mathewhe/aqua_rat huggingface dataset:
Question: Rakesh travelled 1800 kilometre by air which formed 3/5 of the total journey. He travels 1/4 of the trip by car and the remaining trip by train. Find the distance travelled by train.
(A) 350
(B) 450
(C) 550
(D) 650
(E) None of these
Rationale: Explanation :
3/5 of D = 1800. So D = 3000 km,
so distance travelled by train = 3000 – 1800 – 1/4 of 3000 = 450
Answer – B
Answer: (B) 450
Question: If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =
(A)  −48
(B)  −2
(C)  6
(D)  46
(E)  48
Rationale: i.e. if a =-3 then b = 9
or if a = 9 then b =-3
But in each case a+b = -3+9 = 6
Answer: option C
Answer: (C)  6
Question: The average age of the mother and her six children is 12 years which is reduced by 5 years if the age
of the mother is excluded. How old is the mother
(A) 40
(B) 41
(C) 42
(D) 43
(E) 44
Rationale: Answer: Option C
Answer: (C) 42
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 34 years. What is the age of Deepak at present?
(A) 77 years
(B) 15 years
(C) 21 years
(D) 88 years
(E) 55 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 34 => x = 7
Deepak's age = 3x = 21 years.
Answer: C
Answer: (C) 21 years
Question: Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 2 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?
(A) 5
(B) 15
(C) 17
(D) 20
(E) 25
Rationale: Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12
Collective work Time = 12/7 = 1.7 Hrs
Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 2 breaks
=.3/2=.15 hrs = 15 m
so Answer is B) 15 mins
Answer: (B) 15
Question: Write 860,000,000,000 in scientific notation.
(A) 8.6 * 10^11
(B) 800.900 * 10^11
(C) 8.900 * 10^11
(D) 80.9000* 10^11
(E) 08.900 * 10^11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
860,000,000,000 = 8.6* 100,000,000,000 = 8.6 * 10 11**
correct answer A
Answer: (A) 8.6 * 10^11
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 40%?
(A) 700
(B) 882
(C) 772
(D) 652
(E) 271
Rationale: Cost price = Rs.500
profit = 40% of 500 = Rs.200
Selling price = Cost price + Profit
= 500 + 200 = 700
Answer:A
Answer: (A) 700
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.170. Find the unknown rate of two towels?
(A) A)400
(B) B)650
(C) C)500
(D) D)550
(E) E)600
Rationale: 10 * 170 = 1700
3 * 100 + 5 * 150 = 1050
1700 – 1050 = 650
B
Answer: (B) B)650
Question: The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest.
(A) 3052.89
(B) 3052.86
(C) 3092.8
(D) 3052.8
(E) 3052.81
Rationale: R = 100 I / PT
=> R = (100 * 7200)/ (12000 * 5) = 12%
CI = P{ [1 + R /100]n - 1}
= 12000 { [ 1 + 12 / 100]2 - 1} = Rs.3052.80.Answer: D
Answer: (D) 3052.8
Question: If the radius of a circle is increased by 12%, then the area of the circle
(A) decreases by 25.44%
(B) increases by 25.44%
(C) no change in area
(D) decreases by 12%
(E) none
Rationale: A1=pi(100)^2
A2=pi(112)^2
so (A2-A1)/A1*100=25.44
ANSWER:B
Answer: (B) increases by 25.44%
Question: Which of the following is the Highest Common Factor of 121, 99 and 77?
(A) 8
(B) 10
(C) 6
(D) 14
(E) 11
Rationale: the Highest Common Factor is 11Ans is :E
Answer: (E) 11
Question: A certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 120 miles at 60 mph?
(A) 15%
(B) 20%
(C) 27.27%
(D) 30%
(E) 40%
Rationale: Let, Tank capacity = T gallon
Used Fuel = (T-8) gallons
Distance Travelled (@60 miles/hr) = 80 miles
Distance travelled in 1 gallon = Distance travelled in 40 mins (@60 miles/hr) = (60/60)*40 = 40 miles
Fuel used to travel 120 miles = (120/40) = 3 gallon
i.e. Used fuel = (T-8) = 3 gallon
i.e. T = 10 Gallons
i.e. Used Fuel = (3/11)*100 =27,27%
C
Answer: (C) 27.27%
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 65 sec
(B) 12 sec
(C) 77 sec
(D) 44 sec
(E) 11 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: B
Answer: (B) 12 sec
Question: John and Tony began business with Rs.12000 and Rs.14000 after 8 months, John withdraws Rs.2000 and Tony withdraws Rs.4000. At the end of the year, their profits amounted to Rs.4500 find the share of Tony.
