mathewhe/aqua_rat huggingface dataset:
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
(A) 6%
(B) 5%
(C) 12%
(D) 10%
(E) 8%
Rationale: S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 5 years = Rs.	2205/3x 5= Rs. 3675
Principal = Rs. (9800 - 3675) = Rs. 6125.
Hence, rate =(100 x 3675)/(6125 x 5)%	= 12%
answer : C
Answer: (C) 12%
Question: A sum amount to Rs.1344 in two years at simple interest. What will be the compound interest on the same sum at the same rate of interest for the same period?
(A) 10.28%
(B) 10.35%
(C) 10.25%
(D) 14.25%
(E) 11.25%
Rationale: 100
5 ---- I
5
0.25 --- II
-----------
10.25%
Answer: C
Answer: (C) 10.25%
Question: A and B complete a job in 6 days. A alone can do the job in 24 days. If B works alone, how many days will it take to complete the job?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: The rate of A and B is 1/6
A's rate is 1/24
B's rate is 1/6 - 1/24 = 1/8
B can complete the job in 8 days.
The answer is A.
Answer: (A) 8
Question: How many odd three-digit integers greater than 800 are there such that all their digits are different?
(A) 40
(B) 60
(C) 72
(D) 81
(E) 104
Rationale: In the range 800 - 900:
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*5*8 = 40.
In the range 900 - 999:
1 choice for the first digit: 9;
4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*4*8 = 32.
Total: 40+32 = 72.
Answer: C
Answer: (C) 72
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 12 weavers in 12 days?
(A) 12
(B) 18
(C) 24
(D) 30
(E) 36
Rationale: 1 weaver can weave 1 mat in 4 days.
12 weavers can weave 12 mats in 4 days.
12 weavers can weave 36 mats in 12 days.
The answer is E.
Answer: (E) 36
Question: For 1rs 1p interest
wat will be for 2000rs?
(A) 45Rs
(B) 50Rs
(C) 20Rs
(D) 30Rs
(E) 48Rs
Rationale: For 1rs , 1p interest
for 2000rs, x
x= 2000/1 * 1p ==> 2000 paise
To express in rs, 2000/100 = 20rs
ANSWER:C
Answer: (C) 20Rs
Question: If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is:
(A) 8
(B) 9
(C) 12
(D) 14
(E) 13
Rationale: Let the numbers be x and y
Then x2-y2=39
And x-y=3
We get x+y=13
Solving x-y=3, x+y=13
X=8, y=5
Larger number 8
ANSWER A 8
Answer: (A) 8
Question: 10+19
(A) 29
(B) 13
(C) 28
(D) 6
(E) 2
Rationale: A
Answer: (A) 29
Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
(A) 2:5
(B) 3:5
(C) 4:5
(D) 6:7
(E) 7:8
Rationale: Explanation:
Let the third number be x.
Then, first number = 120% of x =120X/100=6X/5
Second number = 150% of x =150X/100=3X/2
Ratio of first two numbers =(6X/5-3X/2)= 12x : 15x = 4 : 5.
ANSWER IS C
Answer: (C) 4:5
Question: Ashle and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashle and Vinnie will be chosen?
(A) 1/10
(B) 3/28
(C) 2/9
(D) 1/4
(E) 1/2
Rationale: I did slightly different and hence obviously ended up with the answer 2/9.
I assumed that because Ashle and Winni have to be chosen, the remaining selection is 3 people from 8.
8C3/10C5= 2/9. Option C.
Answer: (C) 2/9
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 35%, then find the population of city atthe end of the year 2007
(A) 976374
(B) 979923
(C) 1009125
(D) 2356677
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 35/100)
= 1009125
C
Answer: (C) 1009125
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 1:3
(B) 2:1
(C) 3:1
(D) 4:1
(E) None of these
Rationale: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1
ANSWER:C
Answer: (C) 3:1
Question: Abhijit started a business investing 70000. Anuja joined him after six months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, two years after Abhijit started the business?
(A) 4 : 9 : 4
(B) 5 : 9 : 5
(C) 8 : 9 : 8
(D) 7: 9 : 7
(E) 3 : 9 : 4
Rationale: Ratio of their investments
= 70 × 24 : 105 × 18: 140 × 12 = 8 : 9 : 8
Answer C
Answer: (C) 8 : 9 : 8
Question: The population of a bacteria colony doubles every day. If it was started 8 days ago with 4 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 512
(B) 768
(C) 1024
(D) 131072
(E) 409600
Rationale: 4^8(2) = 131072
The answer is D.
