4. Numerical Ability Number Systems Averages & Percentages
Profit and Loss Time and Work Ratio Ages Clock
5. Numbers The citizens of planet nigiet are 6 fingered and
have thus developed their decimal system in base 6. A certain
street in nigiet contains 1000 (in base 6) buildings numbered 1 to
1000. How many 3s are used in numbering these buildings? a) 256 b)
54 c) 192 d) 108 (N-1)*(BASE)(N-2) N=NUMBER OF LAST DIGIT=4(1000
contains 4 digits) base=6 (4-1)*62 = 3*36 = 108.
6. Numbers The citizens of planet nigiet are 8 fingered and
have thus developed their decimal system in base 8. A certain
street in nigiet contains 1000 (in base 8) buildings numbered 1 to
1000. How many 3s are used in numbering these buildings? a) 54 b)
64 c) 265 d) 192 (N-1)*(BASE)(N-2) N=NUMBER OF LAST DIGIT=4(1000
contains 4 digits) base=8 (4-1)*8(4-2) =192
7. NUMBER If a and b are odd numbers, then which of the
following is even ? A. a + b B. a + b + 1 C. ab D. ab + 2 E. None
of these always add two odd number it gives even number
8. FRACTIONS One-third of the marks obtained by Naveen in maths
is the same as the marks he obtained in English. If the total marks
obtained by him in both the subjects is 160, the marks he obtained
in English is: A) 40 B) 30 C) 50 D) None of the options Let the
marks obtained in English be x. Marks obtained in Maths = 3x. Total
marks obtained 4x = 160. Hence marks obtained in English x = 40.
Answer : a) 40
9. Fractions
10. Decimal Number In which of the system, decimal number 184
is equal to 1234? 184= 1*x^3 + 2*x^2 + 3*x + 4 X3 + 2x2 + 3x 180 =
0. Has no integral solution. Hence answer choose none of
these.
12. DECIMALS & FRACTIONS Which pair of rational numbers lie
between 1/5 and 2/5 - a. 262/1000, 275/1000 b. 362/1000, 562/1000
c. 451/1000, 552/1000 d. 121/1000,131/1000 BETWEEN 0.2 AND 0.4 ANS
A.
13. DECIMALS & FRACTIONS
14. FRACTIONS
15. FRACTIONS
16. ALGEBRA Three consecutive whole numbers are such that the
square of the middle number is greater than the product of the
other two by 1. Find the middle number. a. 6 b. 18 c. 12 d. All of
these Let the numbers be x1, x, x + 1. Since x2 = (x1) x (x+1) + 1
it is true for any values of x.
17. A.M & G.M The arithmetic mean of 2 numbers is 34 and
their geometric mean is 16. One of the numbers will be a. 4 b. 16
c. 18 d. 12 a + b = 68 and ab = 256. Hence choice a is
correct.
18. DIVISIBILITY What least number must be subtracted from 9400
to get a number exactly divisible by 65? a. 40 b. 20 c. 80 d. none
of these 65 = 5 X 13 Last digit should be zero or 5. 940040=9360
divisible by 13 & 5 940020=9380, 940080=9320. none of these
divisible by 13. Hence answer is A.
19. Fractions
20. Divisiblity 12 divides, ab313ab (in decimal notation, where
a,b are digits>0, the smallest value of a+b is a)7 b)6 c)2 d) 4
If a number is divisible by 12 then it should be divisible by
4&3 for divisible by 4 last [2 digit]no's should be divisible
by 4 Also sum of digits should be divisible by 3. Hence 2(a+b)+1
should be 3k and ab = 4m. That is a + b = (3k-1)/2 . from the given
choices only first choice is possible k = 5 and smallest should be
7.
21. Divisibility If a number 774958A96B is to be divisible by 8
and 9, the values of A and B, respectively, will be: Using the
divisibility rules, For 8, the last three digits have to divisible
by 8, therefore the number 774958A96B is divisible by 8 if 96B is
divisible by 8. 96B is divisible by 8 if it is 960 or 968 thus B is
either 0 or 8. For 9, the sum of the number has to be divisible by
9, therefore (55 + A + B) is divisible by 9 if (A + B) is 8. Now
either of A or B could be 8, but the other has to be zero.