(A) 2375
(B) 2325
(C) 2300
(D) 3375
(E) 3300
Rationale: (12*8 + 10*4):(14*8 + 10*4)
17:19
19/36 * 4500 = 2375. Answer: A
Answer: (A) 2375
Question: If y is the smallest positive integer such that 7,700 multiplied by y is the square of an integer, then y must be
(A) 29
(B) 58
(C) 63
(D) 74
(E) 77
Rationale: 7700= 5*5*2*2*7*11, so we need one 7 and one 11 to make it a square of a number. so 7*11= 77
Ans: E
Answer: (E) 77
Question: A completes a work in 3 days and B complete the same work in 6 days. If both of them work together, then the number of days required to complete the work will be?
(A) 2 days
(B) 11 days
(C) 21 days
(D) 22 days
(E) 24 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 3 Ã— 6/ 9 = 2 days.
Option 'A'
Answer: (A) 2 days
Question: The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let the members be Old Having age O + other 9 having ages x and New one having age Y
Sum of their ages = (Y + 9 × x) and average = (Y + 9 × x)/10
Before 4 years sum was (O + 9 x – 10 × 4) and average = (O + 9 x – 10 × 4) /10
equating, Y + 9 x = O + 9x – 40
Y = O – 40
Younger is 40 years younger than Old one.
ANSWER:A
Answer: (A) 40
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 1
Rationale: Explanation:
80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: (A) 8
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 10 hours a day?
(A) 28.8
(B) 30
(C) 32
(D) 34
(E) 36
Rationale: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*10=200
Therefore number of days=5760/200=28.8 days
Ans=A
Answer: (A) 28.8
Question: Kiran is younger than Bineesh by 7 years and their ages are in the respective ratio of 7:9. How old is Kiran?
(A) 22.5
(B) 24.5
(C) 23.5
(D) 25.5
(E) 26.5
Rationale: Let age of Kiran and Bineesh be 7x and 9x respectively
7x=9x−7x=72=3.5
Kiran's age =7x=7×3.5=24.5
Answer is B.
Answer: (B) 24.5
Question: A can do a piece of work in 12 days. He worked for 15 days and then B completed the remaining work in 10 days. Both of them together will finish it in.
(A) 12 1/2 days
(B) 10 1/2 days
(C) 12 1/3 days
(D) 10 1/3 days
(E) 11 1/2 days
Rationale: Explanation:
15/25 + 10/x = 1 => x = 25
1/25 + 1/25 = 2/25
25/2 = 12 1/2 days
Answer A
Answer: (A) 12 1/2 days
Question: A man took loan from a bank at the rate of 5% p.a. S.I. After 13 years he had to pay Rs. 1300 interest only for the period. The principal amount borrowed by him was?
(A) 1750
(B) 4000
(C) 3500
(D) 2000
(E) 1000
Rationale: Principal = (100 * 1300) / (5 * 13)
= Rs.2000
Answer: D
Answer: (D) 2000
Question: If A:B = 1/5: 1/3 B:C = 1/2:1/3 then A:B:C?
(A) 9:6:6
(B) 9:6:8
(C) 9:6:2
(D) 9:6:4
(E) 9:15:10
Rationale: A:B = 1/5:1/3 = 3:5
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:15:10
Answer:E
Answer: (E) 9:15:10
Question: When x is even, [x] = x/2 + 1, when x is odd [x] = 2x + 1 then [7]*[8] = ?
(A) [22]
(B) [44]
(C) [75]
(D) [88]
(E) [90]
Rationale: [7]*[8]=(7*2+1)(8/2+1)
=[75].
Ans -C
Answer: (C) [75]
Question: there are two cubes with ratio between volume is 125:64. then what is the value of length of each cube?
(A) 25:16
(B) 16:25
(C) 4:5
(D) 5:4
(E) 150:96
Rationale: given
6a12:a22=150:96
then a12:a22=25:16
a1:a2=5:4
so the answer is D
Answer: (D) 5:4
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/24 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 10/21
(D) (d) 17/35
(E) (e) 7/43
Rationale: This problem is very good example how easy and quick plug-in method might be.
Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 7/24*6=$7/4;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$7/4=$7;
Fraction of total revenue from large cups: 7/(36+7)=7/43.
Answer:E.
Answer: (E) (e) 7/43
Question: Mark purchases a dozen items for $240.00. If Mark sells each item for $30.00 what is his markup%?
(A) 10
(B) 50
(C) 75
(D) 100
(E) 125
Rationale: C.P.=240/12=20
S.P.=30
markup%=((S.P.-C.P.)/C.P.)*100=((30-20)/20)*100=50%
ANSWER:B
Answer: (B) 50
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1100
(B) 1134
(C) 1240
(D) 1340
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: 45 x ? = 40% of 900
(A) 16.2
(B) 4
(C) 5
(D) 500
(E) 8
Rationale: Answer
Let 45 x A = (40 x 900)/100
∴ A = (40 x 9)/45 = 8
Correct Option: E
Answer: (E) 8
Question: 5 percent of 255 =
(A) 5
(B) 12.5
(C) 14.5
(D) 12.75
(E) 25
Rationale: 255/100=2.551% =2.555%= 2.55*5 = 12.75 ANSWER:D
Answer: (D) 12.75
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 45
(B) 40
(C) 39
(D) 37
(E) 38
Rationale: Explanation:
Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2.
x/2 = (83 - 63) => x/2 = 20 => x = 40. Answer: B
Answer: (B) 40
Question: Find out the C.I on Rs.4000 at 4% p.a. compound half-yearly for 1 1/2 years
(A) 244.83
(B) 306.07
(C) 306.04
(D) 306.03
(E) 306.01
Rationale: A = 4000(51/50)3
= 4244.832
4000
-----------
244.83
Answer:A
Answer: (A) 244.83
Question: In a mixed college 160 students are there in one class. Out of this 160 students 3/5 students are girls. How many boys are there ?
(A) A)40
(B) B)64
(C) C)80
(D) D)120
(E) E)140
Rationale: Total Number of Students :160
Total Girls : 160*3/5 =96
Total Boys : 160-96= 64
Answer is B
Answer: (B) B)64
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 5m
(B) 3m
(C) 9m
(D) 2m
(E) 4m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: D
Answer: (D) 2m
Question: 100 + 50 * 2 = ?
(A) 200
(B) 150
(C) 100
(D) 300
(E) 400
Rationale: Explanation:
After applying BOMAS rule,
First Multiplication will be done then addition
So it will be 100 + 100 = 200
Option A
Answer: (A) 200
Question: The G.C.D. of 1.08, 0.36 and 0.8 is:
(A) 0.04
(B) 0.9
(C) 0.18
(D) 0.108
(E) 0.118
Rationale: Given numbers are 1.08, 0.36 and 0.80. H.C.F. of 108, 36 and 80 is 18,
H.C.F. of given numbers = 0.04.
Answer: Option A
Answer: (A) 0.04
Question: If X = Y/Z, -1 < Z < 0 and 4 < Y, which of the following is correct?
(A) X > 4.
(B) 0 < X <4.
(C) -4 < X < 0
(D) X < -4.
(E) X < -20
Rationale: Y is +ve & Z is -ve
Eliminate A & B
For min. value max. numerator and minimize denominator
take Y=4.1 & X=-0.9
X=4.1/-0.9
X<-4
Ans D
Answer: (D) X < -4.
Question: A project scheduled to be carried out over a single fiscal year has a budget of $12,000, divided into 12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $4,540. By how much was the project over its budget?
(A)  $380
(B)  $540
(C)  $1,050
(D)  $1,380
(E)  $1,430
Rationale: Difficulty level: 600
Each month's budget = 12000/12 = 1000
Budget for 4 months = 4*1000 = 4000
Actual amount spent = 4540
Amount spent over the budget = 4540 - 4000 = 540
Answer (B),
Regards,
Answer: (B)  $540
Question: Two trains travel in the same direction at the speeds of 56km/hr. and 29km/hr. respectively. The faster train passes a man in the slower trains in 10 seconds. The length of the faster train (in metres) is
(A) 100
(B) 80
(C) 75
(D) 120
(E) 130
Rationale: Explanation:
The relative speed is 56-29 Km/hr =(27/18) X 5= 7.5 m/s2718×5=7.5m/s
The faster train travels only the length of it’s own = 7.5 x 10 = 75 m
Answer C
Answer: (C) 75
Question: One pump drains one-half of a pond in 6 hours, and then a second pump starts draining the pond. The two pumps working together finish emptying the pond in one-half hour. How long would it take the second pump to drain the pond if it had to do the job alone?
