BANGLADESH BANK (ASSISTANT DIRECTOR) TEST-2009

Problem 01 Consider the following series: 3, 4, 6, 9, 13, --------------- what comes next?(a)15 (b)16 (c)17 (d)18 (e)19

Problem 02 Which of the following is the least like the others?(a)cube (b)sphere (c)pyramid (d)circle (e)none

Problem 03 A farmer had 20 hens. All but 2 died. How many hens are still alive?(a)2 (b)10 (c)15 (d)18 (e)20

Problem 04 A red house is built from red bricks. A blue house is built from blue brick. A white house is built from white bricks. Then what is a green house made from?(a)green bricks (b)wood (c)glass (d)steel (e)none

Problem 05 The hour hand of an analog clock move 1/6th of the degree every minute. Then how many degrees will the hour hand move in one hour?(a) 1degree (b) 2degree (c) 3degree (d) 4degree (e) 5degree

Problem 06 Susan can type 10 pages in 5 minutes. Mary can type 5 pages in 10 minutes. Working together, how many pages can they type in 30 minutes?(a)15 (b)20 (c)25 (d)65 (e)75

Problem 07 Quantity A equal to time to travel 95 miles in 50 miles per hour and quantity B equal to time to travel 125 miles at 60 miles per hour.(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 08 In a class composed of x girls and y boys .What part of the class is composed of girls?(a) y/(x+y) (b) x/xy (c) x/(x+y) (d)y/xy (e)none

Problem 09 r>s>0;Quantity A = rs/r & Quantity B = rs/s(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 10 What is the maximum number of half-pint bottles of cream that can can be filled with a 4-gallon can of cream(2pt.=1at.& 4 qt.=1 gal)(a)16 (b)24 (c)30 (d)64 (e)none

Problem 11 There are 200 questions on a 3 hour examination. Among these questions 50 are mathematics problems. It is suggested that twice as much time be spent on each math problem as for each other question. How many minutes should be spent on mathematics problem?(a)36 (b)72 (c)60 (d)100 (e)none

Problem 12 x = 2y +3 & y = -2;quantity A = x and quantity B = -1(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 13 In a group of 15, 7 have studied Latin, 8 have studied Greek and 3 have not studied either. How many of these studied both Latin and Greek?(a)0 (b)3 (c)4 (d)5 (e)none

Problem 14 Your doctor gives you 3 pills to take one for every half hour. How long does it require to take all the pills?(a) half hour (b)one hour (c)one & half hour (d)two hours (e)none

Problem 15 A is the widow of B; B & C were the only children of E.C is unmarried and is a doctor. D is the grand-daughter of E and studies science. How is A related to D?(a)aunt (b)daughter (c)sister (d)sister-in-law (e)none

Problem 16 If a & b are positive integers and (a-b)/33.5 = 4/7 then

(a)b<a (b)b>a (c)b=a (d)b>=a (e)noneProblem 17 If the operation ^ is defined by the equation x^y = 2x +y then what is the value of a if 2^a = a^3

(a)0 (b)1 (c)-1 (d)4 (e)noneProblem 18 Which of the following fractions has the smallest value?

(a)8/7 (b)10/9 (c)21/20 (d)31/30 (e)noneProblem 19 M men agree to purchase a gift for Taka D. If three men drop out how much more will each

have to contribute towards the purchase of the gift?(a)D/(m-3) (b)MD/3 (c)M/(D-3) (d)3D/(m2-3m) (e)none

Problem 20 If the sum of 3 consecutive integers is 240,then the sum of the two larger integers is:(a)79 (b)159 (c)169 (d)161 (e)none

Problem 21 2/ (a-b) -5/ (b-a) =?Problem 22 Quantity A = (-6)4 and quantity B = (-6)5

(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 23 ½ × ¾ × 8/4 ÷ 8/2 × ½ =?(a)3/32 (b)3/8 (c) 3/2 (d)1/2 (e)3/20

Problem 24 Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $40.They got a bill for $104 and decided to give a tip of $16.They further decided to share the total expense in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is----(a)120 (b)200 (c)60 (d)24 (e)36

Problem 25 After 3 semesters in college, Jim has a 3.0 GPA. What GPA must Jim attain in his fourth semester if he wishes to raise his GPA to a 3.1?(a)2.7 (b)3.1 (c) 3.3 (d)3.4 (e)3.5

Problem 26 If the length and width of a rectangular garden plot were each increased by increased by 20%, what would be the percent increase in the area of the plot?(a)44% (b)24% (c)36% (d)40% (e)none

