ChetanaSforum # Very Urgent : Please solve these Aptitude Questions

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Hi friends, I got CTS exams on sunday.I could not solve these questions.Pls help me in solving it.The answers i gave may be right or wrong.So tell me the method to solve these problems.I have very short time.So tell me soon.1.If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330 2. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other. Ans: 3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans: 4. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12 5. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other 6. A bag contains 3 balls of 11 different colors each. Find the min no of chances to find at least 3 balls of same color?Ans : 23 (i need to know how it is solved)7.There are 1997 doors in a auditorium and as many as people as the no of doors open enter the auditorium .A door was closed and as many as people as no of doors open leave the auditorium . the process was repeated till the no of doors is equal to1.find the total no of peoples enter the auditorium?8. Find the values for the following problem:f(X)= 2X-1 + f(X-1) if X is not equal to zero and if f(X=0)=0 Value of f(5)a)15 b)24 c)22 d)None18.If f(f(X))=81 then the value of X=?9.A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted10. there are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors ion the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 resly. Similarly when the third one goes he does this for 3 6 9 12 15th doors resly. Find number of doors that are open at last11.There is a cube of side 4 cm.The faces are coloured in red.the cube is cut into pieces of size 1 cm.How many cubes have no colour Ans:812.A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 813.using the digits 1,5,2,8 four digit numbers are formed and sum of all possible such numbers ans:10665614. 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:815.four persons can cross a bridge in 3,7,13,17 minutes.only two can cross at a time.find the minimum time taken by the fout to cross the bridge. ans :20

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I tried solving this question:3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the workAns: The answer has come like 10+21/8 days. I wonder why the answer has come in fractions. may be the figures entered by u are wrong. but here am giving the procedure i have followed to solve the sameprocedure: let the work be 'W' A can finish W work in 8 days => A can finish W/8 work in 1 day. Here A worked for 2 days => he completed W/4 work Remaining work = W-W/4 = 3W/4 Now, B can finish work in 14 days => B can finish W/14 in 1 day. Given that B finished 25% of remaining work = 25/100 (3W/4) = 3W/16 i.e., W/14 : 1 :: 3W/16: ? days... on simplification it is 21/8 days. Remaining Work = 3W/4- 3W/16 = W/2 Now C can finish W work in 16 days => C can finish W/16 work in 1 day. so C can finish remaining work ( W/2) in 8 days...( W/16:1 :: W/2: ?) So total days = 2+21/8+8 = 10+21/8 days..

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Hi friends, I got CTS exams on sunday.I could not solve these questions.Pls help me in solving it.The answers i gave may be right or wrong.So tell me the method to solve these problems.I have very short time.So tell me soon.1.If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330 2. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other. Ans: 3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans: 4. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12 5. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other 6. A bag contains 3 balls of 11 different colors each. Find the min no of chances to find at least 3 balls of same color?Ans : 23 (i need to know how it is solved)7.There are 1997 doors in a auditorium and as many as people as the no of doors open enter the auditorium .A door was closed and as many as people as no of doors open leave the auditorium . the process was repeated till the no of doors is equal to1.find the total no of peoples enter the auditorium?8. Find the values for the following problem:f(X)= 2X-1 + f(X-1) if X is not equal to zero and if f(X=0)=0 Value of f(5)a)15 b)24 c)22 d)None18.If f(f(X))=81 then the value of X=?9.A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted10. there are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors ion the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 resly. Similarly when the third one goes he does this for 3 6 9 12 15th doors resly. Find number of doors that are open at last11.There is a cube of side 4 cm.The faces are coloured in red.the cube is cut into pieces of size 1 cm.How many cubes have no colour Ans:812.A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 813.using the digits 1,5,2,8 four digit numbers are formed and sum of all possible such numbers ans:10665614. 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:815.four persons can cross a bridge in 3,7,13,17 minutes.only two can cross at a time.find the minimum time taken by the fout to cross the bridge. ans :20

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1.if all 6 are replaced with 9 from 1 to 100 then algebric sum would varies by 330.

explanation

first take the numbers which have 6 in their unit place - 06,16,26,36,46,56,66,76,86,96.

if all 6 in unit plce is replaced with 9 then in each case the increment would be 3.

so for all ten numbers total increment is 10*3=30.

then take all numbers which have 6 in their tenth place - 60,61,62,63,64,65,66,67,68,69

in each case if we replace 6 with 9 -90,91,92,93,94,95,96,97,98,99

then there is increment of 30 in each case .

so total increment for ten numbers is 10*30==300.

so the total increment including unit and tenth place is 30+300=330.

