Tag: multiplication of numbers

Questions Related to multiplication of numbers

Kunal has only $25$ paise and $50$ paise coins with him. The total amount in $50$ paise denomination is $Rs. 4$ more that the total amount in $25$ paise denomination. The number of $25$ paise coins is $20$ more than the number of $50$ paise coins. What is the total amount with Kunal?

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

  1. $Rs. 32$

  2. $Rs. 36$

  3. $Rs. 40$

  4. $Rs. 24$

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Correct Option: A

The sum of all natural members which multiples of $7$ or $3$ or both and lie between $200$ and $500$ is

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

  1. $45049$

  2. $40149$

  3. $45149$

  4. $45249$

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Correct Option: A

A number when divided by $14$ leaves a remainder of $8$, but when the same number is divided by $7$, it will leave the remainder ?

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

  1. 3

  2. 2

  3. 1

  4. can't be determined

Show answer
Correct Option: C
Explanation:

We have,

When the number is divided by $14$ it gives a remainder of $8$,

The number $= 14N + 8 (14N$ is divisible by $14)$

When same number is divided by $7$ it will give remainder $1.$

hence, this is the answer.

The sum of all two digit numbers which when divided by 4 , yield unity as remainder is 

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

  1. $1012$

  2. $1201$

  3. $1212$

  4. $1210$

Show answer
Correct Option: D
Explanation:

number should be of the form $4k+1$


Smallest 2 digit number that gives remainder $1$ when divided by $4$ $\Rightarrow$ $13 (when \ k=3)$ first term of A.P

Largest 2 digit number that gives remainder $1$ when divided by $4$ $\Rightarrow$ $97 (when \ k=24)$ last term of AP

Series: $13,17,21,....97$

$97=a+(n-1)d$

$97=13+(n-1)4$

$89=(n-1)4$

$(n-1)=21$

$n=22$

Sum of series $=\cfrac{n}{2}$[first term  + last term]

$=\cfrac{22}{2}[13+97]$

$=11\times (110)$

$=1210$

A rectangular cortyard $3.78$ metres long and $5.25$ metres wide is to be paved exactly with square tiles, all of the same size. Then the largest size of the tile which could be used for the purpose is $(n\times 3)\ cm$, then $n$ is equal to

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

  1. $5$

  2. $7$

  3. $2$

  4. $13$

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Correct Option: B

$\dfrac{20}{100}\times 1,70000=20\times 1700=34,000$

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

  1. True

  2. False

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Correct Option: A
Explanation:

$\begin{matrix} \dfrac { { 20 } }{ { 100 } } \times 170000=20\times 1700 \ =34000\, \, \, Ans. \  \end{matrix}$

A train running at the speed of 60$\mathrm { km } / \mathrm { hr }$ crosses a pole in 9 seconds. What is the length of the train

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

  1. $150$ metres

  2. $180$ metres

  3. $324$ metres

  4. Cannot be determined

  5. None of these

Show answer
Correct Option: A
Explanation:

$Speed\>of\>train\>=\>60\>(\frac{Km}{hr})\\=(\frac{60\cdot\>1000\>m}{3600\>sec})\\=(\frac{50}{3})m/sec\\length\>crossed\>in\>9\>seconds\>=\>(\frac{50}{3})\cdot\>9\>=\>150\>m\\\therefore\>length\>of\>train\>=\>150m$

The quotient when  $1 + x ^ { 2 } + x ^ { 4 } + x ^ { 6 } + \dots + x ^ { 34 }$  is divided by  $1 + x + x ^ { 2 } + x ^ { 3 } + \dots + x ^ { 17 }$  is

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

  1. $x ^ { 17 } - x ^ { 15 } + x ^ { 13 } - x ^ { 11 } + \dots + x$

  2. $x ^ { 17 } + x ^ { 15 } + x ^ { 13 } + x ^ { 11 } + \dots + x$

  3. $x ^ { 17 } + x ^ { 16 } + x ^ { 15 } + x ^ { 14 } + \dots + 1$

  4. $x ^ { 17 } - x ^ { 16 } + x ^ { 15 } - x ^ { 14 } + \dots - 1$

Show answer
Correct Option: D
Explanation:
$1+x^2+x^4+\cdots+x^{34}=\dfrac{1-x^{36}}{1-x^2}$

$1+x+x^2+x^3+\cdots+x^{17}=\dfrac{1-x^{18}}{1-x}$

$\implies \dfrac{1+x^2+x^4+x^6+\cdots +x^{34}}{1+x+x^2+\cdots+x^{17}}=\dfrac{1-x^{36}}{1-x^{18}}\times \dfrac{1-x}{1-x^2}=\dfrac{1+x^{18}}{1+x}=x^{17}-x^{16}+x^{15}+\cdots-1$

What should be multiplied by $-23$ to get $575$?

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

  1. $15$

  2. $25$

  3. $-25$

  4. $35$

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Correct Option: C
Explanation:

Let $x $ be multiplied by $-23$ to get $575$


$x (-23) = 575$


$x = \dfrac{575}{-23}$

$\therefore x = -25$

The number of positive n in the range $12\le n\le 40$ such that the product (n -1) (n -2).... 3.2.1 is not divisible by n is :

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

  1. 5

  2. 7

  3. 13

  4. 14

Show answer
Correct Option: B