Tag: division trick

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Multiple choice maths multiply and divide division trick division division of numbers

How many rational numbers exist between any two distinct rational numbers?

  1. 2

  2. 3

  3. 11

  4. Infinite number of rational numbers
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of $\frac { p }{ q } $ where p and q are integers and q $\neq $0.

Multiple choice maths multiply and divide division trick division division of numbers

If $n=2^3\times 3^4\times 7\times15^6$, then find the number of consecutive zeros in natural number n

  1. 6

  2. 3

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Consecutive zeros are formed by factors of 10 (2 * 5). n = 2^3 * 3^4 * 7 * (3*5)^6 = 2^3 * 3^10 * 7 * 5^6. The number of pairs of (2, 5) is min(3, 6) = 3.

Multiple choice maths multiply and divide division trick division division of numbers

State whether the statement is true or false.
$ \displaystyle \frac{4}{-9}   $ and $ \displaystyle \frac{-16}{36}   $ represent the same rational number?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Yes beacause
$ \displaystyle \frac{4}{-9}   $=$ \displaystyle \frac{4\times (-4)}{9\times(-4)}   $= $ \displaystyle \frac{-16}{36}   $ 


or $ \displaystyle \frac{-16}{36}   $= $ \displaystyle \frac{-16\div -4}{36\div -4}   $ =$ \displaystyle \frac{4}{-9}   $

Multiple choice maths multiply and divide division trick division division of numbers

Solve it 
$\dfrac {\left( {{{\left( {245 + 232} \right)}^2} - {{\left( {245 - 232} \right)}^2}} \right)}{\left( {245 + 232} \right)}$

  1. $4$
  2. $2$
  3. $232$

  4. none of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$=\dfrac{{\left(245+232\right)}^{2}-{\left(245-232\right)}^{2}}{\left(245+232\right)}$
$=\dfrac{\left(245+232-245+232\right)\left(245+232+245-232\right)}{\left(245+232\right)}$
$=\dfrac{2\left(232\right)2\left(245\right)}{\left(245+232\right)}$
$=\dfrac{2,27,360‬}{477}=476.65$
Multiple choice maths multiply and divide division trick division division of numbers

Let $Q = \dfrac{x}{y}$ where $x$ and $y$ are real numbers. If both $x$ and $y$ are increased equally then

  1. $Q$ will increase
  2. $Q$ will decrease
  3. $Q$ will remain the same

  4. none of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If x/y = 1, adding 1 to both gives 2/2 = 1 (no change). If x/y < 1, adding a constant increases the ratio. If x/y > 1, adding a constant decreases the ratio. No single outcome is universal.

Multiple choice maths multiply and divide division trick division division of numbers

The value of $0.\bar { 1 } +0.0\bar { 1 } +0.00\bar { 1 } $ is equal to 

  1. $\dfrac{407}{3300}$
  2. $\dfrac { 37 }{ 3000 } $
  3. $\dfrac { 4 }{ 3300 } $
  4. $\dfrac { 1343 }{ 10989 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$0.\bar{1}+0.0\bar{1}+0.00\bar{1}$

Let $x=0.11111...+0.01111...+0.00111....$

$\Rightarrow x=0.12333...$

$\therefore x=0.123333...$

$\Rightarrow 100x=12.333...$

$\Rightarrow 100x-x=12.333333...-0.123333...$

$\Rightarrow 99x=12.210000....$

$\Rightarrow 99x=12.21$

$\Rightarrow x=\dfrac{12.21}{99}$

$\Rightarrow x=\dfrac{1221}{9900}$

$\therefore x=\dfrac{407}{3300}$
Multiple choice maths multiply and divide division trick division division of numbers

 $\displaystyle \frac{3x}{2}-\frac{x}{4}=2$. Find value of x

  1. $2$
  2. $\dfrac85$
  3. $4$
  4. $\dfrac45$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\cfrac { 3x }{ 2 } -\cfrac { x }{ 4 } =2$
$\cfrac { 6x-x }{ 4 } =2$
$\cfrac { 5x }{ 4 } =2$
$x=\cfrac { 4 }{ 5 } \times 2=\cfrac { 8 }{ 5 } $