mathewhe/aqua_rat huggingface dataset:
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:9
(B) 4:3
(C) 4:6
(D) 4:2
(E) 4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer: B
Answer: (B) 4:3
Question: In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 36° of the chart, how much of the Roberts’s $40,000 annual budget is dedicated to clothes and shoes?
(A) $1,500
(B) $3,000
(C) $4,500
(D) $4,000
(E) $5,400
Rationale: Given for clothes and shoes” takes up 36° of the circular chart.
Then clothes and shoes = 36/360 * 40000.
=> 4000.
IMO option D is correct answer...
Answer: (D) $4,000
Question: Ajay spends 25 per cent of his salary on house rent, 5 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajay’s income?
(A) Rs.60000
(B) Rs.80500
(C) Rs.60700
(D) Rs.70500
(E) None of these
Rationale: Explanation:
Savings = Income – expenditure
100 – (25+5+15+10) = 45%
45% of income = Rs.27000
:. Income = 27000 x 100/45 = Rs. 60000.
Answer: Option A
Answer: (A) Rs.60000
Question: A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . How many feet does the squirrel travels if the post is 18 feet tall and 3 feet in circumference?
(A) 10 feet
(B) 12 feet
(C) 13 feet
(D) 15 feet
(E) 18 feet
Rationale: total circuit=18/3=6
total feet squirrel travels=6*3=18 feet
ANSWER:E
Answer: (E) 18 feet
Question: During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.7 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
(A) $2.5
(B) $2.55
(C) $1.53
(D) $3.25
(E) $3.0
Rationale: finding the Harmonic mean here.
HM = 4/(1/12 + 1/14 + 1/17 + 1/21) = 15.31
The calculation is the same either way.
C
Answer: (C) $1.53
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
(A) 5/7
(B) 3/4
(C) 7/18
(D) 5/17
(E) 7/9
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Ans: C
Answer: (C) 7/18
Question: A can do a work in 4 days. B can do the same work in 6days. Both A&B together will finish the work and they got $1000 from that work. Find their shares?
(A) 600,400
(B) 500,500
(C) 300,700
(D) 800,200
(E) 550,450
Rationale: Ratio of their works A:B = 4:6
Ratio of their wages A:B = 3:2
A's share = (3/5)1000 = 600
B's share = (2/5)1000 = 400
correct option is A
Answer: (A) 600,400
Question: Find the odd man out. 742, 743, 633, 853, 871, 990, 532
(A) 532
(B) 742
(C) 990
(D) 633
(E) 871
Rationale: In all numbers except 742, the difference of third and first digit is the middle digit.
Answer is B
Answer: (B) 742
Question: A man sells a horse for Rs.800 and loss something, if he had sold it for Rs.820, his gain would have been trible the former loss. Find the cost price of the horse?
(A) 605
(B) 905
(C) 815
(D) 805
(E) 705
Rationale: CP = SP + 1CP = SP - g
800 + x = 820 - 3x
4x = 20 => x = 5
CP = 800 + 5 = 805
Answer: D
Answer: (D) 805
Question: The average weight of 30 boys sitting in a bus had some value. A new person added to them whose weight was 40 kg only. Due to his arrival, the average weight of all the boys decreased by 2 kg. Find the average weight of first 30 boys?
(A) 150
(B) 122
(C) 30
(D) 120
(E) 102
Rationale: 30x + 40 = 31(x â€“ 2)
x = 102
E
Answer: (E) 102
Question: Dacid obtained 96, 98, 99, 100 and 98 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 79
(B) 99
(C) 88
(D) 88
(E) 98
Rationale: Average = (96+98+ 99+100+98)/5
= 491/5 = 98.
Answer:E
Answer: (E) 98
Question: Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 49 hours and 64 hours respectively. The ratio of their speeds is
(A) 2 : 3
(B) 5 : 9
(C) 6 : 7
(D) 8 : 11
(E) None
Rationale: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √64 : √49
= 8 : 7.
Answer E
Answer: (E) None
Question: The speed of a car is 90 km in the first hour and 80 km in the second hour. What is the average speed of the car?
