Qu@ntose

Aman reaches school every day at 5pm to pick up his children. On a Saturday, the school got over at 4pm and the children started walking towards home. Aman met them on their way and returned home 30 min earlier. How long did the children walk? Solution- Let the meeting point be A. H----------A-------------S As Aman is reaching home 30 min earlier, it means these 30 min are saved by not travelling the distance 'AS' twice. Time taken by Aman to travel distance AS = 30/2 = 15 min As Aman reaches school at 5pm and from A it takes 15 min to reach the point S,that means at 4:45 Aman is at point A. Hence, the children must have walked for 45 min ANS

If the integers m and n are chosen at random between 1 and 100, then the probability that a number of the form 7^m + 7^n is divisible by 5 is: (a)1/5 (b)1/4 (c)1/7 (d)1/49 Solution- (7^m + 7^n) mod 5 = 2^m +2^n Now, the number to be divisible by 5, it must end in 5 or 0. 2^m + 2^n can never end in 5 as it is an even number (minimum value of m,n is 1), so the number must end in 0 if it has to be divisible by 5. Cyclicity of 2 is 4 (2,4,8,6), 2+8 or 6+4 are the only cases when 2^m +2^n is divisible by 5. last digit to be 2 and 8, 2^x must be of the form 2^(k+1) and 2^(k+3) respectively Similarly, last digit to be 4 and 6 it must be of the form 2^(k+2) and 2^(k+4) respectively Now in both of these cases we will have 25 pairs each, Required cases = (25*25 + 25*25)*2  [25*25 +25*25 for both cases and multiplied by 2 as m = 1, n=3 or n=1 or m =3 are both valid cases)  Probability = 25*25*2*2/(100*100) = 1/4 ANS

How much time will an express train of length 150 meters and running at a speed of 75 kmph take to cross a man walking at 5 m/s inside a passenger train of length 200 meters and running at 15 kmph in a direction opposite to that of the express train. The man is walking inside the train and in opposite direction to that of the train. (Assume the man does not reach the end of his train meanwhile.) Solution- Speed of man with respect to passenger train = 5m/sec  or 18km/hr Speed of man with respect to ground = 18 - 15 = 3km/hr Speed of man with respect to express train = 75 - 3 = 72 km/hr or 20m/sec Time taken by express train to cross man = 150/20 = 7.5 sec ANS

                                           Solutions:-

Tony and Harry begin to run in opposite directions on a circular path of radius 35 m at 20 m/sec and 11 m/sec respectively from the same point. What is the time taken by them to meet for the third time at the starting point? (A) 11 min (B) 220 sec (C) 8 min 40sec (D) 325 sec Solution:- Radius = 35 m. Circumference = 2 x 22/7 x 35 = 220 m Time taken for them to meet for the first time at the starting point is LCM [220/20, 220/11] = LCM [11, 20] = 220sec To meet for the third time at the staring point from the start, they need 220 x 3 = 660 sec = 11 minutes

Q1)what is the number of children in the age group 12-15 who like basketball? Q2)If there are 12 boys in the age group 16-18,then how many boys are there in the age group 12-15? Q3)How many boys in England like Football? Q4)What is the number of English boys who like Tennis? Solutions:-

Three children, Rekha, Shankar and Mukesh, were playing the game of Tic-Tac-Toe, on a grid of 3 × 3 squares. Each game was played by all the three children, with the rules slightly modified from the usual, as described below. Each person has his/her own symbol, referred to as his/her 'mark' and in every turn, he/she places the same mark on the grid. The columns are labelled A to C, from left to right, and the rows are numbered 1 to 3, from top to bottom. The position of a mark on the grid is given by the combination of the column and row labels of the square in which it is placed. For example, a mark in position C2 means that the mark is in column C and row 2. The first person to play a game can place his mark on any square in the 3 × 3 grid except B2. In every subsequent turn, each person has to place his/her mark in any empty square, which is not in the same row or column as that of the mark that was placed immediately before his turn not in any diag

A building, which has 200 floors, has exactly three elevators - Elevator A, Elevator B and Elevator C. Only Elevator A stops at the ground floor (i.e., floor 0). Elevator A stops additionally at floors 5, 10, 15 and so on; Elevator B stops only at floors 4, 8, 12 and so on; Elevator C stops only at floors 6, 12, 18, 24 and so on. Further, all the floors are connected by a staircase and any floor can be reached from any other floor using this staircase. Tarun, a network engineer who visits various offices in this building everyday, always tries to reach the desired floor by taking the elevators so that he minimizes the number of floors that he has to walk using the staircase. Q1.     D I R E C T I O N S   f o r   q u e s t i o n s   1   a n d   2 :  Select the correct alternative from the given choices. Tarun got into Elevator A at the ground floor. He got down from Elevator A at the p t h  floor. He got into Elevator B at this floor and got down at the q t h  floor suc

Five teams - A through E - participated in a hockey tournament in which each team played against each of the other teams exactly once. In any match, the winning team is awarded four points and the losing team no points. In case of a draw, the two teams are awarded one point each. At the end of the tournament, B had two points more than E, which, in turn, had two points more than A, which, in turn, had one point less than D, which, in turn, had three points more than C. 1)How many matches did C draw? 2)How many matches did B win? 3)What is the result of the match between C and D? Solutions:-

