Download Test paper 1 1 a>b>c and all three belong to natural numbers find

Test paper 1
1 a>b>c and all three belong to natural numbers find the value of b If
(a+1)(b+1)(c+1)-1=1000
A 10 B11 C 13 D 14
2 . If a,b,c,d are in continued proportion then what is the value of "n' ?
a
d
an +bn+cn
bn+ cn +dn
=
A 2 B 3 C4 D 5
3 If |a|=3,| b|=4 and | a+ b|=1 then | a- b|=?
A
B
C
D
E
5
6
7
8
None of these
4. The population of a bacteria culture doubles every 2 minutes. Approximately
how many minutes will it take for the population to grow from 1,000 to 500,000
bacteria?
A
B
C
D
E
10
12
16
18
20
5 If certain cells are spherical and are 0.008 millimeter in diameter how many
such cells would be required to make a single row 1 millimeter in length?(The
cells are placed so that each is tangent to the next with centers all in a straight
line)
A
B
C
D
E
8
80
100
125
1,250
6. The diagonal of a square is doubled to make another square.The area of the
new square will
A
B
C
D
E
become 4 times
become half
become 5 times
become 2 times
None of thes
7. When the circumference of a circle decrease from 3Π to Π its area decreases
by approximately what %?
A
B
C
D
E
88%
69 8/9%
78 8/9%
44%
88 8/9%
4o brand A television sets and 80 brand B television sets were purchased for a
motel chain. If the price of each brand B set was twice the price of each brand
A set, what percent of the total bill was the price of a brand B set?
8
A
B
C
D
E
0.25%
0.5%
0.625%
0.833%
1.0%
A merchant purchased 2000 fruits at Rs.40/- per 100 and spent Rs.200 on
transport and other expenses. If 10% of them were spoiled, he sold the
remaining at Rs.9/- per dozen. His gain percent in this sale is?
9
A
B
C
D
E
5%
15%
25%
35%
None of the
10. 42. If x + y + z = 1, then xy + yz + zx is
[A] < 1/2 [B] 1/2 [C] >1/2 [D] none of these
11. X,Y,and Z take 20, 30 and 60 days respectively to complete a job independently.
They set out to complete a job together . However Y leaves after 4 days and Z leaves after another
6 days .
How many more days will it take for X alone to complete the job now?
A 4B 3
C 5
D6
12 A rectangular block of dimensions 5*6*7 cm. Is dropped into a cylindrical vesssed of radius 6
cm. And height 10 cm.. If the level of fluid in the cylinder rises by 4 cm.,
What portion of the block is immersed in the fluid?
A22/7*15/18 B22/7*24/35 C22/7*22/34 D22/7*12/15
13. A family uses a mixture of a blend of 2 coffees costing Rs. 30 and Rs. 60 respectively.If the
family uses only the expensive variety, it will have to spend Rs.450 more. The annual consumption
of coffee of the family is 20Kgs. In what ratio are the two blends being used?
A3:1 B2:3 C4:5 D2:1
.14 If x*y*z = (x2+y2)z, then value of 4*3*2 is
A650 B675 C550 D625
15. Ashish travels a distance of 100 km in the following manner, at 20 kmph for the 1 st 50 kms,at 25
kmph for the next 50 kms. He returns at a constant speed of 25kmph.
What was his average speed for the journey?
A22.50 B23.52 C24.60 D22.35
16 X is 25% more efficient than Y and his hourly wages are 25% more.
If X is paid Rs.75, how much will Y receive for the same work?
A65 B90 C75 D110
17 . Anand goes to a shop to buy the walkman costing Rs.2250. The rate of sales tax is 6% he
wants the dealer to reduce the price so that he has to pay Rs.2000 inclusive of tax. Find the
reduction needed in he percent of the walkman.
A15 B16 C17 D18
18.. X buys an apple from Y for Rs.5 and sells it to Z for Rs.10. He later buys the apple back from Z
for Rs.12 and sells it to Y for Rs.15. What is his profit over the venture?
A8 B6 C12 D10
19. A man XY of height 1.75 cm stands at a distance of 4 metres from a pillar AB. If the pillar is at
the height of 5.25 m from the ground, what is the length of the man's shadow on the ground ?
A 1m B2m C5m D6m
20. A spherical ball of 8 cm diameter is melted into a cone with base 20 cm in diameter. Find its
height.
A2.56cm
B3 cm C2 cm
D 3.75 cm
21 . P is the product of all the prime numbers between 1 to 100. Then the number of Zeroes at the
end of P are:
(A) 1
(B) 24
(C) 0
(D) none of these
22. An oil tank is 9/10 full. When 50 litres of oil are removed, the tank is 5/6 full. Find the
capacity of the tank in
litres.
A. 600 B. 750 C 100 D 1200
23. The sum of two prime numbers between 70 and 90 is 162. Their difference is
.A 10 B) 16 C. 14
D 4. or 16
24. Consider a 99 digit number created by writing side by side the first fifty four natural
number as follows:
12345678910111213……5354
The above number when divided by 8 will leave a remainder of
A. 6 B)4 C. 2 .D 0
25. A man engaged a servant on the condition that he would pay him Rs. 90 and also give
him a turban after service of one year. He served only for nine months and received a
turban and Rs. 65. Find the value of the turban in rupees.
A 10 B). 9 C 0 . D 2.50
26 A point P moves in a plane such that its distance from another point Q is always 7 cm.
If the point P moves
from its starting position in the plane, say P1, a distance of 44 cms and halts at point P2,
what is the distance
between P1 and P2?
