The digits of a three number are in AP. If the number is subtracted from the number formed by reversing its digits, the result is 396. What could be the original number?
Answer: B The difference between 3-digit number and its reverse is 99 times the difference between its extreme (hundred and units) digits. As the first difference is 396, the second is 4. Further as the digits are in AP and the hundred's digits is less than the unit's digit, we have following possibilities 135, 246, 357, 468, 579...
Q. No. 8:
Three persons Abhishek, Dishant and Prashant were born on different days in the same year. If the date and month of birth of Abhishek, Dishant and Prashant are numerically equal, then what could be the minimum difference in the ages of youngest and oldest in days?
Answer: C To have the minimum differences in the ages of the oldest and youngest. One of them should be born in February. Also the other two should be born in March and April of January and March. Difference between the youngest and the oldest is the number of days from 2/2 to 4/4 = (26+31+4) = 61 or, 1/1 to 3/3 = 30+28+3 = 61 days.
Q. No. 9:
The total age of some 7 years old and some 5 years old children is 60 years. If I have to select a team from these children such that their total age is 48 years, In how many ways can it be done?
Answer: C Let 'a' children of 7 years and 'b' children of 5 years be taken. Then 7a+5b =48. This is possible only when x=4 and b=4. Hence only one combination is possible.
Q. No. 10:
Out of a group of people, seven times of the square root of a number of people were seen going away for a job and one pair remained unemployed. How many people were there in the group?
Answer: B Let the number of people be 'p' We get, 7{1/2 * x1/2}+2 =x Taking p= 16, Find that the above equation is correct. Thus total number of people in the group be 16.
Q. No. 11:
A and B throws one dice for a stake of Rs 11, which is to be won by the player who first throws a six. The game ends when the stake is won by A or B. If A has the first throw, then what are their respective expectations?
Answer: B Expectation of winning A => [(1/6) + (5/6*5/6*1/6)+...........]*11 => (1/6)/(1- 25/36) * 11 =6 Similarly we get the expectation of B as 5.
Q. No. 12:
There are 2 mean, 3 women and 1 child in Pradeep’s family and 1 man, 1 woman and 2 children in Prabhat’s family. The recommended calorie requirement is- Men: 240, Women: 1990, Children: 1800 and for proteins is: Men: 55 gm, Woman: 45 gm, children: 33 gm. Calculate the total requirement of calories and proteins for each of the two families.
Answer: A The recommended calorie requirements for men, women and children are 2400, 1900 and 1800 respectively and the recommended protein requirements for men, women and children are 55 gm, 45 gm and 33 gm respectively. For Pradeep’s family: Calorie requirement = 2 × 2400 + 3 × 1900 + 1 × 19800 = 12300 Protein requirement = 2 × 55 + 3 × 45 + 1 × 33 = 278 gm For Prabhat’s family: Calorie requirement = 1 × 2400 + 1 × 1900 + 2 × 1800 = 7900 Protein requirement = 1 × 55 + 1 × 45 + 2 × 33 = 166 gm. As option (A) has a match, it is the correct answer.