Problem 27 If b<2 & 2x – 3b = 0, which of the following must be true?(a) x> -3 (b)x<2 (c) x =3 (d) x<3 (e)x>3

Problem 28 If 3/p =6 and 3/q =15 then p-q =?(a)1/3 (b)2/5 (c) 3/10 (d)5/6 (e)none

Problem 29 The average of 5 quantities is 6.The average of 3 of them is 8.What is the average of the remaining two numbers?(a)6.5 (b)4 (c) 3 (d)3.5 (e)none

Problem 30 A father is three times as old as his son. After 15 years the father will be twice as old as his son’s age at that time. Hence the father’s present age is-(a)36 (b)42 (c) 45 (d)48 (e)none

Problem 31 If x = -1, then –(x4 + x3 + x2 + x) =?(a)-10 (b)-4 (c) 0 (d)4 (e)10

Problem 32 A rectangle is 14cm long and 10cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square, then its area changes by :(a)4 (b)144 (c) 12 (d)2 (e)none

Problem 33 Which of the following equations is not equivalent to 25x2 = y2-4.(a)25x2 +4 = y2 (b)75x2 = 3y2 -12 (c) 25x2 = (y+2)(y-2) (d)5x = y-2 (e) none

Problem 34 Quantity A = 1 – 1/27 & Quantity B = 8/9 + 1/81

(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 35 A Zoo keeper counted the heads of the animals in a zoo and found it to be 80.When he counted the legs of the animals he found it to be 260.If the zoo had either pigeons or horses, how many horses were there in the zoo?(a)40 (b)30 (c) 50 (d)60 (e)none

Problem 36 When a student weighing 45kgs left a class, the average weight of the remaining 59 students increased by 200g.What is the average weight of the remaining 59 students?(a)57kgs (b)56.8kgs (c) 58.2kgs (d)52.2kgs (e)none

Problem 37 The average temperature on Wednesday, Thursday and Friday was 250C.The average temperature on Thursday, Friday and Saturday was 240C.If the temperature on Saturday was 270C, what was the temperature on Wednesday?(a)240C (b)210C (c) 270C (d)300C (e)none

Problem 38 If 18 is 15% of 30% of a certain number, what is the number?(a)9 (b)26 (c) 40 (d)81 (e)400

Problem 39 Quantity A = (9/13)2 and Quantity B = (9/13)1/2

(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 40 Average cost of 5 apples and 4 mangoes is 36 taka. The average cost of 7 apples and 8 mangoes is 48 taka. Find total cost of 24 apples and 24 mangoes.(a)1044 (b)2088 (c) 720 (d)324 (e)none

Problem 41 If n and p are both odd numbers, which of the must be an even number?(a)np +2 (b)n+p (c) n+p+1(d)np (e)none

Problem 42 The present ages of A and B are in the ratio 6:4.Five years ago their ages were in the ratio 5:3.Find their present ages.(a)42,28 (b)36,24 (c) 30,20 (d)25,15 (e)none

Problem 43 3.003/2.002 =?(a)1.05 (b)1.50015 (c) 1.501 (d)1.5015 (e)1.5

Problem 44 A predator is chasing its prey. The predator takes 4 leaps for every 6 leaps of the prey and the predator covers as much distance in 2 leaps as 3 leaps of the prey. Will the predator succeed in getting its food?(a)yes (b)in the 6th leap (c) never (d)can’t be determined (e)none

Problem 45 Quantity A = 4/100 and Quantity B = 0.012/3(a)Quantity A is greater (b) Quantity B is greater (c) Quantity A is equal to quantity B (d)Relationship indeterminate (e)None

Problem 46 If u>t,r>q,s>t,t>r;which of the following must be true?I.u>s II.s>q III.u>r(a)I only (b)II only (c) III only (d)I & II only (e)II & III only

Problem 47 Three math classes X, Y, Z take an algebra test. The average score in the class X is 83.The average score in class Y is 76.The average score in class Z is 85.The average score of all students in classes X and Y together is 79.The average score of all students in classes Y and Z together is 81.What is the average for all the three classes?(a)81 (b)81.5 (c) 82 (d)84.5 (e)none

Problem 48 Hasan sold an article for 56taka which cost him x taka. If he had gained x% on his outlay, what was his cost?(a)40 taka (b)45 taka (c) 36 taka (d)25 taka (e)none

Written Math

Problem 49 A boy purchased some chocolates from a shop for Tk. 120.In the next shop he found that the price per piece of chocolate is Tk.3 less than that charged at the previous shop and as such he could have purchased 2 more chocolates. How many chocolates did he buy from the first shop?