A 0 B 14
C 21
D 7
27 The compound interest calculated yearly on a certain sum of money for the second
year is Rs. 880 and for
the third year is Rs. 968. Calculate the rate of interest
A
12 B 10
C 11 D 9
Directions for questions 28 to 33
Each question is followed by 2 statements
Mark (A) if statement a alone is suficient but statement b alone is not sufficient
Mark (B) if statement b alone is sufficient but statement a alone is not sufficient
Mark (C) if both statements a & b together are sufficient but neither statements
alone is sufficient
Mark (D) if each statement alone is sufficient
Mark (E) if statement a & b together are not sufficient
28. What will be Raghu's age 5 year's from now
a. Raghu is 30 years younger than his dad
b. Raghu's dad was 50 years old 5 years ago
29. In a class of 50 students how many girls scored over 80% in chemistry test
a. Exactly 15 boys scored over 80% of the test
b. 1/2 of the class scored over 80%
30. In 1980, what was Vithal's monthly average income
a. he earned Rs. 15000 from Jan to July 1980
b. he earned average income of 1500 from July to Dec. 1980
31. Is X=Z, X,Y,Z are real numbers.
a. X-Y=Y-C
b. X-2Z = Z-2Y
32. What is the value of X? X is a real number
a. X2-X-12=0
b. X2+X-20=0
Directions for questions 33 to 37
Five brothers have among them a pair of twins who are neither the oldest nor the youngest.
E is older than C but younger than B. D is younger than 3 brothers
33. The youngest is
A ) A B) B C)C
D) D
34. One of the twin pair is
A) B
B)
35. The eldest is
C
C)
D
D) E
A) B
B)
C C)
D
D) B
36. The one who has as many elder brothers as younger brothers is
(A ) A
(B)B
(C)E (D) None of these
37. Who is the fourth brother
(A)A (B)B
(C)D (D)E
38.A man invests Rs. 4000 in shares. He invests Rs. 800 in 7%dividend paying
shares at Rs. 8.00,
Rs. 1400 in 8% dividend paying shares at Rs. 7.00 and the remainder in 9%
dividend paying
shares. If all the shares have a face value of Rs. 10.0 each and his % return on
investment is
10.25% at what price did he buy the 9% dividend paying shares ?
A Rs 8 Rs
B Rs 9
C Rs 8.50
D Rs 9.50
39 A boy appears for 5 papers, each of the same number of maximum marks. He
scores in each of
the papers in the ratio of 6: 7: 8: 9: 10. If his average score in all the five papers
together was
60%, then in how many papers did he get more than 50% marks ?
(A)2
(B)3
(C)4
(D)5
40 In between 6 p.m. and 7 p.m. when will both the hands be in oppsite
direction?
A
B
C
D
E
33 3/11 min past 6
36 min past 6
Never happens
25 min past 6
36 min past 7
41 How many kg of Mirchi powder costing Rs.40 kg must be mixed with 16 kg of
Mirchi powder costing Rs.55 kg so that 25% may be gained by selling the
mixture at Rs.60 kg?
24 kg
A
B 14 kg
C 16 kg
D 28 kg
E 12 kg
42 If y,2y+2,3y+3 are in G.P. then their fourth term is
-3
A
B -9
C - 13.5
D -27
E -8
43 If triangle ABC the side BC is extended to D. if angle ABC=60 o and angle
ACD=110oThen angleBAC=
A
B
C
D
E
60o
50
170o
40o
None
44. If y>0 and sqrt(9y+36)= y then y=?
A
B
C
D
E
6
5
4
2
12
45 A frog is in a 19m. deep well. For every 3m jump the frog slips by 1m. How
many jumps would get the frog out of the well?
A
B
C
D
E
8
9
10
7
None of the above
46. When 10 is divided by the positive integer n, the remainder is n-4. Which of
the following could be the value of n?
A
3
B
C
D
E
4
7
8
12
47. A sum of money placed at compound interest doubles itself in 4 years. In how many
years will it amount to eight times itself ?
(A) 8 years
(B) 16 years
(C) 12 years
(D) none of these
48. In an examination, every candidate must take either mathematics or science or may
take both if he so chooses.83.6% of the total took mathematics, 31.2% took science. If 370
candidates took both, find the total number of students.?
(A) 3200
(B) 2800
(C) 3000
(D) 2500
49.When 99 is divided by the positive integer 8, the remainder is ..........
(A) 2
(B) 3
(C) 1
(D) 7
50 How many liters of pure alcohol must be added to 10 liters of a mixture which
is 15% alcohol to make a mixture which will be 25% alcohol?
A 4/5
B 3/5
C 3/4
D 1/2
E 4/3
Answers Test paper 1
1.B (a+1)(b+1)(c+1)-1=1000
= (a+1)(b+1)(c+1) =1000+1 =1001 = 7x11x13
=(12+1)(10+1)(6+1)
a=12 ,b=10 ,c=6
12>10>6
so b=10
Answer is B
a>b>c
2B. a
d
an +bn +cn
bn+ cn +dn
=
Where a b c d are in continued proportion i.e a/b=b/c=c/d
b=ck=dk2
Let a/b=b/c=c/d =k c=dk
a=bk2=dk3
LHS a/d = dk3/d =k3
RHS (dk3)n+(dk2)n+(dk)n
(dk2)n + (dk)n + (d)n
k3
=
kn
assume a continued proportion series 8 ,4 ,2,1 in place of a b c d
=
8n+4n+2n
4n+ 2n +1n
83+43+23
43+ 23 +13
Here 23
point us n may be 3 . Put the value of n=3 and see what happen
672+64+8
=
64 +8 +1
744
=
It satisfies the equations so n=3
=8 =23
73
Answer is B
|a|=3,| b|=4 and | a+ b|=1 then | a- b|=?
|-3|=3,|4 |=4 and | -3+4|=1
or
=
8n+4n+2n
4n+ 2n +1n
=
23 =
3C.If
kn (k2n +kn +1)
(k2n +kn +1)
Answer
Short Cut Method
23
dn (k3n +k2n+kn)
dn (k2n +kn +1) =
kn
n=3
8
1
=
| -3-4|= | -7| =7
|3|=3,|-4 |=4 and | 3-4|=|-1 |=|1|
| 3-(-4)|= | 7| =7
Answer C
4D.Here bacteria population to grow from 1,000 to 500,000 It is a question of GP
Here first we find out nth term
nth term = arn-1
n=? a= 1000
500.000 = 1000 x2n-1
nth term = 500,000
r=2
500 =
2n-1
APPROXIMATELY 29 = 2n-1
n-1 =9
n=10
Growth of bacteria is as follows- 1000
2 000
4000 ,,,,,,,
| ... 2 min ......| ... 2 min ...|
It means - two time intervals among three terms .So there is 9 time intervals
among 10 terms
Total time 2x9 =18 Minutes
so answer is D
5D
OOOOOOOO........
