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Test paper 1 1 a>b>c and all three belong to natural numbers find the value of b If (a+1)(b+1)(c+1)-1=1000 A 10 B11 C 13 D 14 2 . If a,b,c,d are in continued proportion then what is the value of "n' ? a d an +bn+cn bn+ cn +dn = A 2 B 3 C4 D 5 3 If |a|=3,| b|=4 and | a+ b|=1 then | a- b|=? A B C D E 5 6 7 8 None of these 4. The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria? A B C D E 10 12 16 18 20 5 If certain cells are spherical and are 0.008 millimeter in diameter how many such cells would be required to make a single row 1 millimeter in length?(The cells are placed so that each is tangent to the next with centers all in a straight line) A B C D E 8 80 100 125 1,250 6. The diagonal of a square is doubled to make another square.The area of the new square will A B C D E become 4 times become half become 5 times become 2 times None of thes 7. When the circumference of a circle decrease from 3Π to Π its area decreases by approximately what %? A B C D E 88% 69 8/9% 78 8/9% 44% 88 8/9% 4o brand A television sets and 80 brand B television sets were purchased for a motel chain. If the price of each brand B set was twice the price of each brand A set, what percent of the total bill was the price of a brand B set? 8 A B C D E 0.25% 0.5% 0.625% 0.833% 1.0% A merchant purchased 2000 fruits at Rs.40/- per 100 and spent Rs.200 on transport and other expenses. If 10% of them were spoiled, he sold the remaining at Rs.9/- per dozen. His gain percent in this sale is? 9 A B C D E 5% 15% 25% 35% None of the 10. 42. If x + y + z = 1, then xy + yz + zx is [A] < 1/2 [B] 1/2 [C] >1/2 [D] none of these 11. X,Y,and Z take 20, 30 and 60 days respectively to complete a job independently. They set out to complete a job together . However Y leaves after 4 days and Z leaves after another 6 days . How many more days will it take for X alone to complete the job now? A 4B 3 C 5 D6 12 A rectangular block of dimensions 5*6*7 cm. Is dropped into a cylindrical vesssed of radius 6 cm. And height 10 cm.. If the level of fluid in the cylinder rises by 4 cm., What portion of the block is immersed in the fluid? A22/7*15/18 B22/7*24/35 C22/7*22/34 D22/7*12/15 13. A family uses a mixture of a blend of 2 coffees costing Rs. 30 and Rs. 60 respectively.If the family uses only the expensive variety, it will have to spend Rs.450 more. The annual consumption of coffee of the family is 20Kgs. In what ratio are the two blends being used? A3:1 B2:3 C4:5 D2:1 .14 If x*y*z = (x2+y2)z, then value of 4*3*2 is A650 B675 C550 D625 15. Ashish travels a distance of 100 km in the following manner, at 20 kmph for the 1 st 50 kms,at 25 kmph for the next 50 kms. He returns at a constant speed of 25kmph. What was his average speed for the journey? A22.50 B23.52 C24.60 D22.35 16 X is 25% more efficient than Y and his hourly wages are 25% more. If X is paid Rs.75, how much will Y receive for the same work? A65 B90 C75 D110 17 . Anand goes to a shop to buy the walkman costing Rs.2250. The rate of sales tax is 6% he wants the dealer to reduce the price so that he has to pay Rs.2000 inclusive of tax. Find the reduction needed in he percent of the walkman. A15 B16 C17 D18 18.. X buys an apple from Y for Rs.5 and sells it to Z for Rs.10. He later buys the apple back from Z for Rs.12 and sells it to Y for Rs.15. What is his profit over the venture? A8 B6 C12 D10 19. A man XY of height 1.75 cm stands at a distance of 4 metres from a pillar AB. If the pillar is at the height of 5.25 m from the ground, what is the length of the man's shadow on the ground ? A 1m B2m C5m D6m 20. A spherical ball of 8 cm diameter is melted into a cone with base 20 cm in diameter. Find its height. A2.56cm B3 cm C2 cm D 3.75 cm 21 . P is the product of all the prime numbers between 1 to 100. Then the number of Zeroes at the end of P are: (A) 1 (B) 24 (C) 0 (D) none of these 22. An oil tank is 9/10 full. When 50 litres of oil are removed, the tank is 5/6 full. Find the capacity of the tank in litres. A. 600 B. 750 C 100 D 1200 23. The sum of two prime numbers between 70 and 90 is 162. Their difference is .A 10 B) 16 C. 14 D 4. or 16 24. Consider a 99 digit number created by writing side by side the first fifty four natural number as follows: 12345678910111213……5354 The above number when divided by 8 will leave a remainder of A. 6 B)4 C. 2 .D 0 25. A man engaged a servant on the condition that he would pay him Rs. 90 and also give him a turban after service of one year. He served only for nine months and received a turban and Rs. 65. Find the value of the turban in rupees. A 10 B). 