mathewhe/aqua_rat huggingface dataset:
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 4 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 520
(B) 620
(C) 576
(D) 740
(E) 720
Rationale: Distance = (240 x 4) = 960 km.
Speed = Distance/Time
Speed = 960/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = (960 x 3/5) km/hr = 576 km/hr
Answer C) 576 Km/hr
Answer: (C) 576
Question: Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
x 2	+	1 + (30 - x).	2	= 1
75	45	75
11x	+	(60 -2x)	= 1
225	75
11x + 180 - 6x = 225.
x = 9.
B)
Answer: (B) 9
Question: The lengths of the legs of a right triangle are x and y, while the length of the hypotenuse is
x + y- 4. What is the maximum radius of a circle inscribed in this triangle?
(A) 1
(B) 2
(C) 4
(D) 22
(E) cannot be determined from the information given
Rationale: Length of hypotenuse: x + y-4 = a + b. Hence x + y = a + b + 4.
Sum of lengths of legs: x + y = a + b + 2r.
Therefore 2r = 4, so r = 2.
correct answer B
Answer: (B) 2
Question: The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
(A) 19
(B) 27
(C) 16
(D) 15
(E) 17
Rationale: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, (1/3 * 5x)/(1/2 * 6x) = 5/9
15 = 15
Thus, Shaan's age cannot be determined.Answer: D
Answer: (D) 15
Question: In a clothing store, there are six different colored neckties (red, orange, yellow, green, blue, and indigo) and six different colored shirts (red, orange, yellow, green, blue, and indigo) that must be packed into boxes for gifts. If each box can only fit one necktie and one shirt, what is the probability that all of the boxes will contain a necktie and a shirt of the same color
(A) 719/720
(B) 1/120
(C) 2/233
(D) 3/543
(E) 1/720
Rationale: 6 ties and 6 shirts...
red tie can take any of 6 shirts..
orange can take any of the remaining 5 shirts
yellow any of remaining 4..
and so on till last indigo chooses the 1 remaining..
Total ways= 6*5*4*3*2*1= 720
out of this 720, ONLY 1 way will have same colour tie and shirt..
prob = 719/720
A
Answer: (A) 719/720
Question: The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?
(A) 5/7
(B) 5/1
(C) 5/9.
(D) 5/2
(E) 5/8
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
d = 2n - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
d = 2n - 1 => d = 9
Hence the fraction is : 5/9.
Answer: C
Answer: (C) 5/9.
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) 2277
(B) 9261
(C) 686
(D) 1268
(E) 2612
Rationale: A = 8000(21/20)3 = 9261
Answer: OB
Answer: (B) 9261
Question: 1+2=10
2+3=26
3+4=50 then
4+5=?
(A) 80
(B) 81
(C) 82
(D) 83
(E) 84
Rationale: 1+2=10..... (1+2)^2+1 =10
2+3=26....... (2+3)^2+1=26
3+4=50 then...(3+4)^2+1=50
4+5=82........ (4+5)^2+1=82
ANSWER:C
Answer: (C) 82
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 9 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 6 days?
(A) 3
(B) 5
(C) 6
(D) 9
(E) 12
Rationale: Explanation: If six computers require 9 days to process the data, thats
a total of 54 computer-days the product of 6 and 9. If you change the number
of computers or the number of days, 54 will have to remain the product, whether
that means 54 days of one computer or one day with 54 computers.
In 6 days, the number of computers is:
6c = 54
c = 9
9 computers is 3 more than the 6 that it took to do the job in 9 days, so
the correct choice is (A).
Answer: (A) 3
Question: A cube is divided into 125 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: Each side of the cube has 5 x 5 = 25 cubelets.
Only the interior cubelets are painted one colour.
On each side, 3 x 3 = 9 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*9 = 54
The answer is D.
Answer: (D) 54
Question: If x/4 – (x – 3)/5 = 1, then find the value of x.
