# Grade 7 MTAP 2015 Questions with Solutions Part 3

This is the third part of the Metrobank-MTAP Math Challenge Questions for Grade 7. In this post, we discuss the solutions to number 21-30. You can also read the solutions to 1-10 and 11-20.

21.) The average of five numbers is 14. The average of the three of the numbers is 12. What is the average of the other two numbers?

Solution

The average of five numbers is 14 means that their sum is 70. The average of the three of those numbers is 12 means that their sum is 36. Now, 70 – 36 = 34 is the sum of the remaining two numbers. Their average is 34/2 = 17.

22.) A sandwich costs p pesos. A cookie costs Php9 pesos less than a sandwich. How much more expensive are 8 cookies than 5 sandwiches?

Solution

8 cookies – 5 sandwiches = 8(p – 9) – 5p = 8p – 72 – 5p = 3p – 72.

23.) Which values of x satisfy |2x + 1| = |2x – 9|?

Solution
2x + 1 = -(2x – 9)
2x + 1 = -2x + 9
4x = 8
x = 2

24.) A car leaves P at 8 AM and travels to Q at a constant speed. A bus leaves Q at 8:45 AM and travels to P at a speed three times that of the car. If they meet at 10 AM, find the ratio of the distance traveled by the bus to the distance traveled by the car when they meet?

Solution

Let x = speed traveled by the car
3x = speed traveled by the bus
The time traveled by the car from 8:00 AM to 10:00 AM is 2 hours.
The time traveled by the bus from 8:45 to 10:00 AM is 1 hour and 14 minutes or 5/4 hours. Since distance is the product of the rate and the time, the ratio of the distance traveled by the car to the bus is

$\dfrac{2(x)}{\frac{5}{4}(3x)} = \dfrac{8x}{15x} = \dfrac{8}{15}$.

So, the ratio of the distance traveled by the car to the distance traveled by the bus is 8:15.

25.) How many 3-digit numbers are multiple of 18?

Solution

The smallest 3-digit number that is a multiple of 18 is (18)(6) = 108.
The largest 3-digit number that is a multiple of 18 is (18)(55) = 990.
So, there are 55 – 6 + 1 = 50 numbers.

26.) If the perimeter of the square is a 8x + 6, what is its area?

Solution

The side of a square with perimeter $8x + 6 = 2x + \frac{3}{2}$. The area of the square is $(2x + \frac{3}{2})^2 = 4x^2 + 6x + \frac{9}{4}$.

Answer: $4x^2 + 6x + \frac{9}{4}$

27.) Two vertical poles are 3 meters apart. Jack’s climbing one pole well Jill climbs the other. If the distance between Jack and Jill is 5 m, how much higher is Jill than Jack?
Solution

By the Pythagorean Theorem, $3^2 + x^2 = 5^2$, $x^2 = 16$, $x = 4$.

28.) If the circumference of a circle increased by 20% how much is its area increased?

Solution
If we let C be the circumference of the circle and r be its D, then

$C = 2 \pi r$
If we increase the circumference by 20%, we have to multiply C by 1.2. That is,

$1.2C = (1.2)(2 \pi r)$.

Since 2 and pi are constant, we can only change r. That is, we multiply r by 1.2. Now, if we let the area of a circle be A,

$A = \pi (1.2r^2) = 1.44 \pi r^2$.

So, the area increased by 0.44 or 44%.

29.) A camp director prepared enough food for 100 students for six days. If only 75 students came, how long when the food supply last?

Solution

100/75 = x/6
74x = 600
x = 8

30.) How many two digit numbers are not divisible by four nor by five?

Solution

There are 90 two-digit numbers. There are 22 numbers that are divisible by 4 (divide 90 by 4 and get the integer quotient).
There are 18 numbers that are divisible by 5 (divide 90 by 5 and get the integer quotient).
However, numbers which divisible by 20 were counted twice since they are both divisible by 4 and by 5. There are 4 of them (divide 90 by 20 and get the integer quotient). In effect, there are 22 + 18 – 4 = 36 numbers that are either divisible by 4 or 5

Therefore, there are 90 – 36 = 54 numbers that are not divisible by 4 nor by 5.