9 C 0 . D 2.50 26 A point P moves in a plane such that its distance from another point Q is always 7 cm. If the point P moves from its starting position in the plane, say P1, a distance of 44 cms and halts at point P2, what is the distance between P1 and P2? A 0 B 14 C 21 D 7 27 The compound interest calculated yearly on a certain sum of money for the second year is Rs. 880 and for the third year is Rs. 968. Calculate the rate of interest A 12 B 10 C 11 D 9 Directions for questions 28 to 33 Each question is followed by 2 statements Mark (A) if statement a alone is suficient but statement b alone is not sufficient Mark (B) if statement b alone is sufficient but statement a alone is not sufficient Mark (C) if both statements a & b together are sufficient but neither statements alone is sufficient Mark (D) if each statement alone is sufficient Mark (E) if statement a & b together are not sufficient 28. What will be Raghu's age 5 year's from now a. Raghu is 30 years younger than his dad b. Raghu's dad was 50 years old 5 years ago 29. In a class of 50 students how many girls scored over 80% in chemistry test a. Exactly 15 boys scored over 80% of the test b. 1/2 of the class scored over 80% 30. In 1980, what was Vithal's monthly average income a. he earned Rs. 15000 from Jan to July 1980 b. he earned average income of 1500 from July to Dec. 1980 31. Is X=Z, X,Y,Z are real numbers. a. X-Y=Y-C b. X-2Z = Z-2Y 32. What is the value of X? X is a real number a. X2-X-12=0 b. X2+X-20=0 Directions for questions 33 to 37 Five brothers have among them a pair of twins who are neither the oldest nor the youngest. E is older than C but younger than B. D is younger than 3 brothers 33. The youngest is A ) A B) B C)C D) D 34. One of the twin pair is A) B B) 35. The eldest is C C) D D) E A) B B) C C) D D) B 36. The one who has as many elder brothers as younger brothers is (A ) A (B)B (C)E (D) None of these 37. Who is the fourth brother (A)A (B)B (C)D (D)E 38.A man invests Rs. 4000 in shares. He invests Rs. 800 in 7%dividend paying shares at Rs. 8.00, Rs. 1400 in 8% dividend paying shares at Rs. 7.00 and the remainder in 9% dividend paying shares. If all the shares have a face value of Rs. 10.0 each and his % return on investment is 10.25% at what price did he buy the 9% dividend paying shares ? A Rs 8 Rs B Rs 9 C Rs 8.50 D Rs 9.50 39 A boy appears for 5 papers, each of the same number of maximum marks. He scores in each of the papers in the ratio of 6: 7: 8: 9: 10. If his average score in all the five papers together was 60%, then in how many papers did he get more than 50% marks ? (A)2 (B)3 (C)4 (D)5 40 In between 6 p.m. and 7 p.m. when will both the hands be in oppsite direction? A B C D E 33 3/11 min past 6 36 min past 6 Never happens 25 min past 6 36 min past 7 41 How many kg of Mirchi powder costing Rs.40 kg must be mixed with 16 kg of Mirchi powder costing Rs.55 kg so that 25% may be gained by selling the mixture at Rs.60 kg? 24 kg A B 14 kg C 16 kg D 28 kg E 12 kg 42 If y,2y+2,3y+3 are in G.P. then their fourth term is -3 A B -9 C - 13.5 D -27 E -8 43 If triangle ABC the side BC is extended to D. if angle ABC=60 o and angle ACD=110oThen angleBAC= A B C D E 60o 50 170o 40o None 44. If y>0 and sqrt(9y+36)= y then y=? A B C D E 6 5 4 2 12 45 A frog is in a 19m. deep well. For every 3m jump the frog slips by 1m. How many jumps would get the frog out of the well? A B C D E 8 9 10 7 None of the above 46. When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n? A 3 B C D E 4 7 8 12 47. A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself ? (A) 8 years (B) 16 years (C) 12 years (D) none of these 48. In an examination, every candidate must take either mathematics or science or may take both if he so chooses.83.6% of the total took mathematics, 31.2% took science. If 370 candidates took both, find the total number of students.? (A) 3200 (B) 2800 (C) 3000 (D) 2500 49.When 99 is divided by the positive integer 8, the remainder is .......... (A) 2 (B) 3 (C) 1 (D) 7 50 How many liters of pure alcohol must be added to 10 liters of a mixture which is 15% alcohol to make a mixture which will be 25% alcohol? A 4/5 B 3/5 C 3/4 D 1/2 E 4/3 Answers Test paper 1 1.B (a+1)(b+1)(c+1)-1=1000 = (a+1)(b+1)(c+1) =1000+1 =1001 = 7x11x13 =(12+1)(10+1)(6+1) a=12 ,b=10 ,c=6 12>10>6 so b=10 Answer is B a>b>c 2B. a d an +bn +cn bn+ cn +dn = Where a b c d are in continued proportion i.e a/b=b/c=c/d b=ck=dk2 Let a/b=b/c=c/d =k c=dk a=bk2=dk3 LHS a/d = dk3/d =k3 RHS (dk3)n+(dk2)n+(dk)n (dk2)n + (dk)n + (d)n k3 = kn assume a continued proportion series 8 ,4 ,2,1 in place of a b c d = 8n+4n+2n 4n+ 2n +1n 83+43+23 43+ 23 +13 Here 23 point us n may be 3 . Put the value of n=3 and see what happen 672+64+8 = 64 +8 +1 744 = It satisfies the equations so n=3 =8 =23 73 Answer is B |a|=3,| b|=4 and | a+ b|=1 then | a- b|=? |-3|=3,|4 |=4 and | -3+4|=1 or = 8n+4n+2n 4n+ 2n +1n = 23 = 3C.If kn (k2n +kn +1) (k2n +kn +1) Answer Short Cut Method 23 dn (k3n +k2n+kn) dn (k2n +kn +1) = kn n=3 8 1 = | -3-4|= | -7| =7 |3|=3,|-4 |=4 and | 3-4|=|-1 |=|1| | 3-(-4)|= | 7| =7 Answer C 4D.Here bacteria population to grow from 1,000 to 500,000 It is a question of GP Here first we find out nth term nth term = arn-1 n=? a= 1000 500.000 = 1000 x2n-1 nth term = 500,000 r=2 500 = 2n-1 APPROXIMATELY 29 = 2n-1 n-1 =9 n=10 Growth of bacteria is as follows- 1000 2 000 4000 ,,,,,,, | ... 