2.'A' starts at 11 A.M. with speed 4km\hr.B started at 1PM with speed 1km\h in 1st hr,2km\hr in 2nd hr so on.

A travels 2 hours untill B starts .so in 2 hours A traveled 4*2=8km.from 1 PM tll they meet at a point let they traveled t hours.so A traveled 4*t km.

B traveled ikm in 1st hour ,2km in 2nd hour, t km in t hour so total distance traveled is 1+2+3+.....+t=t(t+1)/2.

the distance traveled by each must be same in order to overtake at a point.

so 8+4t=t(t+1)/2 by solving the quadratic eqn t is found tom be 8 hours from 1 pm. so the time is 9 Pm.

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4. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12 ans: let total balls before addition of gray balls = T ratio of white balls and black balls before = 1:2 => white balls = 1*T/3 = T/3 Black balls = 2*T/3 = 2T/3 ratio of white, black and gray balls after addition = 2:4:3 Now total balls = T+9 => White balls = 2(T+9)/9 Black Balls = 4(T=9)/9 Gray balls = 3(T+9)/3 equating the number of black balls before and after addition 2T/3 = 4(T+9)/9 on solving T = 18 number of black balls = 2T/3 = 2*18/3 = 12 balla.

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8. Find the values for the following problem:f(X)= 2X-1 + f(X-1) if X is not equal to zero and if f(X=0)=0Value of f(5)ans: f(5) = 9 + f(4)f(4) = 7+ f(3)f(3) = 5+ f(2)f(2) = 3+ f(1)f(1)= 1+f(0) = 1+0 =1f(2) = 3+1 =4; f(3) = 5+4 =9f(4) = 7+9 =16f(5) = 9+16 =25f(5) = 25

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5. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other Ans: total distance = 500cm each car has to travel 250 cm to collide with each other now, a car travels 100 cm forward with 50 cm/s speed => time taken = 2 secs and 50 cm backward with a speed of 25 cm/s => tiime taken = 2 sec so, for 4 secs each car travels 100 - 50 = 50 cms.. each car has to travel 250 cms to collide therefore time taken to each car to travel 250 sm = 20 sec ( 50cm : 4 sec :: 250 cm : x sec) so both cars collide after 20 secs.

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9. A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted[/b]A cube has, No. of Edges = 12 No. of vertices = 8 No. of faces = 6(a)No. of faces of smaller cubes unpainted in Edges = (No.of edges * No. of smaller cubes per edge * No. of faces of smaller cubes unpainted) = (12 * 3 * 4) = 144(b)No. of faces of smaller cubes unpainted in faces = (No. of faces * No. of smaller cubes per face * No. of faces of smaller cubes unpainted) = (6 * 9 * 5) = 270©No. of faces of smaller cubes unpainted in vertices = (No. of vertices * No. of smaller cubes per vertex * No. of faces of smaller cubes unpainted) = (8 * 1 * 3) = 24Ans = 144 + 270 + 24 = 438

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Q:14--- 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:8Ans:A number is divisible by 4, if its two last digits are zeros or they make a two-digit number, which is divisible by 4.So using our digits -possible combinations of last two digits are--32,36,72,76 which can be divided by 4.(try like---23NA,26NA,27NA,32A,36A....)now use remaining two digits with the above combinations and hence the answer turns upto 8.

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5. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other Ans: total distance = 500cm each car has to travel 250 cm to collide with each other now, a car travels 100 cm forward with 50 cm/s speed => time taken = 2 secs and 50 cm backward with a speed of 25 cm/s => tiime taken = 2 sec so, for 4 secs each car travels 100 - 50 = 50 cms.. each car has to travel 250 cms to collide therefore time taken to each car to travel 250 sm = 20 sec ( 50cm : 4 sec :: 250 cm : x sec) so both cars collide after 20 secs.