(A) 12
(B) 75
(C) 85
(D) 54
(E) 15
Rationale: S = (90 + 80)/2
= 85 kmph
Answer: C
Answer: (C) 85
Question: How many pieces of 85 cm length can be cut from a rod of 34 meters long?
(A) 50
(B) 40
(C) 30
(D) 20
(E) 10
Rationale: Number of pieces = 3400/85 = 40
The answer is B.
Answer: (B) 40
Question: Reema took a loan of Rs 800 with simple interest for as many years as the rate of interest. If she paid Rs. 632 as interest at the end of the loan period, what was the rate of interest.
(A) 8.62%
(B) 8.88%
(C) 8.32%
(D) 8%
(E) 9%
Rationale: Explanation:
Let rate = R% then Time = R years.
=>800∗R∗R /100=632
=>R2=79
=>R=8.88%
Option B
Answer: (B) 8.88%
Question: In the youth summer village there are 175 people, 100 of them are not working,75 of them have families and 125 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
(A) 70
(B) 75
(C) 85
(D) 80
(E) 100
Rationale: total =175
not working =100
having family=75
like to sing in shower = 125
working=175-100=75
not having family = 175-75=100
like to sing in shower = 100
largest possible number is the lowest possible among the above
Thus 75
B
Answer: (B) 75
Question: By selling 18 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 35%?
(A) 11
(B) 13
(C) 15
(D) 18
(E) 12
Rationale: 90% --- 18135% --- ?90/135 * 18 = 12Answer: E
Answer: (E) 12
Question: If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain?
(A) 25%
(B) 28%
(C) 29%
(D) 50%
(E) 55%
Rationale: cp=1*12=12
sp=1.2*15=18
gain=sp-cp=6
gain%=(6/12)*100=50%
ANSWER:D
Answer: (D) 50%
Question: A gardener sells 100 metres of fencing for Rs. 7500 at a loss of Rs. 3 per metre. Find his cost price for one metre of fencing?
(A) 54
(B) 67
(C) 62
(D) 78
(E) 72
Rationale: SP per metre = 7500/100 = Rs. 75 Loss per metre = Rs. 3 CP per metre = 75 + 3= Rs. 78Answer: D
Answer: (D) 78
Question: In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. What is the length of the garden?
(A) 30 m
(B) 28 m
(C) 26 m
(D) 24 m
(E) 22 m
Rationale: Explanation :
Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length
Also, 1 meter is left from all sides of the boundary of the garden.
Hence, length of the garden = (11 × 2) + 1 + 1 = 24 meter
Answer :D
Answer: (D) 24 m
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 281
(B) 284
(C) 288
(D) 255
(E) 122
Rationale: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2
Answer: B
Answer: (B) 284
Question: If 45% of z is 39% of y and y is 75% of x, what percent of x is z?
(A) 200
(B) 160
(C) 100
(D) 65
(E) 50
Rationale: (45/100)z = (39/100)y
and y = (75/100)x i.e. y = (3/4)x
i.e. (45/100)z = (39/100)*(3/4)x
i.e. z = (39*3)x/(45*4)
i.e. z = (0.65)x = (65/100)x
i.e. z is 65% of x
Answer: Option D
Answer: (D) 65
Question: A fort had provision of food for 150 men for 45 days. After 15 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 29	1/5
(B) 37	1/4
(C) 42
(D) 54
(E) 36
Rationale: we have food for 150 men for 45 days.
After 15 days food left for 150 men for 30 days.
so
150 : 30
now we have 125 men and x days
125 : 150 :: 30 : x
x = (150*30)/125 = 36 days.
ANSWER:E
Answer: (E) 36
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.9
(B) 1.5
(C) 1.7
(D) 1.4
(E) 1.1
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer:B
Answer: (B) 1.5
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 54
(B) 76
(C) 87
(D) 80
(E) 82
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer: D
Answer: (D) 80
Question: One millisecond is 0.001 of a second. The costs for a single run of a computer program are $1.07 for operating-system overhead, $0.023 per millisecond of computer time, and $5.35 for the mounting of a data tape. What is the total of these three costs for 1 run of a program that requires 1.5 seconds of computer time ?
