NTS Book for GAT General.pdf


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Building Standards in Educational and Professional Testing


For any posi tive number a there i s a posi tive number b that sati sfi es the
equati on

a =b.

( a )2 = a × a = a .



For any positive integer,



For any posi tive numbers a and b:

ab = a × b

a
=
b

and

o

a
b

a+b ≠ a + b
o


as 5 = 25 = 9 + 16 ≠ 9 + 16 = 3 + 4 = 7
( a )2 = a ,

Al th o u g h i t i s al w a y s t r u e t h a t
posi ti ve as

n

F o r a n y n um b e r a ,



For any number a, b and c:

an = a 2 .

a(b + c) = ab + ac
and i f

a(b − c) = ab − ac

a≠0

(b + c) b c
= +
a
a a



true only if a i s

(−5) 2 = 25 = 5 ≠ −5





a2 = a is

(b − c) b c
= −
a
a a

I ne qua li ti e s


For any number a and b, exactl y one of the foll owi n g i s true:

a>b

a=b

or

or

a < b.



F o r a n y n um b e r a a n d b ,

a > b means

that

a − b is

positi v e.



F o r a n y n um b e r a a n d b ,

a < b means

that

a − b is

n egati v e.



F o r a n y n um b e r a a n d b ,

a = b means

that

a − b is

z ero.



The symbol



means greater than or equal to and the symbol

than or equal to. E.g. the statement
number gr eater than 5.
The statem ent

2 < x < 5 is

x ≥ 5 means

an abbrev i ati on of

2 < x and x < 5 .

A ddi ng or subtracti n g a number to an i n equali ty preserves i t.



If

t h en

means l ess

that x can be 5 or any



a<b,



a + c < b + c and a − c < b − c .

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