I'm afraid the above solution is wrong..answer is 14 secthere are 2 cars moving opposite each other with 50cm/s for 100cm in forward direction and 50cms with 25cm/sec backward directiontherefore it is enough to calculate for 1 car ie 250cmsat 2 sec car moves 100cms forward and by next 2 sec it comes backward by 50cms so total 50cms for 4sec.for 6th sec car moves 150cms forward total and by 8th sec 100cms total.by 10th sec car moves 200cms forward and by 12th sec 150cms total.by 14secs car moves 250cms and collides with other car.so ans is 14sec

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I'm afraid the above solution is wrong..answer is 14 secthere are 2 cars moving opposite each other with 50cm/s for 100cm in forward direction and 50cms with 25cm/sec backward directiontherefore it is enough to calculate for 1 car ie 250cmsat 2 sec car moves 100cms forward and by next 2 sec it comes backward by 50cms so total 50cms for 4sec.for 6th sec car moves 150cms forward total and by 8th sec 100cms total.by 10th sec car moves 200cms forward and by 12th sec 150cms total.by 14secs car moves 250cms and collides with other car.so ans is 14sec

Hi Bindu,You are right.. I missed the logic that each car travells 250 cms, then collides even before coming back to 200. ##### Share on other sites

I tried solving this question:3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the workAns: The answer has come like 10+21/8 days. I wonder why the answer has come in fractions. may be the figures entered by u are wrong. but here am giving the procedure i have followed to solve the sameprocedure: let the work be 'W' A can finish W work in 8 days => A can finish W/8 work in 1 day. Here A worked for 2 days => he completed W/4 work Remaining work = W-W/4 = 3W/4 Now, B can finish work in 14 days => B can finish W/14 in 1 day. Given that B finished 25% of remaining work = 25/100 (3W/4) = 3W/16 i.e., W/14 : 1 :: 3W/16: ? days... on simplification it is 21/8 days. Remaining Work = 3W/4- 3W/16 = W/2 Now C can finish W work in 16 days => C can finish W/16 work in 1 day. so C can finish remaining work ( W/2) in 8 days...( W/16:1 :: W/2: ?) So total days = 2+21/8+8 = 10+21/8 days..

the answer to the 3rd question should be 11 21/8 days . Actually jessu did a mistake in his calculation 3w/4 -3w/16 = 9w/16 and not w/2 so C can solve the remaining work in 9 days .

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Hi friends, I got CTS exams on sunday.I could not solve these questions.Pls help me in solving it.The answers i gave may be right or wrong.So tell me the method to solve these problems.I have very short time.So tell me soon.1.If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330 2. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other. Ans: 3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans: 4. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12 5. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other 6. A bag contains 3 balls of 11 different colors each. Find the min no of chances to find at least 3 balls of same color?Ans : 23 (i need to know how it is solved)7.There are 1997 doors in a auditorium and as many as people as the no of doors open enter the auditorium .A door was closed and as many as people as no of doors open leave the auditorium . the process was repeated till the no of doors is equal to1.find the total no of peoples enter the auditorium?8. Find the values for the following problem:f(X)= 2X-1 + f(X-1) if X is not equal to zero and if f(X=0)=0 Value of f(5)a)15 b)24 c)22 d)None18.If f(f(X))=81 then the value of X=?9.A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted10. there are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors ion the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 resly. Similarly when the third one goes he does this for 3 6 9 12 15th doors resly. Find number of doors that are open at last11.There is a cube of side 4 cm.The faces are coloured in red.the cube is cut into pieces of size 1 cm.How many cubes have no colour Ans:812.A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 813.using the digits 1,5,2,8 four digit numbers are formed and sum of all possible such numbers ans:10665614. 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:815.four persons can cross a bridge in 3,7,13,17 minutes.only two can cross at a time.find the minimum time taken by the fout to cross the bridge. ans :20

question 13using 1,5,2,8 we can make 4! numbers without repetition . of these numbers if 8 is at unit's digit we have 3! such numbers similarly 2 will occur at units palce in 8 such numbers . thus the sum due to units place will be 8(1+ 2+5 +8)=96these numbers can occur at tens place , hunder's palce and thousand's palce at each place we will have there sum as 96 only . so the sum of all such numbers will be 96(1+10+100+1000)=96x1111=106656

