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QUESTION: 1

The grid given below contains the codes of high performing employees from different IT companies. If the number starting with 8206 represents the code of the employees of Infosys, then how many employees of Infosys are high performers?

Solution:

QUESTION: 2

7 5 4 3 2 1 6 8 9

$ > + - # % @ = ×

What is the number indicated by the following symbols?

+ % X $ =

Solution:

QUESTION: 3

From the given alternatives select the word which cannot be formed using the letters of the given word

COMPREHENSION

Solution:

There is only one ‘i’ in the word.

QUESTION: 4

Find the missing term:

Solution:

14 + 9 + 13 = 36 × 3 = 108

17 + 8 + 19 = 44 × 3 = 132

20 + 18 + 15 = 53 × 3 = 159

QUESTION: 5

From among the given alternatives select the one in which the set of numbers is most like the set of numbers given in the question.

Given set: (13, 20, 9)

Solution:

13 + 20 + 9 = 42

Similarly,

17 + 14 + 11= 42

QUESTION: 6

Find the missing term.

Solution:

The pattern is,

18 + 3 = 21, 18 – 2 = 16

21 + 4 = 25, 16 – 3 = 13

25 + 5 = 30, 13 – 4 = 9

30 + 6 = 36, 9 – 5 = 4

QUESTION: 7

**Directions**

Study the following question and based on this, answer the following questions.

C is to the west of I. D is 5m to the north of C. E is 5m to the north of D. F is 9m to the west of E. G is 5m to the south of F. H is 12m to the East of D.

**Q.** How far is G from H?

Solution:

GH = GD + DH

= 9 + 12 = 21m

QUESTION: 8

**Directions**

Study the following question and based on this, answer the following questions.

C is to the west of I. D is 5m to the north of C. E is 5m to the north of D. F is 9m to the west of E. G is 5m to the south of F. H is 12m to the East of D.

**Q. **H is in which direction with respect to E?

Solution:

QUESTION: 9

E is the father of his only child D and Q is grandson of F, who is wife of E. H is mother of T and only daughter-in-law of E. How is D related to T?

Solution:

QUESTION: 10

**Directions**

In each of the questions below are given two/three statements followed by two conclusions numbered I, and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of given conclusions logically follows from the given statements disregarding commonly known facts.

Statement: No cooler is a fan.

All fans are ACs.

No AC is a button.

Conclusion: No fan is a button.

Some ACs are cooler.

Solution:

All fans are ACs(A) + No AC is a button(E) ⇒ No fan is a button(E). Hence conclusion I follows.

No cooler is a fan(E) + All fans are ACs(A) ⇒ Some ACs are not coolers(O). Hence conclusion II will not follow.

QUESTION: 11

**Directions**

In each of the questions below are given two/three statements followed by two conclusions numbered I, and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of given conclusions logically follows from the given statements disregarding commonly known facts.

Statement: Some letters are papers

All papers are objects.

Some objects are subjects.

Conclusion: Some papers are not subjects.

All subjects are objects

Solution:

All papers are objects(A) + Some objects are subjects(I) ⇒ No conclusion. Hence conclusion I will not follow.

Some objects are subjects(I) ⇒ conversion ⇒ Some subjects are objects(I). Hence conclusion II will not follow

QUESTION: 12

If the English alphabetical series in written from right to left, which Letter will be the 6^{th} letter to the right of the 9^{th} letter from the left of the last but one letter from the right.

Solution:

QUESTION: 13

Pick the odd one out:

Solution:

Except MS office, all are operating systems

QUESTION: 14

Which one the following comes in the place of (?)

17 49 ? 592 1578

Solution:

17 × 3 – 2 = 49

49 × 4 + 2 = 198

198 × 3 – 2 = 592

394 × 4 + 2 = 1578

QUESTION: 15

How many such pairs of letters are there in the word ‘APTITUDE’, each of which has many letters between them in the word as they have between them in the English alphabetical series?

Solution:

TU, DE, EI

QUESTION: 16

Eight friends S, T, U, V, W, X, Y and Z are sitting in a straight line facing north, but not necessarily in the same order. U sits third from the left end. Only one person sits between U and Y. W sits on immediate left of T. Z sits on the immediate right of X. Z sits on the left of V. O only one person sits between V and S. V is not on the left S. Who among the following sits between U and Y?