So 1 m.m
.008m.m
= 1000= 125
8
Answer is D
6A
.
A1
=
area =axa = a2
A
2
A
2=
4 times
of A1
Answer
7E 3 Π
x2 + x2 = 4x2 a2
x2 = 4 a2 = 4A1
=
=2Π r1
Π = 2Π r2
A become 4 times
Area
Area
= Π 1.5 x1.5
= 2.25 Π
Π .5 x.5
= .25Π
Area decrease
( 2.25 - .25 )Π = 2.Π
% Area decrease = 2x100Π
2.25Π
=
88 8/9%
. Answer (E)
8E . If price of each brand A tv set is a
Bill of brand A tv set is 40a
Price of each brand Btv set is 2a
Bill of brand B tv set
160a
Total Bill
200a
percent of the total bill was the price of a brand B set
2a x.100 = 1%
200a
Answer E
9.D. Total cost of fruits
Other expenses
2000x40 /100
Spoiled fruits
saleable fruits
Rs800 .00
Rs200.00
1000.00
2000of 10% = 200
1800
1800x 9 = 1350
12
% gain
(1350-1000) x100
1000
35%
Answer D
10 A
(x+y+z ) 2 =1
x2+y2+z2 +2xy+2yz+2zx =1
2xy+2yz+2zx <1
xy+yz+zx <1 /2
Answer is A
11.x will complete 1/20 in one day.
Y will complete 1/30 in one day.
Z will complete 1/60 in one day.
4 days = (1/20 + 1/30 + 1/60)*4
= (3+2+1/60)*4
x2+y2+z2 It must be +ve
= 6/60*4
= 4/10
= 2/5th complete
6 days = (1/20 + 1/60)*6
= (3+1/60)*6
= 4/60*6
= 4/10 = 2/5
total work complete = 2/5+2/5 = 4/5
work remaining = 1/5
1/5/1/20=1/5*20/1
= 4 days
12. volume increase in cylinder=(volume of block *portion of it which is immersed)
22/7*62*4 = 5*6*7( p)
p = 22/7*36*4
5*6*7
p = 22/7*24/35
13.Expensive brand cost = 20*60=1200
Expense now = 1200-450=750
Average cost of the mixture =750/20
Rs.30 Rs. 60
Rs. 750/20
450/20 150/20
3:1
14.= (16+9)2
= 252
= 625
15.
Total time taken = 2.5+2+4=8.5 hour
Distance = 100+100 = 200 kms
Speed = 200/8.5 = 23.52
16. Let wages of y =a, then x=1.25a
X took 75/1.25a = 60/a
Y will take 1.25*60/a
=75/a*a
=Rs.75
17.2250*6% = 135
2250+135= 2385
2385-2000=Rs. 385
discount% = 385/2250*180
= 17%
18... cost price for x = 5
selling price for x = 10
profit = 5
cost price for x = 12
selling price = 15
profit = 3
total profit = 5+3= 8
19.
Triangle SAB is similar to triangle SFL
SA / SF = AB / FL
x /x + 4 = 1.75 / 5.25 = 1/ 3
3x = x + 4
Therefore x = 2m
20.. Volume of cone = volume of sphere
1 / 3 ( 22/ 7) r2h
= 4 /3 ( 22 /7) r2
1 /3 * ( 22 / 7) * 102 h
= 4 /3 * ( 22 /7) * 43
102h= 256
100 h = 256
h=2.56
21 A Prime numbers between 1 to 100 are 2,3,5,7,..................97
Now there is no any prime number which having unit digit 5 or 2 (ie x2,or x5 )
except 2 and 5
SO we get 2x5 =10 and this is only 0 reflect in product of prime numbers
between 1 to 100
answer =1 A
22B Suppose the capacity of tank is x
9/10x -50 = 5/6x
( 9/10-5/6)x= 50
(54 -50/60)x =50
4/60x=50
x= 50x15 = 750
Answer is B
23B . Prime numbers between 70 and 90 are 71 ,73,79,83,89,
Here total of 73 and 89 is 162
difference is 89-73 = 16
Answer is B
24C 12345678910111213……5354 number when divided by 8 will leave a remainder
of ???
Just take last three digit and divide by 8 and find the remainder of this number
only
354 /8 44 2/8 here we get remainder 2 (See one full lesson on this subject
in How to calculate
fast )
Answer isC
25A A point P moves in a plane such that its distance from another point Q is always 7
cm.
Here P moves in a circle keeping a distance of 7 cm .from point Q
If the point P moves from its starting position in the plane, say P1, a distance of 44 cms
and halts at point P2
Here radius of this Circle is 7 cm , circumference of this circle is
a distance of 44 cm and reaches to
P2.
2 x 7x22 /7 = 44 cm .Now
p moves
as a P1
It is nothing but it covers circumference of this circle and reaches
again to original position so distance between P1P2 is 0
answer is A
26B Here no need to find 2 and 3 years compound interest . Compound interest is
interest on interest and it is
calculated at the same rate
Difference of 3rd and 2nd year interest Rs968-880 = Rs88
Extra interest for one year on Rs 880 So % of rate of interest is ( 88 /880 )x100
=10%
Answer is B
28C . Let Raghu’s age now be x
5 years hence will be x +5
from statement I x = f-30
f = 50 +5 = 55
Therefore x = 55-30 =25
5years hence Raghu’s age = 25 + 5 =30
There from both statements together
The answer is [C]
29 C . From statement I  15 boys scored over 80%
From statement II  ½ of 50 = 25 students
Therefore no. of girls = 25-15 = 10
The answer is deduced from I & II both
The answer is [C]
30E
From statement 1 Jan to July is 15000
From statement 2 July to Dec 1500* 6 =9000
Individually the statements don’t tell us about the whole year
Combined Jan to July + July to Dec
1 5000 + 9000 = 24000
Jan to Dec + July = 24000
But salary during July is not know
Therefore average for 12 months cannot be found
Therefore the answer is = [E]
31C . Is x = z, x,y,&z are real numbers
From statement (I) 2y = x + c
From statement (II) 3 z = x + 2y
2y = 3z-x
combined x + c =3z- x
2 x = 2z
Therefore x =z
The answer is (C)
32C.from statement 1  x2 - x – 12 = 0
(x-4) (x +3)=0
Therefore x =4 Or -3
From statement 2 x2 + x –20 =0
( x-4) ( x +5) =0
Therefore x =4 or-5
Therefore x =4 Common in both statement
Answer is [C]
33 to 37
Five brothers have among them a pair of twins who are neither the oldest nor the
youngest.