Hi friends, I got CTS exams on sunday.I could not solve these questions.Pls help me in solving it.The answers i gave may be right or wrong.So tell me the method to solve these problems.I have very short time.So tell me soon.1.If all the 6 are replaced by 9, then the algebraic sum of all the numbers from 1 to 100(both inclusive) varies by Ans: 330 2. A starts at 11:00AM and travels at a speed of 4km/hr. B starts at 1:00PM and travels at 1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time they will meet each other. Ans: 3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the work Ans: 4. The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls. Ans:12 5. Two cars are 500 cm apart. each is moving forward for 100 cm at a velocity of 50 cm/s and receding back for 50 cm at 25 cm/s at what time they will collide with each other 6. A bag contains 3 balls of 11 different colors each. Find the min no of chances to find at least 3 balls of same color?Ans : 23 (i need to know how it is solved)7.There are 1997 doors in a auditorium and as many as people as the no of doors open enter the auditorium .A door was closed and as many as people as no of doors open leave the auditorium . the process was repeated till the no of doors is equal to1.find the total no of peoples enter the auditorium?8. Find the values for the following problem:f(X)= 2X-1 + f(X-1) if X is not equal to zero and if f(X=0)=0 Value of f(5)a)15 b)24 c)22 d)None18.If f(f(X))=81 then the value of X=?9.A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted10. there are 1000 doors that are of the open-close type. When a person opens the door he closes it and then opens the other. When the first person goes he opens-closes the doors ion the multiples of 1 i.e., he opens and closes all the doors. when the second goes he opens and closes the doors 2, 4 6 8 resly. Similarly when the third one goes he does this for 3 6 9 12 15th doors resly. Find number of doors that are open at last11.There is a cube of side 4 cm.The faces are coloured in red.the cube is cut into pieces of size 1 cm.How many cubes have no colour Ans:812.A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 813.using the digits 1,5,2,8 four digit numbers are formed and sum of all possible such numbers ans:10665614. 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:815.four persons can cross a bridge in 3,7,13,17 minutes.only two can cross at a time.find the minimum time taken by the fout to cross the bridge. ans :20

question 18> the only logic in could think of is let say f(x)=x*x so that makes f(f(x))=x*x*x*x=x^4 =81 therefore, x=3.I think o such question u need to go by instinct.

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hi this is sugi.i have got my cts test next week.can u plz explain the problem.A hollow cube of size 5cm is taken , with the thickness of 1cm . it is madeof smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remainunpainted 9. A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted[/b]A cube has, No. of Edges = 12 No. of vertices = 8 No. of faces = 6(a)No. of faces of smaller cubes unpainted in Edges = (No.of edges * No. of smaller cubes per edge * No. of faces of smaller cubes unpainted) = (12 * 3 * 4) = 144(B)No. of faces of smaller cubes unpainted in faces = (No. of faces * No. of smaller cubes per face * No. of faces of smaller cubes unpainted) = (6 * 9 * 5) = 270©No. of faces of smaller cubes unpainted in vertices = (No. of vertices * No. of smaller cubes per vertex * No. of faces of smaller cubes unpainted) = (8 * 1 * 3) = 24Ans = 144 + 270 + 24 = 438

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Q:14--- 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:8Ans:A number is divisible by 4, if its two last digits are zeros or they make a two-digit number, which is divisible by 4.So using our digits -possible combinations of last two digits are--32,36,72,76 which can be divided by 4.(try like---23NA,26NA,27NA,32A,36A....)now use remaining two digits with the above combinations and hence the answer turns upto 8.