(A) 9
(B) 7
(C) 6
(D) 8
(E) 5
Rationale: Explanation:
x/4 – (x - 3)/5 = 1
(5x – 4(x – 3))/20 = 1
5x - 4x + 12 = 20
x = 8
ANSWER:A
Answer: (A) 9
Question: You walk one mile to school every day. You leave home at the same time each
day, walk at a steady speed of 3 miles per hour, and arrive just as school begins. Today you
were distracted by the pleasant weather and walked the rst half mile at a speed of only 2
miles per hour. At how many miles per hour must you run the last half mile in order to arrive
just as school begins today?
(A) 4 miles per hour
(B) 6 miles per hour
(C) 8 miles per hour
(D) 10 miles per hour
(E) 12miles per hour
Rationale: Recall the formula s = v t, where in this case, s is distance (in miles) traveled at a
constant speed of v (miles per hour), for a time of t hours. The rst statement indicates that
it usually takes you only 20 minutes to go to school (solve for t in 1 = 3 t and change units)
Today, it took you 15 minutes to cover the rst half mile (solve for t in 1=2 = 2 t and
change units). You only have 5 more minutes to arrive (that is 1/12th of an hour), and need
to cover another half mile. Solve for v in the equation 1=2 = (1=12) v.
correct answer B
Answer: (B) 6 miles per hour
Question: A train 560 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 56
(C) 41
(D) 42
(E) 34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 560 + 140 = 700 m
Required time = 700 * 2/25 = 40 sec
Answer: Option B
Answer: (B) 56
Question: If {b} denote the remainder when 3b is divided by 2 then which of the following is equal to 1 for all positive integers b?
I. {2b+1}
II. {2b}+1
III. 2{b+1}
(A) I only
(B) II only
(C) I and II
(D) III only
(E) II and III
Rationale: C - I and II
3b/2 = 0 or 1
I just substituted 1 in the equations and solved.
Answer: (C) I and II
Question: Kim can do a work in 3 days while David can do the same work in 2 days. Both of them finish the work together and get Rs. 150. What is the share of Kim?
(A) 22
(B) 60
(C) 88
(D) 66
(E) 12
Rationale: Kim's wages : David's wages = Kim's 1 day work : David's 1 day work = 1/3 : 1/2 = 2:3
Kim's share = 2/5 * 150 = Rs. 60
Answer: B
Answer: (B) 60
Question: A 5-digit code consists of one number digit chosen from 1, 2, 3 and four letters chosen from A, B, C, D, E. If the first and last digit must be a letter digit and each digit can appear more than once in a code, how many different codes are possible?
(A) 375
(B) 625
(C) 1,875
(D) 3,750
(E) 5,625
Rationale: Choose one number from 3 numbers in 3C1 = 3 ways
Choose one position from the middle three for the number in 3C1 = 3 ways
The other four positions can be filled by the 5 letters in 5^4 ways.
Therefore total number of codes possible = 3*3*(5^4) = 5,625
ANSWER:E
Answer: (E) 5,625
Question: A cyclist covers a distance of 750 meter in 2 minutes 50 seconds. What is the speed in km/hr of cyclist
(A) 16 km/hr
(B) 17 km/hr
(C) 15.84 km/hr
(D) 19 km/hr
(E) 20 km/hr
Rationale: Explanation:
Speed=Distance/Time
Distance=750meter
Time=2 min 50sec=170sec
Speed=750/170=4.4m/sec
=>4.4âˆ—18/5km/hr=15.84km/hr
Option C
Answer: (C) 15.84 km/hr
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 288
(B) 277
(C) 274
(D) 270
(E) 281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: (D) 270
Question: A man purchased 1 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?
(A) 278
(B) 277
(C) 278
(D) 450
(E) 650
Rationale: 10 * 150 = 1500
1 * 100 + 5 * 150 = 850
1500 – 850= 650
Answer:E
Answer: (E) 650
Question: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?
