ALGEBRA AND STATISTICS

The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

• A. 5 and 25

• B. 6 and 19

• C. 7 and 18

• D. 8 and 17

Answer explanation

i: 8 + 17=25

ii: 17 - 8 =9

The difference between two numbers is 40. The ratio of the numbers is 5:3. What are the two numbers?

• A.100 and 60

• B. 90 and 50

• C. 80 and 40

• D. 70 and 30

Answer explanation

i: 100 - 60 = 40

ii:

100 /20 = 5

60/20 = 3

 The length of a rectangle is thrice its breadth. If the perimeter is 112 meters, find the length and breadth of the rectangle.

• A. Length - 40 m Breadth - 12 m

• B. Length - 42 m Breadth - 14 m

•  C. Length - 44 m Breadth - 16 m

• D. Length - 46 m Breadth - 18 m

Answer explanation

i: Breadth = x

Length = 3x

ii: 2(x) +2(3x) = 112

2X + 6X = 112

8X = 112

X = 14

iii: Breadth = 14

Length = 3(14) = 42

Abby is 5 years younger than Leah. Four years later, Leah will be twice as old as Abby. Find their present ages.

• A. Leah-6, Abby-1

• B.  Leah -8, Abby-3

• C. Leah-10, Abby-5

• D. Leah -12, Abby -7

Answer explanation

i:Leah's age - Abby's age = 5

6-1 = 5

ii: Leah's age = 6

Abby's age = 1

105 less than 8 times a number is equal to the number. Find the number.

• A.5

• B. 10

• C. 15

• D. 20

Answer explanation

8x - 105 =x

8x - x = 105

7x = 105

x = 105/7

x = 15

Naida has 6 less than 8 times as many skirts as Ynah. Together, Naida and Ynah have 147 skirts. How many skirts does Naida have? How many skirts does Ynah have?

• A. Naida-120, Ynah-27

• B. Naida-117, Ynah-37

• C. Naida-110, Ynah-77

• D. Naida-130, Ynah-17

Answer explanation

i: Number of Yna's skirts : x

Number of Naida's skirts :

8x-6

ii: (8x-6)+ x=147

8x+x -6 =147

9x = 147 +6

9x = 153

x = 153 / 9

x = 17

iii:Number of Yna's skirts : 17

Number of Naida's skirts :

8x-6 = 8(17) - 6 = 136 - 6 = 130

Two planes, which are 2700 miles apart, fly toward each other. Their speeds differ by 50 miles per hour. pass each other after 6 hours. Find their speeds

• A. One's plane speed is 205 mph. The other plane's speed is 240 mph.

• B. One's plane speed is 200 mph. The other plane's speed is 250 mph.

• C. One's plane speed is 195 mph. The other plane's speed is 260 mph

• D. One's plane speed is 190 mph. The other plane's speed is 270 mph.

Answer explanation

To solve this problem, you would use the formula that relates distance, velocity and time as follows:

 

s = (v)(t)

where s= distance

          v = velocity

          t = time

 

'Let us call the faster plane's velocity v₁ and the slower plane's velocity v₂.

 

Then we know that v₁ = v₂ + 50

 

When the planes pass each other at 6 hours we know that the total distance both planes have traveled is 2700 miles.

 

Using the distance/velocity/time equation above we can write the following equation:

 

s = (v)(t)

 

2700 = (v₁)(6) + (v₂)(6)

2700 = (v₂ + 50)(6) + (v₂)(6)

2700 = 6v₂ + 300 + 6v₂

2400 = 12v₂

v₂ = 200 miles per hour

v₁ = v₂ + 50 = 250 miles per hour

Php 70,000 is divided between two accounts. One account pays 4% interest, while the other pays 3.5% interest. At the end of the period, the interest earned was Php 2500. How much was invested in each account?

• A. Php 40,000 was invested at 3.5% and Php 6,000 was invested at 4%.

• B. Php 50,000 was invested at 3.5% and Php 8,000 was invested at 4%.

• C. Php 60,000 was invested at 3.5% and Php 10,000 was invested at 4%.

• D. Php 70,000 was invested at 3.5% and Php 12,000 was invested at 4%.

Answer explanation

60,000 x 3.5% = 2,100

10,000 x 4% = 400

----------------------------

2500

If two equations can be drawn as simple line on graph then these equations are considered

• A. Constant equations

•  B. Solved equations

• C. Equivalent equations

• D. Non-equivalent equations

A set which consists of more than one equations is classified as ________________.

• A. system of equations

• B. system of variables

• C. system of constants

• D. system of coefficients