1.
Find the common factors of 15 and 20.
Correct Answer
A. (A) 1, 5
Explanation
The common factors of 15 and 20 are the numbers that can divide both 15 and 20 without leaving a remainder. The factors of 15 are 1, 3, 5, and 15. The factors of 20 are 1, 2, 4, 5, 10, and 20. The common factors of 15 and 20 are 1 and 5, as they are the only numbers that can divide both 15 and 20 without leaving a remainder.
2.
Find the HCF of 9, 15, and 24.
Correct Answer
C. (C) 3
Explanation
The HCF (Highest Common Factor) of 9, 15, and 24 is 3. This is because 3 is the largest number that can divide evenly into all three numbers. 9 can be divided by 3 to give 3, 15 can be divided by 3 to give 5, and 24 can be divided by 3 to give 8. Therefore, 3 is the highest common factor of all three numbers.
3.
Write in words 1,347,000
Correct Answer
B. (B) one million three hundred and forty-seven thousand
Explanation
The correct answer is (B) one million three hundred and forty-seven thousand. This is because the number 1,347,000 can be written as "one million three hundred and forty-seven thousand", which matches option (B).
4.
Find the LCM of 20, 24, and 30
Correct Answer
A. (A) 120
Explanation
To find the LCM (Least Common Multiple) of 20, 24, and 30, we need to find the smallest number that is divisible by all three numbers. We can start by finding the prime factors of each number: 20 = 2^2 * 5, 24 = 2^3 * 3, and 30 = 2 * 3 * 5. Then, we take the highest power of each prime factor: 2^3 * 3 * 5 = 120. Therefore, the LCM of 20, 24, and 30 is 120.
5.
Find the sum of 695 and 455 and then divide the result by the difference between 39 and 34.
Correct Answer
B. (B) 230
Explanation
To find the sum of 695 and 455, we add them together: 695 + 455 = 1150.
Then, we find the difference between 39 and 34: 39 - 34 = 5.
Finally, we divide the sum (1150) by the difference (5): 1150 / 5 = 230.
Therefore, the correct answer is (B) 230.
6.
Multiply 13/5 and 13/18
Correct Answer
C. (C) 169/90
7.
The 5^{th} multiple of 6 is ……
Correct Answer
C. (C) 30
Explanation
The 5th multiple of 6 can be found by multiplying 6 by 5, which equals 30. Therefore, the correct answer is (C) 30.
8.
Find the sum of 29.34 and 837.5
Correct Answer
D. (D) 866.84
Explanation
The correct answer is (D) 866.84. To find the sum of 29.34 and 837.5, you need to add the two numbers together. Adding the decimal parts, 0.34 and 0.50, gives you 0.84. Adding the whole numbers, 29 and 837, gives you 866. Combining the two results, the sum is 866.84.
9.
Express 84 as a product of prime factors
Correct Answer
B. (B) 2 x 2 x 3 x 7
Explanation
The number 84 can be expressed as a product of prime factors by repeatedly dividing it by prime numbers. Starting with the smallest prime number, 2, we divide 84 by 2 to get 42. We continue dividing 42 by 2 to get 21, and then divide 21 by 3 to get 7. Finally, we divide 7 by itself to get 1. Therefore, the prime factorization of 84 is 2 x 2 x 3 x 7.
10.
Add up 315 and 231
Correct Answer
D. (D) 546
Explanation
The correct answer is (D) 546. To find the sum of 315 and 231, you add the hundreds place, the tens place, and the ones place separately. In the hundreds place, 3 + 2 equals 5. In the tens place, 1 + 3 equals 4. In the ones place, 5 + 1 equals 6. Therefore, the sum of 315 and 231 is 546.
11.
Which one of these numbers is not a common factor of 12 and 24?
Correct Answer
A. (A) 5
Explanation
The number 5 is not a common factor of 12 and 24 because it does not divide evenly into either of them. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the correct answer is (A) 5.
12.
Change to decimal 3/8
Correct Answer
C. (C) 0.375
Explanation
To change a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number). In this case, dividing 3 by 8 gives 0.375. Therefore, the correct answer is (C) 0.375.
13.
