Tag: mental multiplication

Questions Related to mental multiplication

$Table - I$

 Name of City  No. of Govt. employees
 Delhi  4200
 Mumbai  3600
 Chennai  3000

$Table - II$

 Name of City  No. of Govt. employees
 Delhi  $\Box \quad \Box \quad \Box \quad \Box \quad \Box \quad \Box \quad \Box$
 Chennai  $\Box \quad \Box \quad \Box \quad \Box \quad \Box \quad \Box$
 Mumbai    $\Box \quad \Box \quad \Box \quad \Box \quad \Box \quad $

Direction (13-14) : Table-I and Table-II shows the number of Government employees in some cities. Observe the table and answer the questions.
How many employees does each $\square$ represent ?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 500

  2. 600

  3. 700

  4. 800

Show answer
Correct Option: B
Explanation:

Number of government employees in Delhi $= 4200$
Now, $7 \times \square = 4200$
$\Rightarrow \square = \dfrac{4200}{7} = 600$

$6\times 3(3-1)$ is equal to

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $53$

  2. $36$

  3. $20$

  4. $19$

Show answer
Correct Option: B
Explanation:

Given,
$6 \times 3 (3 - 1)$

$= 6 \times 3 (2)$
$= 6 \times 6$ 
$= 36$

Teacher is taking some children on a school trip to the zoo. There are $8$ childrens and $3$ adults. Each children's ticket cost is Rs. $12$ and each adult's ticket cost is rs. $24$. How much will the trip cost?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. Rs. $108$

  2. Rs. $146$

  3. Rs. $168$

  4. Rs. $184$

Show answer
Correct Option: C
Explanation:

We have to find the total cost of the trip.

Since there are $8$ children , that will be $12\times  8= Rs.\ 96$  for the chidren
Since there are $3$ adult  , that will be $24\times 3 = Rs.\  72$  for the adults
which makes total of Rs. $168$

$470988$ books are to be arranged equally in shelves. If $378$ books are arranged in each shelf, how many shelves will be needed?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $1246$ shelves

  2. $1006$ shelves

  3. $2406$ shelves

  4. $3466$ shelves

Show answer
Correct Option: A
Explanation:

There are $470988$ books and are to be arranged in shelves.

Each shelf has $378$ books, So we need $\dfrac{470988}{378}$ shelves 
$\therefore$  We need $ 1246$ shelves.

Repeated addition of same number is called _________.

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. Addition

  2. Subtraction

  3. Multiplication

  4. Division

Show answer
Correct Option: C
Explanation:

Repeated addition is also known as multiplication. If the same number is repeated then in short we can write that in the form of multiplication.
For example : $3+3+3+3+3$

Here $3$ is repeated $5$ times so in short we can write this addition as $3\times 5$ 

In the correctly worked out multiplication problem at the below, each letter represent a different digit. What is the value of B ?

A A
A B

   B B
A A C

A 3 B

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 1

  2. 2

  3. 4

  4. 5

Show answer
Correct Option: B
Explanation:

$B + C = B$

$C = 0$

AA.B $=$ BB $\Rightarrow $ (10 A + A) B $ = $BB= 10 B $+$ B

$AB = B,A = 1$

$ B+A = 3 $

$\Rightarrow B + 1 =3, \Rightarrow B = 2$

1 1 

11

12

22

110

132

If $ \spadesuit \spadesuit \spadesuit = 18$, then $\spadesuit \spadesuit \spadesuit \spadesuit \spadesuit =$ ________.

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $18$

  2. $24$

  3. $30$

  4. $48$

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  $\spadesuit\spadesuit\spadesuit=18$         [Given]

$\therefore$  $3\spadesuit=18$
$\therefore$  $\spadesuit=\dfrac{18}{3}=6$    ----( 1 )
$\Rightarrow$  $\spadesuit\spadesuit\spadesuit\spadesuit\spadesuit=5\spadesuit=5\times 6=30$   [ By using ( 1 ) ]
$\therefore$  $\spadesuit\spadesuit\spadesuit\spadesuit\spadesuit=30$

Find the least number in which multiplied by $1800$ given a perfect cube, then find the sum of the digits of that number.