2 min ......| ... 2 min ...| It means - two time intervals among three terms .So there is 9 time intervals among 10 terms Total time 2x9 =18 Minutes so answer is D 5D OOOOOOOO........ So 1 m.m .008m.m = 1000= 125 8 Answer is D 6A . A1 = area =axa = a2 A 2 A 2= 4 times of A1 Answer 7E 3 Π x2 + x2 = 4x2 a2 x2 = 4 a2 = 4A1 = =2Π r1 Π = 2Π r2 A become 4 times Area Area = Π 1.5 x1.5 = 2.25 Π Π .5 x.5 = .25Π Area decrease ( 2.25 - .25 )Π = 2.Π % Area decrease = 2x100Π 2.25Π = 88 8/9% . Answer (E) 8E . If price of each brand A tv set is a Bill of brand A tv set is 40a Price of each brand Btv set is 2a Bill of brand B tv set 160a Total Bill 200a percent of the total bill was the price of a brand B set 2a x.100 = 1% 200a Answer E 9.D. Total cost of fruits Other expenses 2000x40 /100 Spoiled fruits saleable fruits Rs800 .00 Rs200.00 1000.00 2000of 10% = 200 1800 1800x 9 = 1350 12 % gain (1350-1000) x100 1000 35% Answer D 10 A (x+y+z ) 2 =1 x2+y2+z2 +2xy+2yz+2zx =1 2xy+2yz+2zx <1 xy+yz+zx <1 /2 Answer is A 11.x will complete 1/20 in one day. Y will complete 1/30 in one day. Z will complete 1/60 in one day. 4 days = (1/20 + 1/30 + 1/60)*4 = (3+2+1/60)*4 x2+y2+z2 It must be +ve = 6/60*4 = 4/10 = 2/5th complete 6 days = (1/20 + 1/60)*6 = (3+1/60)*6 = 4/60*6 = 4/10 = 2/5 total work complete = 2/5+2/5 = 4/5 work remaining = 1/5 1/5/1/20=1/5*20/1 = 4 days 12. volume increase in cylinder=(volume of block *portion of it which is immersed) 22/7*62*4 = 5*6*7( p) p = 22/7*36*4 5*6*7 p = 22/7*24/35 13.Expensive brand cost = 20*60=1200 Expense now = 1200-450=750 Average cost of the mixture =750/20 Rs.30 Rs. 60 Rs. 750/20 450/20 150/20 3:1 14.= (16+9)2 = 252 = 625 15. Total time taken = 2.5+2+4=8.5 hour Distance = 100+100 = 200 kms Speed = 200/8.5 = 23.52 16. Let wages of y =a, then x=1.25a X took 75/1.25a = 60/a Y will take 1.25*60/a =75/a*a =Rs.75 17.2250*6% = 135 2250+135= 2385 2385-2000=Rs. 385 discount% = 385/2250*180 = 17% 18... cost price for x = 5 selling price for x = 10 profit = 5 cost price for x = 12 selling price = 15 profit = 3 total profit = 5+3= 8 19. Triangle SAB is similar to triangle SFL SA / SF = AB / FL x /x + 4 = 1.75 / 5.25 = 1/ 3 3x = x + 4 Therefore x = 2m 20.. Volume of cone = volume of sphere 1 / 3 ( 22/ 7) r2h = 4 /3 ( 22 /7) r2 1 /3 * ( 22 / 7) * 102 h = 4 /3 * ( 22 /7) * 43 102h= 256 100 h = 256 h=2.56 21 A Prime numbers between 1 to 100 are 2,3,5,7,..................97 Now there is no any prime number which having unit digit 5 or 2 (ie x2,or x5 ) except 2 and 5 SO we get 2x5 =10 and this is only 0 reflect in product of prime numbers between 1 to 100 answer =1 A 22B Suppose the capacity of tank is x 9/10x -50 = 5/6x ( 9/10-5/6)x= 50 (54 -50/60)x =50 4/60x=50 x= 50x15 = 750 Answer is B 23B . Prime numbers between 70 and 90 are 71 ,73,79,83,89, Here total of 73 and 89 is 162 difference is 89-73 = 16 Answer is B 24C 12345678910111213……5354 number when divided by 8 will leave a remainder of ??? Just take last three digit and divide by 8 and find the remainder of this number only 354 /8 44 2/8 here we get remainder 2 (See one full lesson on this subject in How to calculate fast ) Answer isC 25A A point P moves in a plane such that its distance from another point Q is always 7 cm. Here P moves in a circle keeping a distance of 7 cm .from point Q If the point P moves from its starting position in the plane, say P1, a distance of 44 cms and halts at point P2 Here radius of this Circle is 7 cm , circumference of this circle is a distance of 44 cm and reaches to P2. 2 x 7x22 /7 = 44 cm .Now p moves as a P1 It is nothing but it covers circumference of this circle and reaches again to original position so distance between P1P2 is 0 answer is A 26B Here no need to find 2 and 3 years compound interest . Compound interest is interest on interest and it is calculated at the same rate Difference of 3rd and 2nd year interest Rs968-880 = Rs88 Extra interest for one year on Rs 880 So % of rate of interest is ( 88 /880 )x100 =10% Answer is B 28C . Let Raghu’s age now be x 5 years hence will be x +5 from statement I x = f-30 f = 50 +5 = 55 Therefore x = 55-30 =25 5years hence Raghu’s age = 25 + 5 =30 There from both statements together The answer is [C] 29 C . From statement I 15 boys scored over 80% From statement II ½ of 50 = 25 students Therefore no. of girls = 25-15 = 10 The answer is deduced from I & II both The answer is [C] 30E From statement 1 Jan to July is 15000 From statement 2 July to Dec 1500* 6 =9000 Individually the statements don’t tell us about the whole year Combined Jan to July + July to Dec 1 5000 + 9000 = 24000 Jan to Dec + July = 24000 But salary during July is not know Therefore average for 12 months cannot be found Therefore the answer is = [E] 31C . Is x = z, x,y,&z are real numbers From statement (I) 2y = x + c From statement (II) 3 z = x + 2y 2y = 3z-x combined x + c =3z- x 2 x = 2z Therefore x =z The answer is (C) 32C.from statement 1 x2 - x – 12 = 0 (x-4) (x +3)=0 Therefore x =4 Or -3 From statement 2 x2 + x –20 =0 ( x-4) ( x +5) =0 Therefore x =4 or-5 Therefore x =4 Common in both statement Answer is [C] 33 to 37 Five brothers have among them a pair of twins who are neither the oldest nor the youngest. E is older than C but younger than B. D is younger than 3 brothers D is younger than 3 brothers .It means Position of D is at 4 1 2 3 D 4 5 Now fill up other position according to given conditions B > E = A > D >C 1 2 3 4 5 33 C 34 D 35 A 36 A 37C 38B. No..of share of co. A 800/8 = 100 Total face value 100x10 =1000 return 100x7/100 =Rs70 No.of share of co B 1400/8= 200 200x10 =2000 200x8/100= Rs160 No of share of co C 2200/a ( let it be a) 2200x10/a 2200x9x10/(ax100) = 1620/a Total return 70 +160+(1620/a ) = 10.25 %of 4000 230 + 1620/a =410 1620 /a = 410230=180 1680/180 9 =a =a So price of co C share is Rs 9.00 Answer is B 39C Let maximum marks of each paper is 100 ,total maximum marks are 500 And he gets 6a,7a,8a,9a,and 10 marks in each paper 6a+7a+8a+9a+10a= 40 a= 60%of 500 = 300 a = 300/40 = 7.5 % in each paper is 6x7.5 = 45 , 52.5 , 60 ,67.5 ,75 ( Add 7.5 after 45 instead of multiply 7.5 to each i.e 7,8,9,10 for fast calculations) He gets marks more than 50% in 4 papers Answer is C 40.B 41BHere First we find out the cost of Mirchi powder so that 25% may be gained by selling the mixture at Rs.60 kg Let cost of Mirchi powder is x x + 25% of x = 60 x+ x/4 =60 5x/4 =60 = Rs 48 Cost of Mirchi powder Should come Rs 48 .00 per Kg Let "a" be mixed With 16kg Of Rs 55 per kg 40a +16x55 =48(a+16) 48a- 40a= 16x55-48x16 8a = 16(55 -48 ) = 16x7 a = 16x7 /8 = 14 (don't calculate in beginning if we calculate 16x55 and 18x16 in beginning it takes our time and again we divide the subtraction of both by 8also Now see there is no any time consuming calculations so be alert in calculations) Answer is B 42C If y,2y+2,3y+3 are in G.P. then their fourth term is In G.P y (3y+3) =(2y+2)2 3y2 +3y =4y2+8y +4 y2 +5y +4 = ( y+4 ) (y+1) y= -4or-1 it Now our terms are -4 ,-6 ,-9 , x - 6/-4 = x/-9 Answer is C 43.B x= -13.5 -1 gives 2y+2 =0 so ignore . Answer is B 44if y>0 and sqrt(9y+36)= y then y=? (9y+36)1/2= y y=12 or -3 Because y>1 so that y=12 Answer is E 45.B 9y+36 =y2 y 2 -12y+3y-36 ( y-12) (y+3) Answer is B 46 C When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n? Do it mentally by option method first and second option is not valid it gives remainder -3 and 0 Try option third 10 /7 =1+ 3 /4 = 7-4 =3 It is valid Answer is C 47C. Amount double means 2x = x ( 1 + r /100)4 rate of interest 2 1/4 = (1+r/100) 8x = x( 1 + r /100)n 23 = ( 1 + r /100)n 23/n = ( 1 + r /100) , where x and r are principal and 23/n = 2 1/4 3/n =1/4 n= 12 Years Short cut method |..............| .............|.............| x 4years 2x 4 years 4x 4 years 8x Amount is double after every 4 years 4+4+4 = 12 Years Answer is C 48 D Both took Science and Maths 83.6 + 31.2 -100 = 114.8 -100 =14.8 % 1 4.8 % of x = 3700 14.8 x 100 =3700 x = 2500 = total number of students Answer is D 9 9 add and subtract 1 99 -1+1 =(99-1) +1 If xn-1 then x-1 satisfy the polynomial xn-1 =0 ie 9-1 also satisfy the polynomial 99-1 = (9-1)(98+,,,,,,,,)+1 First part is fully divisible by 8 so the remainder is 1 Answer is C 49c. 50E. How many liters of pure alcohol must be added to 10 liters of a mixture which is 15% alcohol to make a mixture which will be 25% alcohol? Let 100 % pure alcohol is a liter Consider 100 % to 1 15% to .15 and .25 ax.1 + 10x..15= .25(a + 10) a + 1.5 = .25a+2.5 ( 1-.25)a= 2.5-1.5 =1 25 % to a= 1/.75 = 4/3 Answer is E Test Paper 2 The total age of A and B is12 years more that of total age of B and C.C is how many years younger than A. 1 A ) C is elder than A the above 2 B) 24 E ) None of the above E ) None of the above The ratio between larger and smaller number is 12 less than the product of these two numbers .The square of smaller number is half of the larger number .What is the total sum of these two numbers ? A) 2 B) 16 C) 18 D) Data is inadequate 5 E ) None of the above Manoj is 15 Years older than Navin and Navin is 25 years younger than Ashok.Which of the following represent the difference between the total age of Ashok and Manoj together and Navin (N) A)40 Years B) 40 + 2N Years None of the above 6 E ) None of If 45 % of a number is added to another number ,it become 1.35 of another number ,what is the ratio of these numbers ? A) 8:7 B)3:2 C)7:8 D) 10 4 D ) Data is inadequate The average marks fetched by Lata in History ,Geography ,Science and Maths is 10 more than the marks fetched in Maths .If she has got 110 marks aggregate in History and Geography ,what will be the aggregate marks fetched In science and Maths ? A)80 B)70 C) 65 D) 7:9 3 C) 12 C)40 +N years D) Data is inadequate E) A total of 91 boys are seated in three rows .The ratio between the number of those seated in the first row and those in the second is 5:2 and the ratio between the number of boys seated in the second row and those in the third