# Number system

Quiz by Kritika Vohra , updated more than 1 year ago More Less
 Created by Ravindra Patidar over 4 years ago Copied by Kritika Vohra over 1 year ago
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### Description

This test contains 20 MCQ questions for Number System with 2 minutes time limit on each question

## Resource summary

### Question 1

Question
If n = 4p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
Answer
• 2
• 3
• 4
• 6
• 8
• I don't know

### Question 2

Question
For positive integers x and y, which of the following can be written as y^2?
Answer
• (x+1)!
• (x+9)!
• x^2-9
• x^2+1
• (x+1)^2)!
• I Don't Know

### Question 3

Question
What are the last two digits of (301*402*503*604*646*547*448*349)^2 ?
Answer
• 96
• 76
• 56
• 36
• 16
• I don't know

### Question 4

Question
A set of five positive integers has an arithmetic mean of 150. A particular number among the five exceeds another by 100. The rest of the three numbers lie between these two numbers and are equal. How many different values can the largest number among the five take?
Answer
• 18
• 19
• 21
• 42
• 59
• I don't know

### Question 5

Question
Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true?
Answer
• 0<y<4
• 4<y<10
• 10<y<20
• 20<y<30
• y>30
• I don't know

### Question 6

Question
s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits are in s(99)?
Answer
• 350
• 353
• 354
• 356
• 357
• I don't know

### Question 7

Question
If x is an odd negative integer and y is an even integer, which of the following statements must be true? I. (3x - 2y) is odd II. xy^2 is an even negative integer III. (y^2 - x) is an odd negative integer
Answer
• I only
• II only
• I and II
• I and III
• II and III
• I don't Know

### Question 8

Question
A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is
Answer
• 3
• 7
• 21
• 27
• 189
• I don't know

### Question 9

Question
The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have?
Answer
• 1
• 2
• 3
• 4
• 5
• I don't know

### Question 10

Question
How many positive even integers less than 100 contain digits 4 or 7?
Answer
• 16
• 17
• 18
• 19
• 20
• I don't know

### Question 11

Question
Two integers x and y are chosen without replacement out of the set {1, 2, 3,......, 10}. Then the probability that x^y is a single digit number.
Answer
• 11/90
• 13/90
• 17/90
• 19/90
• 23/90
• I don't know

### Question 12

Question
How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
Answer
• 14
• 13
• 12
• 11
• 10
• I don't know

### Question 13

Question
How many prime numbers exist between 200 and 220?
Answer
• 0
• 1
• 2
• 3
• 4
• I don't know

### Question 14

Question
If 3 < x < 100, for how many values of x is x/3 the square of a prime number?
Answer
• 2
• 3
• 4
• 5
• 9
• I don't know

### Question 15

Question
An integer between 1 and 300, inclusive, is chosen at random. What is the probability that the integer so chosen equals an integer raised to an exponent that is an integer greater than 1?
Answer
• 17/300
• 1/15
• 2/25
• 1/10
• 3/25
• I don't know

### Question 16

Question
If two integers are chosen at random out of the set {2, 5, 7, 8}, what is the probability that their product will be of the form a^2 – b^2, where a and b are both positive integers?
Answer
• 2/3
• 1/2
• 1/3
• 1/4
• 1/6
• I don't know

### Question 17

Question
Consider a sequence of numbers given by the expression 5 + (n - 1) * 3, where n runs from 1 to 85. How many of these numbers are divisible by 7?
Answer
• 5
• 7
• 8
• 11
• 12

### Question 18

Question
If x/(11p) is an odd prime number, where x is a positive integer and p is a prime number, what is the least value of x?
Answer
• 22
• 33
• 44
• 66
• 99
• I don't know

### Question 19

Question
When a certain perfect square is increased by 148, the result is another perfect square. What is the value of the original perfect square?
Answer
• 1296
• 1369
• 1681
• 1764
• 2500
• I don't know

### Question 20

Question
If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers? I. P(10) II. P(P(10)) III. P(P(P(10)))
Answer
• I only
• I & II only
• I & III only
• II & III only
• I, II & III
• I don't know

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