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $2$

  2. $3$

  3. $6$

  4. $8$

Show answer
Correct Option: C
Explanation:
factor of $ 1800 - 10 \times 10\times 18 = 3\times 3\times 2\times 2\times 5\times 2\times 5 $

$ = 2^{3}\times 3^{2}\times 5^{2}$

for perfect cube we need $  3\times 5 = 15 $

So, sum of digits $(15) = 1+5=6$

so option (c) is right

The sum of all three-digit natural numbers which leave a remainder $2$ when divided by $3$

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $168450$

  2. $168850$

  3. $165840$

  4. None of these

Show answer
Correct Option: A
Explanation:
First three digit number leaves remainder $2$ is $101$
The next being $104, 107, 110$,...…
Last $3$ digit number $=998$
$\therefore 101, 104, …… 998$
$a=101, d=3$
$n^{th}$ term $\Rightarrow 998=a+(n-1)d$
$998=101+(n-1)3$
$(n-1)\not{3}={\not{897}} _{299}$
$n=300$.
$S _n=\dfrac{300}{2}(2(101)+(300-1)3)=\dfrac{300}{2}(202+897)$
$=164850$.

Given $n =1 + x$ and x is the product of four consecutive integers. Then which of the following is true?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. n is an odd numbers

  2. n is prime

  3. sometimes a perfect square

  4. All the given

Show answer
Correct Option: A,C
Explanation:

$ Let\quad x=a(a+1)(a+2)(a+3)\ Now\quad whether\quad a\quad is\quad even\quad or\quad odd,\quad the\quad four\quad consecutive\quad number's\quad product\quad \ contain\quad 2,\quad 3,\quad 4\quad as\quad factors.\ \therefore \quad x\quad is\quad divisible\quad by\quad 2\times 3\times 4=24----(1)\ Option\quad A\longrightarrow Four\quad consecutive\quad numbers\quad contain\quad two\quad even\quad numbers.\ Therefore\quad product\quad is\quad even.\therefore \quad x+1\quad should\quad be\quad odd.\ Option\quad A\quad is\quad correct.\ Option\quad B\longrightarrow x\quad is\quad divisible\quad by\quad 24\quad (from\quad 1)\ Now\quad there\quad exists\quad no\quad prime\quad of\quad the\quad form\quad 24p+1\quad where\quad p\quad is\quad a\quad natural\quad number.\ e.g.\quad \quad 29=24\times 1+5\ \quad \quad \quad \quad \quad 31=24\times 1+7\ \quad \quad \quad \quad \quad 37=24\times 1+13\ With\quad increasing\quad count\quad the\quad second\quad term\quad increases\quad because\quad difference\quad between\ primes\quad increase\quad with\quad higher\quad count.\quad Therefore\quad x+1=n\quad is\quad not\quad a\quad prime\quad under\quad the\quad \ given\quad condition.\quad For\quad a\quad expanded\quad number\quad to\quad be\quad square,\quad the\quad first\quad and\quad last\quad term\ should\quad be\quad square\quad number.   Option\quad C\longrightarrow x=a(a+1)(a+2)(a+3)\ when\quad a\quad is\quad even\quad a=2p\ \therefore \quad x=2p(2a+1)(2a+2)(2a+3)\ \quad \quad \quad =4p(2p+1)(p+1)(2p+3)\ The\quad product\quad is\quad 4\times 1\times 1\times 3=12\ If\quad we\quad add\quad 1\quad then\quad last\quad term\quad of\quad the\quad product\quad is\quad 13\ which\quad is\quad not\quad a\quad square\quad number.\ So\quad x+1=n\quad is\quad not\quad a\quad square\quad number\quad when\quad a\quad is\quad even.\ (2)\quad When\quad a\quad is\quad odd-\ x=(2p+1)(2p+2)(2p+3)(2p+4)\ The\quad last\quad term\quad of\quad the\quad product\quad is\quad 1\times 2\times 3\times 4=24.\ 24+1=25\quad is\quad a\quad square\quad term.\ \therefore \quad n=x+1\quad is\quad a\quad square\quad number\quad when\quad a\quad is\quad odd.\ \therefore \quad Option\quad C\quad is\quad correct\quad when\quad a\quad is\quad odd.\ Option\quad D\longrightarrow \quad Obviously\quad option\quad D\quad is\quad not\quad correct. $