MYTS 2016 - Grade 7 - Round 1

The interior angles of a quadrilateral are in ratio 1:2:3:4. How many degrees larger is the greatest angle than the smallest?

Points A(3, a) and B(b,17) lie on y=10 x−3. Find a+b.

Real numbers $a, b, c$ satisfy $|a-b|\le 5$, $|b-c|\le 8$, and $|a-c|\le k$. What is the smallest $k$?

In the figure, ABCDE is a regular pentagon with two sides extended. Find angle EFD in degrees.

During a promotion, buying a can of orange juice at the regular price 7 dollars allows a second can for 1 dollar. What is the least cost in dollars for a group of 9 people needing one can each?

Real numbers $a, b, c$ satisfy $a/2=b/3=c/8$ and $ab+bc+ca=414$. Find the maximum of $a-b$.

A taxi company charges a 10000-dong opening fee and 7000 dong per kilometer, then 5000 dong per kilometer beyond the first 20 km. An pays 230000 dong. How many kilometers does she travel?

In a group of 10 friends, each receives a gift from every other friend on their birthday. How many gifts do the group members prepare for one another in a year?

N is a three-digit number with exactly 18 positive divisors. Find the largest N.

A bag contains 25 marbles in three colors: blue, red, yellow. Drawing 21 without looking is necessary to guarantee all three colors. What is the greatest possible number of yellow marbles?

Cut the figure along the grid lines into two congruent pieces. Sum the numbers on each piece. What is the larger sum?

Nine cubes are joined as shown. The surface of the resulting solid is painted. What is its surface area in cm² if every cube has edge length 2 cm?

Five squares of side 7 cm form a cross. A circle passes through eight vertices of the cross. Find the shaded area in cm², using π=22/7.

In how many ways can 8 sweets be distributed to Lam, Hung, Vinh so each receives at least one and no sweet is broken?

Today is Sunday, and in three days it will be Wednesday. Exactly 259 days from today is 11 December 2016, described in the source as South Africa’s national day (independence from Britain in 1931). What day of the week is it? The figure shows calendars for March and April 2016.

Five squares are arranged as shown, with some vertices on a common line and neighboring squares sharing a vertex. The tilted squares have areas x, y cm²; the other three have areas 3,5,10 cm² in order. Find x+y.

Two equal squares have side 120 cm. The first contains 16 equal tangent circles and the second 25 equal tangent circles as shown. Let k and ℓ be their respective total circle areas. Find k−ℓ.

Find the last two digits of $7^{107}$.

A natural number N is generous if divisible by every digit and by the digit sum. For example 12 is generous, but 102 is not. Find the smallest generous number divisible by 11.

Four friends are playing and one breaks a vase. Lan says,“It was not me!” Van says,“Yen did it!” Hang says,“No, Van did it!” Yen says,“Van is lying.” Exactly one tells the truth. Who broke the vase?