Number, Ranking and Time Sequence Test Questions and Answers

Answer: C

There are 45 students in the class.

Suresh has 22 students above him and 22 below him. Counting Suresh himself, the class has 22 + 22 + 1 = 45 students, that is 23 + 23 − 1.

46 forgets that Suresh is counted in both ranks. 47 and 50 do not come out of the counting.

Draw the class as a line: 22 students stand above Suresh, then Suresh, then 22 below. The count is 22 + 1 + 22 = 45. Whenever the rank from the top equals the rank from the bottom, the total is 2n − 1, which gives 45 here.

Answer: D

Rahul is at the 16th position from the left end. Ravi is 20th from the right end in a row of 50, so Ravi is \(50 - 20 + 1 = 31\)st from the left. Rahul is 15th to the left of Ravi, which means 15 places before him, so from the left his position is \(31 - 15 = 16\). The other options come from slips: 15th forgets that the count includes Ravi's own place, 14th subtracts one place too many, and 17th adds a place where it should take one away. Counting a position from either end gives the same row of 50, so the check \(16 + 15 = 31\) holds.

Answer: B

Q is the second youngest. From the statements: T is older than P and R, and T is younger than S, so S > T > P and S > T > R. R is older than Q but younger than P, so P > R > Q. U is younger than Q. Combining, the order from oldest to youngest is S, T, P, R, Q, U. The youngest is U, so the second youngest is Q. P and R are older than Q, and U is the youngest, not the second youngest, so the options P, R and U are wrong. Listing the order oldest to youngest as S, T, P, R, Q, U and counting up from the youngest end gives U first and Q second.

Answer: D

There are 5 persons between them.

Convert the position from the right into a position from the left. In a row of 30, the 16th from the right is

\[ 30 - 16 + 1 = 15\text{th from the left} \]

The people strictly between the 9th and the 15th from the left are in places 10 to 14:

\[ 15 - 9 - 1 = 5 \]

4 is what you get by forgetting the + 1 and taking the 16th from the right as 14th from the left; 8 and 3 do not follow from either position. A quick check: places 1 to 9, the 5 between, and places 15 to 30 (16 people) make 9 + 5 + 16 = 30.

Answer: D

The answer is Data inadequate.

In a row of 35, M is 15th from the right, which is \(35 - 15 + 1 = 21\)st from the left. With ten children between M and R, R is 11 places from M, on either side.

\[ \begin{aligned} \text{R on the left} &: 21 - 11 = 10\text{th} \\ \text{R on the right} &: 21 + 11 = 32\text{nd} \end{aligned} \]

Both positions fit inside the row of 35, and the question does not say on which side of M R stands, so R's position cannot be fixed. Neither 10th nor 32nd is offered anyway: 15th, 5th and 30th do not fit either case.

Answer: A

The tallest is Roshan.

Write the statements as inequalities:

• Roshan > Hardik, and Susheel > Hardik;
• Hardik > Niza > Harry;
• Roshan > Susheel.

Combining them gives Roshan > Susheel > Hardik > Niza > Harry, so Roshan is taller than everyone else.

Susheel is the trap: he is taller than Hardik, but the last statement puts him below Roshan. Hardik is in the middle, and Harry is the shortest of all.

Answer: A

15 students failed.

Ram Kumar is 16th from the top and 21st from the bottom, so the number of students in the class is:

\[ 16 + 21 - 1 = 36 \]

One is subtracted because Ram Kumar is counted in both rankings. With 21 passing, \(36 - 21 = 15\) failed.

Forgetting to subtract 1 gives 37 students and 16 failures, the most common distractor.

Answer: C

8 odd numbers are followed by another odd number.

Walk through the sequence 6 9 2 2 2 6 8 9 1 3 7 5 2 6 7 6 7 7 5 2 9 1 6 4 6 3 9 8 and mark each adjacent odd-odd pair:

• 9 1, 1 3, 3 7, 7 5 (four pairs in the run 9 1 3 7 5)
• 7 7, 7 5 (two pairs in the run 7 7 5)
• 9 1 (one pair)
• 3 9 (one pair)

That is 4 + 2 + 1 + 1 = 8. A run of k consecutive odd numbers contributes k − 1 pairs, which is a quick way to count. Missing the pairs inside the run 7 7 5 gives 6.

Answer: B

2 only is correct.

Statement 1 does not follow. P is taller than Q and R is taller than Q, but nothing compares P with R, so P need not be the tallest; R could be taller than P.

Statement 2 follows. Y and Z run at the same speed, and X is faster than Y, so X is faster than Z.

The difference is that statement 2 chains through an equality, while statement 1 has both comparisons pointing at Q, which leaves P and R unordered.

Answer: C

There are 6 students between them.

Convert Mahesh's position to a count from the left:

\[ \begin{aligned} 60 - 32 + 1 &= 29\text{th from left} \\ 36 - 29 - 1 &= 6 \end{aligned} \]

Mahesh is 29th and Ramesh 36th from the left, so positions 30 to 35 lie between them: 6 students. Forgetting to subtract 1 at either step gives 7 or 8.