**NNPC Mathematics Past Questions And Answers**

1) A rectangle is twice as long as it is wide. If the width is a, what is the length of a diagonal?

A.

B. C.

D. 3a

E. 5a

2) Last year Jose sold a painting for $2000. If he made 25% profit on the sale, how much had he paid for the painting?

A. $1200

C. $1500

C. $1600

D. $2400

E. $2500

Jose made 25% profit, so if he bought the painting for x, he sold it for: x + 0.25x = 1.25x = 2000 ?x

= 2000 ÷ 1.25 = 1600.

The answer is (C).

3) In the figure below what is the value of b?

A. 30

B. 36

C. 45

D. 60

E. 72

Since vertical angles have the same measure, c = d, d = a, and b = a – b a = 2b.

Therefore, c = d = a = 2b. Also, the sum of the measures of all six angles is 3600,

so a + b + c + d + a – b + d = 2a + c + 2d = 360. Replacing c, d, and a by 2b yields

10b = 360 ?b =36.

The answer is (B).

4) A lacrosse team raised some money. The members used 74% of the money to buy uniform, 18% for equipment, and the remaining $216 for a team party. How much money did they raise?

A. 2400

B. 2450

C. 2500

D. 2600

E. 2700

SINCE 74% + 18% = 92%, THE $216 spent on the party presents the other 8 % 0f the money raised. Then: 0.08m = 216 ? m = 216 ÷ 0.08 = 2700. The answer is (E).

5) In the figure below, what is the sum of the degree measures of all of the marked angles? A. 600

B. 620

C. 700

D. 720

E. 750

Each of the 10 marked angles is an exterior angle of the pentagon. If you take one angle at each vertex, the sum of the degree measures of those five angles is 360; the sum of the degree measures of the other five also is 360: 360 + 360 = 720.

The answer is (720).

6) In the figure below, ABCD is a parallelogram. What is the value of y – z?

A. 50

B. 55

C. 60

D. 65

E. 70

The sum of the degree measures of two consecutive angles of a parallelogram is

180, so 180 = (3x – 5) + (2x – 15) = 5x – 20 ? 5x = 200 ? x =40. Since opposite angles of a

parallelogram are equal, y = 3x – 5 = 115 and z = 2x – 15 = 65. Then y

– z = 50. The answer is (50).

7) If the length of a rectangle is 4 times its width, and if its area is 144, what is its perimeter? A. 6

B. 24

C. 30

D. 60

E. 96

8) If the measures of the angles of a triangle are in the ratio of 1:2:3, and if the perimeter of the

triangle is 30 + 10 (3)½, what is the length of the smallest side?

A. 20

B. 18

C. 15

D. 12

E. 10

9) What is the area of Triangle ABC? A. 350

B. 360

C. 370

D. 375

E. 390

The area of Triangle CDE = 0.5(8)(15) = 60. Since the ratio of similitude for the two triangles (as calculated in solution C15) is 2.5, the area of Triangle ABC is (2.5)2 times the area of CDE: (2.5)2 × 60 =

6.25 × 60 = 375. The answer is (375).

10) What is the perimeter of Triangle ABC? A. 80

B. 85

C. 95

D. 100

E. 105

Solution

By the Pythagorean theorem, 82 + 152 = (CE)2 (CE)2 = 64 + 225 = 289 CE = 17. Then the perimeter of

CDE = 8 + 15 + 7 = 40. Triangles ABC and CDE are similar (each has a 900 angle, and the vertical angle

at C are congruent). The ratio of similitude is = 2.5, so the perimeter of ABC is 2.5 × 40 = 100. The

answer is (100).

11) If the difference between the measures of the two smaller angles of a right triangle is 200, what is the measure, in degrees, of the smallest angle?

A. 30

B. 35

C. 40

D. 45

E. 50

- What is the perimeter of Triangle ABC A. 48

B. C. D. 72

E. It cannot be determined from the information given

13) What is the area of Triangle BED in the figure below were ABCD is a triangle?

A. 12

B. 24

C. 36

D. 48

E. 60

You can calculate the area of the rectangle and subtract the area of the two white right triangles, but don’t. The shaded area is a triangle whose base is 4 and whose height is 12. The area is (4)(12) =

The answer is (B).