E is older than C but younger than B. D is younger than 3 brothers
D is younger than 3 brothers .It means Position of D is at 4
1
2
3
D
4
5
Now fill up other position according to given conditions
B > E = A > D >C
1
2
3
4
5
33 C
34
D 35 A 36 A 37C
38B. No..of share of co. A 800/8 = 100 Total face value 100x10 =1000
return 100x7/100 =Rs70
No.of share of co B 1400/8= 200
200x10 =2000
200x8/100= Rs160
No of share of co C 2200/a ( let it be a)
2200x10/a
2200x9x10/(ax100) = 1620/a
Total return
70 +160+(1620/a )
=
10.25 %of 4000
230 + 1620/a =410
1620 /a
= 410230=180
1680/180
9
=a
=a
So price of co C share is Rs 9.00
Answer is B
39C Let maximum marks of each paper is 100 ,total maximum marks are 500 And he
gets 6a,7a,8a,9a,and 10
marks in each paper
6a+7a+8a+9a+10a= 40 a= 60%of 500 = 300
a = 300/40 = 7.5
% in each paper is 6x7.5 = 45 , 52.5 , 60 ,67.5 ,75 ( Add 7.5 after 45 instead
of multiply 7.5 to
each i.e 7,8,9,10 for fast
calculations)
He gets marks more than 50% in 4 papers
Answer is C
40.B
41BHere First we find out the cost of Mirchi powder so that 25% may be gained by
selling the mixture at
Rs.60 kg
Let cost of Mirchi powder is x
x + 25% of x = 60
x+ x/4
=60
5x/4 =60
= Rs 48
Cost of Mirchi powder Should come Rs 48 .00 per Kg
Let "a" be mixed With 16kg Of Rs 55 per kg
40a +16x55 =48(a+16)
48a- 40a= 16x55-48x16
8a
= 16(55 -48 ) = 16x7
a = 16x7 /8 = 14 (don't calculate in beginning if we calculate 16x55 and
18x16 in beginning it
takes our time and again we divide the subtraction of
both by 8also Now
see there is no any time consuming calculations so
be alert in
calculations)
Answer is B
42C If y,2y+2,3y+3 are in G.P. then their fourth term is
In G.P
y (3y+3) =(2y+2)2
3y2 +3y =4y2+8y +4
y2 +5y +4
= ( y+4 ) (y+1) y= -4or-1
it
Now our terms are -4 ,-6 ,-9 , x
- 6/-4 = x/-9
Answer is C
43.B
x= -13.5
-1 gives 2y+2 =0 so ignore
.
Answer is B
44if y>0 and sqrt(9y+36)= y then y=?
(9y+36)1/2= y
y=12 or -3 Because y>1
so that y=12
Answer is E
45.B
9y+36 =y2
y 2 -12y+3y-36
( y-12) (y+3)
Answer is B
46 C When 10 is divided by the positive integer n, the remainder is n-4. Which of
the following could
be the value of n?
Do it mentally by option method
first and second option is not valid
it gives remainder -3 and 0
Try option third
10 /7
=1+ 3 /4
= 7-4 =3
It is valid
Answer is C
47C. Amount double means 2x = x ( 1 + r /100)4
rate of interest
2
1/4
= (1+r/100)
8x = x( 1 + r /100)n
23
=
( 1 + r /100)n
23/n = ( 1 + r /100)
,
where x and r are principal and
23/n
=
2
1/4
3/n =1/4
n= 12 Years
Short cut method
|..............| .............|.............|
x
4years
2x 4 years
4x
4 years 8x
Amount is double after every 4 years
4+4+4 = 12 Years
Answer is C
48 D Both took Science and Maths 83.6 + 31.2 -100 = 114.8 -100 =14.8 %
1 4.8 % of x = 3700
14.8 x
100
=3700
x = 2500 = total number of students
Answer is D
9 9 add and subtract 1
99 -1+1
=(99-1) +1
If xn-1 then x-1 satisfy the polynomial xn-1
=0 ie 9-1 also satisfy
the polynomial 99-1
= (9-1)(98+,,,,,,,,)+1
First part is fully divisible by 8 so the remainder is 1
Answer is C
49c.
50E. How many liters of pure alcohol must be added to 10 liters of a mixture which
is 15% alcohol to
make a mixture which will be 25% alcohol?
Let 100 % pure alcohol is a liter Consider 100 % to 1 15% to .15 and
.25
ax.1 + 10x..15=
.25(a + 10)
a + 1.5 = .25a+2.5
( 1-.25)a= 2.5-1.5
=1
25 % to
a= 1/.75 = 4/3
Answer is E
Test Paper 2
The total age of A and B is12 years more that of total age of B and C.C is how many
years younger than A.
1
A ) C is elder than A
the above
2
B) 24
E ) None of the above
E ) None of the above
The ratio between larger and smaller number is 12 less than the product of these two
numbers .The square of smaller number is half of the larger number .What is the total
sum of these two numbers ?
A) 2 B) 16 C) 18 D) Data is inadequate
5
E ) None of the above
Manoj is 15 Years older than Navin and Navin is 25 years younger than Ashok.Which
of the following represent the difference between the total age of Ashok and Manoj
together and Navin (N)
A)40 Years B) 40 + 2N Years
None of the above
6
E ) None of
If 45 % of a number is added to another number ,it become 1.35 of another number
,what is the ratio of these numbers ?
