Tag: operations on integers

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Questions Related to operations on integers

Multiple choice maths negative numbers and integers odd and even numbers operations on integers different types of numbers

If the number of consecutive odd integers whose sum can be expressed as $50^2 - 13^2$ is k then k, can be 

  1. 33

  2. 35

  3. 37

  4. 39
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of odd $n$ consecutive numbers $n^2$

$\therefore (1+3+5\dots\dots (2n-1))=n^2$
where $n$ represents the number of terms.
$\therefore 50^2=1+3+5\dots 99=50\text{ }terms$
$\therefore 13^2=1+3+5\dots 25=13\text{ }terms$
$\therefore 50^2-13^2$$=(1+3+5\dots 99)-(1+3+5\dots 25)\=(27+29\dots 99)\ =37\text{ }terms.$

Multiple choice maths negative numbers and integers odd and even numbers operations on integers different types of numbers

The sum of even numbers between $1$ and $31$ is:

  1. $6$
  2. $28$
  3. $240$
  4. $512$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ${S} _{n}=(2+4+6+.....+30)$. This is an A.P in which $a=2,d=2$ and $l=30$
Let the number of terms be $n$. Then,
$a+(n-1)d=30$
$\Rightarrow$ $2+(n-1)\times 2=30$
$\Rightarrow$ $n=15$
$\therefore$ ${S} _{n}=\cfrac{n}{2}(a+l)=\cfrac{15}{2}\times (2+30)=(15\times 16)=240$.