GK---->A number is divisible by 4, if its two last digits are zeros or they make a two-digit number, which is divisible by 4.So using our digits -possible combinations of last two digits are--32,36,72,76 which can be divided by 4.the 4 digit no formed 7232,7236,7272,7276, 7632,7636,7672,7676 so the total no of possible combinations are 8.

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I'm afraid the above solution is wrong..

answer is 14 sec

there are 2 cars moving opposite each other with 50cm/s for 100cm in forward direction and 50cms with 25cm/sec backward direction

therefore it is enough to calculate for 1 car ie 250cms

at 2 sec car moves 100cms forward and by next 2 sec it comes backward by 50cms so total 50cms for 4sec.

for 6th sec car moves 150cms forward total and by 8th sec 100cms total.

by 10th sec car moves 200cms forward and by 12th sec 150cms total.

by 14secs car moves 250cms and collides with other car.

so ans is 14sec

YOU ARE RIGHT BUDDY ANSWER IS 14

0_____(2)____________________________100

50______(2+2)_____________!

!_______________(4+2)_____________________________________150

100_____________(6+2)____________!

!________________(8+2)_____________________________________200

150________(10+2)___________!

!_____________________________(12+2)_______250

HENCE 12+2=14.......

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I'm afraid the above solution is wrong..answer is 14 secthere are 2 cars moving opposite each other with 50cm/s for 100cm in forward direction and 50cms with 25cm/sec backward directiontherefore it is enough to calculate for 1 car ie 250cmsat 2 sec car moves 100cms forward and by next 2 sec it comes backward by 50cms so total 50cms for 4sec.for 6th sec car moves 150cms forward total and by 8th sec 100cms total.by 10th sec car moves 200cms forward and by 12th sec 150cms total.by 14secs car moves 250cms and collides with other car.so ans is 14sec

me 2 think that ans is 14 sec

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these typr of questions r not asked in latest cts pattern..

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these typr of questions r not asked in latest cts pattern..

Hi navya,then what type of questions are asked in cts.have you attended the test recently?which city r you from?

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Question 15

The persons will walk across the bridge in the order: 17,13,7,3 or 17,7,13,3. Either way gives a minimum time of 20 minutes.

Explanation

1) First person walks together with second (13 mins walker).

2) 13 mins walker reaches end of bridge and 17 mins walker has 4 mins (17-13) to reach end.

3)At this stage 7 min walker sets off and after 4 mins (when 13 min walker reaches other side) the last walker sets off, leaving the 7 mins walker 3 minutes to reach the other side.

4) The 3 minute walker will arrive at the other side with the 7 minute walker.

Therefore,

Total time taken = Time taken by 17 min walker+ (Time taken by 7 min walker - (Extra time available from 13 min walker arriving before 17 min walker))

=17+(7-(17-13))

=20 mins

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Question 3

6. A bag contains 3 balls of 11 different colors each. Find the min no of chances to find at least 3 balls of same color?

23 chances

Explanation

After picking 12 balls I will have at least 2 balls of the same color (i.e, the other eleven were different colors). Then I pick 10 balls that are not the same color as the ones I picked. So now I have 2 of each color. The next ball I pick will ensure I have 3 balls of the same color.

So total chances=12+10+1=23

I would have liked the question to be phrased: "Find the min. no of chances to definitely find 3 balls of same color?", makes it a bit clearer .

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Question 4

The ratio of white balls and black balls is 1:2. If 9 gray balls is added it becomes 2:4:3. Then what is number of black balls?

12

Alternate Explanation

Let x be white balls. Then there are 2x black balls. Therefore, x/(x+2x+9)=2/9 i.e, writing equation of new proportion of white balls.

Solving gives x=6. Therefore black balls = 12.

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Question 15

The persons will walk across the bridge in the order: 17,13,7,3 or 17,7,13,3. Either way gives a minimum time of 20 minutes.

Explanation

1) First person walks together with second (13 mins walker).

2) 13 mins walker reaches end of bridge and 17 mins walker has 4 mins (17-13) to reach end.

3)At this stage 7 min walker sets off and after 4 mins (when 13 min walker reaches other side) the last walker sets off, leaving the 7 mins walker 3 minutes to reach the other side.