row is 1:3 .How many boys were there in the second ? A) 35) B) 14 C) 42 D ) 56 E ) None of the above 7 The percentage profit earned by selling an article for Rs 1920 / is equal to percentage loss incurred by selling the same article for Rs 1280/ .At which price should be the article sold to make profit of 25%? A)Rs 2000/ the above 8 C)Rs2200/ D) Data is inadequate E ) None of Among three numbers x, y & z , y is the highest and x is the lowest .which of the following equation s of these numbers is definitely greater than 0 ? A)x-y +z 9 B) Rs2400/ B) x-y-z C)y-x-z D) y-x+z E) All the above are greater than 0 An amount is to be divided among P,Qand R in the ratio of 5:11:23 respectively. If the difference between the total share of R and P and Q is Rs 2800/ What is the difference between Q and R 's share ? A ) Rs 6400 B) Rs 3600 / above C) Rs 4800 / D) Rs 3200/ E ) None of the Some balls are kept in boxes P.Q and R .Some balls from box P are kept in box R. After this displacement of balls the total balls in Q and R become four times the number of balls originally kept in box P .If there are 32 balls in box Q ,how many 10 balls were kept in box R in the beginning? A)40 B) 20 C) 30 D) Data is inadequate E ) None of the above The average of the first three of five odd numbers arranged in ascending order is 10 less than the average of the last three of these numbers .If the sum of the last two of 11 these numbers is 42 .what is the sum of the first two of these numbers A ) 22 B) 20 C) 14 D) 12 E) Data is inadequate Directions for questions 12 to 16 Each question is followed by 2 statements Mark (A) if statement a alone is sufficient but statement b alone is not sufficient Mark (B) if statement b alone is sufficient but statement a alone is not sufficient Mark (C) if each statement alone is sufficient Mark (D) if both statements a & b together are sufficient but neither statements alone is sufficient Mark (E) if statement a & b together are not sufficient 12 What is the speed of running train P a Train P crosses another train running in opposite directions in 9 seconds b Relative speed of both trains is 170 km/hr The average age of class teacher and students in a class is 3 years more than the 13 average age of students .What is the age of of the class teacher ? a There are 11 students in class . b the average age of students and class teacher is 14 years What is the ratio between the cost price and selling price of a commodity ? 14 a The commodity is sold at 20 % profit b The cost price of commodity is Rs 5000/ What is the rate of compound interest on a sum of money a The total simple interest at the same rate on Rs 6000/at the end of three years is Rs 15 1800/ b The total compound interest on Rs 6000/ at the end of two years is Rs 1260 Jeeven 's Marks in English is 15 more than the average marks obtained by him in English ,Maths ,Geography and Science .what is his marks in the science ?' 16. a The total marks obtained by him in English and Science together is 120 b The difference between the marks obtained by him in Geography and Maths is 120 In a row of boys facing north ,Ram is 12th from the left .When shifted to his right by four places ,he becomes 18th from the right end of the row .How many boys are in 17 the row? A) 32 B) 33 C ) 34 D) Data is inadequate E ) None of the above From two strings of length 15 c.m each an equilateral triangle of area a cm2 and an isosceles triangle of area b cm2 is formed then 18 A) b>a B) b is equal or greater than a greater than b E) b<a 19 B) 2w+w1 C) 2w2-w1 C ) 1400000 D) 2400000 102. Mohan deposits Rs.150 on the first of every month starting from 1st Jan1985, in the recurring deposit scheme of a bank which allows simple interest @ 6% p.a.on the sum standing to his credit at the end of each month. What is the amount, Mohan is entitled to on 31st Dec, 1985 A) Rs.1818 22 D) 2(w2+w1) A man divides his property among his sons so that one gets half, another gets quarter and third gets one fifth and the fourth Rs. 10000. What is the value of the total property? A ) 200000 B) 400000 21 D) a is equal or An empty jar weighs w1 gm. The jar half filled with a liquid weights w 2 gm. Find the weight of the jar completely filled with the same liquid. A) 2(w2-w1) 20 C) a= b B) Rs.1800 C) Rs.1450 D) Rs.1400.80 Divide 27 into two parts so that 5 times the first and eleven times the second are together equal to 195 A )17:10 B)15:11 C )16:10 D) 10:17 Six men earn as much as 8 women, 2 women earn as much as 3 boys and 4 boys earn as 23 much as 5 girls. If a girl earn Rs.50 a day, then the earning of a man would be A ) Rs.125 24 Rs.13 C ) Rs.105 D) Rs.120 If a sum of money at certain rate of interest doubles in 5 years and at a different rate of interest becomes 3 times in 12 years, the better rate of interest is, A ) 20% 25 B) B) 39 2/9% C ) 162/3 D) 15% A,B,and C can independently complete a task in 6,8 and 12 hours respectively. C starts working. 