Answer: (D) 131072
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
(A) 1/113
(B) 2/213
(C) 1/216
(D) 2/215
(E) 3/211
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: (C) 1/216
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/7%
(B) 33 0/3%
(C) 33 1/3%
(D) 37 1/3%
(E) 32 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3%
Question: The average age of a group of 10 students is 14 years. If 5 more students join the group, the average age rises by 1 year. The average age of the new students is:
(A) 22
(B) 38
(C) 11
(D) 17
(E) 91
Rationale: Explanation:
Total age of the 10 students = 10 × 14 = 140
Total age of 15 students including the newly joined 5 students = 15 × 15 = 225
Total age of the new students = 225 − 140 = 85
Average age = 85/5 = 17 years
Answer: D
Answer: (D) 17
Question: A big container is 30% full with water. If 18 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
(A) 36 liters
(B) 40 liters
(C) 45 liters
(D) 54 liters
(E) 60 liters
Rationale: A big container is 30% full with water and after 18 liters of water is added, the container becomes 75% full. Hence these 18 liters account for 45% of the container, which means that the capacity of it is 18/0.45=40 liters.
OR: if the capacity of the container is x liters then: 0.3x+18=0.75x --> x=40 liters.
Answer: B.
Answer: (B) 40 liters
Question: The average of first 10 odd numbers is?
(A) 44
(B) 10
(C) 99
(D) 77
(E) 62
Rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer: B
Answer: (B) 10
Question: There are 24 students in Chadâ€™s class. He brought 26 cookies to pass out
for his birthday. How many cookies will each student get? Will there be
any cookies left over?
(A) 1-9
(B) 1-7
(C) 2-8
(D) 1-2
(E) 3-10
Rationale: 26/24 = 1 R 2 Chad will give each student 1 cookie and there will be 2
cookies left over
correct answer D
Answer: (D) 1-2
Question: if a@b = a * b^(1/2) then 4@9 = ?
self made
(A) 12
(B) 6
(C) 3
(D) 8
(E) 4
Rationale: a@b = a * b^(1/2)
4@9 = 4*9^(1/2) = 4*3 = 12
Correct Option: A
Answer: (A) 12
Question: If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2k2k is a factor of n?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20
Rationale: There are 10 numbers divisible by 2
There are 5 numbers divisible by 4
There are 2 numbers divisible by 8
There is 1 number divisible by 16.
Hence the total number of 2’s in 20! are 10+5+2+1=18
ANSWER:D
Answer: (D) 18
Question: A batch of widgets costs p + 15 dollars for a company to produce and each batch sells for p(11 – p) dollars. For which of the following values of p does the company make a profit?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: to make profit, selling price should be greater than cost price
p(11-p) - p-15 >0
=> p^2-10*p+15<0
hence p=8
A
Answer: (A) 8
Question: A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 3/4 of the current inventory is Speedsters, of which 3/5 are convertibles. If there are 30 vehicles that are not Speedsters, how many Speedster convertibles are there?
(A) 30
(B) 54
(C) 60
(D) 70
(E) 90
Rationale: Total Vehicle = 3/4 of speedster + 1/4 of others.
Speedster convertibles = 3/4 total vehicle * 3/5
Given : 1/4 constitutes 30 Vehicles. hence 3/4 constitutes 90
Speedster convertibls = 90 * 3/5 = 54
B
Answer: (B) 54
Question: A train passes a man standing on the platform. If the train is 150 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 Â½ sec
(B) 6 Â½ sec
(C) 9 Â½ sec
(D) 8 Â½ sec
(E) 7 Â½ sec
Rationale: E
7 Â½ sec
S = 72 * 5/18 = 20 mps
T = 150/20 = 7 Â½ sec
Answer: (E) 7 Â½ sec
Question: A and B started a business by investing Rs.6000 and Rs. 8000, respectively. After 6 months, B withdrew half of his investment. If after one year they get a profit of Rs.4000 then what is B's share?
(A) Rs.2000
(B) Rs.1000
(C) Rs.3000
(D) Rs.5000
(E) None of the above
Rationale: B's share=2000
6000*12 :8000*6+4000*6=1:1
2 parts=4000
then 1 part=2000
ANSWER:A
Answer: (A) Rs.2000
Question: The average score of a cricketer in 2 matches is 30 and in other 3 matches is 40. Then find the average score in all the 5 matches?