(A)  $7.15
(B)  $8.87
(C)  $28.96
(D)  $35.57
(E)  $40.92
Rationale: Operating system overhead for 1 run = 1.07 $
Mounting of data tape = 5.35$
Cost per 1 millisecond of computer time = .023 $
Total cost of 1 run of a program that requires 1.5 seconds of computer time
= 1.07 + (.023*1500) + 5.35
=1.07 + 34.5 + 5.35
= 40.92$
Answer E
Answer: (E)  $40.92
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 28 sec
(B) 19 sec
(C) 48 sec
(D) 18 sec
(E) 38 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125
= 48 sec.
Answer: C
Answer: (C) 48 sec
Question: 36 people attend a party. 4 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 10
Rationale: Total people = number of men + number of women
36 = 4 + number of married men + 22
number of married men = 36 - 22-4 = 10 men
ANSWER:E
Answer: (E) 10
Question: In a stack of cards, 8 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 1/2. What is the number of cards in the stack?
(A) 10
(B) 11
(C) 12
(D) 15
(E) 18
Rationale: This question can be solved by TESTing THE ANSWERS.
We're told that we have 9 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 1/2. We're asked for the TOTAL number of cards.
Normally, when TESTing THE ANSWERS, we should start with either B or D. Answer B looks easier, so let's start there.
Answer B: 11 total cards
With 11 total cards, and 8 blue cards, the probability of pulling two blue cards is...
(8/11)(7/10) = 56/110~0.509
Since 1/2 = 0.5, this is clearly the answer.
B
Answer: (B) 11
Question: Machine P and Machine Q are each used to manufacture 770 sprockets. It takes Machine P 10 hours longer to produce 770 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
770/x = 770/1.1x + 10
1.1(770) = 770 + 11x
11x = 77
x = 7
The answer is C.
Answer: (C) 7
Question: In a certain accounting class of 100 students, 70% of the students took the final exam on the assigned day while the rest of the students took the exam on a make-up date. If the students on the assigned day had an average score of 60%, and the students on the make-up date had an average score of 90%, what was the average score for the entire class?
(A) 65%
(B) 67%
(C) 69%
(D) 72%
(E) 75%
Rationale: 70% of the class scored 60% and 30% of the class scored 90%.
The difference between 60% and 90% is 30%.
The average will be 60% + 0.3(30%) = 69%.
The answer is C.
Answer: (C) 69%
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20
Rationale: Explanation:
Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5) = 4/5
20x = 4(3x+5)
8x = 20
x = 2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
Answer: A
Answer: (A) 10
Question: A man spends 10% of his income on food and 80% of the remaining income on clothing. If he still has a balance of Rs. 180. what is his total income?
(A) 1100
(B) 1000
(C) 804
(D) 934
(E) 230
Rationale: Total Income = 180 x 100100âˆ’10Ã—100100âˆ’80
= 180 x 10090Ã—10020 = Rs. 1000
correct answer - B
Answer: (B) 1000
Question: An analyst will recommend a combination of 1 industrial stocks, 1 transportation stocks, and 1 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 3 stocks are possible?
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
Rationale: 5C1 * 4C1 * 3C1 = 5*4*3 = 60.
Answer: C
Answer: (C) 60
Question: If x is an even integer, which of the following is an odd integer?
(A) 3x + 2
(B) 7x
(C) 8x +5
(D) x^2
(E) x^3
Rationale: Soln:-
A) 3x + 2
3*Even +2
= Even +Even = Even
(B) 7x
7*Even= Even
(C) 8x +5
8*Even +5
= Even +5
= Odd
(D) x^2
= Even * Even = Even
(E) x^3
= Even *Even * Even
= Even
Answer C
Answer: (C) 8x +5
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 24 times, A has killed:
(A) 27 birds
(B) 72 birds
(C) 30 birds
(D) 80 birds
(E) 20 birds
Rationale: Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of	(5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x	=(3/16)x
3x/16= 27 or x =(24 x 16)/3= 128.
Birds killed by A =(5x/24)	=(5/24*128)= 27.
Answer is A
Answer: (A) 27 birds
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 10
(B) 15
(C) 18
(D) 36
(E) 72
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
2x =(120+120)/12
2x = 20
x = 10.