(A) 2ft. 7 inches
(B) 4ft. 7 inches
(C) 1ft. 7 inches
(D) 3ft. 7 inches
(E) None of them
Rationale: Length of board=7ft. 9 inches=(7*12+9)inches=93 inches.
Therefore, Length of each part = (93/3) inches = 31 inches = 2ft. 7 inches
Answer is A.
Answer: (A) 2ft. 7 inches
Question: Renu can do a piece of work in 6 days, but with the help of her friend Suma , she can do it in 5 days. In what time Suma can do it alone?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 30
Rationale: Renuâ€™s one dayâ€™s work = 1/6
Sumaâ€™s one dayâ€™s work = 1/5 - 1/6 = 1/30
Suma can do it alone in 30 days.
ANSWER:E
Answer: (E) 30
Question: Roycee's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.
(A) 5
(B) 7
(C) 8
(D) 10
(E) 12
Rationale: Roycee's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively.Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.
Hence only M is 8. Now we need to consider only S, (S n R) and R.
(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.
30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.
22 = (12-x) + (5-x) + x + Neither.
Now the max value of x could be 5 and the min value of x could be 0.
When x is 5 (max), Neither is 10.
When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.
Answer 10 (D).
Answer: (D) 10
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
(A) 20%
(B) 30%
(C) 15%
(D) 10%
(E) 35%
Rationale: 900---- 180
100---- 20%
ANSWER A
Answer: (A) 20%
Question: Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 45 minutes. However, if Perry were to work at four Maria’s rate, they would take only 30 minutes. How long would it take Perry, working alone at his normal rate, to tune the warehouse full of instruments?
(A) 1 hr 20 min
(B) 1 hr 45 min
(C) 1 hr
(D) 2 hr 20 min
(E) 3 hr
Rationale: Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/45
converting it to hrs P+M= 1/(45/60) => 1/(3/4) =>4/3
second equation => M+4M =>1/30
converting it to hrs 5M=1/(30/60) =>1/(1/2) =>2
therefore M= 2/5 and P=14/15
Rate of Perry = 14/15
time= work/rate (work = 1 job)
Time ~ 1 hrs
Answer : C
Answer: (C) 1 hr
Question: A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.110/- extra, then how much amount he took?
(A) s.5500/-
(B) s.6000/-
(C) s.4000/-
(D) s.7000/-
(E) s.8000/-
Rationale: Explanation:
2 years = Rs.110/-
year = 110/2
Rate of Interest = 1%
100/1% × 110/2 = Rs.5500/-
P = Rs.5500/-
Answer: Option A
Answer: (A) s.5500/-
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 700 square meters, what is the depth of the channel (in meters)?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 1/2 * d * (12 + 8) = 700
d = 70
The answer is C.
Answer: (C) 70
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
(A) 12003
(B) 12000
(C) 12002
(D) 12022
(E) 12023
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 12000
Answer:B
Answer: (B) 12000
Question: Find the surface area of a cuboid 12 m long, 14 m broad and 7 m high
(A) 868 sq.cm
(B) 600 sq.cm
(C) 700 sq.cm
(D) 900 sq.cm
(E) None of these
Rationale: Explanation:
Surface area = [2 (12 x 14 + 14 x 7 + 12 x 7)] cm2 = (2 x 350)cm2 = 700 cm2.
Answer: C
Answer: (C) 700 sq.cm
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 9%
(B) 4%
(C) 6%
(D) 3%
(E) 5%
Rationale: 65*(90/100)*((100-x)/100)
= 56.16
x = 4%
Answer:B
Answer: (B) 4%
Question: The least number which should be added to 2497, so that the sum is exactly divisible by 5, 6, 4 and 3, is
(A) 3
(B) 13
(C) 23
(D) 33
(E) 43
Rationale: LCM of 5, 6, 4 and 3 = 60
On dividing 2497 by 60, the remainder is 37.
Number to be added = 60 - 37 = 23
Answer : C
Answer: (C) 23
Question: After MM students took a test, there was a total of 64% of correct answers. If the test contains 50 questions, what is the least number of questions that the next student have to get right to bring the total of correct answers to 70% ?
