Bank Probationery Officer M I S C E L L A N I O U S - 1

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1 Bank Probationery Officer Q U A N T I T A T I V E A P T I T U D E M I S C E L L A N I O U S - 1 BINARY NUMBER SYSTEM This system has a base 2, using only 0 and 1. The electric switch has an analogy with binary system. It is either close. i.e. ON representing 1 or it is OFF representing 0. It is this analogy which is responsible for the construction of powerful digital computers. Conversion of Decimal Number to Binary Numbers A popular method to convert decimal numbers to binary numbers is to progressively divide the decimal number is to progressively divide the decimal number by 2 ; writing down the remainders when taken in the reverse order will form the binary number. Example : method to convert decimal numbers to binary numbers by 2 ; writing down the remainders when taken in the reverse order, will form the binary number = 5 with the remainder = 2 with a remainder = 1 with a remainder = 0 with a remainder 1 Now we place the remainder in the reverse order which give binary number equivalent to the decimal number Conversion of Binary Number to Decimal Number Following four steps can be used to convert a Binary Number to Decimal Number. I. Write the binary number. II. Just under the binary write 1, 2, 4, 8, starting from right to left. III. If a Zero appears in a digit position cross out the decimal weight for that position. IV. Add the remaining weights to obtain the decimal equivalent. Example (1) : Conversion of binary number to its decimal equivalent. Step I Step II Step III 4 / 1 Step IV 4 + 1=5 i.e is decimal equivalent of binary number Example (2) : Conversion of binary number to its decimal equivalent. Step I : Step II : Step III : 16 / 4 / 1 Step IV : = 21 Binary Addition Rule = 0 Example = = = 10 1) Add and (2) Add and

2 PRACTICE TEST Directions (Qs. 1-10) : In a certain code, the symbol for 0 (zero) is * and for 1 is. There are no other symbols for other numbers and all numbers greater than 1 are written using these two symbols only : The value of symbol 1 doubles itself every time it shifts one place to the left. Thus 0 is written as * 1 is written as 2 is written as * 3 is written as 4 is written as ** and so on. 1. If ** is added to *, what will be the result? (1) * (2) * * (3) * (4) *** 2. Which of the following will represent 25% of 36? (1) ** (2) *** (3) * * (4) * 3. If is divided by * *, find the result, (1) ** (2) (3) * (4) 4. Which of the following will represent 19? (1) ** (2) * * (3) ** (4) ** 5. Which of the following will represent the value of the expression ? (1) * (2) * (3) ** (4) ** =? (1) (2) (3) (4) 7.? (1) ** (2) ** (3) ** (4) * 8. Find the value of the expression, * 4 (1) (2) ** (3) * (4) * * 9. Which of the following represent 625? (1) ** (2) *** (3) ** (4) *

3 10. Find the value of the expression. (1) *** (2) **** (3) ** (4) ** Direction (Qs ) : As by the above rule, here 0 is written 1 is written as # 2 is written as 3 is written as # # and so on. Then answer the following questions. 11. Which of the following is an odd number? (1) #@@ (2) #@9@ (3)#@#@ (4) #@@## 12. # - =? (1) (2) # (3) # (4) 13. What percent of # # # # is # #? (1) 15 (2) 20 (3) 10 (4) Find the value of #@@@ ] ¼ (1) # (2) # (4) ### 15. Which of the following is an even number? # (2) # # (3) # # # # (4) # 16. What is the representation of # #? (1) 10 (2) 14 (3) 13 (4) What is the ratio # # # and # # (1) 1 : 2 (2) 2 : 1 (3) 3 : 7 (4) 7 : Find the value of (2) (4) 19. Find the value of 796 # (1) @ (2) # (3) # (4) # # # 20. if divide by # what will be the approximate result? (1) # (2) # # # (3) (4) # Direction (Qs ) : by the above questions, here 0 is written as $ 1 is written as 2 is written as $ 3 is written as and so on 21. Find the value of 3 64 $ 3 $$$ (1) (2) $ (3) (4) $$