Speed of each train = 10 m/sec = 10x18/5=36 km/hr
answer :D
Answer: (D) 36
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 4 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
(A) 12
(B) 19
(C) 72
(D) 180
(E) 720
Rationale: 4C3 * 4C2 * 3C2 = 4*6*3 = 72.
Answer: C
Answer: (C) 72
Question: A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is
(A) 4 hours 95 minutes
(B) 4 hours 49 minutes
(C) 4 hours 45 minutes
(D) 4 hours 75 minutes
(E) 7 hours 45 minutes
Rationale: Explanation:
Time taken in walking both ways = 7 hours 45 minutes --------(i)
Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)
By equation (ii)*2 -(i), we have
Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes
Answer: C) 4 hours 45 minutes
Answer: (C) 4 hours 45 minutes
Question: In the formula V = 1/(5r)^2, if r is halved, then V is multiplied by
(A) 64
(B) 8
(C) 1
(D) 1/8
(E) 4
Rationale: Say r=2 => V1 = 1/100
when r=1; V2 = 1/25
V2 = 4*V1.
Answer=E=4
Answer: (E) 4
Question: The mean of set Y does not exceed mean of any subset of set Y. Which of the following must be true about set Y?
I. Set Y contains only one element
II. All elements in set Y are equal
III. The median of set Y equals the mean of set Y
(A) of the three qualities is necessary
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: The only necessary condition seems to be II.
If all nos are equal.... them mean of any subset is the same.
I is obviously ruled out ( e.g. Y = {1,1,1} )
But III, what about 3?
It is not necessary in itself, rather, is automatically implied by II.
All sets that satsify II satisfy III=D
Answer: (D) II and III only
Question: 2, 1, (1/2), (1/4), ?
(A) 1/3
(B) 1/9
(C) 1/5
(D) 1/8
(E) 1/4
Rationale: D
1/8
This is a simple division series; each number is one-half of the previous number.
Answer: (D) 1/8
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
(A) 22
(B) 29
(C) 20
(D) 11
(E) 13
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
«1234.Answer:C
Answer: (C) 20
Question: The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be :-
(A) 101 : 88
(B) 87 : 100
(C) 110 : 111
(D) 85 : 98
(E) 97 : 84
Rationale: Explanation :
Going through the given options,
option 1 :- 101 : 88 = > 189 . [ Divisible by 3 ]
option 2 :- 87 : 100 => 187 . [ Divisible by 11 ]
option 3 :- 85 : 98 => 183 . [ Divisible by 3 ]
option 4 :- 97: 84 = > 181 . [ Prime number ]
Hence, only 181 is the prime number i.e the total number of employee in the company and the required ratio is 97 : 84.
Answer : E
Answer: (E) 97 : 84
Question: Each child has 2 pencils and 13 Skittles. If there are 6 children, how many pencils are there in total?
(A) 16
(B) 12
(C) 18
(D) 22
(E) 08
Rationale: 2*6=12.Answer is B.
Answer: (B) 12
Question: An engineering student has to secure 36% marks to pass. He gets 130 marks and fails by 14 marks. The maximum No. of marks obtained by him is?
(A) 300
(B) 400
(C) 500
(D) 600
(E) 700
Rationale: 130
14
-------
361------ 144
100%------? => 400
ANSWER:B
Answer: (B) 400
Question: Marts income is 60 percent more than Tims income and Tims income is 60 percent less than Juans income. What percentage of Juans income is Marts income
(A) 124%
(B) b) 64 %
(C) c) 96 %
(D) d) 80 %
(E) e) 64 %
Rationale: M = (160/100)T
T = (40/100)J
=> M = (64/100)J
Answer B.
Answer: (B) b) 64 %
Question: What is the 99th digit after the decimal point in the decimal expansion of 2/9 + 3/11?
(A) 1
(B) 2
(C) 4
(D) 7
(E) 9
Rationale: 2/9= 0.22222.... ==> 99th digit is 2
3/11 = 0.27272727.... ==> Every odd digit is 2. So, 99th digit will be 2.