A) 8:7 B)3:2 C)7:8 D) 10
4
D ) Data is inadequate
The average marks fetched by Lata in History ,Geography ,Science and Maths is 10
more than the marks fetched in Maths .If she has got 110 marks aggregate in History
and Geography ,what will be the aggregate marks fetched In science and Maths ?
A)80 B)70 C) 65 D) 7:9
3
C) 12
C)40 +N years
D) Data is inadequate
E)
A total of 91 boys are seated in three rows .The ratio between the number of those
seated in the first row and those in the second is 5:2 and the ratio between the number
of boys seated in the second row and those in the third row is 1:3 .How many boys
were there in the second ?
A) 35) B) 14 C) 42 D ) 56 E ) None of the above
7
The percentage profit earned by selling an article for Rs 1920 / is equal to percentage
loss incurred by selling the same article for Rs 1280/ .At which price should be the
article sold to make profit of 25%?
A)Rs 2000/
the above
8
C)Rs2200/
D) Data is inadequate
E ) None of
Among three numbers x, y & z , y is the highest and x is the lowest .which of the
following equation s of these numbers is definitely greater than 0 ?
A)x-y +z
9
B) Rs2400/
B) x-y-z C)y-x-z
D) y-x+z E) All the above are greater than 0
An amount is to be divided among P,Qand R in the ratio of 5:11:23 respectively. If
the difference between the total share of R and P and Q is Rs 2800/ What is the
difference between Q and R 's share ?
A ) Rs 6400 B) Rs 3600 /
above
C) Rs 4800 /
D) Rs 3200/
E ) None of the
Some balls are kept in boxes P.Q and R .Some balls from box P are kept in box R.
After this displacement of balls the total balls in Q and R become four times the
number of balls originally kept in box P .If there are 32 balls in box Q ,how many
10
balls were kept in box R in the beginning?
A)40
B) 20
C) 30
D) Data is inadequate
E ) None of the above
The average of the first three of five odd numbers arranged in ascending order is 10
less than the average of the last three of these numbers .If the sum of the last two of
11 these numbers is 42 .what is the sum of the first two of these numbers
A ) 22
B) 20 C) 14 D) 12
E) Data is inadequate
Directions for questions 12 to 16
Each question is followed by 2 statements
Mark (A) if statement a alone is sufficient but statement b alone is not sufficient
Mark (B) if statement b alone is sufficient but statement a alone is not sufficient
Mark (C) if each statement alone is sufficient
Mark (D) if both statements a & b together are sufficient but neither statements
alone is sufficient
Mark (E) if statement a & b together are not sufficient
12 What is the speed of running train P
a Train P crosses another train running in opposite directions in 9 seconds
b Relative speed of both trains is 170 km/hr
The average age of class teacher and students in a class is 3 years more than the
13 average age of students .What is the age of of the class teacher ?
a There are 11 students in class .
b the average age of students and class teacher is 14 years
What is the ratio between the cost price and selling price of a commodity ?
14 a The commodity is sold at 20 % profit
b The cost price of commodity is Rs 5000/
What is the rate of compound interest on a sum of money
a The total simple interest at the same rate on Rs 6000/at the end of three years is Rs
15
1800/
b The total compound interest on Rs 6000/ at the end of two years is Rs 1260
Jeeven 's Marks in English is 15 more than the average marks obtained by him in
English ,Maths ,Geography and Science .what is his marks in the science ?'
16.
a The total marks obtained by him in English and Science together is 120
b The difference between the marks obtained by him in Geography and Maths is 120
In a row of boys facing north ,Ram is 12th from the left .When shifted to his right by
four places ,he becomes 18th from the right end of the row .How many boys are in
17 the row?
A) 32 B) 33 C ) 34
D) Data is inadequate
E ) None of the above
From two strings of length 15 c.m each an equilateral triangle of area a cm2 and an
isosceles triangle of area b cm2 is formed then
18
A) b>a
B) b is equal or greater than a
greater than b E) b<a
19
B) 2w+w1
C) 2w2-w1
C ) 1400000
D) 2400000
102. Mohan deposits Rs.150 on the first of every month starting from 1st Jan1985, in
the recurring deposit scheme of a bank which allows simple interest @ 6% p.a.on the
sum standing to his credit at the end of each month. What is the amount, Mohan is
entitled to on 31st Dec, 1985
A) Rs.1818
22
D) 2(w2+w1)
A man divides his property among his sons so that one gets half, another gets quarter and
third gets one fifth and the fourth Rs. 10000. What is the value of the total property?
A ) 200000 B) 400000
21
D) a is equal or
An empty jar weighs w1 gm. The jar half filled with a liquid weights w 2
gm. Find the weight of the jar completely filled with the same liquid.
A) 2(w2-w1)
20
C) a= b
B) Rs.1800
C) Rs.1450
D) Rs.1400.80
Divide 27 into two parts so that 5 times the first and eleven times the second are together
equal to 195
A )17:10
B)15:11 C )16:10
D) 10:17
Six men earn as much as 8 women, 2 women earn as much as 3 boys and 4 boys earn as
23 much as 5 girls. If a girl earn Rs.50 a day, then the earning of a man would be
A ) Rs.125
24
Rs.13
C ) Rs.105
D) Rs.120
If a sum of money at certain rate of interest doubles in 5 years and at a different rate of
interest becomes 3 times in 12 years, the better rate of interest is,
A ) 20%
25
B)
B) 39 2/9%
C ) 162/3
D) 15%
A,B,and C can independently complete a task in 6,8 and 12 hours respectively. C starts
working. 2 hours later she stops and simultaneously A and B starts working. Yet another 2
hours later, B stops working too. Now how long does A have to work alone to complete the
task?
A )3 hour B) 6 hour C )8 hour D)none of these.
26
.I have bought a car for some amount. I sell it to Mr.X at 10% loss due to need of money
urgently. But later I buy it again from him at my original purchase price.
a)What is Mr.X's profit?
b)What is my loss?
