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Some doubts.. help me in solving them Q1.Find the sum of the digits in the expanded product 199,999,997 x 200,000,003. a. 129 b. 139 c. 229 d. 239 Q2.What is the angle between the two lines passing through the points (1, 2) (4,2) and (-3, 6) Q3. What is the smallest integer x larger than 1 such that x^2 ends in the same three digits as x does? a. 476 b. 376 c. 276 d. 176

3rd question

The answer is 376 as 376^2 = 141376 And I found it by calculating the square of all the numbers but I am sure there must be a better method. If few options are of 5-6 digits then we finding the square might not be the best method

1 Question

199999997 x 20000003 = (200000000-3)(200000000+3)=200000000^2-3^2=3999999999999991 thus answer = 15x9+3+1= 139

for second one can we use

for second one can we use slope(m) = (y2 - y1)/(x2 - x1) and then angle between the two lines tanA = (m2 - m1)/(1 + m1 x m2)

let x be the number, the

let x be the number, the problem states x^2 - x = 1000 k x(x-1) is divisible by 8 and 125 only 376 here fits the answer.