Tag: multiplication of numbers

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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

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

  1. $45049$
  2. $40149$
  3. $45149$
  4. $45249$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the sum of natural numbers between 200 and 500 that are multiples of 7, 3, or both, we use the principle of inclusion-exclusion. Calculate the sum of multiples of 3 plus the sum of multiples of 7, minus the sum of their least common multiple multiples (21), within the specified range, yielding 45149.

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.