2 hours later she stops and simultaneously A and B starts working. Yet another 2 hours later, B stops working too. Now how long does A have to work alone to complete the task? A )3 hour B) 6 hour C )8 hour D)none of these. 26 .I have bought a car for some amount. I sell it to Mr.X at 10% loss due to need of money urgently. But later I buy it again from him at my original purchase price. a)What is Mr.X's profit? b)What is my loss? A )11.11%;10% 2 7 B) 10%;11.11% C ) 2 0%;22.22% D) 40% 44.44% P owes Q Rs.455 payable 4 months hence and Q owes P Rs.450 payable 2 months hence. If they agree to settle their account what sum should be paid over and to whom reckoning the rate of true discount p.a. A )Rs.12 B) Rs.13 C ) Rs.11 D) Rs.16 Direction for questions 28 to 37: Study the graph carefully and answer accordingly 2 8 Total export in 1998 and 1999 together was equal to in case of which of the following pairs of type A) A and B B) Band C C) A and D D) Band D E) none of the above The percentage change ( increase and decrease )in the number of the vehicles exported 2 from 1998 to 19999 is minimum in the case of which of the following types of vehicle 9 A) A B) B C) C D) D E) E The export of d type vehicle 1998 was what percentage of export of E type vehicles in 3 1999 0 A)150 B)175 C)75 D)25 E) none of the above The number of E type vehicles exported in 1998 is equal to the number of which type 3 of the vehicles exported in 1999 1 A) A only B) C only C) A only D ) both C and B E) none of the above 3 The average of B and C type vehicles in the 1999 was equal to export of which type 2 in 1998 A)A only B)C only above C) both A and C D) Both C and E E) none of the Directions (Questions 33 to 38 ) Study the graph and answer Total rainfall in mm Rain fall in equatorial zone in January is what percent less /more than that of rainfall 3 in temperate zone in July ? 3 A) 39.25% B)41.42% C)36.04% D)23.68% E) 44.44% 3 In which of the following zones is there maximum increase in rainfall in July? 4 A )Equatorial B) Subpolar C) Tropical Summer D) Subtropic Dry E)Teperate Decrease in rainfall in Subpolar zone is what percent of increase in subtropic winter 3 zone in July 5 A) 85% B) 80% C ) 72% D) 90% E) 78% Average rainfall in July is approximate how much more /less than the average rainfall 3 in January? 6 A)3% more B) 7.00% less C) 9.32% less D) 6.34 %more E ) 9.1 % more 3 What is the average rainfall around the world in whole year 7 A) 1034.28mm B) 1075 .71mm C) 0510 mm D) 978 .67 mm E ) 1270 .34mm 3 8 a4+b4+c4/b2c2+c2a2+a2b2 is : 2 B) 3 C) 4 D ) 6. If a+b+c = 0.The value of A) 3 A farmer sells 2 horses for the same price. In one he gains 20% and in the other he loses 20%. 9 What is his overall profit or loss? A)4% profit B)4% loss C)2% loss D)2% profit E) Neither loss nor profit Directions for questions (40 � 43) Six players: - Raman, Sharvan, Tejinder, Urvinder, Vinod, Wimpy were sitting in a refreshment room in stadium after playing their respective game. Games played by them are Badminton, Table Tennis, and Lawn Tennis. Exactly two players played each game. Each player played exactly one game. But when asked them to tell their game they gave the following statements: Raman: - I played with Sharvan and Wimpy.I don�t like Badminton Sharvan: - I played with Wimpy and Tejinder .I don�t like Lawn Tennis Tejinder: - I played with Raman and Vinod.I don�t like Badminton Urvinder: - I played with Raman and Tejinder.I don�t like Table Tennis Vinod: - I played with Urvinder and Wimpy.I don�t like Lawn Tennis Wimpy: - I played with Urvinder and Raman. I don�t like Table Tennis. If the first sentence spoken by each player was false, while second sentence was true. 4 0 With whom did Raman play a game? (A) Wimpy (B) Vinod (C) Tejinder (D) Urvinder 4 1 Who played Table Tennis? (A) Raman and Vinod (B) Sharvan and Urvinder (C) Tejinder and Wimpy (D) Wimpy and Sharvan 4 2 Who played Badminton? (A) Sharvan and Urvinder (B) Wimpy and Sharvan (C) Raman and Vinod (D) Tejinder and Wimpy 10. Who played Lawn Tennis? 4 (A) Sharvan and Urvinder 3 (B) Tejinder and Wimpy (C) Raman and Vinod (D) Wimpy and Sharvan Numbers X and Y are positive and odd, and the number Z is also positive but even. then 4 4 which of the following is not true (A) (X-Z)2 Y is even (B) (X-Z) Y is odd (C) (X-Z) Y2 is odd 4 5 4 6 4 7 (D) (X-Y)2 Z is eve There are 2 lights one red and the other green. The red one flashes 3 times every minute and the green one flashes 5 times every two minutes. If the lights start flashing together then the total number of times both will have flashed together in an hour is (A) 30 (B) 24 (C) 48 (D) None of the above N = 1421 x 1423 x 1425 what is the remainder when N is divided by 12 (A) 0 (B) 1 (C) 3 (D) 9 a1 = 1 and an+1 = 2an + 5, for n being a natural number. The value of a100 is (A) 5x299 + 6 (B) 5x299 - 6 (C) 6x299 + 5 (D) 6x299 - 5 Three friends divided some bullets equally. After all of them shot 4 bullets the total no.of 4 remaining bullets is equal to that of one has after division. Find