14) What is the value of PS in the triangle below? A.

B. 10

C. 11

D. 13

E

The answer is (D).

15)

Use the Pythagorean Theorem twice, unless you recognize the common right triangle in the figure. Since PR = 20 and QR = 16, PQR is a 3x-4x-5x right triangle with x = 4. Then PQ = 12, and PQS is a right angle triangle whose legs are 5 and 12. The hypotenuse, PS, therefore is 13.

A. 40

B. 45

C. 50

D. 55

E. 57

Solution

Since lines l and k are parallel, the angle marked y in the given diagram and the sum of the angles

marked x and 45 are equal:

Y = x + 45 y – x = 45.the answer is (45).

16) In an office there was a small cash box. One day Ann took half of the money plus $1 more. Then Dan took half of the money plus $1 more. Stan then took the remaining $11. How many dollars were originally in the box?

A. $50

B. $45

C. $42

D. $40

E. $38

Solution

You can avoid some massy algebra by working backwards. Put back the $11 Stan took; then put back the

extra $1 that Dan took. There is now $12, which means that, when Dan took his half, he took $12. Put that

back. Now there is $24 in the box. Put back the extra $1 that Ann took. The box now has $25, so before

Ann took her half, there was $50. The answer is ($50).

17) Each of the 10 players on the basketball team shot 100 free throws, and the average number of baskets made was 75. When the highest and lowest scores were eliminated the average number of baskets for the remaining 8 players was 79.What is the smallest number of baskets anyone could have made?

A. 22

B. 20

C. 18

D. 16

E. 14

Since the average of all 10 players was 75, the total number of baskets made was 10 × 75 = 750. Also, since 8 of the player had an average of 79, they made a total of 8 × 79 = 632 points. The other 2 players, therefore, made 750- 632 = 118 baskets. The most baskets that the player with the highest number could have made was 100, so the player with the lowest number had to have made at least 18. The answer is 18.

18) Karen played a game several times. She received $5 every time she won and had to pay $2 every time she lost. If the ratio of the number of times she won to the number of times she lost was

3:2, and if she won a total of $66, how many times did she play the game?

A. 30

B. 35

C. 40

D. 45

E. 48

Karen won 3x times and lost 2x times, and thus played a total of 5x games. Since she got $5 every time she won, she received $5(3x) = $15x. Also, since she paid $2 for each loss, she paid out $2(2x) = $4x. Therefore, her net winning were $15x – 4x = $11x, which you are told was $66. Then, 11x = 66 ? x = 6, and so 5x = 30.

The answer is 30

19) Since 1950, when martin graduated from high school, he has gained 2 pounds every year. In

1980 he was 40% heavier than in 1950. What percent of his 1995 weight was his 1980 weight?

A. 80

B. 85

C. 87.5

D. 90

E. 95

Solution

Let x = Martin’s weight in 1950. By 1980, he had gained60 pounds (2 pounds per

year for 30 years) and was 40% heavier:

60 = 0.40x x = 60 ÷ 0.4 = 150. In 1980, he weighed 210 pounds, 15 years later, in 1995, he weighed

240:

210/240= 7/8= 87.5%. The answer is C.

20) Henry drove 100 mile to visit a friend. If he had driven 8 mile per hour faster than he did, he would have arrived in of the time he actually toke. How many minute did the trip take?

A. 100

B. 120

C. 125

D. 144

E. 150

21) Two printing presses working together can complete a job in 2.5 hours. Working alone, press

A can do the job in 10 hours. How many hours will press B take to do the job by itself?

A. 10/3

B. 4

C. 5

C. 25/4

E. 15/12

Multiply each term by 10x: 2.5x + 25 = 10x

.Subtract 2.4x from each other: 25 = 7.5x

. Divide each side by 7.5: x = 3 hours. The answer is A.

The table above shows the specializations of North West Medical School graduates in 2005.

Percentages have been rounded to the nearest whole number. One hundred and nineteen students

graduated that year. Use this information to answer the following.

22) If seven students changed their specialization from family practice to paediatrics, approximately what fraction of students would then be specializing in paediatrics?