Problem 50 A loss of 15% is incurred by selling a watch for Tk.612.How much is the sum of money by which it is sold to make a profit of 10%?

Problem 51 Recently Mr. Kamal’s hourly wage has been increased by 10%.Before this increase, Kamal’s total weekly wage was Taka 137.If his weekly working hours were to decrease by 10% from last week’s total working hours, what would be the change, if any, in Kamal’s total weekly wage?

BANGLADESH BANK (ASSISTANT DIRECTOR) TEST-2008

Problem 52 When an object is sold for Tk.250, the seller makes 25% profit. What is the cost price of the object?(a)Tk.200 (b)Tk.180 (c) Tk.220 (d)Tk.160 (e)none

Problem 53 The selling price of 8 apples is equal to the purchase price of 10 apples? What is the profit margin?(a)20% (b)15% (c) 10% (d)12% (e)25%

Problem 54 What annual rate of interest was paid if Tk.60, 000 earned Tk.6000 in interest in 5 years?(a)3% (b)5% (c) 6% (d)2% (e)4%

Problem 55Problem 56Problem 57Problem 58Problem 59Problem 60Problem 61Problem 62Problem 63Problem 64Problem 65Problem 66Problem 67Problem 68Problem 69Problem 70Problem 71Problem 72Problem 73

Problem 74Problem 75Problem 76Problem 77Problem 78Problem 79Problem 80Problem 81Problem 82Problem 83Problem 84Problem 85Problem 86Problem 87Problem 88Problem 89Problem 90Problem 03Problem 04Problem 05Problem 06Problem 07Problem 08

1. Relative Speed ( SR):a) When two objects are running in the same direction-i.e if their speeds are x & y & if x > y then

SR = x -yb) When two objects are running in the opposite direction-i.e. if their speeds are x & y then

SR = x + yProblem 01 Two trains running on the same track travel at the rates of 25 mph and 30 mph. If the slower

train starts an hour earlier, how long will it take the second train to catch up with it?Problem 02 Two ships 1550 miles apart are sailing towards each other. One sails at the rate of 85 miles

per day and the other at the rate of 65 miles per day. How far apart will they be at the end of 9 days?

Problem 03 A and B are walking towards each other over a road 120 miles long. A walks at a rate of 6 mph, and B walks at a rate of 4 mph .How soon will they meet ?

Problem 04 A train 110 m long is running at 60 km/hr. In what time will it pass a man, running in the direction opposite to that of the train at 6 km/hr?

Problem 05 Two trains 128m & 132m long are running towards each other on parallel lines at 42 km/hr and 30 km/hr respectively. In what time will they be clear of each other from the moment they meet?

Problem 06 Two trains are moving in the same direction at 50 km/hr and 30 km/hr. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train.

Problem 07 A man sitting in a train, which is traveling at 50 km/hr, observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 150m long, find its speed.

Problem 08Problem 09

Math lesson: 05: Percent

Formulae:

1. For getting an advantage for quick solving percent (%) problems –knowledge of percent & fraction relationship is required :

Percent Fraction Percent Fraction Percent Fraction Percent Fraction121/2 % 1/8 162/3 % 1/6 20% 1/5 25% 1/4

25% 2/8 331/3% 2/6 40% 2/5 50% 2/4371/2% 3/8 50% 3/6 60% 3/5 75% 3/450% 4/8 662/3% 4/6 80% 4/5 100% 4/4621/2% 5/8 831/3% 5/6 100% 5/575% 6/8 100% 6/6871/2% 7/8100% 8/8

Problem 01 How many sixteenths are there in 871/2%?Problem 02 What is the value of n alter it has been decreased by 162/3%?Problem 03 20 is 331/3% of what number?Problem 04 Find 121/2 % of 96.

2. % increase = (actual increase/original)*100%3. % decrease = (actual decrease/original)*100%4. Simple interest :

a. I = (PRT)/100b. P = (100I)/(RT)c. R = (100I)/(PT)d. T = (100I)/(PR)

Where I = total interest P = principal R = rate of interest T = time in years

Problem 01 An amount deposited for six months at an interest rate of 8% per Nahum yields TK.17.00 as interest. Then what is the amount deposited?

