Interesting side question I posed to myself while looking at part 2 of this question is (and I warn anyone trying to stay on topic to AVOID the rest of this post): How many square integers, x, exist such that 3x+4 is also a perfect square? Very True,That made me spend a minute more on this because ...

Remainder from Sum containing Factorial

(33*32*31*30 * 28!) mod 29 is not equal to (-4 * -3 * -2 * -1 * 28!) mod 29 => Rather, it should be (4*3*2*1*28!) mod 29. Ah, but that isn't a mistake! It'd be a mistake to say that 33 = -4 mod 29, but that isn't what I said ;) Of course, I could see why it would seem that way from what I typed, bu...

Every term other than 33!/29 will still have a 29 in its numerator, so every term other than 33!/29 is divisible by 29. That means that problem can be stated as What is the remainder when 33!/29 is divided by 29? (33*32*31*30*28*27*...*1) mod 29 => (33*32*31*30 * 28!) mod 29 => (-4 * -3 * -2 * -1 *...

A circle is circumscribed around a square such that all the angles of the squares lie on circumference. What is the area of the circle, if area of the square is 100 units? A. 131 B. 137 C. 157 D. 161 E. 174 I'm confused how to set up the formulas here. Can any experts help? Given the are of the squ...

If positive integers a and b are both odd, which of the following must not be odd? A) ab B) a(ab) C) b – a – 1 D) (a + b)/2 E) a – b The OA is E . If we set a=3 and b=5 the (a+b)/2 is 4 and it is not odd. Why option D is wrong? Given a and b are both odd. Just put a = 1 and b = 1, then check ...

As nobody has posted any solution, I am giving first hint. Hint 1 : Please note that S = (33!/1 + 33!/2 + 33!/3 + ..... + 33!/32 + 33!/33). When you divide each term by 29, you will find that every term is divisible by 29 except 33!/29. For example 33!/1/29 is divisible by 29. Similarly, 33!/2/29 is...

As nobody has posted any solution, I am giving first hint. Hint 1 : As both trains meet 10th time, the faster train has to complete 9 one-side trip to meet the another train 10th time. Note : I hope, many viewers will be able to find solution with the above hint. If I don't get solution in another 1...

Journey of Two Trains

Two trains continuously travel between Washington DC and New York, which is 226 miles away. They start simultaneously, train A at Washington and train B at New York, and run at 60 and 40 mph respectively. The station turnaround times are negligible, however, each train stops at destination for 15 mi...