Number, Ranking and Time Sequence Test Questions and Answers

Answer: B

The tallest of the six is S.

From the conditions, T is shorter than R and R is shorter than S, so T < R < S. Also Q is shorter than T, and P is shorter than Q, and U has the same height as R. So the order is P < Q < T < R = U < S, which puts S at the top.

R is equal to U and below S, T is below R, and Q is shorter than T, so R, T and Q cannot be the tallest.

It helps to write the inequalities as a chain: P < Q < T < R = U < S. Everyone is placed between P at the bottom and S at the top, so S is clearly the tallest and P the shortest. The information that R and U are equal does not change this, because both are still below S.

Answer: B

Sachin is 34th from the right end.

The position from the right equals the total number of students minus the position from the left, plus one. So it is 40 − 7 + 1 = 34.

The answer 33 forgets to add one, because Sachin himself is counted in both positions. 32 and 31 are further from the correct figure.

The two ranks always add up to one more than the total, because the same person is counted in both. So rank from the left plus rank from the right equals 41 here, and 41 − 7 = 34. This shortcut works for any row.

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.