D I R E C T I O N S   f o r   q u e s t i o n s   1 3   t o   1 6 :   Answer the questions on the basis of the information given below. Harish, a manager at an FMCG company, conducted a survey to find the most preferred brand of soaps among Luck, Smenthol and Tears. The survey had 240 respondents and each respondent must vote for at least one and at most three brands as his preferred brand. After the survey, Harish found that Luck received twice the number of votes as Smenthol, which, in turn, received forty votes more than Tears. Further, the number of respondents who voted for exactly one, exactly two and all three brands are in the ratio 2 : 3 : 1. Q13.     D I R E C T I O N S   f o r   q u e s t i o n s   1 3   a n d   1 4 :  Type your answer in the text box provided below the question. What is the total number of votes that Luck received? Q14.     D I R E C T I O N S   f o r   q u e s t i o n s   1 3   a n d   1 4 :  Type your answer in the text box provided bel

Six cities, A through F, are connected by certain two-way roads, such that any of the six cities can be reached from any of the other cities, using these roads, either directly or after passing through some of the other cities. The following table provides partial information about the minimum number of cities that one must pass through when travelling between any pair of cities: Q1.     D I R E C T I O N S   f o r   q u e s t i o n   1 :  Select the correct alternative from the given choices. Which of the following pairs of cities are directly connected? E and C D and F B and E   a)  Only (i) and (ii)        b)  Only (ii)        c)  Only (iii)       d)  Only (ii) and (iii)      Q2.     D I R E C T I O N S   f o r   q u e s t i o n s   2   a n d   3 :  Type your answer in the text box provided below the question. In how many ways can a person travel from C to D without passing through any city twice? Q3.     D I R E C T I O N S   f o r   q u

ABC is a right angled triangle. The longest side is 10 cm, and the sum of two of its sides is 12 cm. What is the maximum possible area (in cm) of the triangle ABC? Solution-

Directions for questions 1 to 5: Answer the questions on the basis of the information given below. Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament.The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, each team playing with every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. Every round involves exactly one match for every team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup. The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a

ABCD is a perfect square.Given that C:D=4:1.Find Max[ABCD] Solution:- Search for squares whose last two digits are in the ratio of 4:1 21^2=441 (50(n)+21=21,51)...where n=0,1 (50(n)-21=29,79)...where n=0,1 79^2=6241 Note:-Do memorize Squares upto 25

1)What was the total number of participants in the basket ball selection trials? 1. 147 2 .186 3 .194 4 .None of these 2)What was the total number of baskets done during the whole process? 1 .1211 2 .1225 3 .1048 4 .Cannot be determined 3)If the selection process is divided into three rounds as: The participants who had done less than 4 baskets are eliminated after 1st round, and the participants who did more than 12 baskets were quali􀂡ed directly for the 3rd round and need not participate in the 2nd one. Also for every basket the participant would be awarded ‘1’ point and ‘0’ point for every miss. 4)What is the mean score of the participants who participated in 1st round but not in 2nd round? 1 .3.76 2 .1.69 3 .2.71 4 .13.62 If the number of participants who did 4 baskets were 9, then what is the average number of baskets done by the participants who did between 5 to 12 baskets (both included)? 1 .5.22 2 .7.33 3 .3.91 4 .9.12

Solutions:- Answers:- 1) Thursday         2)   31st            3)9th-tuesday

A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from people already solicited. People already solicited represents 60% of people, the college will ask for donations. If college is to raise exactly the amount needed for the new building, what should be the average donation (in Rs.) from remaining people to be solicited? Solution:- lets consider 100 people 60 people solicited 60 people pay Rs 600 each total money=36000 Now, 75% of total amount =36000 25% of total amount=? (25/75)*36000 =12000

f(x+y)=f(x)*f(y) for al x and y. f(4) = 3,then what is the value of f(-8)? Solution- f(4) = 3 =>f(2+2) = f(2)*f(2) =>3 = f(2)^2 =>±√3 = f(2)----------(1) Now, f(2) =  f(4-2) => f(4 - 2) = f(4)*f(-2) =>±√3 = 3*f(-2) =>f(-2) = ±1/√3------(2) f(-8) = f(-4 - 4) = f(-4)*f(-4) and, f(-4) = f(-2-2) = f(-2)*f(-2) So, f(-8) = f(-2)*f(-2)*f(-2)*f(-2)        f(-8) = f(-2)^4 = (1/√3)^4        f(-8) = 1/9 ANS

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares? (1) 3 (2) 2 (3) 0 (4) 1 Solutions:- N=xxyy                                               N=1000x+100x+10y+y =1100x+11y 11(100x+y) (100x+y) will be of the form     x 0 y  ex:- (100*3 +4)= 3 0 4                             x 0 y  For a number to be divisible by 11 difference of (sum of Unit's digit-sum of tens digit ) must be 0,11 x + y =11 y=11-x 11(100x + 11- x) 121(9x+1) 9x+1 will be a perfect sqaure when x=7                                                          y=4 Ans:- Option 4