Quant Question Bank by VP  Set 2

Q23) How many integers “a” are there such that 9x^2 + 3ax + (a + 5) > 0 for all values of x?

Q24) xy + zy = 37 and xz + zy = 72. Find the number of ordered triplets (x, y and z) such that x, y and z are positive integers

Q25) Two people start swimming from the opposite ends of a swimming pool simultaneously. They meet at a distance of 410 m from one of the ends and continue swimming further till they reach the opposite ends. They take rest for 1 hr each and then start off the return journey. Now they meet at a distance of 230 m from the other end. Find the length of the pool.
(1) 750 m
(2) 1000 m
(3) 1100 m
(4) 840 m

Q26) Lakhjeet had 130 lts of blue paint,160 lts of red paint, and 180 lts of white paint. He painted four equallysized stripes on a wall, making a blue stripe, a red stripe, a white stripe and a pink stripe. Pink paint is a mixture of red and white paints. When lakhjeet finished, he had equal amount of blue, red, and whitepaints left. If he has to paint four more stripes of the same dimensions on another wall in exactly thesame way, then which of the following is true?
(1) lakhjeet requires 30 lts of blue paint, 0 lts of red paint and 40 lts of white paint
(2) lakhjeet requires 30 lts of blue paint, 60 lts of red paint and 60 lts of white paint
(3) lakhjeet requires 30 lts of blue paint, 60 lts of red paint and 80 lts of white paint
(4) lakhjeet requires 80 lts of blue paint, 110 lts of red paint and 130 lts of white paint

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?