Mathematical Critical Thinking and Logical Reasoning

If POINT + ZERO = ENERGY, then E + N + E + R + G + Y = ?

• 14

• 15

• 16

• 17

The ratio between the rates of walking of A and B is 3 : 4. If the time taken by B to cover a certain distance is 24 minutes, then time taken by A to cover that distance is

• 18 minutes

• 32 minutes

• 10(6/7) minutes

• 13(5/7) minutes

The current of a stream runs at 5 kmph. A motor launch goes 25 km upstream and back again to the starting point in 275/2 minutes. The speed of the motor launch in the absence of any current is

• 22.8 kmph

• 10.1 kmph

• 31.6 kmph

• 6 kmph

A and B can fill a cistern in 7.5 minutes and 5 minutes respectively and C can carry away 14 litres per minute. If all the pipes are open when the cistern is full, it is emptied in 1 hour. Then the capacity of the cistern is

• 50 l

• 45 l

• 40 l

• 0.04 kl

The average age of a family of 7 members is 23 years. If the average age of the youngest member be 7 years, then find the average of the family when the youngest member was 1 year old.

• 16 years

• 15 years

• 22 years

• 17 years

If the tax on tea is reduced by 10% by how much percent must the consumption increases so that there is an increase of 8% in the revenue?

• 45.3%

• 58%

• 20%

• 54.7%

How many nine digits number have an even sum of their digits?

• 9!-6!

• 14 × 10⁷

• 45 × 10⁷

• 10⁹ / 2

In how many ways 6 students and 4 teachers be arranged in a row so that no two teachers are together?

• 604800

• 24680

• 25860

• None

Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament was conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprised several rounds. A round involves one match for each team, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.

The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage, teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.

Which of the following statements is true?

• The winner will have more wins than any other team in the tournament.

• At the end of the first stage, no team eliminated from the tournament will have more wins than any of the teams qualifying for the second stage

• It is possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage

• The number of teams with exactly one win in the second stage of the tournament is 4

From a point O, two perpendicular lines are drawn to cut a circle at (A, B and C, D). Let A = 1, OB = 3 and CD = 2. The radius of the circle is

• 2

• √5

• √6

• None