Number System Questions - Test 1

Q1. The integers 1, 2, ........, 40 are written on a blackboard. The following operation is then repeated 39 times: in each repetition, any two numbers say a and b, currently on the blackboard are erased and a new number a+b-1 is written. What will be the number left on the board at the end?

Q2. If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum the first 30 terms?

Q3. How many three-digit positive integers have their hundreds, tens and units’ digits in ascending order?

Q4. From a place P, buses to A leave once every 30 minutes, buses to B leave once every 35 minutes, buses to C leave once every 45 minutes. If buses left for A, B and C simultaneously at 10:00 a.m., from P, when is the next occasion when buses leave together for each of the 3 destinations?

Q6. There are 8375 raisin chocolates, 5025 almond chocolates and 20100 cashew nut chocolates available. The chocolates have to be arranged in boxes such that the combination of chocolates in each box is the same, i.e., each box contains the same number of chocolates of each kind and no chocolates of any kind are left over. Find the number of boxes required if minimum number of chocolates are put in each box.

Q7. When 2^256 is divided by 17 the remainder would be.

Q8. Find the units digit of 34563^20359 + 2358^784.

Q9. A certain number of chocolates which is a perfect square are distributed among 2156 students of a school equally. Find the minimum number of chocolates distributed given that it is greater than 90,000.

Q10. Rahul had some chocolates with him. He had just enough chocolates to distribute them among two groups of children A and B in the following manner. He distributed the chocolates among the children in group A such that each child got as many chocolates as the number of children in it. He distributed the chocolates among the children in group B such that each child got as many chocolates as the square of the number of children in it. He distributed 9 more chocolates to children in group A than in group B. If he had less than 600 chocolates, how many possibilities exist for the number of chocolates with him?

Q11. The number of positive integers valued pairs (x, y), satisfying 4x – 17y = 1 and x≤1000 is.

Q12.  If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be.

Q13. A rich merchant had collected many gold coins. He did not want anybody to know about him. One day, his wife asked, ‘‘How many gold coins do we have 7’’ After pausing a moment, he replied, ‘‘Well! If I divide the coins into two unequal numbers, then 48 times the difference between the two numbers equals the difference between the squares of the two numbers.’’ The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins the merchant has?

Q14. Each of A, B and C had some marbles with them. B distributed half the marbles with him among A and C in the ratio 1: 3. Then C distributed half the marbles with him among A and B in the ratio 1: 3. After that, A distributed half the marbles with him among B and C in the ratio 1: 3. If each of them now has 64 marbles, find the difference between the number of marbles with A and C in the beginning (TITA).

Q15. If a certain amount of money is divided equally among N persons, each one receives Rs 352. However, if two persons receive Rs 506 each and the remaining amount is divided equally among the other persons, each of them receive less than or equal to Rs 330. Then, the maximum possible value of N is (TITA).