Quant Question Bank by VP  Set 2

Q78) The sum of the squares of three consecutive integers is a perfect square. How many such triplets exist?

Q79) Find the number of 3digit numbers that can be formed using the digits 1, 2, 3, 4 and 5, without repetition of digits, such that they are divisible by 6

Q80) A bottle contains a solution of honey and water. If 60 ml of honey and 30 ml of water are added to the solution, the ratio of honey to water becomes 2 : 3. Instead, if 60 ml of water and 30 ml of honey are added to the solution, the ratio of honey to water becomes 7 : 13. What was the original volume of the solution?

Q81) A language school has 2001 students. The percentage of students of this school who study French is between80 and 85 and the percentage of the students of the school who study Spanish is between 30 and 40. Eachstudent of this school studies at least one of the two languages. What is the absolute difference between theminimum and maximum possible numbers of students who study both French and Spanish?

Q82) What is the remainder when 13^66 – 23 is divided by 183?

Q83) Mr. Jha the captain, distributed toffees between players of his team. The first player received50 toffees and then one tenth of the remaining toffees available with Mr. Jha. The second player received 100toffees and then one tenth of the remaining toffees available with the captain. The third player received 150 toffeesand then one tenth of the remaining toffees available with the captain. The sequence continued like this tillMr jha was left with no toffee. After distributing the toffees Mr. Jha found that every player of his teamhad got the same number of toffees. How many players are there in the team including the captain?

Q84) If Sn = 1 – 3 + 5 – 7 + 9 – 11+ .....upto ‘n’ terms, then what is the value of S(1001) – S(1002) + S(1003) ?

Q85) If a, b, c and d are real numbers with a^2 + b^2 + c^2 + d^2 = 100, then what is the maximum value of 2a + 3b + 6c + 24d

Q86) abc is a 3 digit number less than 500. If 63a + 7b + c is div by 72, how many different possible value of 2a + b + c exist ?

Q87) Find the no of pairs of positive integers (x, y) satisfying the equation x^6 = y^2 + 127

Q88) Find the sum of the digits of the least natural number N, such that the sum of the cubes of the four smallest distinct divisors of N is 2N?

Q89) Find the number of primes p, such that p^2 + 3p  1 is also a prime?

Q90) There is a house in Mumbai such that the sum of house numbers on one side is equal to that of the other side .There are more than 50 houses but less than 500 . What is the house number?

Let there be y houses and x be the house no we r looking for
now sum of no on one side of house(x) is 1 + 2 + ... + (x1) = (x  1)x/2
and sum of houses on other side of house = y(y+1)/2  x(x+1)/2
equate both
simplify n u get x^2=y(y+1)/2
multiplying both sides by 8
(2y+1)^2 = 8x^2 +1
let 2y+1 =p and 2x=1
so p^2  2q^2 = 1
this can be solved using pell number
soln will be square triangular no between 50^2 and 500^2
41616 is only such no
so x = root 41616 = 204
and y = 288

Q91) It is given that
f(8)=56
f(7)=42
f(6)=30
f(5)=20
Then what is the possiblr value of f(3) among these
a) 126
b) 64
c) 16
d) 12

Q92) Find 1/( 6 * 11) + 1/(11 * 16) + 1/(16 * 21) + ... 50 terms

Q93) There is a 50m long army platoon marching ahead in a uniform speed . The last person in the platoon wants to give a letter to the first person leading the platoon. So while the platoon is marching he runs ahead, reaches the first person and hands over the letter to him and without stopping he runs and comes back to his original position. In the mean time the whole platoon has moved ahead by 50m. The question is how much distance did the last person cover in that time. Assuming that he ran the whole distance with uniform speed.

Q94) Amit can complete a piece of work in 2.25 days. Badri takes double the time taken by Amit. Chetan takes double that of Badri, and Das takes double dat of Chetan to complete the same task. They are split into two groups (of one or more persons) such that the differnce b/w the times taken by the two groups to complete the same work is minimum. What could be the compostion of the faster group?
a) Amit and Das
b) Badri and Chetan
c) Badri, Chetan and Das
d) Amit alone

Q95) A rope of fixed length is cut into two parts with a single cut. What is the probability that one part is at least twice the other ?

Q96) A and B take a straight route to the same terminal points and travel with constant speed. At the initial moment, the positions of the two and the terminal point form an equilateral triangle. When A moves a distance of 80 km, the triangle becomes right angled. when A is at a distance of 120 km from the end point, B has already reached the end point. Find the distance between them at the initial moment assuming that there are integral distances throughout the movements described.