# MTAP Review: Grade 4 – 6

1. Admission tickets to a variety show cost P80 for adults and P50 for kids. The ratio of adults to kids 5 ∶ 2. If they paid a total of P10,000, find the number of adults in the group.

Ans: A set of 5 adults and 2 kids would pay 5 x P80 + 2 x P50 = P500;

By “Proportionately”, we have P10,000/ P500 = 20 sets. Therefore there are 5 x 20 =100 adults in the group.

2. What is the remainder when 4823 is divided by 11?

Ans: A number is exactly divisible by 11 if the alternating sum of its digits is a multiple of 11.   “By Alternate Elimination and Retention” we have (3 + 8) – (2 + 4) = 5, therefore 5 is the remainder.

3. The sum 9 + 99 + 999 is equal to 9 times what number?

Ans: By “Proportionately”, we can divide each of the terms by 9 and get 1 + 11 + 111 = 123

4. A basketball team scores an average of 53 points per game in its first 4 games and an average of 52 points per game in its first 5 games. How many points did the team score in its 5th game?

Ans: The team scored the average of 52 in the last game plus – 1 for each of the 4 previous games for bringing down the average from 53 to 52. By “using a base” of 52, the team scored 52 + 4 (-1) = 48 in the fifth game.

5. Three guavas and two apples cost P155, while five guavas and four apples cost P285. What is the cost of each guava?

Ans: Use “By Addition and By Subtraction”: Three guavas and two apples cost P155 therefore six guavas and four apples cost P310.  Subtract five guavas and four apples costing P285. We will get one guava is P310 – 285 = P25.

6. The value of √2019 is between what two consecutive integers?

Ans: We know from “By one more than the one before: Squaring numbers ending in 5” that 2025 is the square of 45, therefore √2019 is between 44 and 45.

1. What is the average of 17, 20, 23, 26, 29, 32, and 35?

Ans: The 7 numbers form an arithmetic sequence with 3 as the common difference. The average is the middle term, 26.

2. Given: 1 + 3 = 4; 1 + 3 + 5 = 9; 1 + 3 + 5 + 7 = 16; 1 + 3 + 5 + 7 + 9 = 25. What is the sum of the first 36 odd numbers?

Ans: The sum of the first 36 odd numbers is equal to 362 = 352 + 35 + 36 = 1225 + 71 = 1296.

3. In the set {440, 450, 460, 480}, which of the numbers is a sum of four consecutive whole numbers?

Ans: The average of 4 consecutive numbers is midway between the two middle values. Three of the numbers, 440, 460 and 480 are exactly divisible by 4, so they are not the the sum of 4 consecutive numbers. 450 when divided by 4 will give 112.5, which is the average of the 4 consecutive numbers, 111, 112, 113 and 114.

4. What is the mean of all the dates in the month of October?

Ans: October has 31 days, so the middle date, 16 is the mean.

5. The average of 40 numbers is 38. If three numbers are discarded, namely 40, 24, and 50, what is the average of the remaining numbers?

Ans: The average of the 3 numbers discarded is also 38. Deleting them will not affect the average of the remaining numbers.

1. The price of an article is reduced by 20%. In order to restore the reduced price to the original value, by how much must the reduced price be increased?

Ans: When the price is reduced by 20% it becomes 80% of the original price. To restore it to the original price, we must restore the 20% reduction, which is 1/4  of 80% or 25% of the reduced price.

2. A team’s record is 20 wins and 25 losses. To qualify for the playoffs a team must win 60% of its games played. How many wins of the remaining 15 games are necessary for the team to qualify?

Ans: The team have played 45 games and has to play another 15 more for a total of 60 games. If it has to qualify, it needs to win 60% of all the 60 games or a total of 36 games. Even if wins all the remaining 15 games, the team will win only a total of 20 + 15 or 35 games. Which means it has no chance of qualifying.

3. The selling price of a coat, which normally sells for \$55.00, was reduced by 20% during the spring sale. Since the coat still didn’t sell, the sale price was reduced by 10%. What was the total reduction from the original selling price?

Ans: The price was reduced by 20% so it was offered at 80% of the original price. If the sale price was reduced by 10%, then it would mean that it was reduced by another 8% of the original price. So the total reduction was 28% of the original price.  28% x \$55. 00 = 14% x \$110 = \$15.40

4. The length of a rectangle is increased by 15% and the width is decreased by 20%. Find the percentage change in the area of the rectangle.

Ans: 1.15 L x 0.80W = 2.3 x 0.4 = 0.92 LW. The area will decrease by  100 – 92 or 8%.

5. It took a train 50 seconds to pass a tunnel that was 1000 m long. It took the same train, travelling at the same speed, 75 seconds to pass a bridge that was 1625 m long. How long was the train?

Ans: If L is the length of the train, it took the train 50 seconds to travel L + 1000 m. That means it will need 150 seconds for it to travel 3L + 3000 m. It also needs 75 seconds to travel L + 1625 m or 150 seconds to travel 2L + 3250 m.

3L + 3000 = 2L + 3250; L = 250