(A) 25
(B) 27
(C) 30
(D) 35
(E) 36
Rationale: Average in 5 matches = (2*30 + 3*40)/2+3 = 60+120 / 5 = 180/5 = 36
Answer is E
Answer: (E) 36
Question: find missing number
-5 1 -11 23 29 17 -20 -14,?
(A) -26
(B) -27
(C) -28
(D) -29
(E) -30
Rationale: (-5)+6 = 1 23+6=29 (-20)+6=(-14)
1-12= -11 29-12=17 (-14)-12=(-26)
ans is -26
ANSWER:A
Answer: (A) -26
Question: A vantakes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60 Kmph
(B) 61 Kmph
(C) 62 Kmph
(D) 64 Kmph
(E) 66 Kmph
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
A)
Answer: (A) 60 Kmph
Question: If a/b = 5/4, Then (4a + 3b) / (4a - 3b) = ?
(A) 7
(B) 6
(C) 3
(D) 5
(E) 4
Rationale: Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (4a + 3b) / (4a - 3b) = (4a/b + 3) / (4a/b - 3)
Since a/b = 5/4
this implies that
=[(4*5)/4 +3]/[(4*5)/4 -3)]
= (5+ 3) / (5 - 3)
= 4
Option: E
Answer: (E) 4
Question: (0.756 x 3/4) terms of rate percent is equivalent to ?
(A) 18.9%
(B) 37.8%
(C) 56.7%
(D) 75%
(E) None
Rationale: Answer
(0.756 x 3/4) = (756/1000) x (3/4) x 100 % = 56.7%
Correct Option: C
Answer: (C) 56.7%
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
(A) 23.53 cm
(B) 23.52 cm
(C) 23.51 cm
(D) 23.37 cm
(E) 23.57 cm
Rationale: Explanation:
Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places
Answer: Option E
Answer: (E) 23.57 cm
Question: On dividing 15698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?
(A) 743
(B) 154
(C) 852
(D) 176
(E) 785
Rationale: Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(15698-14)/89=176
Answer(D)
Answer: (D) 176
Question: How many days are there in x weeks x days?
(A) 8x
(B) 14x
(C) 7
(D) 7x
(E) 8
Rationale: x weeks x days = (7x + x) days = 8x days.
Answer is A.
Answer: (A) 8x
Question: If b = 4p, where p is a prime number greater than 2, how many different positive even divisors does b have, including b ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: b=4p
since b = 4p thenevendivisors are:
4p/4p= 1
4p/2p= 2
4p/4= p
4p/2= 2p
so the answer is (C)
Answer: (C)  Four
Question: In a class there are 10 boys and 15 girls. In how many ways can a boy and a girl be selected?
(A) 150
(B) 500
(C) 600
(D) 530
(E) 630
Rationale: Explanation:
We can select one boy from 10 boys in 10 ways.
We select one girl from 15 girls in 15 ways
We select a boy and girl in 10 * 15 ways i.e., = 150 ways.
Answer: Option A
Answer: (A) 150
Question: Average of 10 numbers is zero. At most how many numbers may be greater than zero
(A) 0
(B) 1
(C) 5
(D) 9
(E) 10
Rationale: Option D
Answer: (D) 9
Question: The area of a square is equal to five times the area of a rectangle of dimensions 32 cm *10 cm. What is the perimeter of the square?
(A) 289 cm
(B) 160 cm
(C) 829 cm
(D) 288 cm
(E) 289 cm
Rationale: Area of the square = s * s
= 5(32 * 10)= 1600
=> s =40
= 40 cm
Perimeter of the square
= 4 * 40
= 160 cm.
Answer: B
Answer: (B) 160 cm
Question: The average weight of 10 men is increased by 1 ½ kg when one of the men who weighs 58 kg is replaced by a new man. What is the weight of the new man?
(A)  80 kg
(B)  73 kg
(C)  70 kg
(D)  75 kg
(E)  85 kg
Rationale: Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 58+10x1.5
58+15=73 Kg
Ans: 'B'
Answer: (B)  73 kg
Question: A cycle is bought for Rs.900 and sold for Rs.1160, find the gain percent?
(A) 11
(B) 29
(C) 99
(D) 77
(E) 18
Rationale: 900 ---- 260
100 ---- ? => 29%
Answer: B
Answer: (B) 29
Question: The ratio of male to female in a class is 2:7. the career preference of the students in the class are to be represented in a circle graph. If the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one third of the males and two-third of the females in the class?
