Tag: multiplication methods

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Multiple choice maths ways to multiply and divide mental multiplication multiplication methods 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?

  1. $Rs. 32$
  2. $Rs. 36$
  3. $Rs. 40$
  4. $Rs. 24$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the number of 50 paise coins. Then the number of 25 paise coins is x + 20. The amount in 50 paise is 0.5x, and in 25 paise is 0.25(x + 20). Given 0.5x = 0.25(x + 20) + 4, we solve 0.5x = 0.25x + 5 + 4, so 0.25x = 9, x = 36. Total amount = 0.5(36) + 0.25(56) = 18 + 14 = 32.

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

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 ?

  1. 3

  2. 2

  3. 1

  4. can't be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $1012$
  2. $1201$
  3. $1212$
  4. $1210$
Reveal answer Fill a bubble to check yourself
D Correct answer
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]

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

$=11\times (110)$

$=1210$

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

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

  1. $150$ metres
  2. $180$ metres
  3. $324$ metres

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

  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. $x ^ { 17 } - x ^ { 16 } + x ^ { 15 } - x ^ { 14 } + \dots - 1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$1+x^2+x^4+\cdots+x^{34}=\dfrac{1-x^{36}}{1-x^2}$

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

$\implies \dfrac{1+x^2+x^4+x^6+\cdots +x^{34}}{1+x+x^2+\cdots+x^{17}}=\dfrac{1-x^{36}}{1-x^{18}}\times \dfrac{1-x}{1-x^2}=\dfrac{1+x^{18}}{1+x}=x^{17}-x^{16}+x^{15}+\cdots-1$
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

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 :

  1. 5

  2. 7

  3. 13

  4. 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The product (n-1)! is divisible by n if n is composite and n > 4 (Wilson's Theorem related logic). For n in [12, 40], (n-1)! is not divisible by n only if n is prime. The primes between 12 and 40 are 13, 17, 19, 23, 29, 31, 37. There are 7 such numbers.