Solution:

QUESTION: 17

In a certain coded language DRUM is coded as AOVI and VARY is coded as UBOU, then what is the code of AUTO?

Solution:

DRUM –AOVI

VARY – UBOU

Then, AUTO – BVOP

Every vowel is coded as next consonant and every consonants is coded as previous vowel.

QUESTION: 18

Arrange the following words in a meaningful order.

A. Spawn B. Frog C. Froglet D. Tadpole

Solution:

Spawn → Tadpole → Froglet → Frog

QUESTION: 19

72 : 180 : : 60 : ?

Solution:

72 × 2.5 = 180

Similarly 60 × 2.5 = 150

QUESTION: 20

Interchanging which two operational symbols will make the given equation true?

36 × 5 - 84 ÷ 4 + 50 = 151

Solution:

If we interchange (+ and -) then equation will become correct → 36 × 5 + 84 ÷ 4 - 50

= 180 + 21 - 50 → 201 - 50 = 151

QUESTION: 21

Find the number of triangles in the given figure.

Solution:

The triangles are: ADE, GDE, DFG, EGH, FKB, FGK, GIJ, GHN, HNC, ILK, JMN, AFH, DBN, GKN, EKC, ABC

QUESTION: 22

The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column. e.g. ‘A’ can be represented by 03, 12 etc. and ‘N’ can be represented by 56, 65 etc. Identify the set for the word **DRAW**.

**MATRIX – I**

Solution:

D – 00, 14, 23, 32, 41

R – 57, 66, 75, 89, 98

A – 03, 12, 21, 30, 44

W – 55, 69, 78, 87, 96

QUESTION: 23

In the question one part of the problem figure is subtracted. Select the portion that shows the correct shape by the subtraction.

**Question figure:**

**Answer figure:**

** **

Solution:

QUESTION: 24

In the following questions select the related figure from the given alternatives.

**Question figure:**

**Answer figure:**

Solution:

From the first unit to second unit three line segments are added in a set pattern.

QUESTION: 25

Four positions of dice are given below. Which letter will be opposite to D?

Solution:

The letters A, B, C, D and E are on the adjacent faces of face C. therefore, some other letter lies opposite ‘C’. The letters B, C and E are on the adjacent faces of face D. therefore, A lies opposite D.

QUESTION: 26

India’s longest bridge connects

Solution:

PM Narendra Modi on 26 May inaugurated India’s longest bridge, spanning 9.3 km across the Brahmaputra, promising to turn the north-east into a showpiece of infrastructure development. The road bridge, connecting Dhola in Arunchal Pradesh to Sadiya in Assam.

QUESTION: 27

India’s rank in Global Innovation Index is

Solution:

India move up six places to the 60 position in a survey of innovative capacity among 130 nations on the Global Innovation Index 2017.

QUESTION: 28

In which city in India first three cases of Zika virus has been confirmed by the World Health Organisation (WHO)?

Solution:

The World Health Organisation (WHO) has confirmed the first three cases of Zika virus in India, as having been reported from the city in Gujarat

QUESTION: 29

Who has been awarded with Man Booker Prize recently?

Solution:

Israeli author David Grossman has won the Man Booker International Prize for his novel A Horse Walks into a Bar. His novel is about a failing standup comic.

QUESTION: 30

Every year first Sunday of May is observed as which of the following days?

Solution:

World laughter Day takes place on the first Sunday of May of every year. The first celebration was on January 10, 1998, in Mumbai, India, and was arranged by Dr. Madan Kataria, founder of the worldwide Laughter Yoga movement.

QUESTION: 31

Kanger Ghati National Park is situated in the state of

Solution:

Kanger Ghati National Park was declared a national park in 1982 by the Government of India. Among the various protected areas in the country, the Kanger Valley National Park near Jagdalpur, in the Bastar region of Chhattisgarh is one of the most beautiful and densest national parks, well known for its biodiversity with picturesque landscape, magnificent waterfalls, very famous subterranean geomorphologic limestone caves, and home for the Bastar hill myna, the state bird of Chhattisgarh.

QUESTION: 32

Which is the second highest military award for gallantry during wartime?