Evaluate 3 2/5 + 2 2/3
Correct Answer
D. (D) 6 1/15
Explanation
To evaluate the given expression, we need to convert the mixed numbers into improper fractions. 3 2/5 can be written as (3*5 + 2)/5 = 17/5. 2 2/3 can be written as (2*3 + 2)/3 = 8/3. Now, we can add the fractions: (17/5) + (8/3). To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 15. Converting both fractions to have a denominator of 15, we get: (17/5) * (3/3) = 51/15 (8/3) * (5/5) = 40/15 Adding the fractions: (51/15) + (40/15) = 91/15. Now, we can convert the improper fraction back into a mixed number: 91 ÷ 15 = 6 remainder 1. Therefore, the answer is 6 1/15, which matches option (D).
14.
What is the value of 1 ½ X 2 1/3
Correct Answer
B. (B) 3 ½
15.
Find the common factors of 15 and 20.
Correct Answer
A. (A) 1, 5
Explanation
The common factors of 15 and 20 are numbers that can divide both 15 and 20 without leaving a remainder. The numbers 1 and 5 are the only numbers that can divide both 15 and 20. Therefore, the correct answer is (A) 1, 5.
16.
10/3 is a fraction called …..
Correct Answer
B. (B) improper fraction
Explanation
An improper fraction is a fraction where the numerator is greater than or equal to the denominator. In this case, 10/3 is an improper fraction because the numerator (10) is greater than the denominator (3).
17.
MCM in numeral stands for ……
Correct Answer
D. (D) 1900
Explanation
MCM in numeral stands for "Mille Cent" which is the representation of the number 1900 in Roman numerals.
18.
Add the following 1.23 + 10.23 + 100.23
Correct Answer
B. (B) 111.69
Explanation
The correct answer is (B) 111.69. To find the sum of 1.23 + 10.23 + 100.23, we simply add the three numbers together. 1.23 + 10.23 equals 11.46, and adding 100.23 to that gives us a total of 111.69. Therefore, the answer is 111.69.
19.
Ch Change to mixed fraction 14/9
Correct Answer
B. (B) 15/9
20.
Write as decimal 4/8
Correct Answer
D. (D) 0.5
Explanation
The fraction 4/8 can be simplified to 1/2. When written as a decimal, 1/2 is equal to 0.5.
21.
Express 5/7 as an equivalent fraction
Correct Answer
A. (A) 10/14
Explanation
To express 5/7 as an equivalent fraction, we need to find a fraction that has the same value but with a different numerator and denominator. To do this, we can multiply both the numerator and denominator of 5/7 by the same number. In this case, we can multiply both by 2 to get 10/14. Therefore, the correct answer is (A) 10/14.
22.
I In a leap year, the month of February has ……….. days
Correct Answer
B. (B)29
Explanation
In a leap year, the month of February has 29 days. A leap year occurs every 4 years and has an extra day added to the calendar to keep it synchronized with the solar year. This extra day is added to the month of February, making it 29 days instead of the usual 28 days. Therefore, the correct answer is (B) 29.
23.
Convert 0.88 to percentage
Correct Answer
A. (A) 88%
Explanation
To convert a decimal number to a percentage, you need to multiply it by 100. In this case, 0.88 multiplied by 100 equals 88. Therefore, the correct answer is (A) 88%.
24.
Write in words 30,212,150,615
Correct Answer
C. (C) thirty billion two hundred and twelve million one hundred and fifty thousand six hundred and fifteen
Explanation
The correct answer is (C) thirty billion two hundred and twelve million one hundred and fifty thousand six hundred and fifteen. This is the correct representation of the number 30,212,150,615 in words, following the standard rules of place value and number naming.
25.
Put the following in its lowest term 125/240
Correct Answer
A. 25/48
Explanation
To find the lowest term of a fraction, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 125 and 240 is 5. Dividing both numbers by 5, we get 25/48. Therefore, the correct answer is 25/48.
26.
Which of the following is a pure number?
Correct Answer
B. (B) 31
Explanation
A pure number is a number without any associated units. It's simply a numerical value.
Among the given options:
Option (B) 31 is a pure number.
Option (A) 12^7, Option (C) 6^5, and Option (D) 49^3 are not pure numbers since they represent numbers raised to a power.
So, the correct answer is: (B) 31
27.
Find the difference between 25.00015 and 19.6025
Correct Answer
A. (A) 5.39765
Explanation
The correct answer is (A) 5.39765. To find the difference between 25.00015 and 19.6025, subtract 19.6025 from 25.00015. This gives us 5.39765. Therefore, the difference is 5.39765.
28.