Problem 02 What is the total interest on TK.8000.00 at 12.5% per annum for 9 months?Problem 03 A borrower pays 8% interest/year on the first TK.600.00 he borrows and 7% per year on the

part of the loan in excess of TK.600.00.How much interest Hill the borrower pays on a loan of TK.6000.00 for 1 year?

Problem 04 The rate of interest on a sum of money is 4% per annum for the first 2 years, 6% per annum for the next 4 years and 8% per annum for the period beyond 6 years .If the simple interest accrued by the sum for a total period of 9 years is TK.1120, what is the sum?

5. Compound interest : C = P (1 + r) n

Where C = cumulative amount P = principal r = R/100 n = time in years

6. Compound interest :

C = P (1 + r/m) nm

Where C = cumulative amount P = principal r = R/100 n = time in years m = no of compounding per year

Problem 01 The population of a certain town increases by 50% every 50 years. If the population in 1950 was 810, in what year was the population 160?

Problem 02 Find compound interest on TK.50000 at 16% per annum for 2 years, compounded annually.Problem 03 If the compound interest on a sum of money for 3 years at 10% per year be TK.993, what

would be the simple interest?Problem 04 Find compound interest on TK.100000 at 20% per annum for 2 years 3 months, compounded

annually.Problem 05 Find compound interest on TK.51200 at 15% per annum for 9 months, compounded

quarterly.Problem 06 The value of a machine depreciates every year at the rate of 10% on its value at the beginning

of that year. If the present value of the machine is TK.729, its worth 3 years ago was?Problem 07 Suppose ,you deposit TK.1000 into a bank account which pays a simple interest of 7%.After

a year you empty the bank account, and then take the principal and interest and invest it back into the same account again. Then how much interest will you get in two years?

Problem 08 Frodo invested TK.2000 at 9.5% annual interest rate compounded yearly for 3 years in Bank Alfalfa. Calculate the amount of interest that Frodo would earn by the end of the three years period.

Problem 09 Noa deposited $100 into a saving account that pays an annual compounded interest 2 years ago. At the end of the period, Noa earned $25 as total interest. Find the annual interest rate for Nao’s account.

Problem 10 How long would TK.10000 have to be invested at 2.5%, compounded annually, to amount to TK.12000?

Problem 11 Lucy deposits $700 into a saving account that pays 5% interest rate per annum compounded annually. How many years must Lucy keep her money in that saving account if she wants to earn at least $200 in interest?

Problem 12 Maria has $900 in her saving account that pays 5% interest rate per annum compounded monthly after 48 months. How much did she have to invest as principal? Give your answer to the nearest dollar ($).

Problem 13 A country’s population is increasing by 2.5% per year. If the current population is 43 million, how many more people will there be in that country in two years’ time?

Problem 14 What will TK.1500 amount to three years if it is invested in 20% p.a. compound interest, interest being compounded annually?

Problem 15 The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down line, if the rate of growth of population has been constant over the years and has been compounded annually?

7. Box method : If two pairs of information are given in the % problems then the problems can be solved in the box method :

# Column 1 Column 2 TotalRow 1Row 2Total 100

You can choose any pair in the row/column

Problem 01 In each production lot for a certain toy, 25% of the toys are red and 75% of the toys are blue. Half the toys are size A and half are size B. If out of a lot of 100 toys are red and size A, how many of the toys are blue and size B?

Problem 02 In the Excel Manufacturing Company, 46% of the employees are men. If 60% of the employees are unionized and 70% of these are men. What % of the non-unionized workers are women?

Problem 03 A shipment of banners contains banners of two different shapes, triangular and square, two different colors, red and green. In a particular shipment 26% of the banners are square and 35% of the banners are red. If 60% of the red banners in the shipment are square, what is the ratio of red triangular banners to green triangular banners?

Problem 04 At a certain party attended by 32 people.24 of them was students .If 12 of those in attendance were women and if 6 of the women in attendance were students. Then how many of the men who attended the party were not students?

Problem 05 At a club 70% of the members are women and 60% of the members are married. If 2/3 of the men are single, what fraction of the women is married?

Problem 06 In a class of 80 students, 25% are girls. If 10% of the boys and 20% of the girls attended a picnic. What percent of the class attended the picnic?

Problem 07 If 40% of all women are voters and 52% of the populations are women, what percent of the population are women voters?

Problem 08 In a club 60% of the members are male and 70% are engineers. If 50% of the engineers are male, then what percent of the club members are female and not engineers?

