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When faced with a definition such as AE > EB > 2, is there any strategy in terms of what numbers we should choose? I plugged in 2.5 because I thought both AE = 3 and AE = 4 would fail the condition

Well couldnt understand this

Hi
Nothing is stopping you to choose number, please make sure the number selection falls in criteria if mentioned in the question

and choosing decimal/ fraction will only consume time

Hi,
Let me know what you have not understood?

As a brief, we got a rectangular solid, which is divided to form a triangle.

Now, how can we get the volume of shaded area?

simple, First we need the total volume of the rectangle

second, we need the volume of the triangle

Shaded volume = Total volume of the rectangle - volume of the triangle

I hope this help

This is how I solved it. We know that AB = 6 so AE + EB = 6. We also know that 2<EB<AE which means that 2<EB<3 because if EB was 3 then AE would also have to be 3 which doesn't work as EB must be smaller than AE. This also means that 3<AE<4 because if AE = 4 or greater, than EG=2 or smaller which can't be the case. I then thought of the unshaded area as half of a rectangular prism with the height=AE, W= 5 and L=8. We know that the volume of a rectangular prism is HxLxW. I plugged in 3 and 4 for AE to get the upper and lower limits for the volume. V= 3x8x5 --> 120 and V= 4x8x5 ---> 160. I then divided these by two because the unshaded portion is only half of a rectangular prism. 120/2 = 60 and 160/2=80. Through this we know that the upper unshaded section has a volume between 60 and 80. We can than find what the volume would be in the shaded area by finding the volume of the entire rectangular prism and subtracting the upper and lower limits of the unshaded area. Volume of prism = 6x8x5 --->240 240 - 60 = 180, 240-80= 160. Therefore, the volume of the shaded area must be between 160 and 180. The only answer that falls within this range is D (170).

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