(A) a)160 degree
(B) b) 168 degree
(C) c)191 degree
(D) d)192 degree
(E) e)213 degree
Rationale: here is my approach => males => 2x and females =7x => total =9x
now 9x=> 360
therefore 16x/3 => 213 degree .
P.S => 16x/3 is nothing but total number of students with the given preference
Answer E
Answer: (E) e)213 degree
Question: Two trains 100 meters and 120 meters long are running in the same direction with speeds of 72 km/hr, 54 km/hr In how much time will the first train cross the second
(A) 36 sec
(B) 40 sec
(C) 44 sec
(D) 46 sec
(E) 48 sec
Rationale: Explanation:
Relative speed of the trains = (72 - 54) km/hr = 18 km/hr
= (18 × 5/18) m/sec = 5 m/sec.
Time taken by the trains to cross each other
= Time taken to cover (100 + 120) m at 5 m /sec = (220/5) sec = 44 sec.
Answer: Option C
Answer: (C) 44 sec
Question: What is the remainder when 135^77 is divided by 7 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: (15^77 * 9^77)/7;
(15^77)/7 * (9^77)/7;
1 * 2^77/7;
((2^3)^25 * 2^2)/7;
1 * 4 = 4
ANSWER:E
Answer: (E) 4
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
(A) 1 hour 10 minutes
(B) 1 hour 82 minutes
(C) 2 hour 12 minutes
(D) 1 hour 12 minutes
(E) 1 hour 62 minutes
Rationale: New speed = 6/7 of usual speed
Speed and time are inversely proportional.
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time - usual time = 12 minutes
=> 1/6 of usual time = 12 minutes
=> usual time = 12 x 6 = 72 minutes = 1 hour 12 minutes
Answer :D
Answer: (D) 1 hour 12 minutes
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 76 kmph
(B) 10 kmph
(C) 29 kmph
(D) 25 kmph
(E) 16 kmph
Rationale: Speed of the boat in still water
= (60+80)/2 = 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:B
Answer: (B) 10 kmph
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
(A) 1/7
(B) 1/6
(C) 2/3
(D) 2/5
(E) 3/5
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
B)
Answer: (B) 1/6
Question: A man can swim in still water at 3 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1
(B) 4.2
(C) 5.3
(D) 1.5
(E) 5.2
Rationale: M = 3
S = x
DS = 3 + x
US = 3 - x
3 + x = (3 - x)2
3 + x = 6 -2x
3x = 3
x = 1
Answer:A
Answer: (A) 1
Question: How many positive integers less than 130 are there such that they are multiples of 13 or multiples of 12 but not both?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 28
Rationale: for 13: 13...130=13*10
for 12: 12...130 =12*10
but there is one integer 13*12. so
N=(10)+(10)=20
C
Answer: (C) 20
Question: Find the lowest common multiple of 24, 30 and 40.
(A) 360
(B) 420
(C) 120
(D) 320
(E) 280
Rationale: LCM=2*2*2*3*5=120.
Answer is C
Answer: (C) 120
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
(A) 54.48
(B) 54.68
(C) 54.6
(D) 54.58
(E) 54.9
Rationale: Explanation:
(55×50)+(60×55)+(45×60)/55+60+45
8750/160=54.68
Answer: Option B
Answer: (B) 54.68
Question: Find the LCM of 23,46,827
(A) 227
(B) 83
(C) 23
(D) 827
(E) None of these
Rationale: Explanation:
Whenever we have to solve this sort of question, remember the formula.
LCM = \\begin{aligned} \\frac{HCF of Denominators}{LCM of Numerators} \\end{aligned}
So answers will be option 2,
Please also give attention to the difference in formula of HCF and LCM
Answer: Option B
Answer: (B) 83
Question: A man can row 3 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 2.9
(B) 2.8
(C) 2.4
(D) 2.8
(E) 2.2
Rationale: M = 3
S = 1.2
DS = 3.6
US = 1.8
x/3.6 + x/1.8 = 1
x = 1.2
D = 1.2 * 2 = 2.4
Answer:C
Answer: (C) 2.4
Question: Solution X is 20% chemical A and 80% chemical B by volume; Solution Y is 30% chemical A and 70% chemical B. If a mixture of X and Y is 22% chemical A, what percent of the mixture is Solution X?
(A) 20%
(B) 44%
(C) 50%
(D) 80 percent
(E) 90%
Rationale: 22% of chemical A in X+Y grams of solution comes from 20% chemical A in solution X and 30% chemical A in solution Y, thus:
0.22(X + Y) = 0.2X + 0.3Y --> X = 4Y --> X/(X+Y)=4/5=0.8.