A )11.11%;10%
2
7
B) 10%;11.11%
C ) 2 0%;22.22%
D) 40% 44.44%
P owes Q Rs.455 payable 4 months hence and Q owes P Rs.450 payable 2 months hence. If
they agree to settle their account what sum should be paid over and to whom reckoning the
rate of true discount p.a.
A )Rs.12 B) Rs.13
C ) Rs.11
D) Rs.16
Direction for questions 28 to 37:
Study the graph carefully and answer accordingly
2
8
Total export in 1998 and 1999 together was equal to in case of which of the
following pairs of type
A) A and B
B) Band C
C) A and D
D) Band D E) none of
the above
The percentage change ( increase and decrease )in the number of the vehicles exported
2 from 1998 to 19999 is minimum in the case of which of the following types of vehicle
9
A) A B) B C) C D) D E) E
The export of d type vehicle 1998 was what percentage of export of E type vehicles in
3
1999
0
A)150 B)175 C)75
D)25 E) none of the above
The number of E type vehicles exported in 1998 is equal to the number of which type
3
of the vehicles exported in 1999
1
A) A only B) C only C) A only D ) both C and B E) none of the above
3 The average of B and C type vehicles in the 1999 was equal to export of which type
2 in 1998
A)A only B)C only
above
C) both A and C
D)
Both C and E
E) none of the
Directions (Questions 33 to 38 ) Study the graph and answer
Total rainfall in mm
Rain fall in equatorial zone in January is what percent less /more than that of rainfall
3
in temperate zone in July ?
3
A) 39.25% B)41.42% C)36.04% D)23.68%
E) 44.44%
3 In which of the following zones is there maximum increase in rainfall in July?
4 A )Equatorial B) Subpolar C) Tropical Summer D) Subtropic Dry E)Teperate
Decrease in rainfall in Subpolar zone is what percent of increase in subtropic winter
3 zone in July
5 A) 85% B) 80% C ) 72% D) 90% E) 78%
Average rainfall in July is approximate how much more /less than the average rainfall
3
in January?
6
A)3% more B) 7.00% less C) 9.32% less D) 6.34 %more E ) 9.1 % more
3 What is the average rainfall around the world in whole year
7 A) 1034.28mm B) 1075 .71mm C) 0510 mm D) 978 .67 mm E ) 1270 .34mm
3
8
a4+b4+c4/b2c2+c2a2+a2b2 is :
2 B) 3 C) 4 D ) 6.
If a+b+c = 0.The value of
A)
3 A farmer sells 2 horses for the same price. In one he gains 20% and in the other he loses 20%.
9 What is his overall profit or loss?
A)4%
profit
B)4% loss
C)2% loss
D)2% profit
E) Neither loss nor profit
Directions for questions (40 � 43)
Six players: - Raman, Sharvan, Tejinder, Urvinder, Vinod, Wimpy were sitting in a
refreshment
room in stadium after playing their respective game. Games played by them are
Badminton, Table
Tennis, and Lawn Tennis. Exactly two players played each game. Each player
played exactly one
game. But when asked them to tell their game they gave the following
statements: Raman:
- I played with Sharvan and Wimpy.I don�t like Badminton
Sharvan: - I played with Wimpy and Tejinder .I don�t like Lawn Tennis
Tejinder: - I played with Raman and Vinod.I don�t like Badminton
Urvinder: - I played with Raman and Tejinder.I don�t like Table Tennis
Vinod:
- I played with Urvinder and Wimpy.I don�t like Lawn Tennis
Wimpy:
- I played with Urvinder and Raman. I don�t like Table Tennis.
If the first sentence spoken by each player was false, while second sentence was
true.
4
0
With whom did Raman play a game?
(A) Wimpy
(B) Vinod
(C) Tejinder
(D) Urvinder
4
1
Who played Table Tennis?
(A) Raman and Vinod
(B) Sharvan and Urvinder
(C) Tejinder and Wimpy
(D) Wimpy and Sharvan
4
2
Who played Badminton?
(A) Sharvan and Urvinder
(B) Wimpy and Sharvan
(C) Raman and Vinod
(D) Tejinder and Wimpy
10.
Who played Lawn Tennis?
4 (A) Sharvan and Urvinder
3 (B) Tejinder and Wimpy
(C) Raman and Vinod
(D) Wimpy and Sharvan
Numbers X and Y are positive and odd, and the number Z is also positive but
even. then
4
4
which of the following is not true
(A) (X-Z)2 Y is even
(B) (X-Z) Y is odd
(C) (X-Z) Y2 is odd
4
5
4
6
4
7
(D) (X-Y)2 Z is eve
There are 2 lights one red and the other green. The red one flashes 3 times every
minute and the green one flashes 5 times every two minutes. If the lights start
flashing together then the total number of times both will have flashed together in
an hour is
(A) 30
(B) 24
(C) 48
(D) None of the above
N = 1421 x 1423 x 1425 what is the remainder when N is divided by 12
(A) 0
(B) 1
(C) 3
(D) 9
a1 = 1 and an+1 = 2an + 5, for n being a natural number. The value of a100 is
(A) 5x299 + 6
(B) 5x299 - 6
(C) 6x299 + 5
(D) 6x299 - 5
Three friends divided some bullets equally. After all of them shot 4 bullets the total no.of
4 remaining bullets is equal to that of one has after division. Find the original number of bullets
8
A) 16 B) 18 C) 20 D) 24
There are 27 balls, of which 1 is heavier. Given a balance how many times you need to
49 weigh to find out the odd ball.
A ) 2 B )3 C) 4 D ) None of the above
If the area of the square is increased by 69 % how much the length of the side will
50 increase?
A) 21 B) 31 C) 30
D) None of the above
Answers Paper No2
1C
(A+B)-(B+C)+12
A-C=12
A=C+12 C is 12 years younger than A.
