Consider a set of 11 consecutive integers, each at least −5. Compare:

• Value I: minimum possible average of these 11 integers.

• Value II: minimum possible product of 11 consecutive non-negative integers.

Which relationship is correct?

Three numbers p, q and r have an average of k. The amount by which p exceeds the average is equal to the amount by which q falls below the average. What is the value of r?

How many integers between 1 and 1000, both inclusive, are divisible by 2 or 5 but not by both?

If

P = +, Q = −, R = ×, S = ÷

then insert the proper notations between the successive numbers in the equation:

60 _ 15 _ 3 _ 20 _ 4 = 20

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?

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

A set of 20 pipes can fill 70% of a tank in 14 minutes. Another set of 10 pipes can fill 3/8 of the tank in 6 minutes. A third set of 16 pipes can empty half of the tank in 20 minutes.

If half of the pipes in the first set are closed, half of the pipes in the second set remain open, and all pipes in the third set remain open, how much time will be required to fill 50% of the tank?

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of the runs scored by X to Y is equal to the ratio of the runs scored by Y to 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?

P and Q start from the same point of a circular track at 5:00 AM and move in opposite directions. P completes 5 rounds/hour and Q completes 3 rounds/hour. How many times do they cross between 5:20 AM and 7:00 AM?

A tram overtakes two people walking in the same direction at 3 km/h and 4 km/h. It completely passes them in 8 seconds and 9 seconds respectively. Find the length of the tram.

X can complete one-third of a certain work in 6 days, Y can complete one-third in 8 days, and Z can complete three-fourths in 12 days. All three work together for $n$ days. Then X and Z leave, and Y alone completes the remaining work in $8\frac{2}{3}$ days. Find $n$.

P is the brother of Q and R. S is R's mother. T is P's father.

How many of the following statements are definitely true?

I. S and T are a couple.
II. Q is T's son.
III. T is Q's father.
IV. S is P's mother.
V. R is T's daughter.
VI. P is S's son.

There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG.

A is 6 km south of B.

A is 10 km west of C.

D is 5 km east of E.

C is 6 km north of D.

F is 9 km west of B.

F is 12 km north of G.

A person travels from D to F through these roads. What is the distance covered by the person?

Is $(p + q)^{2} - 4pq$
where $p$ and $q$ are natural numbers, positive?

Statement I: $p < q$

Statement II: $p > q$

Which one of the following is correct?

Let $P,Q,R,S$ be distinct non-zero digits.

If $PP \times PQ = RRSS$

Where $P \leq 3,\ Q \leq 4,$
then what is $Q$ equal to?

Statement I: $R = 1$

Statement II: $S = 2$

Which one of the following is correct?