8. When one % change occurs due to change in two different % changes then this types of problems can be solved by the following formula :

p + q + pq/100be careful in using this formula that you are to use (+) for increment & (-) for decrement.

Problem 01 If the width of a rectangle is increased by 10% and the length is increased by 40%, by what % is the area of the rectangle increased?

Problem 02 Successive discount of 20% and 15% are equal to a single discount of what %?

Problem 03 The price of a television set is discounted by 10%, and the reduced price is then discounted by 10%.The series of successive discounts is equivalent to a single discount of what %?

Problem 04 In redesigning a warehouse, the length is increased by 20%, the breadth is decreased by 40% & the height is decreased by 25%.What is the net increase in the volume of the redesigned warehouse compared to the previous design?

Problem 05 If the assessed value of a piece of property is increased by 25% while the tax rate is decreased by 25%, what is the net effect on the taxes on the property?

Problem 06 The number of passengers on Dhaka-Rongpur route increased by 35% when the fare was reduced by 15%.What will be the percentage increase in revenue?

Problem 07 The number of passengers on Dhaka-Rongpur route increased by 35% when the fare was reduced by 15%.What will be the percentage increase in revenue?

Problem 08 The price of oil is increased by 25%.Then the price again increased by x%. The net effect was the 30% increase of price from the original. What is x?

Problem 09Problem 10

9. Unchanged condition: i) if some system increases and you are to decrease the system in such a way that the system remains the same.

ii) if some system decreases and you are to increase the system in such a way that the system remains the same.

Problem 01 Price of paper has increased by 20%.How much paper usage in % must be curtailed so that expenditure for paper remains the same?

Problem 02 A man intends to run a certain distance in ¼ less time than he usually takes. By what % must he increase his running speed to accomplish this goal?

Problem 03 The length of a rectangle is increased by 60%.By what % would the width have to be decreased to maintain the same area?

Problem 04 Due booming business, a company increased its staff salary by 25%.By what % must it now decrease the salary to return to the original amount?

Math lesson: 06: Permutation & Combination

Formulae:1. Permutation :Let us consider 03 items a,b,c-we can arrange 02 items out of 03 in the following ways :

ab,ba,bc,cb,ca,ac 06 ways ; i.e, when we give importance to the orientation –this is called permutation.

2. Combination :Let us consider 03 items a,b,c-we can arrange 02 items out of 03 in the following ways :

ab or ba bc or cb ca or ac

3. How do we understand that an arrangement is a permutation or combination? Group, team, committee indicate combination Otherwise indicate permutation

4. Notation :For permutation: nPr = n! / (n-r)!In the above example: n = 3, r = 2; 3P2 = 3! / (3-2)! = (3*2*1)/ (1) = 6/1 = 6In the short-cut system: 3P2 = (3) (2) = 6

5. Notation :For combination: nCr = n! / ((n-r)!*r!)In the above example: n = 3, r = 2; 3C2 = 3! / ((3-2)!*2!)= (3*2*1)/ ((1) (1*2)) = 6/2 = 3In the short-cut system: 3C2 = 3P2 /2! = (3*2)/ (1*2) = 6/2 = 3

Problem 01 How many different committees can be chosen out of 5 persons in a group so that one particular person is always chosen?

Problem 02 In how many different ways can 6 people arrange themselves in a row of 6 seats if 2 people insist on sitting in an end seat?

Club A has 20 members and Club B has 28.If a total of 42 people belong to the two clubs, how many people belong to both clubs?Problem 02Problem 03

A singer has memorized 12 different songs. If every time he performs he sings any three of these songs, how many different performances can he give?

03 ways; i.e, when we donot give importance to the orientation –this is called combination.

If 75% of a class answered the first question on a certain test correctly, 55% answered the second question on the test correctly and 20% answered neither of the questions correctly, what % answered both correctly?Problem 03In examination 70% students passed in English and 65% passed in Mathematics, 27% of the students failed in both subjects. If only 248 students passed in both subjects, what was the total number of students appearing at the examination?Problem 04In a certain shipment of 120 new cars, 2/3 of the equipped with radios and 2/5 are equipped with air conditioners. If 20 of the cars are equipped neither a radio nor with an air conditioner, how many cars in the shipment are equipped with both a radio and an air conditioner?Problem 05In a group of 15 married couples, 16 people have brown hair and blue eyes and 9 people have both brown hair and blue eyes. How many people have neither brown hair nor blue eyes?

