Quantitative Aptitude focuses on several topics like Problems on numbers in Arithmetic, which is the science that studies the relationships between numbers. It includes all methods that apply to numbers. Numbers are expressed as figures – 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 known as digits. 0 is considered as inconsequential digit, but the remaining digits are considered significant.
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Numerals are groups of figures that represent a number. Numbers are classified into the following types:
- Natural numbers: Natural numbers are numbers that we use to count objects. They are denoted by ‘N’. N= {1, 2, 3, 4, 5,….}
- Whole numbers are formed by including ‘zero’ in natural numbers. They are identified by the letter ‘W’. W={0, 1, 2, 3, 4, 5,…….}
- Prime Number: A number other than one is referred to as a prime number, if it can only be divided by one and itself.
- Composite Numbers: A composite number is any number other than 1 that is not a prime number. e.g. 4,6, 8,9,12,14
- Even Number: A number divisible by two is known as an even number. e.g., 2, 4, 8, 12, 24, 28…. It also has the form 2n (where n is a whole number).
- Odd number: Odd number is a number that is not divisible by two. e.g.,3,9,11,17,19,…….
- Consecutive Numbers: A succession of numbers that are all greater than the one before it by one is referred to as a consecutive number. 2. e.g., 6, 7, 8, 13, 14, 15, 16, or 101, 102, 103, 16.
- Integers: Integers are a set of numbers that includes both whole and negative values. It is denoted by I. For example, I ={- 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5…}.
- Rational numbers: Rational numbers are can be expressed as fractions. They are denoted by Q. For example, 1/2, 3 /4, 8/9, and 13/15 are rational numbers. Rational numbers are those that can be expressed as a/b, where a and b are integers and b is not 0.
- Irrational numbers: Irrational numbers are cannot be expressed as p/q (where p and q are integers and q is not zero). For example, √3 = 1.732, √2 = 1.414. However, repeating decimals, such as 8/3 = 2.666 or 2. overline 6 form, are rational numbers.
- Real numbers: Real numbers encompass rational and irrational numbers.
Practice Quizzes
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Problems on Numbers Quiz 1 – Coming Soon |
Problems on Numbers Quiz 2 – Coming Soon | Problems on Numbers Quiz 3 – Coming Soon |
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Some Important Formulas To Solve Problems on numbers
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Example problems on Problems on numbers
Q1. If the product 4864*9 P 2 is divisible by 12, the value of p:
A) 1
B) 2
C) 3
D) 4
Answer: A) 1
Explanation:
Clearly 4864 is divisible by 4
So, 9 P 2 must be divisible by 3. So (9+P+2) must be divisible by 3.
So P=1.
Q2. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :
A) 553681
B) 555181
C) 555681
D) 556581
Answer: C) 555681
Explanation:
987 = 3 * 7 * 47.
So, the required number must be divisible by each one of 3, 7, 47
553681 => (Sum of digits = 28, not divisible by 3)
555181 => (Sum of digits = 25, not divisible by 3)
555681 is divisible by each one of 3, 7, 47.
Q3. How many terms are in the G.P. 3, 6, 12, 24, ……., 384 ?
A) 8
B) 9
C) 10
D) 11
Answer: A) 8
Explanation:
Here a = 3 and r = 6/3 = 2. Let the number of terms be n.
Then, t = 384 => a * r^(n-1) = 384
=> 3 * 2^(n-1) = 384 => 2^(n-1) = 128 = 2^(7)
=> n-1 = 7 => n = 8.
Q4. What is the simplified result of following the steps below in order?
1.Add 5y to 2x
2.Multiply the sum by 3
3.Substract x+y from the product
A) 5x + 14y
B) 5x + 16y
C) 5x + 5y
D) None
Answer: A) 5x + 14y
Explanation:
Step 1 :2x + 5y
Step 2 :3(2x + 5y) = 6x + 15y
Step 3 :(6x + 15y) – (x +y) = 6x + 15y – x – y (watch that last minus sign!)
This gives 5x + 14y
Q5. If three numbers are added in pairs, the sums equal 10, 19 and 21. Find the numbers?
A) 2,3 and 5
B) 6,8 and 10
C) 6, 4 and 15
D) 12, 9 and 15
Answer: C
Explanation:
Smart Approach:
By ‘Hit & Trial’ method
(2 + 3) ≠ 10. Option ‘A’ gets eliminated
(6 + 8) ≠ 10. Option ‘B’ gets eliminated too.
(6 + 4) = 10
(4 + 15) = 19
& (15 + 6) = 21
It’s evident that the numbers in option ‘C’ satisfy the given condition.
Hence, option ‘C’ is the correct answer.
Traditional Approach:
Let the numbers be x, y and z. then
x + y = 10 …..(1) y + z = 19 …..(2) x + z = 21 ….(3)
Adding (1), (2) and (3),
we get : 2(x + y + z) = 50 or (x + y + z) = 25.
Thus, x = (25 – 19) = 6; y = (25 – 21) = 4; z = (25 – 10) = 15.
Hence, the required numbers are 6, 4 and 15.
Hence, option C is correct.
Q6. The least number by which 1470 must be divided to get a number which is a perfect square is ?
A) 5
B) 6
C) 15
D) 30
E) None of these
Answer: D
Explanation:
1470 = 7 × 7 × 6 × 5
To make it a perfect square, it must be divided by 5 × 6 = 30.
Hence, option D is correct.
Q7. Of three numbers, the sum of the first two is 45, the sum of the second and the third is 55, and the sum of the third and thrice the first is 90. Find the third number.
A) 20
B. 25
C) 30
D) 15
E) None of these
Correct Option: C
Let the number be x, y and z.
Then x + y = 45 ….(i)
y + z = 55 ….(ii)
z + 3x = 90 …. (iii)
Now, from (i)
y = 45 – x
And from (ii) z = 55 – y
∴ z = 55 – (45 – x)
z = 10 + x
Putting the value of z in equn. (iii) , we have
3x + 10 + x = 90
∴ x = 20
y = 45 – 20 = 25 and z = 10 + 20 = 30.
Hence, option C is correct.
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