National Bank Ltd - Probationary Officer - 22.03.2013/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ For which of the following values of n is 100+n/n not an integer?

বর্ণনাঃ

এখানে নিঃশেষে বিভাজ্যতা পরীক্ষার সূত্র/নিয়ম ব্যবহার করতে হবে। 
১. দিয়ে যে কোনাে সংখ্যা বিভাজ্য। 
২. সকল জোড় সংখ্যা 2 দ্বারা বিভাজ্য। 
৩. যে সংখ্যার অঙ্কগুলাের সমষ্টি 3 দ্বারা বিভাজ্য সে সংখ্যা 3 দ্বারা বিভাজ্য। 
৪. যে সংখ্যার একক ও দশক স্থানীয় অঙ্কে গঠিত সংখ্যা 4 দ্বারা বিভাজ্য সে সংখ্যা 4 দ্বারা বিভাজ্য। 
৫. যে সংখ্যার শেষ অঙ্ক 0 অথবা 5 সে সংখ্যা 5 দ্বারা বিভাজ্য এই তথ্য জানলে সমস্যাটি মুখে মুখেই solve করা যায়।

প্রশ্নঃ Robi has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

বর্ণনাঃ

General rule for such kind of problems: to maximize one quantity, minimize the others; to minimize one quantity, maximize the others. The lowest number of pairs we can make from 7 individual socks is 3 pairs and 1 sock from a fourth pair. Hence, the greatest number of pairs of matched socks Robi can have left is 10-4=6. So the answer is (b) 6.

প্রশ্নঃ In a certain population, there are times as many people aged 21 or under as there are people over 21. The ratio of those 21 or under to the total population is :

বর্ণনাঃ

Let the number of people over 21 years be x. 
Given that the number of people aged 21 or under = 3x 
So total population = 4x 
Required ratio = 3x : 4x = 3:4 
So the answer choice is (e) 3 to 4.

প্রশ্নঃ If the sum of three consecutive integers is odd, then the first and the last integers must be -

বর্ণনাঃ

Try for 2,3,4-2 +3 +4 = 9 (9 is odd) 
Here, the First and the last integers, must be even 
You can try for such any consecutive integers.

প্রশ্নঃ Of 30 applicants for a job, 14 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree. How many of the applicants had at least 4 years experience and a degree?

বর্ণনাঃ

Process of elimination : 30-3 = 27; 27 - 14 - 18 = -5 
Then 5 are in the intersection between 4 years experience and degree.

প্রশ্নঃ A person makes a profit of 10% on 25% of the quantity and a loss of 20% on the rest. What is the percentage gain or loss on the whole?

বর্ণনাঃ

Suppose cost price = 100 Tk.
Gain on 25Tk = 2.50 Tk = Selling price = 25 +2.50 = 27.50 TK 
Loss on 75 Tk = 15 Tk Selling price = 75 - 15 = 60 Tk 
Total selling price = 60 + 27.50 = 87.50 
Loss = 100 - 87.50 = 12.50

প্রশ্নঃ If the radius of a circle is increased by 6%, then the area of the circle is increased by ---

বর্ণনাঃ

Area of circle increased by $$\begin{gathered} =r+r+\frac{r\times r}{100}=radius \\ =6+6+\frac{6\times 6}{100} \\ =12+0·63 \\ =12·36 \end{gathered}$$

প্রশ্নঃ A person invested 2/3 th of his capital 3%, 1/6th at 6% and the remainder at 12%. If his annual income is Tk. 25, then the capital is

বর্ণনাঃ

We have, $$\begin{gathered} \frac{1}{a}=\frac{2}{3},\frac{1}{b}=\frac{1}{6}, \\ \frac{1}{c}=1-\left(\frac{2}{3}+\frac{1}{6}\right)=\frac{1}{6} \\ {R}_1=3\%,R_2=6\%,R_3=12\% \\ \therefore A=25 Tk. \\ Capital=\frac{A\times 100}{{\displaystyle \frac{R_1}{a}+\frac{R_2}{b}+\frac{R_3}{c}}}=\frac{25\times 100}{{\displaystyle 3\times \frac{2}{3}+\frac{6}{6}+\frac{12}{6}}} \\ =\frac{2500}{5} \\ =500 \end{gathered}$$

প্রশ্নঃ which of the following is the value of $\sqrt{\sqrt[3]{0.000064}}$?

বর্ণনাঃ

$\sqrt{\sqrt[3]{0·000064}}=\sqrt{0·04}=0·2$

প্রশ্নঃ Morshed has d books, which is 3 times as many as Salam and 1/2 as many as Roni. How many books do the three of them have altogether, in terms of d?

বর্ণনাঃ

Morshed has d books; Salam has d/3 books; Roni has 2d books;
Total = $d+\frac{d}{3}+2d=\frac{10d}{3}$
So, answernis (c) $\frac{10}{3}d.$

প্রশ্নঃ Mr.Nazim was planning on depositing a certain amount of money each month into a college fund for his children. He then decided not to make any contributions during June and July. To make the same annual contribution that he had originally planned, by what percent should he increase his monthly deposits?

বর্ণনাঃ

Assume we conteributes 100 Tk per month, for an annual total of 1200 Tk.Seeing that he missed two months : 1200 - 1000 = 200
$$\begin{gathered} 1 have\frac{200}{1200}\times 100 \\ =16\frac{2}{3}\% \end{gathered}$$

প্রশ্নঃ In the figure above, if PQRS is a parallelogram, then y-x=?

বর্ণনাঃ

In parallelogram corresponding angles are equal and consecutive angles supplementary (supplementary angles are two angles that add up to 180°), thus : 
140 = 2y 	2y + x = 180 
y =70 		=> 140 + x = 180
                => x= 40 
Now, y - x = 70-40 = 30 
So, the answer choice is (a) 30