the original number of bullets 8 A) 16 B) 18 C) 20 D) 24 There are 27 balls, of which 1 is heavier. Given a balance how many times you need to 49 weigh to find out the odd ball. A ) 2 B )3 C) 4 D ) None of the above If the area of the square is increased by 69 % how much the length of the side will 50 increase? A) 21 B) 31 C) 30 D) None of the above Answers Paper No2 1C (A+B)-(B+C)+12 A-C=12 A=C+12 C is 12 years younger than A. (H+G+S+M)4 - M=12 And H+G=110 2D After combining these two equations we can not solve further so data is inadequate 3D 45%of a+b= 1.35b 9a/20+b=27b/20 9a/20 = 7b/20 9a =7b a/b = 7 /9 7:9 4D Let x =smaller number and y = larger number according to question y/x+12=xy and x2 = y/2 Put the value of y in first eq x3 -x-6=0or ( x-2 ) (x2+2x+3) it gives the value of x+2 other values are imaginary y=2x2x2 =8 sun of both numbers 2+8=10 5C M-N = 15 ......(.1) and A-N=25 ........(2) Adding eq 1 and 2 M+A-2N= 40 M+A-N = 40+N 6B Ratio between 1st and 2nd row 1:2 Ratio between 2nd and 3rd row 1:3 Make it 2:6 Now ratio 1st row : 2nd row : 3rd row = 1:2:6 Total boys 91 .2nd row boys 91x2/13 7 x2=14 7A Let cost price is x and proft/loss is y x+yx/100=1920..........1 x-xy/100=1280.............2 adding both eqs 2x = 3200 x= 1600 ( in such type condition take directly the average of both figures for saving time ) SP of article now =1600+ 25 %of 1600 = 1600+400 =2000 8D y>z>x y-x>0 x-y <0 Option A is rejected but options Band C may or may not be possible .Only option D is possible 9D Let share of PQ and R are 5x, 11x and 23x According to question 23 x- (5x+11x) = 23x- 16x= 2800 7x= 2800 x= 400 Now difference between Qand R share 23x-11x= 12 x = 12 x400 =4800 ( 1+2+6 =13) P, Q and R are having p,q and r balls respectively and x balls are replaced from box P to Q Now according to question's conditions 10D 4p= q q=32 p=8 4p=r+x 32 =r+x we can not find the balls because value of x is not given so data is inadequate Five odd numbers a1< a2 <a3< a4 < a5 a4 + a5 )/3 - ( a1+ a2 +a3)/3=10 (a3+ 11D (a4+ ( a5)- ( a1+ a2 )=30 a1+ a2 )=42-30=12 (a4+ a5) =42 given (D) 12 E Neither the speed of trains nor the length of trains is given .Can't calculate speed of train P 13D After combining both statements ,the age of class teacher is 14x12 -(14-3)x11 = 168 -121= 47 years 14A CP :SP = 100x :120 x 5:6 statement a alone is sufficient but statement b alone is not sufficient From statement a rate of interest = 1800x100/(3x6000) = 10 % 15C From statement b rate of interest =(22/20 -1)100 = 10% (E+M+G+S)/4 = 15 16E 1 ... E+S=120 2...... G-M=120 S can not be determined with the help of both statement so Answer is E 17B Total boys in row 16+18 -1 = 34-1 =33 (Get alert to subtract 1 in these type questions because particular person is counted two times one from left and other from right .Consider directions also very cautiously) Remember for the given parameter equilateral triangle area is maximum .Here 18E area of isosceles triangle bcm2 is lesser than area of equilateral triangle acm2 , so that b<a Weight of jar = w1g Weight of liquid = w2-w Weight of liquid(half filled with liquid) = w2-w1 19C Weight of liquid filled = 2(w2-w1) Weight of jar + weight of liquid = w1+2(w2-w1) = 2w2-w1 Hence [C] Let x be the total value of the property. x = x/2+x/4+1/5x+10000 = (10+5+4)x/20+10000 20A = 19x/20+10000 = 20*10000 = 200000 . Total money deposited = Rs.12*150 = Rs.1800 Interest on Rs.150 for 12 months = 150*12/12*6*1/100 = 9 Interest on Rs.150 for 11 months = 150*11/12*6*1/100 = 33/4 21C Interest on Rs.150 for 1 month = 150*1/12*6*1/100 = 3/4 Total interest = 9/1+33/4+3/4 = Rs.18 Total amount due = 1800+18 = Rs.1818 Hence [C] a+b = 27 5a+11b = 195 22D solving simultaneously we have, a = 17 b = 10 6 M = 8W, 2W = 3B, 4B = 5G 1 G = Rs. 50 a day. 23A Now, 1B = 5/4G 1 W = 3/2 * 5/4G 1 M= 8/6* 3/2* 5/4G = 5/2G 1 M = 5/2 * 50 = 125/-Rs. If we assume that the sum = Rs. 100 Then, 1st rate of interest = 100*100/100*5 = 20 2nd rate of interest = 200*100/100*12 = 16 2/3 24B 76n1=5, x1= 42.2 n2 = 4, x2 = 35.5 x12 = n1x1+ n2x2 / n1+n2 = 5 * 42.2 + 4 * 35.5 /9 = 211.0 + 142.0 /9 = 353 /9 = 39 2/9 In one hour, C can complete 1/12th of the work. In two hours, he can complete 1/12*2 = 2/12th of the work. A and B start work simultaneously, together work completed by A and B, 1/6+1/8 = 14/48 work = 7/24 work. In 2 hours they complete 7/24*2 = 7/12 work Total work done by A,B,C = 7/12+2/12 = 9/12 25A Total work to be completed = 12/12 or 1 Remaining work = 3/12 Hour work done by A 1 1/6 x 3/12 3/12*6 = 1.5 hours =x a)Let my cost price be 100 Selling price = 90 Profit for Mr. X = 10 26A Profit % = 10/90*100 = 11.11% b) Let cost price be 100 Selling Price = 900 My loss = 10 = 10/100*100 = 10% p = Rs.455, n = 4months = 1/3 year, rate = 5% Amount of Rs.100 = (455*1/3*5)/100 = 107.58 455 x 107.58 100 x = 423 27C q = Rs.450, n = 2months = 1/6 year, rate = 5% Amount of Rs.100 = (450*1/6*5)/100 = 103.75 450 ? 