Answer: D.
Answer: (D) 80 percent
Question: Pipe A and pipe B fill water into a tank of capacity 2000 litres, at a rate of 200 l/min and 50 l/min. Pipe C drains at a rate of 25 l/min. Pipe A is open for 1 min and closed, then pipe B is open for 2 min and closed. Further the pipe c is opened and drained for another 2 min. This process is repeated until the tank is filled. How long will it take to fill the tank?
(A) 14 min
(B) 18 min
(C) 25 min
(D) 32 min
(E) 40 min
Rationale: tank capacity: 2000 L,
1st- 200 l/min for 1 min, volume filled: 200 L
2nd- 100 l/min for 2 min, volume filled: 100 L
3rd (water draining) : 25 l/min*2 : 50 L
total : (200+100)-50 =250 L filled for 1 cycle
number of 250 in 2000 L tank :2000/250 = 8
time taken to fill: 8* total time= 8*5 = 40 (option E)
Answer: (E) 40 min
Question: 2 pipes P1 and P2 together can fill a tank in 6 hrs and P3 alone can fill the tank in 10 hrs if they work together what is the time taken to fill the tank?
(A) 7/4 hrs
(B) 9/4 hrs
(C) 13/4 hrs
(D) 15/4 hrs
(E) 16/4 hrs
Rationale: Explanation:
(P1 +P2) can fill 1/6 tank in 1 hr
P3 can fill 1/10 tank in 1 hr
(P1+P2+P3) can fill tank (1/6+1/10)= 4/15
=>3 pipes can fill the tank in 15/4 hrs
Answer: Option D
Answer: (D) 15/4 hrs
Question: Three candidates contested an election and received 561, 716 and 1111votes respectively. What percentage of the total votes did the winning candidate got?
(A) 46%
(B) 35%
(C) 50%
(D) 25%
(E) 62%
Rationale: Total number of votes polled = (561 + 716 + 1111) = 2388
Required percentage = 1111/2388 * 100 = 46% (approximately)
Answer: Option A
Answer: (A) 46%
Question: The total of the ages of Jayant, Prem and Saransh is 75 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Jayant?
(A) 20 years
(B) 32 years
(C) 34 years
(D) 38 years
(E) None
Rationale: Solution
Let the ages of Jayant, Prem and Saransh 10 years ago be 2x, 3x and 4x years respectively. Then,
(2x + 10)+(3x + 10)+(4x + 10)	= 75.
‹=›9x = 45
x = 5.
∴ Jayant's present age = 2x + 10 = 20 years.
Answer A
Answer: (A) 20 years
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 7 1/7 sec
(B) 7 7/2 sec
(C) 7 1/8 sec
(D) 7 1/2 sec
(E) 7 3/2 sec
Rationale: 70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 1/2 sec
Answer: D
Answer: (D) 7 1/2 sec
Question: Laura has a deck of standard playing cards with 14 of the 70 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
(A) 1/4
(B) 12/42
(C) 5/26
(D) 1/5
(E) 13/42
Rationale: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 14/70 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 14/70 = 1/5 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
D
Answer: (D) 1/5
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is
(A) 288
(B) 278
(C) 245
(D) 397
(E) 252
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: (C) 245
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 3/4
(B) 1/3
(C) 7/19
(D) 8/21
(E) 9/21
Rationale: 7C1/21C1=7/21=1/3
ANSWER:B
Answer: (B) 1/3
Question: If |z|/w = 2, which of the following must be true?
(A) z = -2w
(B) z = 2w
(C) z^2 = 4w^2
(D) z^2 = 4w^3
(E) z^3 = 8w^3
Rationale: |z|/w = 2.
|z| = 2w.
Then z = 2w or -2w and so z^2 = 4w^2.
The answer is C.
Answer: (C) z^2 = 4w^2
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
(A) 15 kmph
(B) 17 kmph
(C) 75 kmph
(D) 18 kmph
(E) 87 kmph
Rationale: 90 * 10/60
= 15 kmph
Answer: A
Answer: (A) 15 kmph
Question: The ratio of the ages of Mona and Sona is 4:5. Twelve years hence, their ages will be in the ratio of 5:6. What will be Sona's age after 6 years?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 66
Rationale: Let their present ages be 4x & 6x
Then (4x + 12)/(5x + 12) = 5/6 ; x=12
Sona's age after 6 years = (5x +6) = 66 years
ANSWER:E
Answer: (E) 66