# SMO JUNIOR SECTION 2015

Problem 1 :

Among the five numbers 5/9, 4/7, 3/5, 6/11 and 13/21 which one has the smallest value ?

(A)  5/9     (B) 4/7     (C)  3/5   (D)  6/11     (E)  13/21

Solution

Problem 2 :

Adrian, Biliy, Christopher, David and Eric are the five starters of a school's basketball team. Two among the five shoot with their left hand while the rest shoot with their right hand. Among the five, only two are more than 1.8 meters in height. Adrian and Billy shoot with the same hand, but Christopher and David shoot with different hands. Biliy and Christopher are respectively the shortest and tallest member of the team, while Adrian and David have the same height. Who is more than 1.8 meters tall and shoots with his left hand?

(a)  None (B) Only Christopher (C) Only Eric

Christopher and Eric (E) Not enough information to ascertain

Solution

Problem 3 :

How many ways are there to arrange 3 identical blue balls and 2 identical red balls in a row if the two red balls must always be next to each other?

(A) 2   (B) 4    (c) 5    (D) 10    (E) 20

Problem 4 :

If. a,b and c are positive real numbers such that

Problem 5 :

In the figure below, each distinct letter represents a unique digit such that the arithmetic sum holds. What is the digit represented by the letter B?

(A) 0   (B) 2    (c) 4    (D) 6    (E) 8

Problem 6 :

Find the minimum value of the function

2015  -  [10/(x2 -4x + 5)]

(A) 2000   (B) 2005    (c) 2010

(D) 2013    (E) None of these

Solution

Problem 7 :

It is known that 99900009 is the product of four consecutive odd of squares of these four odd numbers.

(A) 40000  (B) 40010   (c) 40020

(D) 40030    (E) 40040

Problem 8 :

The lengths of the sides of the triangle are

x2, 22 - x and x - 2

The total number of possible integer value of x is.

(A) 0       (B) 1      (C) 2       (D) 3    (E) 4

Solution

Problem 9 :

Find the value of

Solution

Problem 10 :

If x and y satisfy the equation 2x2 + 3y2 = 4x, the maximum value of 10x + 6y2 is

(A) 2       (B) 9/2      (C) 20       (D) 81/4    (E) None

Solution

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