A. 1/7

B. 1/4

C. 1/7

D. 1/5

E. 1/15

Answer: D

Explanation: Thirteen percent of 119 students (119/100) * 13 = 15 specialized in paediatrics. If 7 students joined them then there would be 22 students studying it. This equates to

22/119 = 0.18 which is approximately 1/5.

23) What is the approximate ratio of students specializing in sports medicine, emergency medicine and family practice?

A. 6:4:10

B. 1:4:5

C. 2:8:10

D. 3:2:10

E. 3:2:5

Answer: D

Explanation: The ratio of students specializing in each is (15:11:48) which approximates to 3:2:10.

24) One twelfth of the students who chose to specialize in family practice plan to work abroad. How many is this?

A. 7

B. 8

C. 5

D. 9

E. 3

Answer: C

Explanation: Forty eight percent of 119 students (119/100) * 48 = 57 specialized in family practice. One twelfth of these equates to 57/12 = 5 who planned to work abroad.

25) How many students decided to specialize in immunology? A. 9

B. 11

C. 14

D. 7

E. 15

Answer: B

Explanation: Nine percent of 119 students decided to specialize in immunology. This equates to

(119/100) * 9 = 11 students

The table above shows the amount spent by Ace Marketing Consultancy to promote their clients.

‘Marketing’ spend does not include the time of any Ace employees, this is billed separately as ‘Personnel’.

Use this information to answer the following questions.

26) Approximately what percentage of Ace Marketing’s total business is accounted for by their three

smallest clients?

A. 18% B. 17% C. 20% D. 16% E. 22%

Answer: C

Explanation: The total value of Ace’s business is $41,427 (marketing) plus $40,614 (personnel) which gives

$82,041. Since we know that Aardvark account for 54% of the business, the quickest way to work out

how much the three smallest clients account for is to calculate how much Blue Arrow accounts for

($21,659 which is 26%), add this to the

54% to give 80%, which leaves 20% to be accounted for by the smallest three

27) Approximately what percentage of Ace Marketing’s total business is for Aardvark Cellular?

A.49% B. 57% C. 50% D. 54% E. 56%

Answer: D

Explanation: The total value of Ace’s business is $41,427 (marketing) plus $40,614 (personnel) which gives

$82,041. Aardvark Cellular account for (21,340+22,749 =) $44,089.

This equates to (44,089/82,041) * 100 = 54%.

28) If flyers for Aardvark Cellular cost $150 per thousand. Approximately, how many thousand have been produced?

A. 23

B. 20

C. 17

D. 14

E. 18

Answer: B

Explanation: Fourteen percent of $21,340 was spent on flyers for Aardvark Cellular. This equates to

(21340/100) * 14 = $2,987. If flyers cost $150 per thousand then approximately (2987/150 =) 20,000 have

been produced.

29) If Ace charges their clients cost price plus 20%, how much will they bill Aardvark Cellular for their website?

A. $1,536

B. $1,174

C. $1,744

D. $1,280

E. $1,474

Answer: A

Explanation: Six percent of $21,340 was spent on the website for Aardvark Cellular. This equates to (21340/100) * 6 = $1,280. If Ace add 20% then they will bill Aardvark for

$1,280 * 1.2 = $1,536.

30) Approximately how much was spent by on brochures for Aardvark Cellular? A. $4,994

B. $4,774

C. $4,632

D. $4,694

E. $4,624

Answer: D

Explanation: Twenty two percent of $21,340 was spent on brochures for Aardvark Cellular. This equates to (21340/100) * 22 = $4,694.

The table above shows the numbers of passengers flying from New York to four European capital cities

by low cost airline SleazyJet. These numbers have been rounded to the nearest thousand. Use this

information to answer the following questions.

31) Approximately, what fraction of passengers who travelled in Q4 2005 flew to Berlin? A. 1/8

B. 1/4

C. 1/7

D. 1/5

E. 1/15

Answer: C

Explanation: The number of passengers travelling in Q4 2005 was: London 10,000

Paris 14,000

Rome 20,000

Berlin 7,000

This gives a total of 51,000 of whom 7,000 were travelling to Berlin.

This equates to (7,000/51,000 = 1/7.