a. For double overlap system : n(AUBUC) = n(A) + n(B) + n(C) – n(A ∩ B)-n(B∩ C) –n(C ∩ A) + n ( A ∩ B∩ C )

= 1’s – 2’s + 3’sHere 1’s = n (A) + n (B) + n(C) 2’s = n (A ∩ B) + n (B∩ C) + n(C ∩ A) 3’s = n (A ∩ B∩ C)

n(AUBUC) = total circle valuen(AUBUC) + n (out of circle) = total

Problem 01

Club Number of studentsChess 40Drama 30Math 25

The table above shows the number of students in three clubs at McAuliffe school. Although no student is in al three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

Problem 02 20% of the families in Dhaka city have a car, 30% have a refrigerator and 40% have a TV set. Again 10% have a car and a refrigerator, 15% have a refrigerator and a TV and 8% have a car and TV, 5% of the families have all three items.What % of families have none of the three items?

Problem 03 At Milltown High School 315 girls play at least one varsity sport; 100 play a fall sport, 150 play a winter sport, and 200 play a spring sport. If 75 girls play exactly two sports, how many play three?

2. Mixture : two types :

Dry mixtureProblem 01 How many pounds of nuts selling for 70 cents per pound must he mix with 30 pounds of nuts

Dry mixture

Wet mixture

Mixture of two types of tea. Example: 5Kg tea @ TK.300.00 per Kg is mixed with 10 Kg @ TK.250.00 per Kg.

Mixture of two concentration alcohols. Example: 5 litre 50% alcohol is mixed with 10 litre 80% alcohol.5Kg tea @ TK.300.00 per Kg

Sum of all terms

selling at 90 cents per pound to make a mixture which sells for 85 cents per pound?Problem 02 A dealer mixes a lbs. of nuts worth b cents per pound with c lbs. of nuts worth d cents per

pound .At what price should he sell a pound of the mixture if he wishes to make a profit of 10 cents per pound?

Wet mixture Cross method: consider 02 persons are carrying a palki (one person:P1 :P2 other person). Who will carry higher load & lower load? Certainly the person who is closer to the palki (resultant load) will carry higher load & the person who is

far away to the palki (resultant load) will carry lower load.Example:

90 %(?)50 %( 3litre)

60-50 = 10 90-60 = 30

60%

3 1

Therefore quantity of 90% liquid = 1 litre.

Problem 01 How many quarts of pure alcohol must be added to 15 quarts of a solution which is 40% alcohol to strengthen it to a solution which is 50% alcohol?

Problem 02 Barbara invests $2400 in the security National Bank at 5%.How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

Problem 03 How many quarts of a 90% solution of alcohol should be mixed with a 75% solution of alcohol in order to make 20 quarts of 78% solution?

Problem 04 How many ounces of pure acid must be added to 20 ounces of a solution that is 5% acid to strengthen it to a solution that is 24% acid?

Problem 05 How much alcohol, in pints, must be added to 80 pints of a solution of alcohol and iodine that is 20% iodine, in order to produce a 15% solution of iodine?

Math lesson: 03: Basic ArithmeticConceptual terms:

1. Integers : Whole numbers Positive or negative ------------- -3,-2,-1,0,1,2,3 ------------------ Odd numbers(1,3,5,7--------------)/even numbers(2,4,6,8-----------------)

2. Prime numbers :

Any whole number which is divisible by 1 and itself Total prime numbers from 1 to 100 is =25

4422322321 =25 (sum of all the digits =25)Explanation: from 1 to 10 prime nos = 4

11 to 20 prime nos = 4 & so on. Test whether a number is a prime number or not :Consider a number 329 you are to test whether this number is a prime number or not Find an approximate square root of 329 say √329=18 Now up to 18 the prime numbers are : 2,35,7,11,13,17 329 is not divisible by 2,35,7,11,13,17 So 329 is a prime number

3. Digits: 0, 1, 2-----------9: there are ten digits.4. Distinct: which are not same 3, 2 are distinct numbers but 4,4are not distinct numbers.5. Reciprocal :(x)(1/x) = 1 ; 1/x is the reciprocal of x 6. Number line: when numbers are arranged on a line this is the number line.7. Absolute value: is the magnitude of any number always positive of any nonzero number.8. Test of divisibility :

A number is divisible by Check to see2 It is even3 Sum of the digits is divisible by 34 Number formed by last two digits is divisible by 45 End in 5 or 06 Even & sum of its digits is divisible by 38 Number formed by last three digits by 89 Sum of digits is divisible by 910 Ends in 011 Difference of (sum of even places digits) & (sum of odd places digits) is

divisible by 11

9. Factors & multiple : Factors of 6 = 1,2,3,6

So number is divisible by factors Multiples of 6 = 6×1, 6×2, 6×3, 6×4------------ etc

So multiples are divisible by the number.

