1.If 3y+x>2
and x+2y≤3, what can be said about the value of y?

a)y=-1 b)y>-1 c)y<-1 d)y=1

2.If m is an
odd integer and n an even integer, which of the following is definitely odd?

a)(2m+n)(m-n) b)(m+n^{2})+(m-n^{2}) c)m^{2}+mn+n^{2} d)m+n

3.If the
price of an item is decreased by 10% and then increased by 10%, the net effect
on the price of the item is:

a)A decrease
of 99% b)no change c)a decrease of 1% d) an increase of 1%

4. what is
the sum of all even integers between 99 and 301?

a)40000 b)20000 c)40400 d)20200

5.There are
20 balls which are red,blue or green. If 7 balls are green and the sum of red
balls and green balls is less than 13, at most how many red balls are there?

a)4 b)5 c)6 d)7

6.If n is
the sum of two consecutive odd integers and less than 100, what is the greatest
possibility of n?

a)98 b)94 c)96 d)99

7.x^{2}<1/100,
and x<0. What is the tightest range in which x can lie?^{ }

a)-1/10<x<0 b)-1<x<0 c)-1/10<x<1/10 d)-1/10<x

8.There are
4 boxes colored red, yellow, green and blue. If 2 boxes are selected, how many
combinations are there for atleast one green box or one red box to be selected?

a)1 b)6 c)9 d)5

9.All faces
of a cube with an eight-meter edge are painted red. If the cube is cut into
smaller cubes with a two meter edge, how many of the two-meter cubes have paint
on exactly one face?

a)24 b)36 c)60 d)48

10.In a
sequence of integers, A(n)=A(n-1)-A(n-2), where A(n) is the nth term in the
sequence, n is an integer and n>=3, A(1)=1,A(2)=1. Calculate S(1000), where S(1000) is the sum
of the first 1000 terms.

a)2 b)3 c)4 d)0

11.If x^{2}-16>0,which of the following
must be true?

a)-4>x>4 b)-4>x<4 c)-4<x<4 d)4<x

12.Two
cyclists begin training on an oval racecourse at the same time. The
professional cyclist completes each lap in 4 mins. The novice takes 6 mins to
complete each lap. How many minutes after the start will both cyclists pass at
exactly the same spot where they began to cycle?

a)10 b)8 c)14 d)12

13.M,N,O and
P are all different individuals; M is the daughter of N; N is the son of O; O
is the father of P; Among the following statements, which one is true?

a) M is the
daughter of P

b)If B is
the daughter of N, then M and B are sisters.

c) if C the
granddaughter of O, then C and M are sisters.

d) P and N are
brothers

14.

In the above
diagram, ABCD and EFGH are squares of side 1 unit such that they intersect in a
square of diagonal length(CE)=1/2. The total area covered by the squares is

a) Cannot be found from the information

b) 1 ½

15. There are 10
stepping stones numbered 1 to 10 as shown at

the side. A fly jumps from the first stones as follows:

every minute it jumps to the 4^{th} stone from where
it started- that is

from 1^{st}
it would go to 5^{th} and from 5^{th} it would go th 9^{th}
and from 9^{th}

it would go to 3^{rd} etc. where would the fly be at
the 60^{th} min if it

starts at 1?

16.What is the remainder when 6^{17}+17^{6}
is divisible by 7?

a)1 b)6 c)0 d)3

17.In base
7, a number is written only using the digits 0,1…..6. the number 135 in base 7
is 1*7^{2}+3*7+5=75 in base 10. What is the sum of the base 7 numbers
1234 and 6543 in base 7?

a)11101 b)11110 c)10111 d)11011

18.The
sequence {A_{n}} is defined by A_{1}=2 and A_{n+1}=A_{n}+2n.
what is the value of A_{100}.

a)9902 b)9900 c)10100 d)9904

19.Find the
number of rectangles in the figure given
below.(a square is also considered a rectangle)

20.A,B,C and
D go for a picnic. When A stands on a weighing machine, B also climbs on, and
the weight shown was 132 kg. when B stands, C also climbs on , and the machine
shows 130 kg. similarly the weight of C and D is found as 102kg and that of B
and D is 116 kg. what is D’s weight?