(A) + 20
(B) + 35
(C) + 15
(D) + 20
(E) + 45
Rationale: Denote xx as the required number of correct answers. xx must satisfy the equation 0.64∗M∗50+x/50M+50=7/10 or 350M+350=320M+10x or x=3M+35
Answer: B
Answer: (B) + 35
Question: A and B together invested Rs. 20,000 in a business. At the end of the year, out of total profit is Rs. 5,000 B's share was Rs. 2000. A's investment was
(A) s. 4,500
(B) s. 8,250
(C) s. 10,500
(D) s. 11,250
(E) s. 12,000
Rationale: A+B=20000
total profit=5000
5000-2000=3000
3000;2000=3:2
then 3*20000/5=12000
ANSWER:E
Answer: (E) s. 12,000
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 19 m
(B) 17 m
(C) 18 m
(D) 14 m
(E) 12 m
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: (B) 17 m
Question: Nine highschool teachers gather at allocacting the subject, Three subject of 3 people each will be created. How many ways are there to create these 3 teams?
(A) 45
(B) 51
(C) 90
(D) 175
(E) 280
Rationale: Arrange the 6 teachers in a straight line in 6! ways.
The first three form team 1, next three form team 2 and last three form team 3. But in each team, the boys are arranged in first, second third positions so you need to un-arrange them by dividing by 3! three times (once for each team). You get 6!/(2! * 2! * 2!)
Also, there are no distinct teams - team1, team2 and team3. You just have three teams. So you also need to un-arrange the three teams by dividing by another 3!.
You get 6!/(2! * 2! * 2!) * 2! = 45
Answer (A)
You get 6!/(2! * 2! * 2!) * 2!
Answer : A
Answer: (A) 45
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?
(A) 65
(B) 17
(C) 12
(D) 18
(E) 15
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.
Answer: C
Answer: (C) 12
Question: A company has 60 employees, of which 22 studied accounting, 15 studied finance and 14 studied marketing. Nine employees have done just two courses and only one made ​​the three courses. How many employees have no training?
(A) A)0
(B) B)9
(C) C)10
(D) D)20
(E) E)26
Rationale: Total employees=60
studied accounting=22
studied finance=15
studied marketing=14
9 employees have been double counted and one employee has been counted thrice.
Therefore employees who have received training=22+15+14-9-(2*1)
=51-11
=40
Employees with no training
=60-40
=20
Ans=D
Answer: (D) D)20
Question: The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
(A) 400
(B) 277
(C) 268
(D) 191
(E) 123
Rationale: T.D.
=	B.D. x 100
100 + (R x T)
= Rs. 420 x 100
100 + 15 x	1
3
= Rs. 420 x 100
105
= Rs. 400.
Answer: A
Answer: (A) 400
Question: If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true?
I. c - a = 2
II. abc is an even integer.
III. (a + b + c)/3 is an integer.
(A)  I only
(B)  II only
(C)  I and II only
(D)  II and III only
(E)  I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then a = c + 2, from which it follows that c - a = -2. So, I is false.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is true.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: D.
Answer: (D)  II and III only
Question: The units digit of (35)^(87) + (93)^(47) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: The units digit of powers of 3, cycles in a group of 4: {3, 9, 7, 1}
47 has the form 4k+3, so the units digit of 93^47 is 7.
The units digit if powers of 5 is always 5.
7+5 = 12, so the units digit is 2.
The answer is A.
Answer: (A) 2
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647
(A) ?= 17
(B) 18
(C) 13
(D) 10
(E) 20
Rationale: A
17
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: (A) ?= 17
Question: How many words can be formed from the letters of the word ‘DIRECTOR’
So that the vowels are always together?
(A) 360
(B) 60
(C) 36
(D) 2160
(E) 2010
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
ANSWER D 2160
Answer: (D) 2160
Question: Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for t dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?