10. Fraction =

Fractions are three types Proper fraction : Numerator < Denominator ; example : 3/5 Improper fraction : Numerator > Denominator ; example : 5/3 Mixed number : integer + proper fraction ; example : 12/3 ( here 1 = integer , 2/3 = proper fraction) Equivalent fraction : 2/3 = 20/30 = 4/6

Denominator

Numerator

Reducing fraction : 20/30 = 2/3 Squares of fractions : * for proper fraction : PF

2 < PF ; example : (2/3)2 < 2/3 * for improper fraction : IPF

2 > IPF ; example : (3/2)2 >3/2

Problem 01 Find the unit’s digit in the product (256 × 27 × 159 × 182).Problem 02 Find the unit’s digit in the product (367 × 639 × 753).Problem 03 If n is any positive integer, then (34n – 43n) is always divisible by?Problem 04 -1 ≤ x ≤ 2 & 1 ≤ y ≤ 3; least possible value of (2y – 3x) =?Problem 05 The number 0.01 is how many times as great as the number (0.0001)2?Problem 06 32a+b = 16a+2b, then a = ?Problem 03 On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37.Find the

divisor.What least number must be subtracted from 2000 to get a number exactly divisible by 17?Find the number which is nearest to 3105 & exactly divisible by 21?A number when divided by 342 gives a remainder 47.When the same number is divided by 19, what would be the remainder?

Problem 07 A 3-digit number 4a3 is added to another 3-digit number 984 to give the 4 digit number 13b7, which is divisible by 11. (a + b ) = ?

Problem 08 If x & y are the 2 digits of the number 653xy such that this number is divisible by 80, then x + y =?

Problem 09Problem 10

Math lesson: 02: Ratio & ProportionConceptual terms:

1. Ratio : the ratio of two quantities in the same units is a fraction that one quantity is of the other a to b is a ratio (a/b) , written as a : b a = antecedent, b = consequent 2/3 = (2*4)/ (3*4) = 8/12 when both numerator & denominator are multiplied by the

same number the ratio will be same. 20/30 = (20 ÷ 10)/ (30÷10) = 2/3 when both numerator & denominator are divided by

the same number the ratio will be same.

2. Proportion: the equality of two ratios is called proportion. example : 2 : 3 = 8 : 12

Problem 01 The prices of a washing machine and a television set are in the ratio 3:2. If a washing machine costs TK.6000 more than the television set, the price of the television set is?

Problem 02 The students in three classes are in the ratio 2:3:5.If 20 students are increased in each class, the ratio changes to 4:5:7.The total number of students before the increase was?

Problem 03 TK.1050 is divided among P, Q & R .The share of P is 2/5th of the combined share of Q & R.

Find the share of P?Problem 04 The speeds of 3 cars are in the ratio 3:4:5.The ratio between times taken by them to travel the

same distance is? Problem 05 In a mixture of 60 liters, the ratio of milk and water is 2:1.What amount of water must be

added to make the ratio 1:2?Problem 06 Average age of 3 girls is 20 years and their ages are in the proportion 3:5:7.The age of the

youngest girl is?Problem 07 1 year ago the ratio between A’s & B’s salary was 3:4.Ratios of their individual salaries

between last year’s & this year’s salaries are 4:5 & 2:3 respectively. At present the total of their salary is TK.4160.The salary of A now is?

Problem 08 In a mixture of 60 liters, the ratio of milk and water is 2:1.If the ratio of the milk and water is to be 1:2, and then the amount of water to be further added is?

Problem 09 The ratio of milk and water in 66kg of adulterated rated milk is 5:1.Water is added to it to make the ratio 5:3.The quantity of water added is?

Problem 10 A can is filled with a mixture of two liquids A & B in the proportion 7:5.When 9 liters of the mixture are drawn off and the can is filled with B, the proportion of A & B becomes 7:9.How many liters of liquid A were contained by the can initially?

Problem 11 Equal amounts of water were poured into two empty jars of different capacities, which made one jar ¼ full and the other jar 1/3 full. If the water in the jar with the lesser capacity is then poured into the jar with the greater capacity. What fraction of the larger jar will be filled with water?