Solution:

The Maha Vir chakra is the second highest military decoration in India, after the Param Vir Chakra, and is awarded for acts of conspicuous gallantry in the presence of the enemy, whether on land, at sea or in the air.

QUESTION: 33

‘Rand’ is the currency of which of the following countries?

Solution:

Nigeria – Naira

South Africa – Rand

Namibia – Shilling

Ethiopia – Birr

QUESTION: 34

Increase in the focal length of eye lens and Stiffening of ciliary muscles is caused by

Solution:

A person suffering from hypermetropia can see the distant objects clearly but not the near object.

QUESTION: 35

Which of the following disease is caused by the deficiency of iodine in food?

Solution:

Goitre is the disease caused by the deficiency of iodine in food. In this disease the shape of the thyroid gland enlarges abnormally.

QUESTION: 36

The India’s First Woman Governor of India is

Solution:

Sarojini Naidu was the first female to become the governor of an Indian state. She governed Uttar Pradesh from 15 August 1947 to 2 March 1949.

QUESTION: 37

Mercalli scale is the instrument used for measuring the intensity of ___________

Solution:

The Mercalli intensity scale is a seismic scale used for measuring the magnitude and intensity of an earthquake. It measures the effects of an earthquake.

QUESTION: 38

The first Chairman of Finance commission was

Solution:

The First Finance Commission of India was appointed in 1951, for the period 1952-57 by the President of India and was chaired by K.C.Neogy.

QUESTION: 39

Nadir Shah took away Kohinoor Diamond during the period of _____________

Solution:

In 1738-39, Nadir Shah raided India and took away Thakht-i-Taus (The Peacock throne) and Kohinoor Diamond during the period of Muhammad Shah.

QUESTION: 40

The Polymer used for Electrical insulation buttons is

Solution:

Bakelite was used for its electrical non-conductivity and heat-resistant properties in electrical insulators, radio and telephone casings and such diverse products as kitchenware, jewellery, pipe stems, children toys and firearms.

QUESTION: 41

The Emblem of the Chola Dynasty was

Solution:

The Tiger or Jumping Tiger was the royal emblem of the Cholas and was depicted on coins, seals and banners.

QUESTION: 42

Match the following Important Books on Economics with their respective Authors.

**Books on Economics Author**

(i) The Wealth of Nations A. Irwin Fisher

(ii) Money Illusion B. Adam Smith

(iii) The Value and Capital C. J.M.Keynes

(iv) General Theory of Employment D. Hicks

Solution:

QUESTION: 43

Which of the following metal has the highest Melting point?

Solution:

Of all the metals in Pure form, tungsten has the highest melting point, Lowest vapour pressure and the highest tensile strength.

QUESTION: 44

The Study of lizards is known as

Solution:

Study of Lizards is Saurology

-Study of Pulse and arterial pressure is Sphygmology

-Study of serum, interaction of antigen and antibodies in the blood is Serology

-Study of parasites is Parasitology.

QUESTION: 45

Which of the following rock is not sedimentary rock?

Solution:

Granite is a common type of Igneous rock that is granular and phaneritic in nature.

QUESTION: 46

Article __ of the Indian Constitution ensures Abolition of Untouchability.

Solution:

Under Article 17, Untouchability is abolished and its practice in any form is forbidden. The enforcement of any disability arising out of Untouchability shall be an offence punishable in accordance with law.

QUESTION: 47

Who was the first king to have the image of Lord Buddha inscribed on his coins?

Solution:

Kanishka's coins portray images of Indian, Greek, Iranian and even Sumero – Elamite divinities, demonstrating the religious syncretism in his beliefs. Kanishka's coins from the beginning of his reign bear legends in Greek language and script and depict Greek divinities

QUESTION: 48

DNA fingerprinting is a technique used for the detection of:

Solution:

The first methods for finding out genetics used for DNA profiling involved RFLP analysis. DNA is collected from cells, such as a blood sample, and cut into small pieces using a restriction enzyme (a restriction digest).

QUESTION: 49

Foramen Magnum is an aperture of

Solution:

The foramen magnum (Latin: great hole) is a large oval opening (foramen) in the occipital bone of the skull in humans and various other animals. It is one of the several oval or circular openings (foramina) in the base of the skull.The foramen magnum is a very important feature in bipedal mammals.

