Number, Ranking and Time Sequence Test Questions and Answers

Answer: B

Gagan is 73rd from the left and 79th from the right, so the row has 73 + 79 - 1 = 151 students. The student is counted once in each position, which is why one is subtracted.

\[ 73 + 79 - 1 = 151 \]

The options 152, 153 and 154 are what one gets by counting Gagan twice or adding extra students. Counting the places to the left (72) and to the right (78) of Gagan and then adding Gagan himself gives 72 + 78 + 1 = 151, which checks the answer.

Answer: C

The statement that is false is 'Kisan is taller than Jason'. Putting the given facts in order: Kisan is shorter than Sarim and taller than Prajwal; Sarim is shorter than Jason; Jason is shorter than Urvasi. Together this gives Urvasi > Jason > Sarim > Kisan > Prajwal.

So Urvasi is the tallest, Prajwal is the shortest and Sarim is shorter than Urvasi, which makes the first, second and fourth statements true. Kisan stands below Sarim, who stands below Jason, so Kisan is shorter than Jason and the third statement is false.

Answer: C

Two people are younger than F.

Only two people are older than D, and B and E are older than D (E is older than B, B older than D), so those two are B and E and no one else can be above D. F is younger than E, so F can only sit below D. The full order is E, B, D, F, A, C, with C the youngest and A younger than F. Those younger than F are A and C.

None, one and three do not match this order.

The key step is the sentence that only two people are older than D. Because B is older than D, and E is older than B, those two are all there is above D, so every other person, including F, must be younger than D. The statement that F is younger than E and older than A then gives the order E, B, D, F, A, C.

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: A

Correct answer: Friday

From 25 June to 15 August is \( 5 + 31 + 15 = 51 \) days. Since \( 51 = 49 + 2 \), the day moves on by two from Wednesday, giving Friday.

Answer: D

Correct answer: 6 : 34

In each pair the second number is the square of the first plus two: \( 4^2+2 = 18 \), \( 7^2+2 = 51 \), \( 9^2+2 = 83 \). For 6 the rule gives \( 6^2+2 = 38 \), not 34 - so 6 : 34 is the odd pair.