Problem 12 Saif, Noman & Morshed divided a sum of money among themselves in the ratio 2:3:7.Find the share of Saif if the total share of Saif and Noman together is TK.1500 less than that of Morshed.

Problem 13 Four liters of milk are to be poured into a 2 liter bottle and a 4 liter bottle. If each bottle is to be filled to the same fraction of its capacity, how many liters of milk should be poured into the 4 liter bottle?

Problem 14 A group of workers can do a piece of work in 24 days. However as 7 of them were absent it took 30 days to complete the work. How many people actually worked on the job to complete it?

Problem 15 The proportion of milk and water in 3 samples is 2:1, 3:2 & 5:3.A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is?

Math lesson: 04: InequalityFormulae:

1. If a > b & a > 0 ; b > 0 then a + x > b + x a – x > b-x -a < -b -a + x < -b + x -a - x < -b - x ax> bx (if x > 0) ax < bx ( if x< 0) a/x > b/x ( if x > 0) a/x < b/x ( if x <0 )

Problem 01 If p & q both positive and q<p, which of the following is false?(A) -4q>-4p (B) q/2 < p/2 (C) 5-q < 5-p (D) –p/3 < -q/3 (E) 1/q >1/p

Problem 02 If a & b both positive and a>b, which of the following is always true? (A) b2/a2 > b/a (B) a/b> a2/b2 (C) b2/a2 > 1 (D) b2/a2 > a2/b2 (E) a2/b2 > a/b

Problem 03 If x<z and x <y, which of the following statements are always true? Assume x<0I. y<z II. x<yx III. 2x<y + z(A) only I (B) only II (C) only III (D) II and III only (E) I,II & III

Problem 04 If x>y, z<y and w<x, which of the following statements is always true?(A)z>w (B)y>w (C) y = w (D) z<x (E) x<z

Problem 05Problem 06Problem 07Problem 08

2. If a b > 0 then a > 0 , b > 0 i.e a (+) & b(+) OR

a< 0 , b< 0 i.e a(-) & b(-)Problem 01 If ab>0 and a<0, which of the following is negative?

(A)-a (B) b (C) –b (D) (a-b) (E) –(a+b)Problem 02 If xy>0 and y<0 which of the following must be positive?

(A) x-y (B) x+y (C) (x+10)/y (D) (y-2)/x (E) NoneProblem 03 If xy>0 and x<0 which of the following must be negative?

(A) -x (B) y (C) -y (D) (x-y) (E) –(x + y)Problem 04Problem 05Problem 06

3. If a b < 0 then a > 0 , b < 0 i.e a (+) & b(-) OR a< 0 , b> 0 i.e a(-) & b(+)

Problem 01 If xyz<0 and z<0 then which of the following must always be true?(A) xy>0 (B) xy<0 (C) xy>z (D) xy<z (E) None

Problem 02Problem 02Problem 03Problem 01Problem 02Problem 03

4. If a>b & a>c then We donot know the relationship between b & c i.e *) b>c *)b<c *) b = c possible we cannot make any exact argument about (b-c) or (c-b) so if the question says which of the following must be true in that case we should just

omit those answer choices relating to (b-c) or (c-b)

Problem 01 If x>y and y<z, which of the following is the most appropriate?(A) x>z (B) z>x (C) x = z (D) any of the following may be true (E) None

Problem 02 If a>b and a>c, which of the following must be greater than 0?(A) (b-c)/(b+c) (B) (c-b)/(a-b) (C) (b-c)/(b-a) (D) (b-a)/(c-a) (E) None

6. Average =

7.8. Special case : for the case of consecutive integers

9.10.

11. i) Average =

j)k)

Number of terms

First number + last number

2

l) ii) Average = middle number (for odd number of terms: average = (n+1)/2 number of terms)m)

n) iii) Average = average of middle two terms (for even number of terms: average = (n+1)/2 number of terms)o)p)q)r)s)t)u)v)w)

x) Math lesson: 07: Venn Diagram & Mixturey) Formulae:

3. Venn diagram :4. We cannot get an instant idea from language but we can get a clear concept from diagram: the

relationship of 02 objects single overlap system 03 objects double overlap system

5. Venn diagram : formulae :a. For single overlap system :b. n (AUB) = n(A) + n(B) – n(A B)c. = 1’s – 2’s

d. Here 1’s = n (A) + n (B) e. 2’s = n (A ∩ B)f. n (AUB) = total circle valueg. n (AUB) + n (out of circle) = total h. i. Problem 01