QUESTION: 50

Fermentation is a

Solution:

Fermentation is a metabolic process that converts sugar to acids and gases, or alcohol. It occurs in yeast and bacteria, and also in oxygen-starved muscle cells, as in the case of lactic acid fermentation. Fermentation is also used more broadly to refer to the bulk growth of microorganisms on a growth medium, often with the goal of producing a specific chemical product.

QUESTION: 51

At present, Naveen is six years younger than Mohit. Mohit’s age fifteen years hence will be equal to thrice that of Naveen three years ago. What will be the sum of their present age?

Solution:

Mohit = x

Naveen = (x-6)

15 years hence, Mohit’s age = (x + 15) years

3 years ago, Naveen = x - 6 - 3

= (x - 9) years

Now, (x+15) = 3 (x-9)

x + 15 = 3x - 27

42 = 2x

x = 21 years

Hence, Mohit = 21 years

Naveen = 21 - 6 = 15 years

Sum of the present ages of Mohit and Naveen = 21 + 15 = 36 years

QUESTION: 52

The distance between two places P and Q is 550 km. A car departs from place P for place Q at a speed of 60 km/hr. at 5 am. Another car departs from place Q for place A at a speed of 40 km/hr at 10 am. At what time will both the car meet each other?

Solution:

Distance travelled by the first car in 5 hours = 60 × 5 = 300 km

Remaining distance = 550 - 300

= 250 km

Time for both cars to meet = distance/(relative speed )

= 250/(60+40) = 250/100

= 21/2 hrs = 2 hrs 30 min

∴ Both the cars will meet after 2 hrs 30 min means (10 am + 2 hrs 30 min) = 12 hrs 30 min

QUESTION: 53

Amit started a business by investing Rs. 60,000. After 4 months, Harish joined him with a capital of Rs. 48,000. At the end of the years Harish received Rs. 2800 as profit. What is the total profit at the end of the year?

Solution:

Ratio of Amit’s profit to Harish’s profit = 60 × 12 : 48 × 8

= 15 : 8

Now, lets Amit’s profit be 15x and that of Harish be 8x.

Given, 8x = 2800

x = 350

∴ Total profit = 15x + 8x

= 23x = 23 × 350

= 8050

QUESTION: 54

Abhishek, Rohit and Pankaj working together completed a job in 20 days. The ratio of their efficiencies is 3 : 4 : 5. How many days will be required by the fastest worker alone to complete the whole work?

Solution:

Ratio of efficiencies = 3 : 4 : 5

Ratio of time required = 1/3 : 1/4 : 1/5

= 20 : 15 : 12

Suppose Abhishek, Rohit and Pankaj complete the work in 20x, 15x, 12x days respectively.

Then,

1/20x + 1/15x + 1/12x = 1/20

(3x+4x+5x)/60x

12/60x = 1/20

x = (12×20)/60 = 4 days

Hence, the fastest worker (Pankaj) can complete the work = 12x

= 12 × 4

= 48 days

QUESTION: 55

A man rows to a place 221 km away and comes back to the starting point. If the speed of the stream is 2 km/hr and the speed of the boat in still water is 15 km/hr. Then what is the total time taken by him?

Solution:

221/((15+2)) + 221/((15-2)) = 13 + 17 = 30 hrs

QUESTION: 56

A shopkeeper marks the price of an article Rs. 3200. What will be the selling price if he allows two successive discounts of 30% each?

Solution:

Marked price

∴ SP = 3200 × 70/100 × 70/100 = Rs. 1568

QUESTION: 57

Two Poles are 12 metres apart horizontally and the height of one is double that of the other. If from the mid-point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary. Then the height of the shorter post is:

Solution:

Let AB = taller pole

CD = shorter pole = h

OB = OD =( 12)/2 = 6m

In ∆OCD,

tanθ = h/6 ............................(i)

In ∆AOB

tan 〖(90- θ)〗 = 2h/6 = h/3

cotθ= h/3 .............................(ii)

Multiplying (i) and (ii), we get

tanθ ×cotθ = h/6 × 4/3

1 = h²/18

h² = 18

h=3√2 m

QUESTION: 58

In a mixture of 85 litres, the ratio of milk to water is 2 : 3. If this ratio is to be 1 : 3, then what is the quantity of water needed to be added?

