DIRECTIONS for questions 1 to 10:In each of these questions, two quantities are mentioned, at column A and at column B. To mark the answers to the questions, use the following instructions. Choose 1: If the quantity in column A is greater. Choose 2: If the quantity in column B is greater. Choose 3: If the two quantities are equal. Choose 4: If the relationship cannot be determined.
Set T consists of all the three digit numbers greater than 450 that contain the digits 2, 4 and 5 with no digit repeated.
Column A
The number of 3 digit nos. in set T
Column B
4
Answer Key: 2 Explanation: T = {452 , 524 ,542}, n (T) = 3
Set T consists of all the positive integer multiples of 2 that are less than 50, and set R consists of all the positive integer multiples of 7 that are less than 50.
Column A
The number of integers that set T and R have in common
Column B
4
Answer Key: 2 Explanation: T = {2, 4, 6, 8…44,48}, R = { 7, 14, 21,……49 },
T ∩R = { 14, 28, 42 }, n (T ∩ R) = 3
Column A
The number of different prime factors of 28 that are greater than 2
Column B
The number of different prime factors of 24 that are greater than 2
Answer Key: 3 Explanation: The different prime factors of 28 are 2 and 7 and that of 24 are 2 and 3,
So, both 28 and 24 have 1 prime factor other than 2
The product of two consecutive positive integers equals 6 times the smaller integer.
Column A
The sum of the two integers
Column B
10
Answer Key: 1 Explanation: Let consecutive positive integers be x and (x + 1), x × (x + 1 ) = 6x, x + 1 = 6, x = 5, So, the other integer is 5+1 = 6. Hence sum of these two integers is 5 + 6 = 11.So, answer is option 1
Integers t, u, v, w, x and y are equally spaced on the number line, y – t = 30
Column A v – u
Column B
6
Answer Key: 3 Explanation:y – t = 30 is divided equally in 5 segments of 6 units each , v – u is equal to the segment uv which is 6.
Column A
The sum of 3 greatest distinct integers that are less than 2
Column B
The sum of 2 least distinct integers that are greater than -1
Answer Key: 2 Explanation: The 3 greatest distinct integers < 2 are -1, 0, 1. The sum is = 0.
The 2 least distinct integers greater than -1 are 0, 1. The sum is 1. Hence answer is option 2.
Let (m, n) be defined as the set of all integers between m and n, excluding m and n. For example, (0, 3.5) = {1, 2, 3}. x is in (2, 6), y is in (6,9)
Column A x
Column B y
Answer Key: 1 Explanation: The values of ‘x’ are 3, 4 and 5 and the values of y are 7 and 8.
Hence, x > y.
Column A
Number of integers between 15 and 51 that are squares of integers
Column B
Number of integers between 6 and 126 that are cubes of integers
Answer Key: 3 Explanation: The squares of integers between 15 and 51 are (16, 25, 36, 49). They are 4 in number.
The numbers which are cubes and between 6 and 126 are (8, 27, 64, 125). They are also 4 in number.
Hence answer is 3.