Basic Numeracy

A natural number N is such that it can be expressed as N = p + q + r, where p, q, and r are distinct factors of N. How many numbers below 50 have this property?

The 5-digit number PQRST (all distinct digits) is such that T is not equal to 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?

Three prime numbers p, q, and r, each less than 20, are such that p – q = q – r. How many distinct possible values can we get for (p + q + r)?

X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in days. What is n equal to?

What is the 489th digit in the number 123456789101112...?

Consider a set of 11 numbers:

Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ –5.
Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers.
Which one of the following is correct?

There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

Let x be a real number between 0 and 1. Which of the following statements is/are correct?

Select the correct answer using the code given below:

Let be a 3-digit number. What is the HCF of P and 481?

Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR − PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?

Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had Team Y's average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by Team X?

A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the train?

The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?

A 4-digit number N is such that when divided by 3, 5, 6, 9 it leaves a remainder of 1, 3, 4, 7 respectively. What is the smallest value of N?

What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999?

How many possible values of (p + q + r) are there satisfying where p, q, and r are natural numbers (not necessarily distinct)?

Let p + q = 10, where p, q are integers.
Value-I = Maximum value of p × q when p, q are positive integers.
Value-II = Maximum value of p × q when p ≥ 6, q ≥ 4.
Which one of the following is correct?

The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?

A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?

If n is a natural number, then what is the number of distinct remainders of when divided by 4?

If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?

Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

If N² = 12345678987654321, then how many digits does the number N have?

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to the ratio of number of runs scored by Y to number of runs scored by Z.
Value-I = Runs scored by X
Value-II = Runs scored by Y
Value-III = Runs scored by Z
Which one of the following is correct?

What is the remainder when is divided by 6?

Consider the following statements:

1. There exists a natural number which when increased by 50% can have its number of factors unchanged.
2. There exists a natural number which when increased by 150% can have its number of factors unchanged.

Which of the statements given above is/are correct?

P and Q walk along a circular track. They start at 5:00 am. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k?

The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹ 90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?

What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35ⁿ?

What is the sum of the first 28 terms in the following sequence?
1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,..

What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?

Consider the following:

Which of the above are correct?

Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10:

Which of the statements given above are correct?

Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?

Consider the following:
Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women
If the average weight of the women is 63 kg, then what is the average weight of the boys?

X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?

A can X contains 399 liters of petrol and a can Y contains 532 liters of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of liters is an integer.
How many different bottle sizes are possible?

How many consecutive zeros are there at the end of the integer obtained in the product
$1^2\times 2^4\times 3^6\times 4^8\times ...\times {25}^{50}$?

Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X+Y) is the greatest two-digit number, then what is the number of possible values of X?

In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

What is the rightmost digit preceding the zeros in the value of 30³⁰?

A number is mistakenly divided by 4 instead of multiplying by 4. What the percentage change in the result due to this mistake?

Two persons P and Q enter into a business. P puts ₹14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹400 more than Q’s share out of the total profit of ₹2,000, what is the capital contributed by P?

Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements:

Which of the statements given above are correct?

In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, –, × each at most two times. What is the smallest non-negative value of the expression?

A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?

Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?

On January 1^st, 2023, a person saved ₹1. On January 2^nd, 2003, he save ₹2 more than that on the previous day. On January 3^rd, 2023, he saved ₹2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube?

222³³³ + 333²²² is divisible by which of the following numbers?

The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples.

Consider the following statements:

Which of the statements given above is/are correct?

If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?

421 and 427, when divided by the same number, leave the same remainder 1.
How many numbers can be used as the divisor in order to get the same remainder 1?

What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?

32⁵ + 2²⁷ is divisible by

A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?

What is the number of fives used in numbering a 260-page book?

Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements:

A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so an.

Consider the following statements:

Which. of the above statements is/are correct?

A box contains 14 black balls, 20 blue balls, 26 green balls, 28 Yellow balls, 38 red balls 54 white balls. Consider the following Statements:

Which of the above statements is/are correct?

ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?

What is the remainder when $85\times 87\times 89\times 91\times 95\times 96$is divided by 100?

A flag has to be designed with 4 horizontal strips using some or all of the colour red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?

How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers?

D is a 3-digit number such that the ratio of the number of the sum of its digits is least. What is the difference between the digit at the hundred’s place and the digit at the unit’s place of D?

There are large numbers of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:

Which of the statements given above is/are correct?

A rectangular floor measures 4 m in length and 2.2 m in breadth. Tiles of size 140cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?

Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following:

Which of the above statements is/are correct?