPA is higher than L’s but lower than H’s.

GPA: H > K > L

> I has a higher GPA than J.

GPA: I > J

> Both F and G have higher GPA’s than  H.

GPA: F, G > H > K > L

1. At max, only three students can possibly have a lower GPA than K. These students are L, I and J. Therefore, the statement given in option (D) cannot be true. So, D is the correct option.

2. If J has a higher GPA than K, then F, G, H, I, J and K all have a higher GPA than L. Therefore, L has the lowest GPA. Hence, D is the correct option.

3. If J has a higher GPA than F, then we will have this order of GPA:

I > J > F > H > K > L and G > H

There are four possible orders:

1. G > I > J > F > H > K > L

2. I > G > J > F > H > K > L

3. I > J > G > F > H > K > L

4. I > J > F > G > H > K > L

Hence, C is the correct option.

4. If H has a higher GPA than I, then both F and G would also have a higher GPA than I. Therefore, I’s GPA cannot be equal to the average of F’s and G’s. So, A is the correct option.

Practice Exercise 4: There are five books A, B, C, D and E. Book C lies above D. Book E is below A; D is above A; B is below E. Which is at the bottom?

A. B

B. E

C. A

D. C

 Book B is at the bottom. So, A is the correct option.

Practice Exercise 5: In a queue, Andrew is the last person while his friend is standing at seventh position from the front. If the person standing exactly between Andrew and his friend is on 23rd position from the front, what is Andrew’s position in the queue? 

A. 37

B. 36

C. 38

D. 39

Position of the person standing exactly between Andrew and his friend from the front = (Andrew’s position from the front + Andrew’s friend’s position from the front)/2

Therefore, Andrew’s position from the front  = 2 × (Position of the person standing exactly between Andrew and his friend from the front) – Andrew’s friend’s position from the front

= 2 × 23 – 7 = 39

Therefore, D is the correct option.

Practice Exercise 6: In a class of 35 students, Kiran is placed 7th from the bottom whereas Mohan is placed 9th from the top. Sohan is placed exactly between Kiran and Mohan. What is Kiran’s position from Sohan?

A. 13th

B. 11th

C. 10th

D. 9th

Kiran’s position from the top = (Total number of students in the class) – (Kiran’s position from the bottom) + 1

= 35 – 7 + 1 = 29th

Sohan’s position from the top = (Kiran’s position from the top + Mohan’s position from the top)/2

= (29 + 9)/2 = 19th

Therefore, Kiran’s position from Sohan is 10th. So, C is the correct option.