What is the place value of 8 in 238056
Correct Answer
D. (D) 8000
Explanation
The place value of a digit in a number is determined by its position in the number. In the given number, 238056, the digit 8 is in the thousands place. Therefore, its place value is 8000.
29.
Write the number in words: 4510015
Correct Answer
B. (B) four million five hundred and ten thousand and fifteen
Explanation
The correct answer is (B) four million five hundred and ten thousand and fifteen. This is because the number 4510015 can be broken down into four million (4,000,000), five hundred and ten thousand (510,000), and fifteen (15).
30.
Write as improper fraction 22/3
Correct Answer
A. (A) 7 1/3
Explanation
The given fraction is 22/3. To write it as an improper fraction, we divide the numerator (22) by the denominator (3). 22 divided by 3 equals 7 with a remainder of 1. So, the improper fraction is 7 1/3.
31.
An integer is any positive or negative numeral True/False
Correct Answer
A. True
Explanation
An integer is any positive or negative numeral, which means it can be a whole number that is either positive or negative. Therefore, the statement "An integer is any positive or negative numeral" is true.
32.
Wh Which is the greatest in the following -19, -7, +4, +3, -5.
Correct Answer
C. (c) +4
Explanation
The greatest number among the given options is +4. When comparing negative numbers with positive numbers, the positive numbers are always greater. Therefore, +4 is greater than -19, -7, +3, and -5.
33.
Express 23.725 correct to the nearest whole number
Correct Answer
C. (c) 24
Explanation
The question asks to express 23.725 to the nearest whole number. To do this, we look at the decimal part of the number. Since the decimal part is greater than 0.5, we round up the whole number to the next higher number, which is 24. Therefore, the correct answer is (c) 24.
34.
Find the value of (+3) – (+7)
Correct Answer
A. (a) -4
Explanation
The given expression is (+3) - (+7). When subtracting a positive number from another positive number, we can think of it as adding the opposite of the second number. So, (+3) - (+7) can be rewritten as (+3) + (-7). Adding 3 to the opposite of 7 gives us -4. Therefore, the value of (+3) - (+7) is -4.
35.
Simplify 6 + 1 + (-4)
Correct Answer
A. (a) +3
Explanation
The given expression can be simplified by adding the numbers together. 6 + 1 = 7, and then adding -4 to 7 gives us 3. Therefore, the simplified form of the expression is +3, which is the correct answer.
36.
Simplify - 14a
7
Correct Answer
A. -2a
Explanation
To simplify the expression negative fourteen a over seven, divide the coefficient negative fourteen by seven. This results in negative two. The variable 'a' remains unchanged. So, the simplified expression is negative two a.
37.
Convert 92% to fraction
Correct Answer
B. (b) ^{23}/_{25}
Explanation
To convert a percentage to a fraction, we divide the percentage by 100 and simplify the fraction if possible. In this case, we divide 92 by 100 to get 0.92. Since 92 and 100 have a common factor of 4, we can simplify the fraction by dividing both the numerator and denominator by 4. This gives us 23/25, which is the equivalent fraction for 92%. Therefore, the correct answer is (b) 23/25.
38.
Simplify (-4a) x (+3b)
Correct Answer
A. (a) -12ab
Explanation
The given expression (-4a) x (+3b) represents the product of -4a and +3b. To find the product, we multiply the coefficients (-4 and +3) and the variables (a and b) separately. The product of -4 and +3 is -12. The variables a and b are both present in the expression, so we include them in the product. Therefore, the simplified form of the expression is -12ab, which matches option (a).
39.
Which is greatest 3^{4} or 2^{4 }?
Correct Answer
D. (d) 3^{4}
Explanation
In this question, we are asked to determine which number is greater between 34 and 24. The number 34 is greater than 24, so the correct answer is 34.
40.
Express correct 14.467 to 2 decimal places
Correct Answer
C. (c) 14.47
Explanation
The correct answer is (c) 14.47. When expressing a number to 2 decimal places, we round the number to the nearest hundredth. In this case, 14.467 is closer to 14.47 than it is to 14.46, so we round up to 14.47.
41.
Find the value of +72 + (-168)
Correct Answer
D. (d) -96
Explanation
The given expression is +72 + (-168). When we add a positive number and a negative number, we subtract the absolute value of the smaller number from the absolute value of the larger number and keep the sign of the larger number. In this case, the absolute value of -168 is larger than the absolute value of +72. So, we subtract 168 from 72 and keep the negative sign, resulting in -96.