# 2019 Grade 7 Math Challenge Divisionals Questions and Answers (with PDF)

Below are the 2019 MTAP Grade 7 Math Challenge Division Finals questions and answers. Solutions will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Easy

1.) If 1 megabyte is equal to $10^6$ bytes and 1 gigabyte is equal to $10^9$ bytes, how many gigabytes are there in 1 megabyte?

2.) Divide $2.4 \times 10^{-8}$ by $6 \times 10^8$ and write the quotient in scientific notation.

3.) Point Q lies midway between points  P and R on a number line. What is the coordinate of R if P and Q have coordinates -16 and -7, respectively.

4.) How many sides does a regular polygon have if the measure of each interior angle is $160^\circ$?

5.) Assume A and B are subsets of the set of integers. If A is the set of multiples of 2, and B is the set of multiples of 3, describe the elements of A ∩ B.

6.) Find the value of b so that $x = 3$ is the solution of the equation $b^2 + b(x - 3) + 3b = (b - x)^2$

7.) Find the product: $(1 - x)(1 + x + x^2 + x^3 + \cdots + x^{2018})$.

8. Simplify $\dfrac{1 - w^2}{1 - |w|}$ given that $w < 0$.

9.) Find the solution set of the inequality $x^3 - 3x^2 > 0$ and express it in interval notation.

10.) If the polynomial $10x^2 - 7x - 12$ is divided by $2x + 3$, the quotient is $5x + b$ and the remainder is $21$. Find the value of $b$.

11.) Assume ∗ is a rule for combining any two real numbers a and b given by ab = ab − 2. What is the value of b such that ab = a?

Average

1.) A camera drone travels at a speed of 40 miles per hour. Ho many feet can it travel if its maximum flight time is 20 minutes

2.) If $6 \cdot 16^{x-1} = 24 \cdot 2^{2x+6}$, what is the value of $x$?

3.) Express the repeating decimal 8.121 212 . . . as a fraction in lowest terms.

4.) Solve for $x$: $\dfrac{x + 3}{3} - \dfrac{x + 2}{2} = \dfrac{x + 6}{6}$

5.) In a pie chart that shows the monthly family expenditures on different items, the central angle of the sector representing the expenses on food is $144^\circ$. How much is spent on food if the monthly family income is Php22 000?

6. What is the solution set of the equation $5 - |1 - 2x| = 2$.

Difficult

1.) Each student in a class of 40 has an active account on at least one of the following social networking sites: Facebook, Instagram, or WhatsApp. Thirty students are active on Facebook, 20 on Instagram, and 17 on WhatsApp. If 13 students are active on both Facebook and Instagram, 7 on both Instagram and WhatsApp, and 5 on all three sites, how many students are active on either Facebook or Instagram but not on WhatsApp?

2.) If the sum of $2^x$ and its reciprocal is 3, what is the sum of $8^x$ and its reciprocal?

3.) A data set consisting of 8 whole numbers has mean, median, and mode that are all equal to 3. What is the largest possible number in the data set if the smallest number is 2?

4.) In the figure, the areas of the shaded region and the rectangle are in the ratio 2 ∶ 3, and the areas of rectangle and the circle is 21 square units, what is the area of the shaded region?

5.) Write the product $(a^2 + b^2)(c^2 + d^2)$ as a sum of two squares.

6.) John has Php100 and Php500 bills. How many Php500 bills does he have if there are 34 bills altogether and the total amount is Php11 800?

Tiebreaker

1.) On January 1, 2019, the NASA New Horizons spacecraft returned a sharp image of the farthest object ever explored by a spacecraft. The image consists of two spheres, one smaller than the other, joined together like a giant snowman. Scientists called the smaller sphere Thule and the bigger sphere Ultima. If the volume of Ultima is three times the volume of Thule, how many times is the diameter of Ultima bigger than the diameter of Thule?

2.) On a quiz, the mean of the scores of five students is 13.6. If the highest score is deleted, the mean of the four remaining scores is 12.5. Find the highest score?

3.) In an isosceles triangle, the measure of the exterior angle adjacent to one of the base angles is $115^\circ$.

Do or Die

If $n! = n(n - 1)(n - 2) \cdots 1$, what is the remainder if $1! + 2! + 3! + \cdots + 2019!$ is divided by 15?