(A) 1 hour
(B) 1.09 hour
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: The tricky part here, I believed is one half hour = 1/2. Then everything would be easy.
We have the 1st pump working rate/hour = 1/2 :6 = 1/12
Working rate of 2 pumps: 1/2 : 1/2 = 1.
Working rate of 2nd pump: 1 -1/12= 11/12 --> Time taken for the 2nd pump to finish: 1 : 11/12 = 12/11 = 1.09 hours.
B
Answer: (B) 1.09 hour
Question: A person got Rs.40 more when he invested a certain sum at compound interest instead of simple interest for two years at 10% p.a. Find the sum?
(A) 7500
(B) 4000
(C) 5000
(D) 4500
(E) 2671
Rationale: P = (d * 1002) / R2
=> (40 * 100 * 100) / 10 * 10 = Rs.4000
Answer:B
Answer: (B) 4000
Question: A farmer had d animals, all of which the farmer bought for the same price. The farmer decided to sell the animals. 14 of the animals were sold at a profit of 10% each while the rest were sold at a loss of 20% each. Overall, the farmer made neither a profit nor a loss. Which of the following is equal to d?
(A) 21
(B) 24
(C) 27
(D) 33
(E) 36
Rationale: Let P be the price the farmer paid for each animal.
The total profit on the 14 animals is 14*0.1*P.
The total loss on the other (d-14) animals is (d-14)*0.2*P.
(d-14)*0.2*P = 14*0.1*P
0.2*d = 1.4 + 2.8
d = 21
The answer is A.
Answer: (A) 21
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
(A) 12
(B) 10
(C) 11
(D) 09
(E) 03
Rationale: Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
Answer:C
Answer: (C) 11
Question: A chair is bought for Rs.800/- and sold at Rs.720/- find the loss percentage
(A) 10% Loss
(B) 10% Gain
(C) 12% Loss
(D) 12% Gain
(E) None of these
Rationale: Explanation:
Formula = (Selling price ~ Cost price)/Cost price * 100
= (720 ~ 800)/800 = 10% Loss
Answer: Option A
Answer: (A) 10% Loss
Question: What is the difference between the place value of 5 in the numeral 7559?
(A) 150
(B) 160
(C) 180
(D) 190
(E) 450
Rationale: 500 - 50 = 450
E
Answer: (E) 450
Question: Thabo owns exactly 180 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: I think we can use double-matrix method and solve using only one variable.
Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.
Double-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction
P H Total
F 2x+40 0
NF x+20 x
Total 3x+60 x 180
3x + 60 + x = 180
x = 30
Answer (C.)
Answer: (C) 30
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) Rs.486
(B) Rs.455
(C) Rs.487
(D) Rs.480
(E) Rs.489
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125]
= Rs.480
Answer: D
Answer: (D) Rs.480
Question: Out of 12 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) A)5/11
(B) B)5/11
(C) C)5/1
(D) D)9/11
(E) E)5/3
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃
= 1 - (6 * 5 * 4)/(10 * 11 * 12)
= 9/11
Answer:D
Answer: (D) D)9/11
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 12, find the other?
(A) 100
(B) 600
(C) 120
(D) 200
(E) 150
Rationale: Other number = 12*600/12= 600
Answer is B
Answer: (B) 600
Question: Find the odd man out. 8,40,42,60,96
(A) 8
(B) 40
(C) 42
(D) 60
(E) 96
Rationale: All except 42 are multiples of 4
Answer is C
Answer: (C) 42
Question: 40 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
(A) 13.2
(B) 17.5
(C) 12.8
(D) 34.25
(E) 31.25
Rationale: x/7 = y/9 => x:y = 7:9
7/16 * 40 = 17.5
ANSWER:B
Answer: (B) 17.5
Question: A part-time employee whose hourly wage was increased by 15 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?
(A) 9
(B) 13.04
(C) 10
(D) 11
(E) 12
Rationale: Let original hourly wage be x and let the no of hours worked be y
Total wage will be =x*y
After the increment the wage will be=1.15 x
Now we need to find number of hours worked so that
x*y=1.15x*z i.e z=1/1.15 y
%decrease = (y-1/1.15y)/y *100=13.04%
Thus my answer is B.
