What is the least possible number of cuts required to cut a cube into 64 identical pieces?

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

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?

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?

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

On January 1st, 2023, a person saved ₹1. On January 2nd, 2023, he saved ₹2 more than that on the previous day. On January 3rd, 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?

$222^{333} + 333^{222}$ is divisible by which of the following numbers?

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

What is the rightmost digit preceding the zeros in the value of $30^{30}$?

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?

A can X contains 399 litres of petrol and a can Y contains 532 litres 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 litres is an integer. How many different bottle sizes are possible?

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:

1. The unit digit of $S$ can be 0.

2. The unit digit of $S$ can be 9.

3. The unit digit of $S$ can be 5.

Which of the statements given above are correct?

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?

P's salary is 20% lower than Q's salary which is 20% lower than R's salary. By how much percent is R's salary more than P's salary?

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

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?

A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?

Consider the following:

1. 1000 litres = 1 m³

2. 1 metric ton = 1000 kg

3. 1 hectare = 10,000 m²

Which of the above are correct?

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 $X$?

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?

How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?

The calendar for the year 2025 is same for

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

1. $(p - r) (qs)$ is even.

2. $(q - s) q^2 s$ is even.

3. $(q + r)^2 (p + s)$ is odd.

Which of the statements given above are correct?

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

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

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, ...

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?

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?

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?

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:

1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.

2. The total cost of one orange and one mango is equal to the cost of one apple.

Which of the statements given above is/are correct?

$32^5 + 2^{27}$ is divisible by

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?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

If the average marks in a class are 60, then what is the number of students in the class?

Statement-I:

The highest marks in the class are 70 and the lowest marks are 50.

Statement-II:

Exclusion of highest and lowest marks from the class does not change the average.

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

Is $(x + y)$ an integer?

Statement-I:

$ (2x + y) $ is an integer.

Statement-II:

$ (x + 2y) $ is an integer.

Which one of the following is correct in respect of the above Question and the Statements?

If P means 'greater than (>); Q means 'less than (<)'; R means 'not greater than (≤)'; S means 'not less than (≥) and T means 'equal to (=)', then consider the following statements:

1. If 2x(S)3y and 3x(T)4z, then 9y(P)8z.

2. If x(Q)2y and y(R)z, then x(R)z.

Which of the statements given above is/are correct?

What will come in place of * in the sequence 3, 14, 39, 84, *, 258?

In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q - S = 2S and T = R + S + 3, then what is the value of P + R - T?

Which of the following statements best reflect the most logical and rational inferences that can be made from the passage?

1. The current methods of food distribution are solely responsible for the loss and wastage of food.

2. Land productivity is adversely affected by the prevailing trend of food loss and wastage.

3. Reduction in the loss and wastage of food results in lesser carbon footprint.

4. Post-harvest technologies to prevent or reduce the loss and wastage of food are not available.

Select the correct answer using the code given below.

Based on the above passage, the following assumptions have been made:

1. The food distribution mechanism needs to be reimagined and made effective to reduce the loss and wastage of food.

2. Ensuring the reduction of wastage and loss of food is a social and moral responsibility of all citizens.

Which of the assumptions given above is/are valid?

Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage?

Based on the above passage, the following assumptions have been made:

1. Fiscal policies of governments are solely responsible for higher prices.

2. Higher prices do not affect the long-term government bonds.

Which of the assumptions given above is/are valid?

Which one of the following statements best reflects the most logical and rational inference that can be made from the above passage?

Based on the above passage, the following assumptions have been made:

1. India needs a new generation of urban professionals with knowledge relevant to modern urban practice.

2. Indian universities at present have no capacity or potential to impart training in systems approach.

Which of the assumptions given above is/are correct?

Which one of the following statements best reflects the central idea of the above passage?

Based on the above passage, the following assumptions have been made:

1. Internet is not inclusive enough.

2. Internet can adversely affect the quality of politics in a country.

Which of the assumptions given above is/are valid?

Which one of the following statements best reflects the thinking of the author about the science?

Which of the following is/are emphatically conveyed by the author of the passage?

1. Without science, mankind could not have continued to exist till today.
2. It is the science that will ultimately determine the destiny of mankind.

Select the correct answer using the code given below.

Based on the above passage, the following assumptions have been made:

1. The horrors of modern life are the inevitable result of the progress of science.
2. The aspect of truth likely to be overlooked is that science is what man has made it.

Which of the assumptions given above is/are correct?

When we meet other people while we travel, we learn to differentiate between

With reference to the above passage, the following assumptions have been made :

1. Travel leads to an understanding of humans.

2. Travel helps those who wish to learn fundamental common values.

3. A person with long experience in travel can resolve differences amongst people.

Which of the assumptions given above are valid?

Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage?

1. In conventional classroom learning, the central goal is duration of learning rather than attainment of competency.

2. Conventional classrooms encourage one-size-fits-all approach and stamp out all differentiation.

Based on the above passage, the following assumptions have been made:

1. As a large number of workers in our country are employed in unorganized sector, India does not need to change its present conventional classroom system of education.

2. Even with its present conventional classroom system of education, India produces sufficient number of skilled workers to fully realize the benefits of demographic dividend.

Which of the assumptions given above is/are valid?

Based on the above passage, the following assumptions have been made:

1. The adolescent does not feel comfortable with his parents because they tend to be dominating and assertive.

2. The adolescent of modern times does not have much respect for parents.

Which of the assumptions given above is/are valid?

Which one of the following statements best reflects the central idea of the above passage?

(a) Parents in general may not be of much help when children are on their way to becoming adults.

(b) When children reach adolescence, involvement of parents in their lives is unnecessary.

(c) Modern-day nuclear families are not capable of bringing up children properly.

(d) In modern societies, adolescents tend to be stubborn, disobedient and careless.

Which one of the following statements best reflects the most logical, rational and practical suggestion implied by the passage?

Based on the above passage, the following assumptions have been made:

1. Giant icebergs have a bearing on primary productivity and food chains of the Southern Ocean.

2. Melting of giant icebergs can produce climate change effects and impact world fisheries.

Which of the assumptions given above is/are valid?

Which one of the following statements best reflects the most logical, rational and practical message conveyed by the passage?

Which one of the following statements best reflects the crux of the above passage?

Which one of the following statements best reflects the most logical and rational message conveyed by the above passage?

Based on the above passage, the following assumptions have been made:

1. The author of the passage believes that flowers are creations of Nature’s luxury.

2. The author of the passage does not believe in the usefulness of flowers except as things of beauty.

Which of the assumptions given above is/are valid?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

What are the values of m and n, where m and n are natural numbers?

Statement-I:

m + n > mn and m > n.

Statement-II:

The product of m and n is 24.

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:

What is the time required to download the software?

Statement-I:

The size of the software is 12 megabytes.

Statement-II:

The transfer rate is 2.4 kilobytes per second.

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question :

What are the unique values of $x$ and $y$, where $x, y$ are distinct natural numbers?

Statement-I : $x / y$ is odd.

Statement-II : $x y=12$

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

A certain amount was distributed among $X, Y$ and $Z$.

Question :

Who received the least amount?

Statement-I :

$X$ received $4 / 5$ of what $Y$ and $Z$ together received.

Statement-II :

$Y$ received $2 / 7$ of what $X$ and $Z$ together received.

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

There are three distinct prime numbers whose sum is a prime number.

Question:

What are those three numbers?

Statement-I:

Their sum is less than 23.

Statement-II:

One of the numbers is 5.

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

A person buys three articles p, q and r for ₹50. The price of the article q is ₹16 which is the least.

Question : What is the price of the article p?

Statement-I : The cost of p is not more than that of r.

Statement-II : The cost of r is not more than that of p.

Which one of the following is correct in respect of the above Question and the Statements?

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

P, Q, R and S appeared in a test.

Question : Has P scored more marks than Q?

Statement-I : The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.

Statement-II : The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.

Which one of the following is correct in respect of the above Question and the Statements?

A question is given followed by two Statements I and II. Consider the Question and the Statements.
The age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

Question:
What is the difference of their ages?

Statement-I:
The age of P is greater than the age of Q.

Statement-II:
The sum of their ages is 11/6 times their difference.

Which one of the following is correct in respect of the above Question and the Statements?

Consider the sequence:

A_BCD_BBCDABC_DABC_D

that follows a certain pattern. Which one of the following completes the sequence?

A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?

A Statement is given followed by two Conclusions numbered I and II. Consider the Statement and the Conclusions.

Statement :
India is the world's largest producer of milk.

Conclusion–I :
India is the world's largest exporter of milk.

Conclusion–II :
India does not import milk.

A Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement.
Main Statement: Pradeep becomes either a Director or a Producer.

Statement P: Pradeep is a Director.

Statement Q: Pradeep is a Producer.

Statement R: Pradeep is not a Director.

Statement S: Pradeep is not a Producer.

Select the correct answer.

If a+b means a−b ; a−b means a×b ; a×b means a+b; then what is the value of 10+30−100×50+25? (Operations are to be replaced simultaneously)

If in a certain code, 'ABCD' is written as 24 and 'EFGH' is written as 1680, then how is 'IJKL' written in that code?

If in a certain code, 'POT' is written as ATOP and 'TRAP' is written as APART, then how is 'ARENA' written in that code?