(H+G+S+M)4 - M=12
And H+G=110
2D
After combining these two equations we can not solve further so data is
inadequate
3D
45%of a+b= 1.35b
9a/20+b=27b/20
9a/20 = 7b/20
9a =7b
a/b = 7 /9 7:9
4D
Let x =smaller number and y = larger number
according to question
y/x+12=xy
and x2 = y/2
Put the value of y in first eq
x3 -x-6=0or ( x-2 ) (x2+2x+3) it gives the value of x+2 other values are imaginary
y=2x2x2 =8
sun of both numbers
2+8=10
5C
M-N = 15 ......(.1) and A-N=25 ........(2)
Adding eq 1 and 2
M+A-2N= 40
M+A-N = 40+N
6B
Ratio between 1st and 2nd row 1:2
Ratio between 2nd and 3rd row
1:3
Make it 2:6
Now ratio 1st row : 2nd row : 3rd row = 1:2:6
Total boys 91 .2nd row boys
91x2/13
7 x2=14
7A
Let cost price is x and proft/loss is y
x+yx/100=1920..........1
x-xy/100=1280.............2
adding both eqs
2x = 3200 x= 1600 ( in such type condition take directly the average of both
figures for saving time )
SP of article now =1600+ 25 %of 1600 = 1600+400 =2000
8D
y>z>x
y-x>0
x-y <0
Option A is rejected but options Band C may or may not be possible .Only option
D is possible
9D
Let share of PQ and R are 5x, 11x and 23x
According to question
23 x- (5x+11x) = 23x- 16x= 2800
7x= 2800
x= 400
Now difference between Qand R share 23x-11x= 12 x = 12 x400 =4800
( 1+2+6 =13)
P, Q and R are having p,q and r balls respectively and x balls are replaced from
box P to Q
Now according to question's conditions
10D 4p= q
q=32 p=8
4p=r+x
32 =r+x we can not find the balls because value of x is not given so data is
inadequate
Five odd numbers a1< a2 <a3< a4 < a5
a4 + a5 )/3 - ( a1+ a2 +a3)/3=10
(a3+
11D
(a4+
(
a5)- ( a1+ a2 )=30
a1+ a2 )=42-30=12
(a4+
a5) =42 given
(D)
12
E
Neither the speed of trains nor the length of trains is given .Can't calculate speed
of train P
13D
After combining both statements ,the age of class teacher is
14x12 -(14-3)x11 = 168 -121= 47 years
14A CP :SP = 100x :120 x
5:6 statement a alone is sufficient but statement b alone is not
sufficient
From statement a
rate of interest = 1800x100/(3x6000) = 10 %
15C
From statement b
rate of interest =(22/20 -1)100
= 10%
(E+M+G+S)/4 = 15
16E 1 ... E+S=120
2...... G-M=120
S can not be determined with the help of both statement so Answer is E
17B
Total boys in row 16+18 -1 = 34-1 =33 (Get alert to subtract 1 in these type
questions because
particular person is counted two times
one from left
and other from right .Consider
directions also very
cautiously)
Remember for the given parameter equilateral triangle area is maximum .Here
18E area of isosceles triangle bcm2 is lesser than area of equilateral triangle acm2 ,
so that b<a
Weight of jar = w1g
Weight of liquid = w2-w
Weight of liquid(half filled with liquid) = w2-w1
19C Weight of liquid filled = 2(w2-w1)
Weight of jar + weight of liquid = w1+2(w2-w1)
= 2w2-w1
Hence [C]
Let x be the total value of the property.
x = x/2+x/4+1/5x+10000
= (10+5+4)x/20+10000
20A
= 19x/20+10000
= 20*10000
= 200000
. Total money deposited = Rs.12*150 = Rs.1800
Interest on Rs.150 for 12 months = 150*12/12*6*1/100 = 9
Interest on Rs.150 for 11 months = 150*11/12*6*1/100 = 33/4
21C Interest on Rs.150 for 1 month = 150*1/12*6*1/100 = 3/4
Total interest = 9/1+33/4+3/4 = Rs.18
Total amount due = 1800+18 = Rs.1818
Hence [C]
a+b = 27
5a+11b = 195
22D
solving simultaneously we have,
a = 17 b = 10
6 M = 8W, 2W = 3B, 4B = 5G
1 G = Rs. 50 a day.
23A Now, 1B = 5/4G 1 W = 3/2 * 5/4G
1 M= 8/6* 3/2* 5/4G = 5/2G
1 M = 5/2 * 50 = 125/-Rs.
If we assume that the sum = Rs. 100
Then, 1st rate of interest = 100*100/100*5 = 20
2nd rate of interest = 200*100/100*12 = 16 2/3
24B 76n1=5, x1= 42.2 n2 = 4, x2 = 35.5
x12 = n1x1+ n2x2 / n1+n2
= 5 * 42.2 + 4 * 35.5 /9
= 211.0 + 142.0 /9
= 353 /9
= 39 2/9
In one hour, C can complete 1/12th of the work.
In two hours, he can complete 1/12*2 = 2/12th of the work.
A and B start work simultaneously,
together work completed by A and B,
1/6+1/8 = 14/48 work = 7/24 work.
In 2 hours they complete 7/24*2 = 7/12 work
Total work done by A,B,C = 7/12+2/12 = 9/12
25A Total work to be completed = 12/12 or 1
Remaining work = 3/12
Hour
work done by A
1
1/6
x
3/12
3/12*6 = 1.5 hours =x
a)Let my cost price be 100
Selling price = 90
Profit for Mr. X = 10
26A Profit % = 10/90*100 = 11.11%
b) Let cost price be 100
Selling Price = 900
My loss = 10 = 10/100*100 = 10%
p = Rs.455, n = 4months = 1/3 year, rate = 5%
Amount of Rs.100 = (455*1/3*5)/100 = 107.58
455
x
107.58
100
x = 423
27C
q = Rs.450, n = 2months = 1/6 year, rate = 5%
Amount of Rs.100 = (450*1/6*5)/100 = 103.75
450
?