22. Divisibility 311311311311311311 is divisible by: a)3 and
11. b)11 but not 3. c)3 but not 11. d)none of the above. a.3 and 11
the sum of digits is 30 which is divisible by 3 the differences of
odd place digits - even place is divisible by 11
23. DIVISIBILITY What least number be added to 5200 to get a
number exactly divisible by 180? (1) 160 (2) 60 (3) 20 (4) 180 180
= 5 X 4 X 9. 5200 + 160 = 5360 NOT DIVISIBLE BY 9. 5200 + 60 = 5260
NOT DIVISIBLE BY 9 5200 +20 = 5220 DIVISIBLE BY 9 5200 + 180 NOT
DIVISIBLE BY 9.
24. DIVISIBILITY A number when divided by 32 leaves the
remainder 29. This number when divided by 8 will leave the
remainder (1) 3 (2) 5 (3) 7 (4) 29 Let the number be 32k + 29. 32k
+ 29 = 32k + 24 + 5 8(4k+3) + 5. The remainder is 5.
25. Powers The unit digit in the expression ( 36234 x 33512 x
39180) (5429 x 25123 x 31512) will be (a) 2 (b) 6 (c) 8 (d) 4 Power
of 6 end in 6 Fourth power of 3 end in 1 Even power of 9 end in 1
Odd power of 4 end in 4 Power of 5 end in 5 Power of 1 end in 1
Ans: 6 4 = 2.
26. POWERS If x increases linearly, how will a-x behave
(a>1) ? a. Increase linearly b. Decrease linearly c. Increase
exponentially d. Decrease exponentially Since x increases linearly,
x decreases linearly and ax decreases exponentially. Ans d.
27. POWERS What is x if xx 3 3 1 9 81 1 3 27 1 100 Rewrite each
term as a power of three, then combine exponents: 12932 4 100 3 333
3 1 3 3 1 xxx Since the bases are the same, the exponents must be
equal: 1293 xx which has the solution x = 94
28. LOGARITHM What is the value of the following expression: 2
log105 + log104 ? a. 2 b. 2.5 c. 3 d. None of these Log10 25*4 =
log10100 = 2.
29. LCM Find the greatest number of five digits, which is
exactly divisible by 7, 10, 15, 21 and 28. The number should be
exactly divisible by 15 (3, 5), 21 (3, 7), 28 (4, 7). Hence, it is
enough to check the divisibility for 3, 4, 5 and 7. Lcm of 3,4,5
and 7 is 420. 105/420 = 238 is quotient 238* 420 = 99960 is the
only number which satisfies the given condition.
30. HCF The ratio of two numbers is 3 : 4 and their H.C.F. is
4. Their L.C.M. is: A. 12 B. 16 C. 24 D. 48 Let the numbers be 3x
and 4x. Then, their H.C.F. = x. So, x = 4(given) the numbers are 12
and 16. LCM of 12,16 is 48. So, ans is OPT (D)
31. HCF & LCM
32. HCF & LCM Four different electronic devices make a beep
after every 30 minutes, 1 hour, 3/2 hour and 1 hour 45minutes
respectively. All the devices beeped together at 12 noon. They will
again beep together at: i) 12 Midnight ii) 3 a.m iii) 6 a.m. iv) 9
a.m Interval after which the devices will beep together = (L.C.M.
of 30, 60, 90, 105) min. = 1260 min. = 21 hrs. So, the devices will
again beep together 21 hrs. after 12 noon i.e., at 9 a.m.