4 22. If K 3 48, find K. (1) $ (2) $$ (3) $ (4) 23. What is represent for 22? (1) $ (2) $$ $ (3) $ $ (4) $ 24. Find the value of (1) (2) $$ (3) ( ) $ (4) ( $ ) $ 25. Four of the following five are alike in a certain way and so form a group. Which is the one does not belong to that group? (1) $$$ (2) $$ (3) $ (4) (5) $ Directions (Qs ) : - The answering the questions below, use the following information. A "B means 'add B to A' B means 'divide A by B' A 'B means 'subtracte B from A' A*B means 'multiply A into B' 26. The average age df 30 boys in a class in equal to 14 years. When the age of class teacher is included the average becomes 15 years. To find the age of class teacher, which of following is suitable. (1) 15' 1) (2) (30 * 14)" (31 15) (3) 15 "(30 * 1) (4) (30 * 14)' (31 * 14) 27. A shopkeeper maifcs the price at 15% more than the original price. Due to increase indemand he further increased the price by B%. How much % profit will he get? (1) 15' B" (15 * B)* 100 (2) 15' B" B) 100 (3) 15" B" (15 * B)@ 100 (4) 15" (15 * B)@ Find the compound intrest on Rs.P at R % compounded annually for N years. (1) P * ( R " 100) N * P (2) P * ( 100) N * P (3) P * ( 1 ' 100) N * "P (4) ( 1" R* 100) N " P 29. Express the following equation into the above give rule : 8 4 (3-2) (1) 4 (3 " 2) * 5 " 6 " 9 (2) 4 (3 ' 2) * 5 ' 6 " 9 (3) 8 * 4 (3 " 2) * 5 " 6 ' 9 (4) 4 (3 * 2) * 5 " 6 " One-fifth of one - fourth of one - ninth of a number R is given by (1) 5)* R (2) 5)* 9)* R (3) 5)* 9) * R (4) Can't be determined 31. The LCM of (a³ + b³) and (a 4 - b 4 ) is (1) (a³ " b³) (a² ' b²) (a ' b) (2) (a " b) (a² "ab " b²) (a³ " b³) (3) (a³ " b³) (a " b) (a² ' b²) (4) (a " b³) (a² " b²) (a ' b)

5 1 x 32. If a 2 x, find the value 1 2a 1 a 1 2 a 1 (1) (1" x) 2x'1 (2) (1" x) 1'2x (3) (1" x) (2' 2x'1 (4) (1" x) 2x'1 33. A man walks at the rate of 5km/hour for 6 hours and at the rate of 4km/hour for 12 hours. The average speed of the man (in/hour) is (1) (5 * 6" 4* (6' 12) (2) (12 "6) (3) (5* 6"4* 12 (6 "12) (4) (5 4" 6* (12 "6) The value of 1 x x x x 4 is (1) (x"1) (2) (x"1) (3) (x"5) (4) (x"5) P 35. How will the formula 2 be written in the coded formula? 100 (1) P)* 100 (2) (P'P)*100 (3) 100 (4) (P"P)@100 Directions (Qs.36-45) : To answer the following questions use the information below : M *N means 'add N to M' M # N means 'subtract N from M' M'N means 'multiply M into N' M N means 'divided M by N' % of 20% of 30% of Q can be written as (1) Q' (10 100)' (20 100)' (30 100) (2) Q(10 100) (20 100) (30 100) (3) Q' (10 100)' (20 100) (30 100) (4) Q' (10 100)' (20 100) (30 100) 37. Anil buys a toy at 20% discount. He sells it at a profit of 5% on his cost price. What price does he sell it at if the labelled price of the article be L? (1) L # (80 100) # ( ) (2) L'(80 100)' ( ) (3) L (80'100) (105' 100) (4) L* (80'100) * (105'100) 38. One fifth of one-sixth of one -tenth of D is give by (1) D # (1 5) (1 6) (1 10) (2) D'(1 5)' (1 6)' (1 10) (3) D' (1# 5) ' (1 6)' (1 10) (4) D' (1 5)' (1 6)' (1 10)

