প্রশ্নঃ If the product of 3 different positive integers is 6, then twice the sum of the integers is ----
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There is no way of solving this problem mathematically, as no relation between the integers is given. Now, it is said the integers are positive only 1, 2, 3 is the possible combination (1×2×3 = 6). So, their sum = 1+2+3 = 6. Twice of the sum is 12.
প্রশ্নঃ 0.1+(0.1)2+(0.1)3=?
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0.1+(0.1)2+(0.1)3=0.1+0.01+0.001=0.111
প্রশ্নঃ Sum of P and Q is 72 and the value of R is 42. What is the average of P, Q and R?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
P + Q = 72; R = 42
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> P + Q + R = 72 + 42 = 114
Their average = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>114</mn><mn>3</mn></mfrac></math> = 38
প্রশ্নঃ If x+y=9 and x/y=2, then x equals to ----
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x + y = 9 and <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>y</mi></mfrac></math> = 2 or x = 2y
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mn>2</mn><mi>y</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>9</mn><mspace linebreak="newline"/><mo>⇒</mo><mn>3</mn><mi>y</mi><mo>=</mo><mn>9</mn><mspace linebreak="newline"/><mo>⇒</mo><mi>y</mi><mo>=</mo><mn>3</mn><mspace linebreak="newline"/><mo>∴</mo><mi>x</mi><mo>=</mo><mn>2</mn><mi>y</mi><mo>=</mo><mn>2</mn><mo>×</mo><mn>3</mn><mo>=</mo><mn>6</mn></math>
প্রশ্নঃ Find the largest number of apples not exceeding 1000, which can be equally divided among 6, 20, 24 boys?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
The number that would be divisible by the L.C.M of 6, 20, 24 is the correct answer option
Now, the L.C.M of 6, 20,, 24 is found.
2 6, 20, 24
3 3, 10, 12
2 1, 10, 4
1, 5, 2
So L.C.M = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><mn>3</mn><mo>×</mo><mn>2</mn><mo>×</mo><mn>5</mn><mo>×</mo><mn>2</mn><mo>=</mo><mn>120</mn></math>
Now, only 960 is divisible by 120, so 960 is the correct answer.
প্রশ্নঃ The ratio of boys to girls in a class 2/5. If 2 boys leave and 4 girls join the class, the ratio of the boys to the girls becomes 1/4. Originally, how many girls were in the class?
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Let, Originally, there were 2x boys and 5x girls in the class
Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>2</mn></mrow><mrow><mn>5</mn><mi>x</mi><mo>+</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mspace linebreak="newline"/><mo>⇒</mo><mn>4</mn><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>=</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>4</mn><mspace linebreak="newline"/><mo>⇒</mo><mn>8</mn><mi>x</mi><mo>-</mo><mn>8</mn><mo>=</mo><mn>5</mn><mi>x</mi><mo>+</mo><mn>4</mn><mspace linebreak="newline"/><mo>⇒</mo><mn>8</mn><mi>x</mi><mo>-</mo><mn>5</mn><mi>x</mi><mo>=</mo><mn>4</mn><mo>+</mo><mn>8</mn><mspace linebreak="newline"/><mo>⇒</mo><mn>3</mn><mi>x</mi><mo>=</mo><mn>12</mn><mspace linebreak="newline"/><mo>∴</mo></math> x = 4
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Originally number of girls = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>×</mo><mn>4</mn><mo>=</mo><mn>20</mn></math>
প্রশ্নঃ What annual rate was paid if Tk. 60000 earned Tk. 6000 interest in 5 years
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I= <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>p</mi><mi>n</mi><mi>r</mi></mrow><mn>100</mn></mfrac></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>r</mi><mo>=</mo><mfrac><mrow><mi>I</mi><mo>×</mo><mn>100</mn></mrow><mrow><mi>p</mi><mo>×</mo><mi>n</mi></mrow></mfrac><mspace linebreak="newline"/><mo>=</mo><mfrac><mrow><mn>6000</mn><mo>×</mo><mn>100</mn></mrow><mrow><mn>60000</mn><mo>×</mo><mn>5</mn></mrow></mfrac></math>
= 2
প্রশ্নঃ What will be the profit or loss if 4 mangoes are sold at the same price which 5 were bought?
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এ ধরনের math, যেখানে বিক্রয়ের unit ক্রয়ের unit থেকে 1 কম, সেক্ষেত্রে সবসময় লাভ হবে, এবং লাভের % = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>100</mn><mrow><mi>ব</mi><mi>ি</mi><mi>ক</mi><mi>্</mi><mi>র</mi><mi>য়</mi><mi>ে</mi><mi>র</mi><mo> </mo><mi>u</mi><mi>n</mi><mi>i</mi><mi>t</mi></mrow></mfrac><mfrac><mn>100</mn><mn>4</mn></mfrac></math> = 25%
পূর্ণ নিয়ম:
Let, the cost price of 5 mangoes is x
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>1</mn><mo> </mo><mfrac><mi>x</mi><mn>5</mn></mfrac></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>4</mn><mo> </mo><mo> </mo><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mn>5</mn></mfrac></math>
Now, selling price of 4 mangoes is x
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Profit <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>-</mo><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mn>5</mn></mfrac></mstyle></mrow><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mn>5</mn></mfrac></mstyle></mfrac><mo>×</mo><mn>100</mn><mo>%</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn><mi>x</mi><mo>-</mo><mn>4</mn><mi>x</mi></mrow><mn>5</mn></mfrac></mstyle><mstyle displaystyle="true"><mfrac><mrow><mn>4</mn><mi>x</mi></mrow><mn>5</mn></mfrac></mstyle></mfrac><mo>×</mo><mn>100</mn><mo>%</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mi>x</mi><mn>5</mn></mfrac><mo>×</mo><mfrac><mn>5</mn><mrow><mn>4</mn><mi>x</mi></mrow></mfrac><mo>×</mo><mn>100</mn><mo>%</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>×</mo><mn>100</mn><mo>%</mo><mspace linebreak="newline"/></math>
= 25%
প্রশ্নঃ What's the area of a square in square meter if its perimeter is 80?