32) How many more passengers travelled to Rome in Q2 2005 than in the same quarter the previous year?

A. 5,000

B. 4,000

C. 3,000

D. 2,000

E. 1,000

Answer: E

Explanation: The number of passengers travelling in to Rome Q2 2004 was 12,000. The number of passengers travelling in to Rome Q2 2005 was 13,000.

Therefore 1,000 more passengers travelled in Q2 2005.

33) What was the ratio of passengers travelling to London and Paris in Q2 2004? A. 2.2:1

B. 1.8:1

C. 2:1

D. 0.75:1

E. 1:2

Answer: B

Explanation: The number of passengers travelling in to London Q2 2004 was 18,000. The number of passengers travelling in to Paris Q2 2004 was 10,000.

This equates to a ratio of 1.8:1

34) How many passengers travelled in Quarter 4 2004? A. 46,000

B. 44,000

C. 43,000

D. 45,000

E. 42,000

Answer: A

Explanation: The number of passengers travelling in Q4 2004 was: London 11,000

Paris 14,000

Rome 13,000

Berlin 8,000

This gives a total of 46,000.

The table above shows the total sales figures for three models of SUV. It also shows the percentage of

customers who specified additional equipment when buying from the dealer network. Use this

information to answer the following questions.

35) How much extra profit would be generated if dealers doubled the number of Body Kits fitted when they sold a FreeRanger?

A. $2,268

B. $4,534

C. $1,130

D. $1,238

E. $226

Answer: A

Eplanation: Twenty percent of the 10,804 FreeRangers sold (2,161) were fitted with body kits. The total revenue generated was 2,161 * $350 = $756,000. The profit margin on this is 30%, therefore (756,000/100) * 30 = ) $2,268. If dealers doubled the number sold then the additional profit would be

$2,268.

The table above shows the total sales figures for three models of SUV. It also shows the percentage of customers who specified additional equipment when buying from the dealer network. Use this information to answer the following questions.

36) How much profit (margin), in millions of dollars, can be attributed to Cruise Control fitted to the

FreeRanger?

A. 0.61

B. 0.48

C. 0.21

D. 4.80

E. 3.60

Answer: B

Explanation: Fifty percent of the 10,804 FreeRanger customers (5,402) specified cruise control. The total revenue generated was 5,402 * $220 = $1.19 million. The profit margin on

this is 40%, therefore (1.19/100) * 40 = ) $0.48 million.

37) How much profit (margin), in millions of dollars, can be attributed to Body Kits fitted to the

SportRanger?

A. 0.49

B. 1.48

C. 4.80

D. 0.36

E. 0.21

Answer: A

Explanation: Sixty percent of the 7,762 SportRangers sold (4,657) were fitted with body kits. The total revenue generated was 4,657 * $350 = $1.63 million. The profit margin on

this is 30%, therefore (1.63/100) * 30 = ) $0.49 million

38) How much total revenue, in millions of dollars, did Alloy Wheels generate for FreeRanger sales? A. 1.41

B. 1.28

C. 1.30

D. 1.36

E. 11.20

Answer: D

Explanation: Sixty percent of the 10,804 FreeRangers sold (6,482) were fitted with alloy wheels. Therefore the total revenue generated was 6,482 * $210 = $1.36 million.

39) How many customers specified cruise control when ordering a FreeRanger?

A. 5,320

B. 2,566

C. 4,861

D. 2,861

E. 5,402

Answer: E

Explanation: Fifty percent of the 10,804 FreeRanger customers (5,402) specified cruise control.

The table above shows agricultural imports for the island of South Cerney for a period of five months. Use this information to answer the following questions

40) Approximately what fraction of the total tonnage of imports is rice? A. 1/5

B. 1/4

C. 1/3

D. 2/5

E. 3/10

Answer: E

Explanation: Total tonnages imported over the 5 months are as follows:

Rice 141

Wheat 176

Potatoes 152

This means that the total tonnage of imports was 469 tons of which 141 tons were of

rice. Therefore (141/469 = 0.3) which is 3/10

41) Identify the missing number at the end of the series.

100, 96, 91, 85, ?

