NMTC Stage 2 GAUSS Primary Level 2026

$$ABCD$$ is a parallelogram. The measure of $$\angle ABC = 60^\circ$$. The bisector of $$\angle BAD$$ (dividing $$\angle BAD$$ in two equal halves) meets the side $$DC$$ in point $$E$$ such that $$E$$ is the midpoint of side $$DC$$. If the length of segment $$AE = 6\text{ cm}$$, then find Perimeter of $$\triangle ADE$$ + perimeter of $$\square ABCE$$.

Form the smallest seven-digit number, completely divisible by 99, by using the digits 0, 2, 4, 6, 8 each at least once. Give the detailed justification.

In the following Alphametic addition problem, each letter represents a unique digit. It is known that when the digit represented by $$A$$ is even and the digit represented by $$N$$ is odd, then the Alphametic addition problem has two different solutions. Find these two solutions.
$$\text{AMTI} + \text{NMTC} = \text{FINAL}$$

If $$\frac{1}{y} - \frac{1}{x} = 7$$, then evaluate $$\left(\frac{11x + 5xy - 11y}{5x - 33xy - 5y}\right)\left(\frac{35x + 26xy - 35y}{3x - 20xy - 3y}\right)$$.

In $$\triangle ABC$$, $$AB = BC$$. Point $$D$$ is on side $$AC$$ and point $$E$$ is on side $$AB$$ such that $$BD = BE = AD$$. It is known that $$\angle ADE = 30^\circ$$. Then find the measure of $$\angle ABC$$, $$\angle ACB$$, $$\angle BDC$$, $$\angle DEA$$.

Call a number prime looking if it is composite but not divisible by 2, 3, or 5. The three smallest prime-looking numbers are 49, 77, and 91. There are 95 prime numbers less than 500. How many prime-looking numbers are there less than 500?

Raj is to select six chocolates from a tray containing the chocolates of type (i) fruit & nut, (ii) roasted almond, (iii) milky-bar, (iv) blueberry. All chocolates of each type are identical. There are at least six chocolates of each of these four types in the tray. How many different assortments of six chocolates can be selected?

Each side of square $$ABCD$$ with side length of $$5\text{ cm}$$ is divided into equal five parts by four points. Choose one of the four points from each side, and connect the points consecutively to obtain a quadrilateral (One example is shown in the adjoining figure). Write all possible areas of the quadrilateral so obtained.