IAS 2017 — Maths

There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers?

A 2-digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder?

In a city 12% of households earn less than `30,000 per year, 6% households earn more than Rs 2,00,000 per year, 22% households earn more than Rs 1,00,000 per year and 990 households earn between Rs 30,000 and Rs 1,00,000 per year. How many households earn between Rs 1,00,000 and Rs 2,00,000 per year?

There are three pillars, X, Y and-Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance. A climbs on X by 6cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of the requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar?

If for a sample data - Mean < Median < Mode, then the distribution is

P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings?

A freight train left Delhi for Mumbai at an average speed of 40 km/hr. Two hours later, an express train left Delhi for Mumbai, following the freight train on a parallel track at an average speed of 60 km/hr. How far from Delhi would the express train meet the freight train?

Certain 3-digit numbers have the following characteristics: 1. All the three digits are different. 2. The number is divisible by 7. 3. The number on reversing the digits is also divisible by 7. How many such 3-digit numbers are there?

The monthly incomes of X and Y are in the ratio of 4: 3 and their monthly expenses are in the ratio of 3 : 2. However, each saves Rs 6,000 per month. What is their total monthly income?

Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?

The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again?

P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), Where, A is greater than B. In this context, which of the following statements is correct?

If there is a policy that 1/3rd of a population of a community has migrated every year from one place to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period?

There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?

What is the total number of digits printed, if a book containing 150 pages is to be numbered from to 150

If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there?

Suppose the average weight of 9 persons is 50kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg, Then the weight of the 5th person will be

A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

There is a milk sample with 50% water in it. If 1/3rd of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to

Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal's position if he agreed?

The average rainfall in a city for the first four days was recorded to be 0.40 inch. The rainfall on the last two days was in the ratio of 4 : 3. The average of six days was 0.50 inch. What was the rainfall on the fifth day?

A clock strikes, once at 1o'clock, twice at 2o'clock and thrice at 3 o'clock, and soon. If it takes 12 seconds to strike at 5 o'clock, what is the time taken by it to strike at 10 o'clock?

There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?

How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place?