# NTS Book for GAT General.pdf

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Building Standards in Educational and Professional Testing
e. g.

a &lt; b and

c&lt;d,

then

a+c &lt;b+d .

Mul ti pl yi n g or di vi di ng an i n equali ty by a posi ti ve number pres e rves i t. If

a &lt; b and c i s

5 − 10 &lt; 6 − 10

and

A ddi n g i n equ al i ti es i n sam e di recti on preserv es i t:
If

5 &lt; 6 ⇒ 5 + 10 &lt; 6 + 10

a posi tive number, then

a×c &lt; b×c

a b
&lt;
c c.

and

Mul ti pl yi n g or di vi di ng an i n equali ty by a negati ve number reve rses i t. If

a &lt; b and c i s

a negati ve number, then

a×c &gt; b×c

and

a b
&gt;
c c.

If si des of an i n equality are both posi ti ve and both ne gati ve, taki ng the
reci procal reverses th e i n equali ty .

If

0 &lt; x &lt; 1 and a i s

If

0 &lt; x &lt; 1 and m and n are

If

0 &lt; x &lt; 1,

If

t h en

0 &lt; x &lt; 1 , then

pos i t i v e , t h en

xa &lt; a .

integers wi th

m&gt;n,

t h en

xm &lt; xn &lt; x .

x &gt; x.

1
1
&gt;x
&gt;1
x
and x

Pro per ties of Ze ro

0 i s the only number that i s nei ther negati ve nor posi ti ve.

0 i s smal l er than every posi tive number and great er than every negati ve
number.

0 i s an even i n teger.

0 i s a m ul ti pl e of ev ery i n teger.

For every number

a

:

For every number

a

: a×0 = 0.

For every posi ti ve i n teger

For every number

a

(incl u di ng 0):

For every number

a

(other than 0):

a + 0 = a and a − 0 = a .

National Testing Service Pakistan

n : 0n = 0 .

a ÷ 0 and

0÷a =

a
0

are undefi n ed symbol s.

0
= 0.
a

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