Question number 25. Anurag chooses four of the numbers 2, 3, 4, 5, and 6, and writes one in each box so that the calculation in the diagram to the right is correct. How many of the five numbers can Anurag write in the shaded box? Ok, so the first thing that we can do is rearrange this equation that we're given up here at the top. So we can move this box to this side of the equation, and now we have that square 1 plus square 2 equals square 4 plus square 3. And that is quite similar to an equation that we see over here. 2 plus 6 equals 3 plus 5. So how does that help us? Well, subtracting any of these numbers from both sides gives us an equation of the same form as above. What does that mean? Well, let's say we subtract 6 from both sides of this equation. We have 2 plus 6 minus 6, so that's just 2 on this side. 2 equals 3 plus 5 minus 6. Is that true? Yes, it is. 3 plus 5 is 8, minus 6 is 2. So we have 3, 5, 6, and then 2. Similarly, we can try, what if we subtract 2 from each side? So the 2's cancel out on this side, 6 equals 3 plus 5 minus 2. 3 plus 5 is 8, 8 minus 2 is 6. 3, 5, 2, 6. So once we've created this equation of this form, we can tell immediately that every single one of these numbers is going to work. Even if we use the other side. If we subtract the 3 out, then we have 2 plus 6 minus 3, 8 minus 3 equals 5. 2, 6, 3, 5. So this is a handy little equation for telling us that all four of these numbers will work in this scenario. But yes, there is one number that hasn't been included, and that's just because this equation can only contain four numbers at a given time. So we can create a new equation. 2 plus 5 equals 3 plus 4. Both of these are equal to 7. So now in this equation, similarly, all four of these numbers can be in the shaded box. We can have 2 plus 5 minus 3 equals 4, or 2 plus 5 minus 4 equals 3. So that means that all five numbers can appear in the shaded box, and the answer is E.

number selection

equation flexibility

number pairing

shaded box

solution explanation