alleryStart learning →If $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?
- $14$
- $10$
- $21$
- $28$
Show answer and solution
Correct answer: C. $21$
Use the difference-of-squares identity $a^2 - b^2 = (a+b)(a-b) = 7 \times 3 = 21$.
MAT Number System — practice questions
Explore 48 free Number System questions in MAT Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.
Practise Number System with Quill →Number System questions and exercises with answers
Showing questions 1–30 of 48.
If $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?Read the answer and worked solution →Expand $(x + 5)^2$.Read the answer and worked solution →If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?Read the answer and worked solution →Factorise $a^3 - b^3$.Read the answer and worked solution →If $x + \dfrac{1}{x} = 5$, find $x^3 + \dfrac{1}{x^3}$.Read the answer and worked solution →If $a + b + c = 6$ and $a^2 + b^2 + c^2 = 14$, find $ab + bc + ca$.Read the answer and worked solution →What is the prime factorisation of 360?Read the answer and worked solution →For which value of n does $6^n$ end with the digit zero?Read the answer and worked solution →How many divisors does the number $N = 2^3 \times 3^2 \times 5$ have?Read the answer and worked solution →What is the HCF of 18 and 24?Read the answer and worked solution →What is the LCM of 12 and 18?Read the answer and worked solution →HCF of two positive integers a and b is 5. Their LCM is 200. If a = 25, what is b?Read the answer and worked solution →Which of the following is a rational number?Read the answer and worked solution →Which fraction has a TERMINATING decimal expansion?Read the answer and worked solution →The product of a non-zero rational number and an irrational number is always:Read the answer and worked solution →Which property is this?Read the answer and worked solution →True or false: closureRead the answer and worked solution →Complete the identity elementsRead the answer and worked solution →Match each property to its statementRead the answer and worked solution →Identities and propertiesRead the answer and worked solution →True or false: how many rationals lie between two rationalsRead the answer and worked solution →Order the steps: find a rational number between two othersRead the answer and worked solution →Tap every property rational numbers have under additionRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Flip and pair: property with its equationRead the answer and worked solution →Complete distributivityRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Additive or multiplicative?Read the answer and worked solution →
Worked practice questions
Expand $(x + 5)^2$.
- $x^2 + 10x + 10$
- $x^2 + 5x + 25$
- $x^2 + 25$
- $x^2 + 10x + 25$
Show answer and solution
Correct answer: D. $x^2 + 10x + 25$
$(a+b)^2 = a^2 + 2ab + b^2$.
With $a=x, b=5$: $x^2 + 10x + 25$.
If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?
- $3abc$
- $-3abc$
- $0$
- $abc$
Show answer and solution
Correct answer: A. $3abc$
The general identity $a^3+b^3+c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ collapses when $a+b+c = 0$: the RHS is zero, so $a^3+b^3+c^3 = 3abc$.
A frequent slip is to pick option A — that would require *all three* numbers to be zero, not just their sum.
How to practise
- Choose a Number System question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
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