Number system: practice set 5

Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M − N is

There are three types of rectangular tiles: 3′ × 3′, 3′ × 7′ and 3′ × 11′. An area of rectangular shape of dimensions 3′ × 100′ is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x − y is

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)?

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

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

1. I.x² > x³.
2. II.x > √x.

Select the correct answer using the code given below:

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?

32⁵ + 2²⁷ is divisible by

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:

1. 1.p + q + r − s − t is definitely even.
2. 2.2p + q + 2r − 2s + t is definitely odd.

Which of the above statements is/are correct?

Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?

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

1. 1.To buy 78 gm of coins one must buy at least 7 coins.
2. 2.To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct?

A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?

What is the value of X in the sequence 2, 12, 36, 80, 150, X?

Consider the following multiplication problem:

(PQ) × 3 = RQQ, where P, Q and R are different digits and R ≠ 0.

What is the value of (P + R) ÷ Q?

Let p, q, r and s be natural numbers such that

p − 2016 = q + 2017 = r − 2018 = s + 2019

Which one of the following is the largest natural number?

How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?

How many pairs of natural numbers are there such that the difference of whose squares is 63?

If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

If $ means ‘divided by’; @ means ‘multiplied by’; # means ‘minus’, then the value of 10#5@1$5 is

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?

There are five hobby clubs in a college — photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?