# Edition 21

1. In a rectangular coordinate system, the vertices of triangle ABC are A(3, 3), B(7, 7), and C(12, 3). How many lattice points (points with integral x and y coordinates) are located on the sides of the triangle?

• (A) 14
• (B) 17
• (C) 8
• (D) 9
• (E) None of these

2. Consider the triangle PQR shown in the figure, where S is a point on PQ such that QR = 20 cm, SQ = 16 cm, RS = 8 cm, and ∠QRS = ∠QPR. What is the ratio of the perimeter of the triangle PRQ to that of the triangle RSQ?

• (A) 4 : 3
• (B) 5 : 4
• (C) 8 : 7
• (D) 9 : 8
• (E) 1 : 2

3. How many four-digit positive integers are divisible by 12 and consist of entirely prime digits?

• (A) 43
• (B) 54
• (C) 87
• (D) 98
• (E) 16

1. Problem #2) Solution :
B D=x cm;;
C o s
Or (A B ^2+ B D ^2-A D ^2)/(2 * A B* B D)=(A C ^2+C D ^2-A D ^2)/(2* A C * C D);
Or ( 1 7^2 +x ^2 -1 5 ^2/(2* 17 * x)=(1 7^2 + 4 ^2-1 5 ^2)/(2 * 17* 4);
Or (64+ x^2)/x= (80)/4=20;
Or 64+ x^2=20 *x; or x=4 or 16 ;
Admissible value of x=16B D= x cm=16 cm

1. Thank you sir for another solution

2. Rajan kumar says:

Solution of problem1.
First we will measure 3 conis each side.
Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.
Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

2. Rajan kumar says:

Solution of problem1.
First we will measure 3 conis each side.
Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.
Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

3. Question 1 solution :
(c)
As 10 houses have less than 6rooms, they are to be excluded.
Given,
4 houses have more than 8 rooms .
Therefore, number of houses having either less than 6 or greater than 8 rooms = 10 + 4 = 14.
The remaining houses, that is 11 houses fulfill the above mentioned criteria.