33. HCF & LCM
34. Factorization 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 n is A*A*B*C =A^2*B*C no. of
factors=(2+1)(1+1)(1+1) =12 A HAS POWER OF 2,B HAS POWER OF 1,C HAS
POWER 1 SO PRIME FACTORIZATION CAN BE CALCULATED AS: IF
A^P+B^Q+C^R,THEN PRIME FACTORIZATION IS (P+1)*(Q+1)*(R+1) SO IN
THIS CASE P=2,Q=1,R=1 SO (2+1)(1+1)(1+1)=12 FACTORS
35. RACES & GAMES An athlete decides to run the same
distance in 1/4th less time that she usually took. By how percent
will she have to increase her average speed
36. RACES & GAMES In August, a cricket team that played 120
matches won 20% of the games it played. After a continuous winning
streak, this team raised its average to 52%. How many matches did
the team win to attain this average? A) 40 B) 52 C) 68 D) 80 (24+x)
/ (120+x) = 0.52, where x is the number of games played and 24 is
20% of 120 24 + x = 0.52(120 + x) 24+x = 62.4 + 0.52x 0.48x =
62.4-24 0.48x=38.4 x=38.4/0.48 x=80
37. PERCENTAGE
38. PERCENTAGE
39. PERCENTAGE Find the percentage of prime numbers present
between 1 and 100 (including both). A) 20 B) 25 C) 24 D) 23 2, 3,
5, 7, 11, 13, 17, 19 =8 23,29, 31, 37, 41, 43, 47, 53 =8 61,67, 71,
73, 79, 83, 89, 97 =8 24%
40. PERCENTAGE
41. PERCENTAGE If 7% of A is 42, then find 27% of A. A) 162 B)
62 C) 600 D) 126 Ans: 162 Another method 7 is prime number and the
last digit of given number is 2. Hence 27% of A also should have
last digit is 2 and so C and D are not possible. B is also not
possible because it is not divisible by 9(ie 27).
42. PERCENTAGE
43. PERCENTAGE
44. PERCENTAGE 4% is equal to one out of every: A) 12 B) 20 C)
40 D) 25 Answer 25
45. PERCENTAGE The difference between a discount of 35% and two
successive discounts of 20% and 20% on a certain bill was Rs. 22.
Find the amount of the bill. (1) Rs. 1100 (2) Rs. 200 (3) Rs. 2200
(4) Data inadequate Successive 20% discount means 36% discount. The
difference between 35% and 36% is 1%. 1% = 22 means the answer is
2200.
46. Percentage An athlete decides to run the same distance in
1/4th less time that she usually took. By how much percentage will
she have to increase her average speed? let original speed be s1
and time be t1 then s1=d/t1 ---eqn 1 new speed be s2 and time given
is 3t1/4 therefore s2=d/(3t1/4) -----eqn 2 dividing eqn 2 by eqn 1
s2=4s1/3 increased speed = 4s1/3-s1 =1s1/3 percent
increase=[(1s1/3)/s1]*100 =33.33%
47. FRACTIONAL POWERS
48. NEGATIVE POWERS What is the value of 0-10? i) 0 ii) 1 iii)
-10 iv) None of these 0.
49. 2525 is divided by 24, the remainder is 1) 23 2) 22 3) 1 4)
2 2525 = (24 + 1)25 = 24K + 1. CHOICE 3.
50. AVERAGE The average age of a group of nine men today is the
same as it was six years ago, with one of the men having been
replaced by another much younger man. The difference in ages of the
man being replaced and the man replacing him is how many years? (a)
53 (b) 54 (c) 55 (d) 56 Six years ago the average is x and now also
x. the number is same. Hence No of persons * time elapsed = 9 * 6 =
54.
51. AGE The average age of A and B is 20 years. If C were to
replace A, the average would be 19 and if C were to replace B, the
average would be 21. What are the ages of A, B and C? (1) 22, 18,
20 (2) 18, 22, 20 (3) 22, 20, 18 (4) 18, 20, 22
52. RATIO If a:b=3:4 and b:c=2:7, then what is the value of
a:b:c? A) 3:4:14 B) 3:4:7 C) 6:4:7 D) 6:8:12 A) 3:4:14
53. RATIO The prices of a refrigerator and a cell phone are in
the ratio 3:2. If the refrigerator costs Rs. 6000 more than the
cell phone, what is the price of the cell phone? A) Rs. 1200 B) Rs.
12000 C) Rs. 8000 D) Rs. 9000 Let the price of refrigerator be 3x
and cellphone be 2x. X =6000 price of cellphone = 12000.
54. RATIO
55. PROFIT / LOSS A man buys a watch for Rs.135. His overhead
expenses were Rs.50. If he sells the watch for Rs.254, what is his
approximate profit/loss in percent? A) 39% profit B) 37% profit C)
37% loss D) 39% loss B) 37% profit Wild guess 185 divisible by 37.
and S.P > C.P.