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Side of the square = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>p</mi><mi>e</mi><mi>r</mi><mi>i</mi><mi>m</mi><mi>e</mi><mi>t</mi><mi>e</mi><mi>r</mi></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>80</mn><mn>4</mn></mfrac><mo>=</mo><mn>20</mn></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Area of the square = <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>20</mn><mn>2</mn></msup></math> = 400 sq.m
প্রশ্নঃ What is the sum of the following series? 1+2+3.........+100=?
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Sum = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>n</mi><mfenced><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mn>2</mn></mfrac></math>; here, n = 100
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>100</mn><mfenced><mrow><mn>100</mn><mo>+</mo><mn>1</mn></mrow></mfenced></mrow><mn>2</mn></mfrac><mspace linebreak="newline"/><mo>=</mo><mn>50</mn><mo>×</mo><mn>101</mn></math>
= 5050
প্রশ্নঃ In England is written as 1234526 and France as 785291, the Greece will be written as ---
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England = 1234526, so E = 1, n = 2, g = 3, 1 = 4, a = 5, d = 6
France = 785291, so f = 7 r = 8, c = 9
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Greece = 381191
[পরীক্ষার হলে, খেয়াল করুন Greece এ মাঝে তিনটি E আছে England এর E = 1 এবং France এর E ও 1 so Greece এর তিনটি E তে 1 আছে যেটিতে সেই Option টিই সঠিক, একমাত্র C অপশনটিতেই এটি করা হয়েছে। ]
প্রশ্নঃ six persons A, B, C, D, E and F are standing in a circle. B is between D and C. A is between E and C. F is to the right of D. who is between A and F?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
The sequence is : <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>→</mo><mi>B</mi><mo>→</mo><mi>C</mi><mo>→</mo><mi>A</mi><mo>→</mo><mi>E</mi><mo>→</mo><mi>F</mi><mo>.</mo></math>
প্রশ্নঃ What is the missing letter in the series of D H L R ---?
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The letters are arraned this way :
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mi>C</mi><mo>→</mo><mi>D</mi><mo>,</mo><mo> </mo><mi>E</mi><mi>F</mi><mi>G</mi><mo>→</mo><mi>H</mi><mo>,</mo><mo> </mo><mi>I</mi><mi>J</mi><mi>K</mi><mo>→</mo><mi>L</mi></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>N</mi><mi>O</mi><mi>P</mi><mi>Q</mi><mo>→</mo><mi>R</mi><mo>,</mo><mo> </mo><mo>∴</mo><mo> </mo><mi>S</mi><mi>T</mi><mi>U</mi><mi>V</mi><mi>W</mi><mo>→</mo><mi>X</mi></math>
প্রশ্নঃ If SUMMER is coded as RUNNER, the code for WINTER will be ----
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
S of SUMMER is replaced by the previous letter of S which is R. U is kept unchanged. MM is repalaced by the letter following M which is N.ER is kept unchanged.
W of WINTER is replaced by the letter of W which is V.
I is kept unchanged. N and T is replaced by the letter following N and T which are O and U, ER is kept unchnged. So we ge VIOUER
প্রশ্নঃ What is the difference between the salesperson of company A and B in 2015?
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NO correct answer is given. Correct answer is 20 - 15 = 5.
প্রশ্নঃ What is the percentage change in the profit per salesperson in 2015 over 2014 in case of company B?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
For company B:
2014 Profit/salesperson = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>25</mn><mn>10</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn></math>
2015 " " = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>50</mn><mn>20</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn></math>
So no change.
প্রশ্নঃ What is the growth rate in sales of company B in 2015 over 2014?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
For company B: growth rate in sales = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>600</mn><mo>-</mo><mn>200</mn></mrow><mn>200</mn></mfrac><mo>×</mo><mn>100</mn><mo>%</mo></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>400</mn><mn>200</mn></mfrac><mo>×</mo><mn>100</mn><mo>%</mo></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>200</mn><mo>%</mo></math>
প্রশ্নঃ What is the difference between the growth rate of salesperson in 2015 over 2014 of the company?
Best One ব্যাখ্যা যোগ করুন।বর্ণনাঃ
For A: growth rate of salesperson = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>15</mn><mo>-</mo><mn>10</mn></mrow><mn>10</mn></mfrac><mo>×</mo><mn>100</mn><mo>%</mo></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>5</mn><mn>100</mn></mfrac><mo>×</mo><mn>100</mn><mo>%</mo></math>
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>50</mn><mo>%</mo></math>
For B : growth rate of salesperson = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>20</mn><mo>-</mo><mn>10</mn></mrow><mn>10</mn></mfrac><mo>×</mo><mn>100</mn><mo>%</mo></math>
= 100%
<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Their difference = (100-50)% = 50%
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