Quant Question Bank by VP  Set 2

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.

Q97) In a certain country there are four states. Each state has four major cities. All the major cities in a state are connected with each other via three different modes of transport namely rail, road and air. But a city is connected a another city via only one mode of transport if it belongs to the other states. What is the total number of different routes constructed among the major cities in the given country?

Q98) If x = (a  1)(b  2)(c  3)(d  4)(e  5), where a, b, c, d and e are distinct natural numbers less than 6. If x is a non zero integer, then the number of sets of possible values a, b, c, d and e are

Q99) There's 14 seats in a row and 7 couples. 6 Couples sit next to each other, but the 7th couple cannot. How many different ways can they be seated?

Q100) A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One dice has 4 red face and 2 blue faces. How many red and blue faces should the other dice have for both the to players have same chances of winning?
a) 3 red and 3 blue faces
b) 2 red and remaining blue
c) 6 red and 0 blue
d) 4 red and remaining blue