Solution:

Quantity of milk in the mixture = 85 × 2/5 = 34 liters

Quantity of water in the mixture = 85 × 3/5 = 51 liters

Let x liters water be added to the mixture then,

34/(51+ x) = 1/3

102 = 51 + x

x = 102 - 51

= 51 litres

QUESTION: 59

The ratio of P’s to Q’s salary is 5 : 7. If Q’s salary is increased by 35%, his total salary becomes Rs. 52,920. What is the salary of P?

Solution:

Let the salary of P and Q be 5x and 7x respectively.

Then,

7x × 135/100 = 52,920

x = (52920×100)/(135×7)

= Rs. 5600

∴ P’s salary = 5x

= 5 × 5600

= Rs. 28000

QUESTION: 60

How much water must be added to a cask which contain 32 litre of milk at a cost price of Rs 45 per litre so that the cost of milk reduces to Rs. 40 per litre?

Solution:

Let x litre water be added in the mixture.

Then,

(32+ x) 40 = 45 × 32

1280 + 40x = 1440

40x = 160

x = 4

Therefore, 4 litre water must be added in the mixture.

QUESTION: 61

A train running at the speed of 35 metre per second crosses a bridge in 30 seconds. Another which is 130 metre shorter than the previous train crosses the same bridge at the speed of 40 metre per second. Find the time taken by the second train to cross the bridge?

Solution:

Let the length of the bridge be x m and that of the first train be y m

(x+y)/35 = 30

x+y = 1050

Again = (x+(y-130))/40 = t

(x+y-130)/40

(1050-130)/40 = 920/40

= 23 seconds

QUESTION: 62

The Value of (sin38˚)/(cos52˚)+ (cos12˚)/(sin78˚)- 4cos²60˚ is

Solution:

(sin38˚)/(cos52˚)+ (cos12˚)/(sin78˚)- 4cos²60˚

(sin (90-52)˚)/(cos52˚)+ (cos (90-78)˚)/(sin78˚)- 4cos²60˚

(cos52˚)/(cos52˚)+ (sin78˚)/(sin78˚)- 4cos²60˚

⇒1 + 1 - 4×(1/2)²

⇒1

QUESTION: 63

A tradesman **offers **8% discount on the marked price and 1 article free with every 19 article bought and still gains 35%. If the marked price is 35% more than the cost price of Rs. 100. Then what is the selling price?

Solution:

Total discount = 8% + 1/((19+1)) × 100

= 8% + 1/20 × 100

= 8 + 5

= 13%

CP = Rs. 100

MP = Rs. 135

SP = 135× 88/100 × 135/100

= Rs. 160.38

QUESTION: 64

In physics examination a student scored 45% marks in the first paper out of 160. How much percent marks should he score in the second paper out of 140 marks if he is to get an overall of 66% marks?

Solution:

Marks obtained in first paper = 45/100 × 160 = 72

Marks to be obtained in both the papers (160+140) × 66/100

= 198

∴ Marks to be obtained necessarily is second paper = 198 - 72

= 126

∴ Percentage of marks to be obtained in second paper = 126/140 × 100 = 90%

QUESTION: 65

A rectangle with a diagonal of length 28m is inscribed in a circle. Find the area of a circle?

Solution:

Radius of circle = 28/2 = 14 m

Area of circle = π/4 r²

= 22/7 × 14 × 14

= 616 cm²

QUESTION: 66

A wire is moulded into a circle of radius 21 cm. Then the wire is bent and shaped into a rectangle of length 36 m. Find the area of the rectangle thus formed?

Solution:

Circumference of circle = Perimeter of a rectangle = 2πr

= 2 × 22/7 × 21

= 132 m

Perimeter of a rectangle = 2(l + b)

132 = 2(l + b)

36 + b = 66

B= 66 – 36 = 30 m

∴ Area of the rectangle = l × b = 36 × 30

= 1080 m²

QUESTION: 67

Suraj is one third as good as workman as Pankaj and together they finish a piece of work in 36 days. The number of days taken by Suraj alone to finish the work is

Solution:

Panjkaj’s 1 day work = 1/x

Suraj’s 1 day’s work = 1/3x

Then,

1/x + 1/3x = 1/36

4/3x = 1/36

x = (4×36)/3 = 48 days

Suraj alone can complete the work in 3×48 = 144 days

QUESTION: 68

Find the value of X in the given figure:

Solution:

In the given figure

∠ABF + ∠CBF = 180˚ (Angles in a straight line)

75˚ + ∠CBF = 180˚

∠CBF = 105˚

Now, in ∆CBE

∠CBE + ∠BCE + ∠CEB = 180˚

105˚ + ∠BCE + 44˚ = 180˚

∠BCE = 180˚ - (105˚+ 44˚)

∠BCE = 31˚

∠BCE + ∠DFB = 180˚ (Sum of opposite sides of Cyclic Quadrilateral)

∠DFB = 180˚ - 31˚ = 149˚

∠DFB + ∠AFB = 180˚

∠AFB = 180˚ - 149˚ = 31˚

In ∆ABF

∠AFB + ∠FAB + ∠AFB = 180˚

∠FAB = 180˚-(75˚+31˚) = 74˚

QUESTION: 69

A man takes a total of 5 hrs 30 min by walking to a certain place and coming back by cycle. He would have gained 2 hrs 30 min by cycling both the ways. The time he would take to walk both ways is

Solution:

By cycling + by walking = 5 hrs 30 min .......... (i)

One way by cycling = (5 hrs 30 min 〖- 2 hrs 30 min〗)/2

= 1 hrs 30 min

∴ By walking both ways = 2 (5 hrs 30 min - 1 hrs 30 min) = 8 hrs.

QUESTION: 70

The slope of the equation 24x+8y=56 is

Solution:

For the equation

y=mx+c

Where ‘m’ is the slope

24x+8y=56

8y= -24x+56

y= (-24x)/8+ 56/8

y= -3x+7 Slope = -3

QUESTION: 71

Find the value of ‘x’ in the given expression

(49/16)^{x }× (64/343)^{x-1} = 4/7

Solution:

(49/16)^x× (64/343)^(x-1) = 4/7

⇒(7/4)^2x× (4/7)^(3x-3) = 4/7

〖

⇒(4/7)〗^(-2x)× (4/7)^(3x-3) = 4/7

⇒ -2x+3x-3=1 ⇒ x = 4

QUESTION: 72

**Directions**

Study the graph and answer the following questions:

**Q. **What is the ratio of the students who are learning Bharatanatyam from school Q to the total number of students who are not learning Bharatanatyam from school S?

Solution:

No. of students who are learning Bharatanatyam from school Q = 250 × 34/100

= 85

No. of students who are not learning Bharatanatyam from school S = 450 × 68/100

= 306

∴ Required ratio = 5 : 18

QUESTION: 73

**Directions**

Study the graph and answer the following questions:

**Q.** In school R, out of the total number of students learning Bharatanatyam, 1/9 are below 15 years of age. If out of the total students who are below 15 years of age 30% are females, then what is the male number of students who below 15 years of age learning Bharatanatyam?

Solution:

No. of students who are below 15 years of age in school R = 300 × 20/100

= 60

No. of male students who are learning Bharatanatyam in school R = 60 × 70/100

= 42

QUESTION: 74

**Directions**

Study the graph and answer the following questions:

**Q.** What is the difference between the total number of students learning Bharatanatyam from school P and R to the number of students who are not learning Bharatanatyam from school T?

Solution:

P = 550 × 18/100

= 99

R = 300× 20/100 = 60

Total students from P and R

= 99 + 60

= 159

T - 420 × 70/100 = 294

∴ Required difference = 294 - 159 = 135

QUESTION: 75

**Directions **In each question, there are three sentences. Each has a pair of words that are italicised and highlighted. From the italicised and highlighted words, select the most appropriate words (A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may be selected to correctly complete the set of sentences. From the options given, choose the most appropriate one.

The focus on jobs is obviously vital (A)/ peripheral (B). At the root of the crisis is the step (A) / steep (B) fall in the prices of agricultural goods. Growth can come about without any substantial (A) / sustainable (B) job-creation in the formal sectors of the economy, but through improvements in productivity.

Solution:

vital means important peripheral means unimportant step means move, pace, stairs steep means sharp, abrupt substantial means significant sustainable means able to be maintained at a certain rate or level

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