Answer: (B) 13.04
Question: 81*82*83*84*85*86*87*89. What should be in the unit place in this product?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: It should be zero in the unit place in this product.
85*82 will give zero in unit place.
ANSWER:A
Answer: (A) 0
Question: At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $162.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
(A) $21
(B) $35
(C) $31
(D) $41
(E) It cannot be determined
Rationale: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:
3B+7S+C=120
4B+10S+C=162.5
Subtracting the first equation from the second gives us B+3S=42.5
Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=35. In any case, there is no necessity to know each item's price, just the sum.
Answer: B
Answer: (B) $35
Question: A number is selected at random from the first 40 natural numbers. What is the probability that the number is a multiple of either 2 or 21?
(A) 21/40
(B) 2/5
(C) 7/15
(D) 4/15
(E) 11/30
Rationale: Number of Multiples of 2 from 1 through 40 = 40/2 = 20
Number of Multiples of 21 from 1 through 40 = 40/21 = 1
Number of Multiples of 2 and 21 both from 1 through 40 = Number of Multiples of 21*2(=42) = 0
Total favourable cases = 20 + 1 - 0 = 21
Probability = 21 / 40
Answer: option A
Answer: (A) 21/40
Question: A train running at the speed of 60 km/hr crosses a pole in 27 seconds. Find the length of the train?
(A) 150 meter
(B) 876 meter
(C) 167 meter
(D) 450 meter
(E) 169 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 27
= 450 meter
Answer: D
Answer: (D) 450 meter
Question: At what time between 7 and 8 o’clock will the hands of a clock be in the same straight line but, not together?
(A) 5 min. past 7
(B) 5 2⁄11 min. past 7
(C) 5 3⁄11 min. past 7
(D) 5 5⁄11 min. past 7
(E) None of these
Rationale: When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o’clock, they are 25 min. spaces apart.
∴ Minute hand will have to gain only 5 in. spaces.
55 min.spaces are gained in 60 min.
5 min. spaces are gained in (60⁄55 × 5)min. = 5 5⁄11 min.
∴ Required Time = 5 5⁄11 min. past 7
Answer D
Answer: (D) 5 5⁄11 min. past 7
Question: The average marks of 25 students in a class is 100. But a student mark is wrongly noted as 60 instead of 10 then find the correct average marks?
(A) A)78
(B) B)82
(C) C)98
(D) D)91
(E) E)85
Rationale: correct avg marks = 100+(10-60)/25
avg = 100-2 = 98
Answer is C
Answer: (C) C)98
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 48, the dividend is:
(A) 5324
(B) 5334
(C) 5336
(D) 5356
(E) 5808
Rationale: Divisor = (5 * 48) = 240
= 10 * Quotient = Divisor
=> Quotient = 240/10 = 24
Dividend = (Divisor * Quotient) + Remainder
Dividend = (240 * 24) + 48 = 5808.
E
Answer: (E) 5808
Question: The average age of a college is 21.8 years. If the average age of students of college is 24.2 years and Average age of lecturers of college is 20.6 years. Find the ratio of the number of students to that of Lecturers?
(A) 3:1
(B) 1:3
(C) 2:1
(D) 1:2
(E) 3:2
Rationale: 1:2
Option 'D'
Answer: (D) 1:2
Question: If v = 4p, where p is a prime number greater than 2, how many different positive even divisors does v have, including v ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: v=4p
since v = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Answer: (C)  Four
Question: A car is running at a speed of 108kmph. What distance will it cover in 15sec?
(A) 300m
(B) 150m
(C) 200m
(D) 450m
(E) 500m
Rationale: Speed = 108kmph = 108*5/18 = 30 m/s
Distance covered in 15sec = 30*15 = 450m
Answer is D
Answer: (D) 450m
Question: Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $40 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?
(A)  $781
(B)  $755
(C)  $765
(D)  $773
(E)  $775
Rationale: = (750*6+ 790 *20)/26
= 781
Answer is A.
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Answer: (A)  $781
Question: Eleven animals of a circus has to be placed inside in eleven cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
(A) 604800
(B) 808250
(C) 502450
(D) 784200
(E) 302400
Rationale: first we will fill the smaller cages-
these 4 cages will require to be filled by 11-6 = 5 animals => 5C4∗4!=120.
remaining 6 and 1 out of the above 5 can be filled in7∗6∗5∗4∗3∗2=5040
total ways = 120∗5040=604800
ANSWER:A
Answer: (A) 604800