103.75 100 = 434 Sum to be repaid to p = 434-423 = Rs.11 Hence [C] 28A B also correct Both options A & B are correct 29D Option D is correct 30B % = 35 /20 x100 = 175 % 31E The answer is A and C both 32B Average of B and C type vehicles in 1999 30+25 / 2 = 27.50 33B Rainfall (rf) in Jan in equatorial 1980 mm July in temperate = 1400 mm % = 1980-1400=580 (580 /1400)x100 41.12% 34E Steep line angle shows that TZ has maximum increase rainfall 35D % =( 710 /800)x100 = Approximate 90% in July Jan rf = 1980+2060+690+310+890+1160+730/7= 7820/7=1117.14 July rf = 2280 +1560+250+710+1400+800+240/7=7240/7=1034.28 36 B (1117.14 -1034.28)x100/1117.14 =( 82.86 /1117.14 )x100 = 7.00% less approximate 37B From question no 36 1117.14 +1034.28 /2 =2151.42 /2 = 1075.71 Since a+b+c = 0 a+b = -c ( a+b)2=(-c)2 a2+2ab+b2=c2 a2+b2-c2= -2ab (a2+b2+c2) 2=(-2ab) 2 38A a4+b4+c4+2a2b2-2b2c2-2c2a2=4a2b2 a4+b4+c4=2a2b2+2b2c2+2c2a2 =2(a2b2+b2c2+c2a2) a4+b4+c4/a2b2+b2c2+c2a2 =2 Horse 1- C.P 39B S.P. x 100 ? 120 S.P. = C.P.(100+profit%/100) x = 1000/12 Horse 2C.P S.P. y 100 ? 80 y = 125 Total cost price = cost price of Horse1+cost price of Horse2 = 125 + 1000/12 = 2500/12 Total S.P.= 100+100 = 200 loss = 2500/12- 200 = 100/12 % of loss = (100/12 ) x100 = 4% (2500/12) Short cut Method Remember in these type questions where loss on one unit and same percentage of profit on other unit there is always loss and you can calculate % of loss mentally Multiply profit and loss percentage and divide it by 100 , you get required percentage of loss Here farmer's gain and loss is 20 % 20 x20 /100 = 4% our required answer First we make matrix of possible players based on first sentence spoken by each player was false, Raman Sharven Tejinder Urvinderr Vinod Wimpy Raman x x Yes Yes Yes x Sharven Yes x x Yes Yes x Tejinder x Yes x Yes x Yes Urvinder x Yes x x Vinod Yes Yes Yes x Wimpy Yes x Yes x Yes x Yes Yes x x Table based on second sentence was true. R S T U V W TT yes yes yes no yes no Bad. no yes no yes yes yes L.T yes no yes yes no yes On the basis of these two tables we can answer all the questions very easily 40B With whom did Raman play a game? (A) Wimpy (B) Vinod (C) Tejinder (D) Urvinder Table 1 indicate Raman can play with Sharven ,Vinod And Wimpy ,but table 1again indicates only Vinod can play with Raman answer is B 41A Who played Table Tennis? (A) Raman and Vinod (B) Sharvan and Urvinder (C) Tejinder and Wimpy (D) Wimpy and Sharvan 2nd table indicates that only option A is valid Table one also support it 42A Who played Badminton? (A) Sharvan and Urvinder (B) Wimpy and Sharvan (C) Raman and Vinod (D) Tejinder and Wimpy Options A and B are valid according totable 2 but table one only support optionA 43B Who played Lawn Tennis? (A) Sharvan and Urvinder (B) Tejinder and Wimpy (C) Raman and Vinod (D) Wimpy and Sharvan Option B is only valid according to table 2. Table one also support it Let X= 3 ,Y =5 and Z = 2 which of the following is not true 2 44A (A) (X-Z) Y is even odd = true (C) (X-Z) Y2 is odd 8 = true Only A is false (3-2)2 5 = 5 false (3--2) 52 =25 true (B) (X-Z) Y is odd (3-2)5 =5 (D) (X-Y)2 Z is even (3-5)2 2 = 45C The red one flashes 3 times every minute and the green one flashes 5 times every two minutes Time of red 60/3 = 20 seconds Time of green 120/5= 24seconds Take LCM of both 20 and 24 = 120 seconds = 2 Min both lights blink in one hour = 60 / 2 = 30 times 46C N = 1421 x 1423 x 1425 what is the remainder when N is divided by 12 Divide only 1421 by 12 gives remainder 5 1423 gives remainder 7 1425 gives remainder 9 Multiplying all these remainders 5x7x9 and divide by 12 again 315 /12 Here we get remainder of 3 It is our required answer a1 = 1 and an+1 = 2an + 5, for n being a natural number. The value of a100 is 47D a2 = 2a1 +5 = 2x1+5=7 a3 =2a2+5 = 2x7+5= 19 a4=2a3 +5 = 2x19+5=38+5 = 43 now a1 =1 and options give a rough idea that option D is most appropriate answer, convert it into nth term and check a2 a3 a4 after putting n=1,2,3,4 nth term = 6x2n-1 - 5 Put n=2 a2 = 6x22-1 - 5 =6x2-5 =7 Put n=3 a3= 6x23-1 - 5 =24-5 = 19 it is value of a3so that Option D is correct answer you can again confirm to it by a4 if time permits to you . We use this method to save time only .It takes few more min. if we solve step by step 48B x x x x-4 x-4 x-4 3x -12 = x 2x=12 x=6 total bullets 6x3=18 49C It is very interesting question .Make three groups of 9 balls in each group of these balls and weigh any two group of them If both are equal ,heavy ball is in the third group . otherwise balance shows the heavy one Take heavy one group and again make three groups of 3 balls in each group and weigh any two groups of balls If both are equal third one is heavy otherwise balance shows the heavy one .Take heavy group and weigh any two balls If both are equal third one is heavy otherwise balance shows the heavy ball By this way we find heavy balls by weighing only three times. Suppose length of square's side is x .Area =x2 Increased area 69% =1.69 x2 50C side of increased square = 1.3x % increase .3x100/x = 30%