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<ul><li> 1. NAC QUESTIONS </li> <li> 2. 25/5 = ? </li> <li> 3. Numerical analytical </li> <li> 4. Numerical Ability Number Systems Averages & Percentages Profit and Loss Time and Work Ratio Ages Clock </li> <li> 5. Numbers The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 6) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? a) 256 b) 54 c) 192 d) 108 (N-1)*(BASE)(N-2) N=NUMBER OF LAST DIGIT=4(1000 contains 4 digits) base=6 (4-1)*62 = 3*36 = 108. </li> <li> 6. Numbers The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? a) 54 b) 64 c) 265 d) 192 (N-1)*(BASE)(N-2) N=NUMBER OF LAST DIGIT=4(1000 contains 4 digits) base=8 (4-1)*8(4-2) =192 </li> <li> 7. NUMBER If a and b are odd numbers, then which of the following is even ? A. a + b B. a + b + 1 C. ab D. ab + 2 E. None of these always add two odd number it gives even number </li> <li> 8. FRACTIONS One-third of the marks obtained by Naveen in maths is the same as the marks he obtained in English. If the total marks obtained by him in both the subjects is 160, the marks he obtained in English is: A) 40 B) 30 C) 50 D) None of the options Let the marks obtained in English be x. Marks obtained in Maths = 3x. Total marks obtained 4x = 160. Hence marks obtained in English x = 40. Answer : a) 40 </li> <li> 9. Fractions </li> <li> 10. Decimal Number In which of the system, decimal number 184 is equal to 1234? 184= 1*x^3 + 2*x^2 + 3*x + 4 X3 + 2x2 + 3x 180 = 0. Has no integral solution. Hence answer choose none of these. </li> <li> 11. DECIMALS & FRACTIONS 892.7 - 573.07 - 95.007 =? i) 224.623 ii) 224.777 iii) 233.523 iv)414.637 Choice 1. </li> <li> 12. DECIMALS & FRACTIONS Which pair of rational numbers lie between 1/5 and 2/5 - a. 262/1000, 275/1000 b. 362/1000, 562/1000 c. 451/1000, 552/1000 d. 121/1000,131/1000 BETWEEN 0.2 AND 0.4 ANS A. </li> <li> 13. DECIMALS & FRACTIONS </li> <li> 14. FRACTIONS </li> <li> 15. FRACTIONS </li> <li> 16. ALGEBRA Three consecutive whole numbers are such that the square of the middle number is greater than the product of the other two by 1. Find the middle number. a. 6 b. 18 c. 12 d. All of these Let the numbers be x1, x, x + 1. Since x2 = (x1) x (x+1) + 1 it is true for any values of x. </li> <li> 17. A.M & G.M The arithmetic mean of 2 numbers is 34 and their geometric mean is 16. One of the numbers will be a. 4 b. 16 c. 18 d. 12 a + b = 68 and ab = 256. Hence choice a is correct. </li> <li> 18. DIVISIBILITY What least number must be subtracted from 9400 to get a number exactly divisible by 65? a. 40 b. 20 c. 80 d. none of these 65 = 5 X 13 Last digit should be zero or 5. 940040=9360 divisible by 13 & 5 940020=9380, 940080=9320. none of these divisible by 13. Hence answer is A. </li> <li> 19. Fractions </li> <li> 20. Divisiblity 12 divides, ab313ab (in decimal notation, where a,b are digits>0, the smallest value of a+b is a)7 b)6 c)2 d) 4 If a number is divisible by 12 then it should be divisible by 4&3 for divisible by 4 last [2 digit]no's should be divisible by 4 Also sum of digits should be divisible by 3. Hence 2(a+b)+1 should be 3k and ab = 4m. That is a + b = (3k-1)/2 . from the given choices only first choice is possible k = 5 and smallest should be 7. </li> <li> 21. Divisibility If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be: Using the divisibility rules, For 8, the last three digits have to divisible by 8, therefore the number 774958A96B is divisible by 8 if 96B is divisible by 8. 96B is divisible by 8 if it is 960 or 968 thus B is either 0 or 8. For 9, the sum of the number has to be divisible by 9, therefore (55 + A + B) is divisible by 9 if (A + B) is 8. Now either of A or B could be 8, but the other has to be zero. </li> <li> 22. Divisibility 311311311311311311 is divisible by: a)3 and 11. b)11 but not 3. c)3 but not 11. d)none of the above. a.3 and 11 the sum of digits is 30 which is divisible by 3 the differences of odd place digits - even place is divisible by 11 </li> <li> 23. DIVISIBILITY What least number be added to 5200 to get a number exactly divisible by 180? (1) 160 (2) 60 (3) 20 (4) 180 180 = 5 X 4 X 9. 5200 + 160 = 5360 NOT DIVISIBLE BY 9. 5200 + 60 = 5260 NOT DIVISIBLE BY 9 5200 +20 = 5220 DIVISIBLE BY 9 5200 + 180 NOT DIVISIBLE BY 9. </li> <li> 24. DIVISIBILITY A number when divided by 32 leaves the remainder 29. This number when divided by 8 will leave the remainder (1) 3 (2) 5 (3) 7 (4) 29 Let the number be 32k + 29. 