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 $a^2 - b^2 = (a+b)(a-b) = 7 \times 3 = 21$.
ITBP Number System — practice questions
Explore 47 free Number System questions in ITBP 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 47.
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 square of 349?Read the answer and worked solution →What is the three-digit number which is 2 more than a perfect square and 2 less than a perfect cube?Read the answer and worked solution →Which of the following numbers is NOT a perfect cube?Read the answer and worked solution →What is the HCF of 16, 72 and 28?Read the answer and worked solution →The HCF of 156, 312 and 195 is:Read the answer and worked solution →If the number x3339 is divisible by 11, what is the digit x?Read the answer and worked solution →The least common multiple (LCM) of 14, 42 and 77 is:Read the answer and worked solution →If the number x4738 is divisible by 9, what is the value of x?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 →True or false: reading the propertiesRead 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.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.