Alternatively:
Imagine a 3-digit integer: PQR
P has 4 values, Q has 4 values, R has 4 values
There are 4^3 = 48 combinations
If we dismiss P=Q=R, that removes 4 combinations
If we dismiss P=Q, Q=R and P=R, that removes 3 x 4 = 12 combinations

So, 48 - 4 - 12 = 32 combinations

Using the Equation of a Circle is certainly the right way to go. However for speed, you could try this: With a range from y = -1 to y = 7, it is easy to recognise that the radius is 4. As the centre of the circle is not lying on the x-axis, it means that it must intersect the x-axis at a value less...

Rate = w/time: w/x = w/(y + 2) or w/y = w/(x - 2) where x and y are measures of time Together: w/x + w/(x - 2) = (5w/4)/3 So, 12(x -2) + 12x = 5x(x-2) Rearrange to make a quadratic: 5x^2 - 34x + 24 = 0 (5x-4)(x-6) = 0 x = 4 or 6 As X takes 2 days longer than Y, then x = 6, y = 4 to make w widgets Th...

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Note that Answer 5 should be: >=20 (not <=20) An integer when divided by 6 has remainder 2 and when divided by 8 gives remainder 4. What is the remainder when the integer is divided by 48? 1. 0 2. between 1 and 6 3. between 7 and 12 4. between 13 and 19 5. <= 20 [spoiler]OA: E[/spoiler]

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How can I find out how many times number 3 appears in 1 to 1000 ?

Assuming "number" means digit,
in binary it doesn't appear at all!

Alternative method, perhaps?

By comparing sides of similar triangles (ratio), area and other geometric facts, can anyone find a way of using the attached graph to solve this problem? I've labelled all intersections to help a writer describe their solution.