32k + 29 = 32k + 24 + 5 8(4k+3) + 5. The remainder is 5. </li> <li> 25. Powers The unit digit in the expression ( 36234 x 33512 x 39180) (5429 x 25123 x 31512) will be (a) 2 (b) 6 (c) 8 (d) 4 Power of 6 end in 6 Fourth power of 3 end in 1 Even power of 9 end in 1 Odd power of 4 end in 4 Power of 5 end in 5 Power of 1 end in 1 Ans: 6 4 = 2. </li> <li> 26. POWERS If x increases linearly, how will a-x behave (a>1) ? a. Increase linearly b. Decrease linearly c. Increase exponentially d. Decrease exponentially Since x increases linearly, x decreases linearly and ax decreases exponentially. Ans d. </li> <li> 27. POWERS What is x if xx 3 3 1 9 81 1 3 27 1 100 Rewrite each term as a power of three, then combine exponents: 12932 4 100 3 333 3 1 3 3 1 xxx Since the bases are the same, the exponents must be equal: 1293 xx which has the solution x = 94 </li> <li> 28. LOGARITHM What is the value of the following expression: 2 log105 + log104 ? a. 2 b. 2.5 c. 3 d. None of these Log10 25*4 = log10100 = 2. </li> <li> 29. LCM Find the greatest number of five digits, which is exactly divisible by 7, 10, 15, 21 and 28. The number should be exactly divisible by 15 (3, 5), 21 (3, 7), 28 (4, 7). Hence, it is enough to check the divisibility for 3, 4, 5 and 7. Lcm of 3,4,5 and 7 is 420. 105/420 = 238 is quotient 238* 420 = 99960 is the only number which satisfies the given condition. </li> <li> 30. HCF The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: A. 12 B. 16 C. 24 D. 48 Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4(given) the numbers are 12 and 16. LCM of 12,16 is 48. So, ans is OPT (D) </li> <li> 31. HCF & LCM </li> <li> 32. HCF & LCM Four different electronic devices make a beep after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45minutes respectively. All the devices beeped together at 12 noon. They will again beep together at: i) 12 Midnight ii) 3 a.m iii) 6 a.m. iv) 9 a.m Interval after which the devices will beep together = (L.C.M. of 30, 60, 90, 105) min. = 1260 min. = 21 hrs. So, the devices will again beep together 21 hrs. after 12 noon i.e., at 9 a.m. </li> <li> 33. HCF & LCM </li> <li> 34. Factorization The prime factorization of integer N is A*A*B*C where A, B and C are all distinct prime integers. How many factors does N have? a)12 b)24 c)4 d)6 n is A*A*B*C =A^2*B*C no. of factors=(2+1)(1+1)(1+1) =12 A HAS POWER OF 2,B HAS POWER OF 1,C HAS POWER 1 SO PRIME FACTORIZATION CAN BE CALCULATED AS: IF A^P+B^Q+C^R,THEN PRIME FACTORIZATION IS (P+1)*(Q+1)*(R+1) SO IN THIS CASE P=2,Q=1,R=1 SO (2+1)(1+1)(1+1)=12 FACTORS </li> <li> 35. RACES & GAMES An athlete decides to run the same distance in 1/4th less time that she usually took. By how percent will she have to increase her average speed </li> <li> 36. RACES & GAMES In August, a cricket team that played 120 matches won 20% of the games it played. After a continuous winning streak, this team raised its average to 52%. How many matches did the team win to attain this average? A) 40 B) 52 C) 68 D) 80 (24+x) / (120+x) = 0.52, where x is the number of games played and 24 is 20% of 120 24 + x = 0.52(120 + x) 24+x = 62.4 + 0.52x 0.48x = 62.4-24 0.48x=38.4 x=38.4/0.48 x=80 </li> <li> 37. PERCENTAGE </li> <li> 38. PERCENTAGE </li> <li> 39. PERCENTAGE Find the percentage of prime numbers present between 1 and 100 (including both). A) 20 B) 25 C) 24 D) 23 2, 3, 5, 7, 11, 13, 17, 19 =8 23,29, 31, 37, 41, 43, 47, 53 =8 61,67, 71, 73, 79, 83, 89, 97 =8 24% </li> <li> 40. PERCENTAGE </li> <li> 41. PERCENTAGE If 7% of A is 42, then find 27% of A. A) 162 B) 62 C) 600 D) 126 Ans: 162 Another method 7 is prime number and the last digit of given number is 2. Hence 27% of A also should have last digit is 2 and so C and D are not possible. B is also not possible because it is not divisible by 9(ie 27). </li> <li> 42. PERCENTAGE </li> <li> 43. PERCENTAGE </li> <li> 44. PERCENTAGE 4% is equal to one out of every: A) 12 B) 20 C) 40 D) 25 Answer 25 </li> <li> 45. PERCENTAGE The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was Rs. 22. Find the amount of the bill. (1) Rs. 1100 (2) Rs. 200 (3) Rs. 2200 (4) Data inadequate Successive 20% discount means 36% discoun...</li></ul>

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