(A) (x – s)t – sd
(B) xt – (xd – sd)
(C) xd – st
(D) (x – s)d – xt
(E) (s – t)d – xt
Rationale: Answer D:
The amount of hotdogs she can sell is x-s. The price per pound is d, so the revenue is (x-s)d. The total costs are x time t, so the profit is (x-s)d-xt.
Answer: (D) (x – s)d – xt
Question: For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 1 order of $300 ?
(A)  $1
(B)  $2
(C)  $3
(D)  $4
(E)  $5
Rationale: Total cost involved for each 75 $ shipment: 3+2 = 5 $. Thus, for two such orders = 10$
Total cost involved for a 300$ shipment: 3+3 = 6$.
The difference = 4$.
D.
Answer: (D)  $4
Question: Which is the middle even number between 9 and 23?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: (a+l)/2
here a=9,b=23=>ans=16
ANSWER:B
Answer: (B) 16
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 87
(B) 69
(C) 40
(D) 72
(E) 21
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
(A) 22
(B) 11
(C) 77
(D) 88
(E) 12
Rationale: (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: D
Answer: (D) 88
Question: If 32455 × 3145208 × K^3 is divisible by 3, which of the following could be the value of K?
(A) 27
(B) 10
(C) 34
(D) 11
(E) 9
Rationale: The first two terms are not divisible by 3, so we need the third term to be divisible by 3. The only way that (k^2) is going to be a multiple of 3 is if k is a multiple of 3. Therefore, we need the single answer that is a multiple of 3.
Answer =(A)
Answer: (A) 27
Question: A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per liter of petrol if he spends Rs. 4000 each year?
(A) Rs. 7.98
(B) Rs. 9.98
(C) Rs. 10
(D) Rs. 11
(E) Rs. 12
Rationale: Total quantity of petrol
consumed in 3 years
= 4000	+	4000	+	4000 litres
7.50	8	8.50
= 4000 2	+	1	+	2 litres
15	8	17
= 76700 litres
51
Total amount spent = Rs. (3 x 4000) = Rs. 12000.
Average cost = Rs. 12000 x 51 = Rs.	6120 = Rs. 7.98
76700	767
A)
Answer: (A) Rs. 7.98
Question: The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?
(A) p − 2pq
(B) q − pq
(C) p + q − 2pq
(D) p + q − pq
(E) p + q
Rationale: Probability of A occuring = p , Probability of A NOT occuring = 1-p
Probability of B occuring = q , Probability of B not occurring = 1-q
Probability of atleast of one of A and B occuring = 1-(1-p)(1-q) = p+q -pq
Answer:D
Answer: (D) p + q − pq
Question: Find the ones digit of 73^353
(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: The units digit of 73^353 will be the same as the units digit of 3^353.
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {3, 9, 7, 1}, ... Now, since 353=352+1=(multiple of 4)+1, then the units digit of 3^353 will be the first number in the pattern thus 3.
Answer:A.
Answer: (A) 3
Question: The markup on a box of apples is 10 percent of the cost. The markup is what percent of the selling price?
(markup = selling price - cost)
(A)  9.09 %
(B)  10%
(C)  12 1/2%
(D)  15%
(E)  16 2/3%
Rationale: MP = 0.1 CP
SP = CP + 0.1 CP = 1.1 CP
hence MP = 0.1/1.1 SP = 1/1 SP. Hence MP is 9.09 % of SP
Answer A
Answer: (A)  9.09 %
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
(A) 22
(B) 75
(C) 44
(D) 28
(E) 12
Rationale: S = (90 + 60)/2 = 75 kmph
Answer: B
Answer: (B) 75
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
(A) 32
(B) 29
(C) 30
(D) 37
(E) 12
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer:D
Answer: (D) 37
Question: The maximum number of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
(A) 91
(B) 910
(C) 1001
(D) 1911
(E) None of these
Rationale: Explanation:
Required number of students = H.C.F of 1001 and 910 = 91. Answer: A
Answer: (A) 91