In a range of consecutive numbers starting with 1, all the even numbers are removed. From the remaining, consider the first 7 numbers. The sum of these 7 numbers is [#1699]

1+3+5+7+9+11+13 = 49

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1+3+5+7+9+11+13 = 49

41

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41

The smallest number amongst them is 13 => X + (X+2) + (X+4) + (X+6) = 64 => 4X + 12 = 64 => 4X = 64 - 12 => 4X = 52 => X = 13

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The smallest number amongst them is 13 => X + (X+2) + (X+4) + (X+6) = 64 => 4X + 12 = 64 => 4X = 64 - 12 => 4X = 52 => X = 13

5 : (5² + 2) = 5 : 27 Hence 9 : (9² + 2) = 9 : 83

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5 : (5² + 2) = 5 : 27 Hence 9 : (9² + 2) = 9 : 83

A bisector is a line that divides a shape into two equal parts, like a line that cuts a triangle into two equal areas or a line that divides a circle into two equal parts (semi-circles).

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A bisector is a line that divides a shape into two equal parts, like a line that cuts a triangle into two equal areas or a line that divides a circle into two equal parts (semi-circles).

The difference of speed = 22m/s - 20m/s = 2m/s As the train with speed 22m/s will cross the other, hence this train have to go the smallest length of the trains distance ahead of the other to cross completely. Hence This train will be ahead of 100m with a speed of 2m/s. Hence The time to cross each other will take = 100m / (2m/s) = 50 sec

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The difference of speed = 22m/s - 20m/s = 2m/s As the train with speed 22m/s will cross the other, hence this train have to go the smallest length of the trains distance ahead of the other to cross completely. Hence This train will be ahead of 100m with a speed of 2m/s. Hence The time to cross each other will take = 100m / (2m/s) = 50 sec

76

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76

$\frac{45}{100}*X = \frac{30}{100} * Y$ = $\frac{X}{Y} = \frac{30*100}{100*45}$ = $\frac{X}{Y} = \frac{2}{3}$ = X:Y = 2:3

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$\frac{45}{100}*X = \frac{30}{100} * Y$ = $\frac{X}{Y} = \frac{30*100}{100*45}$ = $\frac{X}{Y} = \frac{2}{3}$ = X:Y = 2:3

1

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1

3.5 m

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3.5 m

(1000+100)m / (20m/s) = 55 seconds

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(1000+100)m / (20m/s) = 55 seconds