A. 74

B. 75

C. 77

D. 78

E. 79

Answer: D

Explanation: The difference between the numbers in this series increases by 1 each time: -4, -5, – 6, etc. This will produce a difference of -7 between 85 and the next number in the series, which is therefore 78.

42) Identify the missing number at the end of the series.

11, 16, 26, 41, ?

A. 51

B. 56

C. 61

D. 66

E. 46

Answer: C

Explanation: The difference between the numbers in this series increases by 5 each time – 5, 10, 15, etc.

This will produce a difference of 25 between 41 and the next number in the series, which is therefore 66.

43) Identify the missing number at the end of the series.

5, 12, 19, 26, ?

A. 31

B. 33

C. 35

D. 34

E. 37

Answer: B

Explanation: The numbers in this series increase by 7 each time. Therefore the next number is 33.

44) Anna bought $4,000 of company stock. She sold 75% of it when the value doubled, and the remainder at four times the purchase price. What was her total profit?

A.$4,000

B. $6,750

C. $6,000

D. $6,500

E. $5,000

Answer: C

Explanation: Anna sold 75% of her stock when it was worth $8000. So she took $6000 cash, leaving her

with $2000 worth of stock, which she had purchased for $1000. When this stock increased in value to

$4000 she sold it and added this to the first $6000 giving her $10,000 in cash. Subtracting the initial

$4000 coat of the stock, Anna has made $6,000.

45) A total of 1600 copies of a CD were sold. 30% were sold at 55% discount, 10% were sold at 30% discount and the remainder were sold at the full price of $7.95. What was the approximate total revenue in dollars?

A. 10,369

B. 10,569

C. 10,569

D. 10,234

E. 10,669

Answer: D

Explanation: Of the 1600 CDs sold:

60% or 960 were sold at $7.95 = $7632

10% or 160 were sold at $5.56 = $889

30% or 480 were sold at $3.57 = $1713

Therefore the total revenue was $10,234

46) Anna and John both receive stock as part of their remuneration. Anna receives $400 worth plus a bonus of 12%. John receives $300 worth plus a bonus of 20%. What is the difference between the values of the two bonuses?

A. $12.00

B.$10.00

C. $20.00

D. $14.00

E. $11.50

Answer: A

Explanation: Anna receives a bonus of ($400 * 0.12 =) $48. John receives a bonus of ($300 * 0.20 =) $60.

The difference between their bonuses is therefore $12.

47) Components X,Y and Z are ordered in the ratio 1:5:4. How many Z components will be in an order for 8000 components?

A.3,200

B.1,600

C. 6,400

D. 4,600

E. 1,800

Answer: A

Explanation: The components are ordered in the ratio 1:5:4 and the total order is for 8,000. To work out the numbers of each add 1+5+4 = 10.

Divide $8,000 by 10 = 800. You can then calculate that the number of Z components will be (800 * 4 =)

3,200.

48) A bank offers 10% per annum interest which is calculated and added at the end of the year. Another bank offers 10% per annum which is calculated and added every six months. What is the difference on a deposit of $800 after one year?

A. $2.00

B. $2.60

C. $2.40

D. $2.20

E. $4.00

Answer: A

Explanation: At the bank paying 10% interest calculated each year, the amount will be $880 ($800 * 1.10) at the end of the first year. At the bank paying 10% per annum added every 6 months, the amount will be $840 ($800 * 1.05) at the end of the first six months and $882 ($840 * 1.05) at the end of the year. Therefore the difference will be $2.00.

49) It costs a manufacturer X dollars per component to make the first 500 components.

All subsequent components cost X÷5 each. When X = $4.50 How much will it cost to manufacture 4,000

components?

A. $5,600

B. $4,600

C. $5,400

D. $5,200

E. $5,450

Answer: C

Explanation: The first 500 components are $4.50 each which gives $2,250. The 3500 subsequent components cost $0.90 each which gives $3,150. Therefore the run of 4000 components will cost $5,400

50) Identify the missing number.

2 6 44 8 10

15 19 ? 21 23

A. 72

B. 66

C. 73

D. 57

E. 55

Answer: D

Explanation: The numbers on the bottom row are 13 more than those on the top row. Therefore the missing number is 44 + 13 = 57..