#Numbers - 18

F(x) is a fourth order polynomial with integer coefficients and with no common factor. The roots of F(x) are -2,-1,1,2.If P is a prime number greater than 97,then the largest integer that divides F(p) for all the values of p is

(a)72
(b)120
(c)240
(d)360
(e)None of these

Solution -
F(x) = (x-2)(x-1)(x+1)(x+2)
P must be of the form - 6k+1/6k-1
Substituting the value of p(6k-1) in the eqn,
(6k-3)(6k-2)(6k)(6k+1)
3*2*6=36 
Substituting the value of p(6k+1) in the eqn,
(6k-1)(6k)(6k+2)(6k+3)
6*2*3=36
so 72 must be a factor 
now options (a),(d) and (e) are left,
now they are 5 consecutive numbers with middle term missing, starting with an odd number
(6k-1)(6k+2)(6k)(6k+3)or
(6k-3)(6k-2)(6k)(6k+1)
the number will always contain a multiple of 5
36*2*5=360 ANS

Comments

Post a Comment

Popular posts from this blog

#Profit&Loss-1

A shopkeeper uses false weights thereby cheats customer by giving 750 gm instead of 1 kg. He also claims that he sells rice at the cost price. In order to increase his sales he offered 125 gm of rice free with every 1 kg of rice. What is his overall percentage(approximate) profit if a customer buys 1 kg of rice and if the shopkeeper uses false weight to measure 125 gm also? Solution- Let the cost price of 1 gm of rice = Re 1 Cost Price of 750 gm = Rs. 750 Selling Price = Rs. 1000 We know that, SP = CP*(1 + Profit%) He is offering 125 gm for free but actually he is just giving 125*3/4 gms for free => SP = 1000*1 + 125*(3/4)*0 =>CP = 750 + 125*(3/4) => 1000 = (750 + 125*0.75)*(1 + Profit%) => Profit% = 18.51% Ans
Read more

# DILR-1

The currency of the country Banama is Rupas (Rp). There are exactly five denominations in which the currency is available – Rp 2, Rp 3, Rp 7, Rp 17 and Rp 19. Each of five persons, A through E, had notes of exactly one denomination with him and no two persons among the five had notes of the same denomination. On a particular day, the five persons visited a shop and each of them purchased a different product. The amounts that A through E paid the shopkeeper were Rp 102, Rp 357, Rp 399, Rp 238 and Rp 147, in that order. Further, the number of notes that each person gave the shopkeeper was distinct. However, the amount that each person paid the shopkeeper was more than the price of the product that he purchased. Therefore, the shopkeeper returned the excess amounts to each of A through E in the form of 2 notes, 4 notes, 1 note, 2 notes and 1 note respectively, but in denomination(s) different from that in which the person had paid the shopkeeper. Q1)What is the total numb
Read more

#DILR-18

Image
A building, which has 200 floors, has exactly three elevators - Elevator A, Elevator B and Elevator C. Only Elevator A stops at the ground floor (i.e., floor 0). Elevator A stops additionally at floors 5, 10, 15 and so on; Elevator B stops only at floors 4, 8, 12 and so on; Elevator C stops only at floors 6, 12, 18, 24 and so on. Further, all the floors are connected by a staircase and any floor can be reached from any other floor using this staircase. Tarun, a network engineer who visits various offices in this building everyday, always tries to reach the desired floor by taking the elevators so that he minimizes the number of floors that he has to walk using the staircase. Q1.     D I R E C T I O N S   f o r   q u e s t i o n s   1   a n d   2 :  Select the correct alternative from the given choices. Tarun got into Elevator A at the ground floor. He got down from Elevator A at the p t h  floor. He got into Elevator B at this floor and got down at the q t h  floor suc
Read more