National Testing Service Pakistan

(Building Standards in Educational & Professional Testing)

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National Testing Service Pakistan

Overseas Scholarship Scheme for PhD Studies

Building Standards in Educational and Professional Testing

PATTERNS AND PRACTICE

National Testing Service Pakistan

Overseas Scholarship Scheme for PhD Studies

Building Standards in Educational and Professional Testing

2

Quantitative Ability

The Quantitative section measures your basic mathematical skills, understanding of elementary mathematical concepts, and the ability to reason quantitatively and solve problems in a quantitative setting. There is a balance of questions requiring basic knowledge of arithmetic, algebra, geometry, and data analysis. These are essential content areas usually studied at the high school level. The questions in the quantitative section can also be from • • • Di screte Quanti tative Questi on Quanti tative Compari son Questi on Data Interpretati on Questi on etc.

The distribution in this guide is only to facilitate the candidates. This distribution is not a part of test template, so, a test may contain all the questions of one format or may have a random number of questions of different formats. This chapter is divided into 4 major sections. The first discusses the syllabus /contents in each section of the test respectively and the remaining three sections address the question format, guide lines to attempt the questions in each format and some example questions.

2.1

2.1.1

General Mathematics Review

Arithmetic

The following are some key points, which are phrased here to refresh your knowledge of basic arithmetic principles.

Basic arithmetic

• For any number a, exactl y one of the fol l owi ng i s true: o a i s n egativ e o a i s z ero o a i s posi ti ve Th e on l y nu m ber th at i s equ al to i ts opposi te i s 0 (e. g.

•

a = − a only if a = 0 )

• •

If 0 i s m ul ti pli ed to any oth er n um ber, i t will m ak e i t zero ( a × 0 = 0 ) . Product or quoti ent of two numbers of t h e same si gn are al ways posi ti ve and of a d i fferent si gn are al ways negati ve. E. g. i f a po si ti ve number i s mul ti pli ed to a negati ve number the r esul t wi ll be nega ti ve and i f a negati ve number i s d i vi ded by another ne gati ve number the r esul t will be posi ti ve.

S ee th e f oll owi n g tables f or all com bi n ati ons.

National Testing Service Pakistan

Overseas Scholarship Scheme for PhD Studies

Building Standards in Educational and Professional Testing

+ + − −

• • •

÷ or × ÷ or × ÷ or × ÷ or ×

+ − + −

= = = =

+ − − +

The sum of two posi tive numbers i s al ways posi ti ve. The sum of two negative numbers i s al ways negati ve. S u btracti ng a number from another i s the same as ad di ng i ts opposi te

a − b = a + (−b)

• •

The reci pro cal of a number a i s

1 a

The produc t of a number and i ts reci procal i s al ways one

a×

•

1 =1 a 1 b

D iv i di n g by a n u m ber i s th e same as m u l ti pl yi n g by i ts reci procal

a ÷b = a×

• •

Every i n teger has a fini te set of factor s (di v i sors) an d an i nfi ni te set of m u l t i p l i e r s. If a and o o o o b are two i n tegers, the f oll owi n g four terms are synonyms a i s a divisor o f b a i s a factor o f b b i s a divisible b y a b i s a multiple o f a

They al l mean that when a i s divi ded by b there i s no r e m a i n der . • • • Posi ti ve i n tegers, other than 1, have at l east two posi tive factors. Posi ti ve i n tegers, other than 1, whi ch have exactl y two factors, are known as p r i m e nu m b e r s. Every i n teger greater than 1 that i s not a pri m e can be wri tten as a product of pri m es. T o f i n d t h e p r i m e f a c to r i z a ti o n of a n i n t e g e r , fi n d a n y t w...