56. PROFIT/ LOSS
57. PROFIT / LOSS
58. PROFIT / LOSS After giving a discount of Rs.45 the
shopkeeper still gets a profit of 20%, if the cost price is Rs.180.
Find the mark up percent. A) 0.4 B) 0.55 C) 0.45 D) 0.48 LET THE
S.P = X C.P = 180. S.P = 180 + 36 = 216. M.P = S.P + 45 = 216+45 =
261. M.P% = 0.48 PROFIT COST PRICE DISCOUNT MARKED PRICESELLING
PRICE
59. PROFIT / LOSS
60. PROFIT / LOSS In a shop 80% of the articles are sold at a
profit of 10% and the remaining at a loss of 40%.what is the
overall profit/loss? a.10% profit b.10% loss c.15% profit d. no
profit, no loss Option d no profit,no loss 80*1.1+20*0.6/100=1
61. PROFIT / LOSS If a pen is being sold at 4% profit instead
of 4% loss the actual profit is Rs 16. What is the actual cost
price of the pen ? Let x be the CP. (104/100)x - (96/100)x = 16
Solving we get x = Rs.200.
62. PROFIT / LOSS
63. PROFIT / LOSS John buys a cycle for 31 dollars and given a
cheque of amount 35 dollars. Shop Keeper exchanged the cheque with
his neighbor and gave change to John. After 2 days, it is known
that cheque is bounced. Shop keeper paid the amount to his
neighbor. The cost price of cycle is 19 dollars. What is the
profit/loss for shop keeper? a) loss 23 b) gain 23 c) gain 54 d)
Loss 54 CP of cycle = 19$ SP of cycle = 31$ Profit = 31$-19$ = 12$
Again, shopkeeper gave 35$ to neighbour. Loss = 35$ So, net loss =
35$-12$ = 23$
64. PROFIT & LOSS -5 x = - 1000 X = 200
65. A man can do a job in 25 days. He worked at it for 15 days
and then gave up. After that, B completed the work in 10 days.
Together, both can finish the job in ________days. a) 12 days b) 25
days c) 6 days d) 12 days
66. TIME & WORK If 50 people finish a job in 10 days, how
long will it take 20 people to finish the same job? A) 25 B) 50 C)
4 D) None of the options Answer : A) 25.
67. TIME & WORK
68. TIME WORK Ten men can paint a room in 3 hours. How many
hours would 5 men take to paint the room, if they work at the same
rate? A) 6 hours B) 1.5 hours C) 10 hours D) None of the options A)
6 hours.
69. PIPES & CISTERNS Pipe A takes 16 min to fill a tank.
Pipes B and C, whose cross- sectional circumferences are in the
ratio 2:3, fill another tank twice as big as the first. If A has a
cross-sectional circumference that is one-third of C, how long will
it take for B and C to fill the second tank? (Assume the rate at
which water flows through a unit cross-sectional area is same for
all the three pipes.) a. 66/13 b. 40/13 c. 16/13 d. 32/13 If A has
a cross sectional circumference is x and area will be proportional
to x2 cross section of C is 3x and area will be proportional to 9x2
.Hence cross sectional circumference of B will be (2/3)*3x = 2x so
area is proportional to 4x2. Pipe A fills in 16 min. Pipe B and C
sum of area is proportional to 13x2. will fill the same tank in
16/13 min. The second tank is twice big in size require 2 * 16 / 13
= 32/13 min
70. AGES 20) If the ages of a husband and a wife are in the
ratio 5:4 and the sum of their ages is 45, what is the difference
between their ages? A) 4 years B) 5 years C) 3 years D) 6 years Let
the ages be 5x and 4x. Sum 9x = 45 x = 5 years. Difference between
their ages is 5 years.
71. CLOCK Samarth asked his friend: .What will be the time
after 2 hours 30 mins, if the time was 3:45 p.m. half an hour ago?"
What should be his friends reply? A) 6:30 p.m. B) 6 p.m. C) 6:45
p.m. D) None of the options Time now = 3:45 + 0:30 = 4:15 min After
2:30 time will be 6:45 min.
