Quant Question Bank by VP  Set 2

Q27) N is a natural number which gives remainders 1 and 2 when divided by 6 and 5, respectively. All such N’s are written in the ascending order, side by side from left to right. What is the 99th digit from the left?

Q28) Boxes of 2 types viz. A and B are used for packing balls of 2 different colours. Each of the type A boxescan hold a maximum of 17 blue balls or 19 green balls, and each of the type B boxes can hold amaximum of 18 blue balls or 23 green balls. When all the boxes of type A are to be completely filledwith blue balls and all the boxes of type B with green balls, the total number of balls required is 566. Butwhen the boxes of type A are to be completely filled with green balls and the boxes of type B with blueballs, the total number of balls required is 49 less. How many boxes are there? (All balls of the same colour and are identical.)

Q29) If bhavya and Karmveer work on alternate days to complete a work, then the work gets completed in
exactly 24 days. If B and K denote the number of days required by bhavya and Karmveer respectively tocomplete the work independently, then how many ordered pairs of integral values of R and K are possible?

Q30) How many fourdigit numbers, having distinct digits, using the digits 1, 2, 3, 4 and 5 can be formedsuch that the numbers formed are divisible by each of the digits used in the number ?

Q31) The product of three positive integers is 6 times their sum. One of these integers is the sum of the othertwo integers. If the product of these three numbers is denoted by P, then find the sum of all distinctpossible values of P.

Q32) Find the range of x where x  3  4 > 3

Q33) N coins are lying on a table. Two friends A and B play a game in which they have to pick at least one coin and at most eight coins from the table turn by turn. The person who clears the table last looses the game. A starts the game. No player is allowed to pass his turn without picking any coin. Find the maximum value of N (a two digit number) such that no matter how many coins A pick at the start, he will always lose.

Q34) Three distinct numbers are randomly selected from the first 20 natural numbers. Find the probabilitythat the selected numbers are in a geometric progression having common ratio greater than 1.

Q35) After the addition of 35 liters of water to a 'can' of diluted milk, the concentration of milk in the 'can'
becomes 30%. Now, further 40 liters of water is added to the can and the concentration of milk in thecan gets reduced by 10 percentage points. How many more liters of water must be added to the cannow such that the concentration of milk in the can becomes 8%?

Q36) If log2(X) + log4(X) = log0.25 (√6) and x > 0, then x is

Q37) A page is torn from a novel. The sum of the remaining page numbers is 10000. What is the sum of the two pagenumbers on the torn page of this novel?

Q38) A number 4^16 + 1 is divisible by x. Which among the following is also divisible by x?
a) 4^96 + 1
b) 4^32 + 1
c) 4^8 + 1
d) 4^48 + 1

Q39) Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?

Q40) If the highest power of 20 in n! is x, then x can take the following values except
a. 27
b. 28
c. 30
d. 31

Q41) Three horses : Kanishka, Silver Streak and Arabian Knight are the only horses competing in a race and
only one of these three can win the race. If Kanishka is twice as likely to win as Silver Streak and SliverStreak is twice as likely to win as Arabian Knight, then what is the probability of Arabian Knight losing this race?

Q42) In how many ways can 3 identical books be distributed among 5 students such that no student gets more than 2 books?

Q43) There is a railway line that passes through a tunnel of length 200 metres. A road runs parallel with the
tunnel. One day when the driver of a 150 metre long train is exactly at the middle of the tunnel, a man Schumi, who is on the road parallel to the tunnel starts from one of the ends of the tunnel towards the other end. If Schumi and the train cross the tunnel simultaneously, then what is the ratio of the time taken by them to cross each other when they move in the same direction to the time taken by them to cross each other when they move in the opposite direction

Q44) On any given day, the bank balance of a person A is the sum of his bank balance on the previous day
and his bank balance on the next day. If the bank balance of A on 18th November 2007 and 19th November 2007 is Rs.4000 and Rs.2000 respectively, then what will be his bank balance on 16th November 2008? (Assume that the bank balance of A can be negative.)

Q45) Nando starts reading all the letters of the English alphabets starting from ‘a’ at the rate of 1 letter per second. Nachi, his younger brother reads the vowels only starting from ‘a’ at the rate of 1 vowel per second. This cycle of reading letters at the uniform rate continues indefinitely. If the two of them start reading together, after how much time, will they just complete reading the letter ‘u’ together?

Q46) There is a group of 11 people namely: A1, A2, A3 ... A11. The number of balls with A1 through A11 in that order is in arithmetic progression. If the number of balls with A1, A3, A5, A7, A9 and A11 is equal to 72, then what is the number of balls with A1, A6 and A11 put together?
(a) 24
(b) 36
(c) 48
(d) Cannot be determined