2 +2 = 4
ANSWER:C
Answer: (C) 4
Question: If A is an even integer and q is an odd integer, which of the following must be an odd integer?
(A) A/q
(B) Aq
(C) 2A+q
(D) 2(A+q)
(E) 3A/q
Rationale: this is a must question:
A. A/q
can be a non-integer
B. Aq
always even
C. 2A+q
2A = even -> even+odd = odd
D. 2(A+q)
always even - A+q = odd *2 -> even
E. 3A/q
might be a non integer.
C
Answer: (C) 2A+q
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 29
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: The time it took car P to travel 900 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
(A) 40
(B) 54
(C) 62
(D) 70
(E) 80
Rationale: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(900/x)-(900/(x+10))=2
Solving for x=62 miles\hr.
C
Answer: (C) 62
Question: If a truck is traveling at a constant rate of 216 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters)
(A) 10
(B) 24
(C) 30
(D) 36
(E) 48
Rationale: Speed = 216 Km/hr => 216,000 m/hr
In one minute => 216000/60 = 3600 meters
In one sec => 3600/60 = 60 meters
Time = Total distance need to be covered / Avg. speed
=> 600/ 60 = 10 and hence the Answer : A
Answer: (A) 10
Question: A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is
(A) 22030
(B) 220030
(C) 23030
(D) 24030
(E) 25030
Rationale: Explanation:
(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
Answer: Option B
Answer: (B) 220030
Question: In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-two students are registered for Math, and thirty-five students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
(A) 13
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: A U B U C = A + B + C - AB-BC-AC + ABC
68 = 25 + 22+ 35 -AB-BC-AC +3 => AB+BC+AC = 17
Exactly Two classes = AB+BC+AC - 3ABC = 17 -3*3 = 8
Hence D
Answer: (D) 8
Question: Sum of the squares of three numbers is 579 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 29
(E) 28
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 579 + 2* 131
a + b + c = √841 = 29
D
Answer: (D) 29
Question: If the sides of a triangle are 52 cm, 48 cm and 20 cm, what is its area?
(A) 480 cm2
(B) 765 cm2
(C) 216 cm2
(D) 197 cm2
(E) 275 cm2
Rationale: The triangle with sides 52 cm, 48 cm and 20 cm is right angled, where the hypotenuse is 52 cm.
Area of the triangle
= 1/2 * 48 * 20
= 480 cm2
Answer: A
Answer: (A) 480 cm2
Question: If a and b are integer numbers which is greater then one, which of the following CANNOT be the value of ab?
(A) 9
(B) 14
(C) 21
(D) 23
(E) 25
Rationale: 23 is a prime number itself and so cannot be multiple of two prime numbers which is greater then one..
ans D
Answer: (D) 23
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
(A) 2 hours
(B) 3 hours
(C) 4 hours
(D) 5 hours
(E) 6 hours
Rationale: Speed downstream = (13 + 4) km/hr = 17 km/hr.
Time taken to travel 68 km downstream =68/17hrs = 4 hrs
Answer: Option C
Answer: (C) 4 hours
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 40 per kg. His profit percent is:
(A) No profit, no loss
(B) 5%
(C) 8%
(D) 40%
(E) None of these
Rationale: Explanation :
C.P. of 56 kg rice = (26 * 20 + 30 * 36) Rs. = (520 + 1080) Rs. = 1600 Rs.
S.P. of 56 kg rice = (56 * 40) Rs. = 2240 Rs.
Profit % = (2240−1600/1600∗100)% = 40%
Answer : D
Answer: (D) 40%
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 24 candies so that now Rebecca has four times as many candies as Tina has. Rebecca has now how many candies?
(A) 36
(B) 64
(C) 54
(D) 55
(E) 60
Rationale: T = R
T - 24 ;R + 24
R + 24 = 4 ( T - 24 )
R + 24 =4T - 96
R - 4T = - 120
We knowR = T, so
R - 4T = - 120
Or, R - 4R = -120
Or, - 3R = - 120
Or, R = 40( This is the initital no of Candies Rebecca had)
Candles now she possesses is 40 + 24 = 64
So , Rebecca now has 64 candies.
Answer will be (B) 64
Answer: (B) 64