6 39. Find the average runs scored by Sachin if he scored12, 20 and 75 in three successive innings. (1) 12* 20 * 75) # 3 (2) (12 * 20 ' 75) 3 (3) (12* 20 * 75) ' 3 (4) 12 # 20 # 75) How will 103% of % of 103 be written in the coded formula? (1) ( ) 92* (81 100) 103 (2) ( ) 92* (100 81) 103 (3) ( ) 92* (81 100) 103 (4) ( )* 92* (81 100) The area of a circle is 27.4 sqm. Find the circumstance (in m). (1) 2N * 27.4 (3) 2 ' ' 27.4 (2) (4) 2 ' ' 27.4# 42. A can do a piece of work in 9 days and B in 7 days. How many days will both take to finish the work? (1) 1 (1 9 # 1 7) (2) 1 (8 * 5) (3) 1 (1 9*1 7) (4) 1 (1 11 # 1 8) 43. If you add 20 to 70, you get A. If you add to 40 to 80 and subtract 32, you get B. How will you write A B? (1) (20 *70 ) (80* 40* 32) (2) (20*70) (80* 4 # 32) (3) (20 * 70) (40* 80 # 82) (4) (20 70) # (40* 80 # 32) 44. What sum of money (in Rs.) will yield Rs. 350 as interest at the rate of 5% in 3 years? (1) 100* (2) ( )(8 3) (3) (200*100) (8' 3) (4) (200'100) B (8'3) 45. Mohan bought a bag with 8% discount on the original price. He got a profit of Rs. 25 by selling it at a price of 112% of that which he bought it. If the original price is x, how will you write the equation? (1) (x # (8 x) * 100) (12* 100) = 25 (2) (x # (8x) 100) (12 100) =25 (3) (x # (8 x) 100) (12 100) = 25 (4) (x* (8 x) 100) (12 # 100) = 25

7 Direction (Qs ) : For the following questions the symbols used are,,, with the following meanings. A B means A B A B means A - B A B means A + B A B means A B 46. The perimeter of a circle is 100m, find the area of the circle. (1) (2) (3) (4) The perimeter of a rectangle cardboard is A cm. The difference between the lengths of the side is Mcm. Then the length (in cm) of the cardboard is (1) (A M) 2 (2) (A M 2) 2 (3) (A 2 M ) 2 (4) (A 2 M ) In a class the average height of a group of 12 persons is 165 cm. If Vimal leaves the group, the average height reduces to 164cm. Then find the height of Vimal (in cm) (1) (2) (3) (4) The sum of the two numbers is 24. Their difference is 10. Then their product may be expressed as (1) ( ) 4 (2) ( ) 4 (3) ( ) 4 (4) Can't say 50. A man purchases a horse of Rs. M and sells it to B at a profit of x % who in turn sells the horse at a loss of y%. Find the price at which the horse was last sold. (1) M[(1 100)(1 y 100)] (2) M[(1 100)(1 y 100)] (3) M[(1 100)(1 y 100)] (4) M[(1 100)(1 y 100)] 1. (3) = 1110 = * 2. (1) 25% of 36 = 9 ANSWERS In the binary form, 9 is written as 1001 = ** 3. (2) = 15 and * = 5 result is a 3 = 11two

8 4. (3) 5. (5) = 4 3 = 12 = = ** 6. (2) (4) (1) 9. (1) 10. (2) = = 16 = = **** 11. # # = (3) The result is (2) 14. (5) ] ¼ 8 = (5) 16. (3) 17. (1) = 2 2 = 4 = (1) = = (2) = 784 = 28 = (4) = 5 = (5) 2-2 = 0 = $ 22. (2) 48 = (3) 22 = (10110) (3) (5) $ = 2 which is a prime no. All others are composite numbers. 26. (5) 27. (3) 28. (2) 29. (5) 30. (2) 31. (3) 32. (3) 33. (1) 34. (2) 35. (3) 36. (1) 37. (2) 38. (4) 39. (5) 40. (1) 41. (3) 42. (3) 43. (2) 44. (5) 45. (2) 46. (2) 47. (5) 48. (1) 49. (2) 50. (4)