4) The 3 minute walker will arrive at the other side with the 7 minute walker.

Therefore,

Total time taken = Time taken by 17 min walker+ (Time taken by 7 min walker - (Extra time available from 13 min walker arriving before 17 min walker))

=17+(7-(17-13))

=20 mins

good thinking ##### Share on other sites

--18.If f(f(X))=81 then the value of X=3, consider f(X)=X²in that case f(3)=3²=9and f(f(3))=f(9)=9²=81Ans. X=3----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------9. A hollow cube of size 5cm is taken , with the thickness of 1cm . it is made of smaller cubes of size 1cm . if the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?total 1cm cubes in 5cm cube=5x5x5=125hollow part of 5cm cube with 1cm thick edges=(no. of cubes forming side length-(2 x no. of cubes forming edge thickness))³=> hollow part = (5-(2x1cm))³ = (5-2)³ = 3³ = 27Now number of blocks that form edge or surface of hollow 5cm cube = 125-27 = 98total sides of all 98 1cm cubes= 98x6 = 588number of 1 cm sides painted = (5x5)x6 = 150, since 5x5 1cm squares on each of six sides of bigger cubetotal sides not painted = 588-150 = 438Ans. 438--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------11.There is a cube of side 4 cm.The faces are coloured in red.the cube is cut into pieces of size 1 cm.How many cubes have no colour Ans:812.A cube of 12 mm is painted on all its side. If it is made up of small cubes of size 3mm. If the big cube is splitted into those small cubes, the number of cubes that remain unpainted is Ans: 8both these questions have same logic except that the numbers are different. Its the same as calculating the hollow part of a cube. (no. of cubes forming side length-(2 x no. of cubes forming edge thickness))³in 11., (4-(2 x 1))³ = 2³ = 8in 12., [(12/3)-{2 x (3/3)}]³ = [4-{2 x 1}]³ = [4-2]³= 2³ = 8--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------13.using the digits 1,5,2,8 four digit numbers are formed and sum of all possible such numbers ans:106656[1000 x 3! x (1+5+2+8)] + [100 x 3! x (1+5+2+8)] + [10 x 3! x (1+5+2+8)] + [1 x 3! x (1+5+2+8)]==> 3! x (1+5+2+8) [1000 + 100 + 10 + 1]==> 6 x 16 x 1111==> 106656--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------14. 2,3,6,7 using these numbers form the possible four digit numbers that are divisible by 4. ans:8Among the permutations from the above 4 digits, the numbers ending in 32,36,72 and 76 are only divisible by 4.Therefore, 2! x 4 =2 x 4 = 8The numbers are: 6732, 7632, 2736, 7236, 3675, 6372, 2376, 3276!  i hope am right abt all.. ##### Share on other sites

I tried solving this question:3. A,B,C, can do a work in 8,14,16 days respectively. A does the work for 2 days. B continues from it and finishes till 25% of the remaining work. C finishes the remaining work. How many days would have taken to complete the workAns: The answer has come like 10+21/8 days. I wonder why the answer has come in fractions. may be the figures entered by u are wrong. but here am giving the procedure i have followed to solve the sameprocedure: let the work be 'W' A can finish W work in 8 days => A can finish W/8 work in 1 day. Here A worked for 2 days => he completed W/4 work Remaining work = W-W/4 = 3W/4 Now, B can finish work in 14 days => B can finish W/14 in 1 day. Given that B finished 25% of remaining work = 25/100 (3W/4) = 3W/16 i.e., W/14 : 1 :: 3W/16: ? days... on simplification it is 21/8 days. Remaining Work = 3W/4- 3W/16 = W/2 Now C can finish W work in 16 days => C can finish W/16 work in 1 day. so C can finish remaining work ( W/2) in 8 days...( W/16:1 :: W/2: ?) So total days = 2+21/8+8 = 10+21/8 days..hi this is aswin i hv infy on 28th.. can any one tell me the specific pattern? was the following topics present?venn diagramstabl,bar,pie charts..?data sufficiency..?statements and assumtions..?is reading of shkanthula devi useful nw..? else wht book wld help..?waiting 4 ur replies..

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