72. Four bells ring at intervals of 10 min, 12 min, 15 min, and
20 min, respectively. If they ring together at 8 a.m., find out the
interval of time after which they will ring together again. a) 9
a.m. b) 10 a.m. c) 11 a.m. d) 1 p.m.
73. PERMUTATION The letters of the word WOMAN are written in
all possible orders and these words are written out as in a
dictionary ,then the rank of the word 'WOMAN' is a. 117b. 120 c.
118 d. 119 5!=120 120/5=24 Since W is the last in rank WOMAN is in
the last 24. O is in the last rank of the remaining 4 letters. 24/4
= 6 Therefore WOMAN is in the last 6 in rank. M is between A and N
so WOMAN is in rank 117 or 118. A is before N so WOMAN's rank is
117. There are 120 possible arrangements of the letters in WOMAN.
Since WOMAN is near the end, I'll list out the ones after WOMAN:
WONMA WONAM WOMNA There are only three, so these account for the
118th, 119th, 120th words, and it places WOMAN 117th.
74. PROBABILITY What is the probability of getting the sum 5 in
two throws of the dice? a. 1/12 b. 1/5 c. 1/9 d. None of these
75. PROBABILITY The probability of A solving a problem is 2/3.
The probability of B solving a problem is . If the same problem is
given to both of them, what is the probability of neither of them
solving it? (a) 3/4 2/3 (b) (1- ) x 2/3 (c) 1/3 + 1/4 (d) 1/3 x
1/4
76. CUBES A 4 inch cube is taken and it is painted in green
colour and then it is cut into 1 inch cubes. How many cubes are 2
faces painted? (a) 12 (b) 24 (c) 36 (d) 48
77. TRAINS Two trains start from stations Chennai and
Villupuram spaced 150 km apart at the same time and speed. As the
trains start, a bird flies from one train towards the other and on
reaching the second train; it flies back to the 1st train. This is
repeated till the trains collide. If the speed of the train is
75kmph and that of the bird is 100kmph. How much did the bird
travel till collision? (a) 100km (b) 120km (c) 220km (d) 175km
78. distance between trains is 150 km. one train travels 75 km
/ hr. other train travels 75 km / hr. they will meet when the total
distance traveled by both of them is equal to 150 km. rate * time =
distance. We know that the time that each train travels will be the
same. We let h = the time each train travels. train 1 travels 75 km
/ hr * h hours. train 2 travels 75km / hr * h hours. the total
distance they travel is 150 km. 75 * h + 75 * h = 150 h = 1 They
will meet in 1 hour. the bird was flying at 100 km/h. in the same 1
hour the bird flew a total of 100 km. bird flies 50 km in one
direction, then travels back 50 km when the trains meet.
79. RACES & GAMES
80. The difference between the simple interest and compound
interest obtained on a principal amount at 5% per annum after two
years is Rs.35. What is the principal amount? a) Rs.15,000 b)
Rs.10,000 c) Rs.14,000 d) Rs.13,000
81. ATTENTION TO DETAIL Follow the directions given below to
answer the questions that follow. Your answer for each question
below would be: A. If all the THREE items given in the question are
exactly ALIKE B. If only the FIRST and SECOND items are exactly
ALIKE. C. If only the FIRST and THIRD items are exactly ALIKE. D.
If none of the above 49 A0067DF667016 A0067DF667016 A0067DF667106
(a) A (b) B (c) C (d) D 50 Janmasthami Janmasthhami Jamnasthami (a)
A (b) B (c) C (d) D
82. If * stands for +, + stands for -, and - stands for /, then
27/5*8+11-7=? (a) 141.4 (b)38.4 (c) 16.4 (d)36.1 If * stands for -,
/ stands for +, + stands for / and stands for *, then which of the
following is TRUE? A)8/12*4+20-8=18.4 B)12*8/4+20-8= -5.6
C)8*4/12+8-8= -12.2 D)8*8/4+20-8= -4 (a) A (b) B (c) C (d) D
Identify the correct match 345611242627 A) 345612414627 B)
345611426227 C)345611624227 D) 345616242227 (a) A (b) B (c) C (d)
D