a)58kg b)78kg c)44kg

21.Roy is
now 4 years older than Erik and half of
that amount older than Iris. If in 2 yrs,Roy will be twice as old as Erik, then
in 2 yrs what would be Roy’s age multiplied by Iris’s age?

a)28 b)48 c)50 d)52

22.X,Y,Z and
W are integers. The expression X-Y-Z is even and the expression Y-Z-W is odd.
If X is even what must be true?

a)W must be
odd b)Y-Z must be odd c)W must be odd d)Z must be odd

23.Given the
following information, which option must be true?

a) A occurs
only if either B or C occurs.

b)B occurs
only if both D and E occur.

c)F occurs
only if C does not occur.

d)G occurs
only if both A and F occur

i)5040

ii)3584

iii)4096

iv)7200

24.Mr and
Mrs Smith have invited 9 of their friends and their spouses for a party at the
Waikiki beach resort. They stand for a group photograph. If Mr Smith never
stands next to Mrs Smith(as he says they are always together otherwise), how
many ways the group can be arranged in a row for the photograph?

a)20! b)19!+18! c)18*19! d)
2*19!

25.Tim and
Elan are 90 km away from one another. They are starting to move towards each
other simultaneously, Tim at a speed of 10 kmph and Elan at a speed of 5 kmph.
If every hour they double their speeds, what is the distance that Tim will pass
until he meets Elan?

a)45km b)60km c)30 d)80km

26.In a
rectangular coordinates system, what is the area of a triangle whose verstices
have the coordinates (4,0),(6,3) and (6,-3)?

a)6 b)7 c)7.5 d)6.5

27.A drawer
holds 4 red hats and 4 blue hats. What is the probability of getting exactly
three red hats or exactly three blue hats when taking out 4 hats randomly out
of the drawer and immediately returning every hat to the drawer before taking
out the next?

a)1/2 b)1/8 c)1/4 d)3/8

28.In how
many ways can we distribute 10 identical looking pencils to 4 students so that
each student gets at least one pencil?

a)5040 b)210 c)84 d)none
of these

29.The prime
factorization of integer N is A*A*B*C, where A,B and C are all distinct prime
integers. How many factors does N have?

a)12 b)24 c)4 d)6

30.N is an
integer and N>2, at most how many integers among N+2, N+3,N+4,N+5,N+6 and
N+7 are prime integers?

a)1 b)3 c)2 d)4

31.A turtle
is crossing a field. What is the total distance(in metres) passed by the
turtle? Consider the following two statements.

(X) the
average speed of the turtle is 2 metres per minute.

(Y) had the
turtle walked 1 metre per sec faster than his average speed it would have
finished 40 min earlier.

i)statement
X alone is enough to get the answer.

ii)both
statements X and Y are needed to get the answer.

iii)statement
Y alone is enough to get the answer.

32.Given the
following information, who is the youngest?

C is younger
than A; A is taller than B

C is older
than B; C is younger than D

B is taller
than C; A is older than D

a)D b)B c)C d)A

33.Given the
information, which option must betrue?

i)A occurs
only if either B or C occur.

ii)B occurs
only if both D and E occur.

iii) F
occurs only if C does not occur.

iv) G occurs
only if both A and F occur

a)A occurs
whenever F occurs.

b)F never
occurs

c)G does not
occur if D does not occur

d) none of
these

34.If
P(x)=ax^{4}+bx^{3}+cx^{2}+dx+e has roots at x=1,2,3,and
4, and P(0)=48, what is P(5)?

a)48 b)24 c)0 d)50

35.How many
workers does factory W employ? Consider the following two statements to get the
answer.

(X) 220
workers at W install batteries, and 300 workers knit socks.

(Y) every
worker of W either installs batteries or knits socks, or both.

i)statement
X alone is enough to get the answer.

ii)statements
X and Y are together not enough to get the answer, and additional data ia
needed.

iii)statement
Y alone is sufficient to get the answer

iv)both statements
X and Y are needed to get the answer