103.75
100
= 434
Sum to be repaid to p = 434-423 = Rs.11
Hence [C]
28A
B also correct Both options A & B are correct
29D
Option D is correct
30B
% = 35 /20 x100 = 175 %
31E
The answer is A and C both
32B
Average of B and C type vehicles in 1999
30+25 / 2 = 27.50
33B
Rainfall (rf) in Jan in equatorial 1980 mm
July in temperate = 1400 mm
% = 1980-1400=580
(580 /1400)x100 41.12%
34E
Steep line angle shows that TZ has maximum increase rainfall
35D
% =( 710 /800)x100 = Approximate 90%
in July
Jan rf = 1980+2060+690+310+890+1160+730/7= 7820/7=1117.14
July rf = 2280 +1560+250+710+1400+800+240/7=7240/7=1034.28
36 B
(1117.14 -1034.28)x100/1117.14 =( 82.86 /1117.14 )x100 = 7.00% less
approximate
37B
From question no 36
1117.14 +1034.28 /2
=2151.42 /2 = 1075.71
Since a+b+c = 0
a+b = -c
( a+b)2=(-c)2
a2+2ab+b2=c2
a2+b2-c2= -2ab
(a2+b2+c2) 2=(-2ab) 2
38A
a4+b4+c4+2a2b2-2b2c2-2c2a2=4a2b2
a4+b4+c4=2a2b2+2b2c2+2c2a2 =2(a2b2+b2c2+c2a2)
a4+b4+c4/a2b2+b2c2+c2a2
=2
Horse 1- C.P
39B
S.P.
x
100
?
120
S.P. = C.P.(100+profit%/100)
x = 1000/12
Horse 2C.P
S.P.
y
100
?
80
y = 125
Total cost price = cost price of Horse1+cost price of Horse2
= 125 + 1000/12 = 2500/12
Total S.P.= 100+100 = 200
loss = 2500/12- 200 = 100/12
% of loss = (100/12 ) x100 = 4%
(2500/12)
Short cut Method
Remember in these type questions where loss on one unit and same percentage of
profit on other unit there is always loss and you can calculate % of loss mentally
Multiply profit and loss percentage and divide it by 100 , you get required
percentage of loss
Here farmer's gain and loss is 20 %
20 x20 /100 = 4% our required answer
First we make matrix of possible players based on first sentence spoken by each
player was false,
Raman Sharven Tejinder Urvinderr Vinod Wimpy
Raman
x
x
Yes
Yes
Yes
x
Sharven Yes
x
x
Yes
Yes x
Tejinder x
Yes
x
Yes
x
Yes
Urvinder
x
Yes
x
x
Vinod
Yes
Yes
Yes
x
Wimpy
Yes
x
Yes
x
Yes
x
Yes
Yes
x
x
Table based on second sentence was true.
R
S
T
U
V
W
TT
yes
yes
yes
no
yes
no
Bad.
no
yes
no
yes
yes
yes
L.T
yes
no
yes
yes
no
yes
On the basis of these two tables we can answer all the questions very easily
40B
With whom did Raman play a game?
(A) Wimpy
(B) Vinod
(C) Tejinder
(D) Urvinder
Table 1 indicate Raman can play with Sharven ,Vinod And Wimpy ,but table
1again indicates only Vinod can play with Raman answer is B
41A
Who played Table Tennis?
(A) Raman and Vinod
(B) Sharvan and Urvinder
(C) Tejinder and Wimpy
(D) Wimpy and Sharvan
2nd table indicates that
only option A is valid Table one also support it
42A
Who played Badminton?
(A) Sharvan and Urvinder
(B) Wimpy and Sharvan
(C) Raman and Vinod
(D) Tejinder and Wimpy
Options A and B are valid according totable 2 but table one only support optionA
43B
Who played Lawn Tennis?
(A) Sharvan and Urvinder
(B) Tejinder and Wimpy
(C) Raman and Vinod
(D) Wimpy and Sharvan
Option B is only valid according to table 2. Table one also support it
Let X= 3 ,Y =5 and Z = 2
which of the following is not true
2
44A (A) (X-Z) Y is even
odd = true
(C) (X-Z) Y2 is odd
8 = true
Only A is false
(3-2)2 5 = 5 false
(3--2) 52 =25 true
(B) (X-Z) Y is odd
(3-2)5 =5
(D) (X-Y)2 Z is even
(3-5)2 2 =
45C
The red one flashes 3 times every minute and the green one flashes 5 times
every two minutes
Time of red 60/3 = 20 seconds
Time of green 120/5= 24seconds
Take LCM of both 20 and 24
= 120 seconds = 2 Min
both lights blink in one hour = 60 / 2 = 30 times
46C
N = 1421 x 1423 x 1425 what is the remainder when N is divided by 12
Divide only 1421 by 12 gives remainder 5
1423 gives remainder 7
1425 gives remainder 9
Multiplying all these remainders
5x7x9 and divide by 12 again
315 /12 Here we get remainder of 3
It is our required answer
a1 = 1 and an+1 = 2an + 5, for n being a natural number. The value of a100 is
47D
a2 = 2a1 +5 = 2x1+5=7
a3 =2a2+5 = 2x7+5= 19
a4=2a3 +5 = 2x19+5=38+5 = 43
now a1 =1 and options give a rough idea that option D is most appropriate answer,
convert it into nth term and check a2 a3 a4 after putting n=1,2,3,4
nth term = 6x2n-1 - 5
Put n=2
a2 = 6x22-1 - 5 =6x2-5
=7
Put n=3
a3= 6x23-1 - 5 =24-5 = 19 it is value of a3so
that Option D
is correct answer you
can again
confirm to it by a4 if time
permits
to you .
We use this method to save time only .It takes few more min. if we solve step by
step
48B
x
x
x
x-4 x-4 x-4
3x -12 = x
2x=12
x=6
total bullets 6x3=18
49C
It is very interesting question .Make three groups of 9 balls in each group of these
balls and weigh any two group of them If both are equal ,heavy ball is in the third
group . otherwise balance shows the heavy one Take heavy one group and again
make three groups of 3 balls in each group and weigh any two groups of balls If
both are equal third one is heavy otherwise balance shows the heavy one .Take
heavy group and weigh any two balls If both are equal third one is heavy
otherwise balance shows the heavy ball By this way we find heavy balls by
weighing only three times.
Suppose length of square's side is x .Area =x2
Increased area 69% =1.69 x2
50C
side of increased square
= 1.3x
% increase
.3x100/x = 30%