This is the 2017 MTAP Grade 7 Math Challenge questions 26 to 30. Questions 1-25 including can be found **here**. The pdf can be downloaded **here**. Solutions and answer will be posted later.

Questions in the previous years can be accessed on the **Past Tests** page and all questions can be found in the** All Posts** page.

26.) What should be the value of if the value of is when ?

27.) There are five less spoons than forks in a party. If represents the number of spoons and the number of forks, express in terms of .

28.) It takes three times as long to finish Task A than it is to finish Task B. If A and B represent the time needed to finish Task A and B, respectively, give an equation relating A and B.

29.) The temperature of coffee decreased from Celsius to Celsius a few minutes after it was poured in a cup. By how many degrees Fahrenheit did the coffee cool?

30.) If , what is the largest integer that can take?

31.) Simplify .

32.) A vehicle traveled 60 km in 1 hour. Express its average speed in meters per second.

33.) A rectangular tank measures 3 m × 4 m × 5 m. How many liters of water can this tank hold?

34.) Solve for x:

.

35.) The ages of Dina and Danny are in the ratio of 2 : 3. Five years later, the sum of their ages will be 40. What are their present ages?

36.) Solve: . Give the answer in interval notation.

37.) Solve the inequality . Give the answer in set notation.

38.) What set satisfies the inequality ?

39.) Twice the measure of plus the measure of its complementary angle is . Find .

40.) Each exterior of a regular polygon measures . How many sides does it have?

41.) If the number of sides of a polygon is increased by 5, by how much would the sum of the interior angles of the polygon increase?

42.) Suppose . List all the angles that must be congruent to ∠8.

43.) Suppose , , and . Find .

44.) Suppose , , and . Find .

Numbers 45 and 46 refer to the following data values, arranged in descending order, representing the number of ambulances in seven hospitals:

**14 13 12 k 7 7 4**

45.) Find all possible values of so that the seven numbers have a unique mode.

46.) Find all possible values of k so that the median of the seven numbers is 8.

47.) In a 10-point quiz, 16 scored 10, 8 scored 9, 9 scored 8, 2 scored 7, and 5 scored 6. Find the mean score of the students.

48.) For the month of February, Ramon spent P 15,000. He spent P 8,000 for rent, P 4,500 for food, P2,000 for utilities, P500 for others. In a pie graph representing Ramon’s expenses, what is the central angle of the region representing the “other” expenses?

49.) Give tne mean deviation of the following data set: 3, 5, 5, 5, 6, 9.

50.) The population growth rate of twenty Philippine cities are 2.2, 4.5, 8.3, 9.4, 11.8, 12.2, 13.9, 14.9, 16.5, 18.0, 19.0, 19.5, 21.3, 22.2, 24.2, 25.6, 29.4, 32.6, 38.5, 53.4. Suppose you represent this data in a histogram with five classes, each having a class width of 10. The class mark of one of these classes is 16.5. How many data values will fall in this class?

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