mathewhe/aqua_rat huggingface dataset:
Question: which of the following inequalities indicates the set of all values of d for which the lengths W of the three sides of a triangle can be 3,4, and d?
(A) 0<d<1
(B) 0<d<5
(C) 0<d<7
(D) 1<d<5
(E) 1<d<7
Rationale: This question is a good way to apply one of the most basic relation between the 3 sides of a triangle. In a triangle (ANY TRIANGLE), any side MUST be greater than the positive difference of the other two sides and less than than the sum of the other 2 sides. Let the sides of a triangle be a,b,c .
Thus,
|a-b| < c < a+b
|b-c| < a < b+c
|c-a| < b < a+c
Thus, if the sides of the triangle are 3,4 and d,
4-3<d<4+3 ---> 1<d<7. Thus E is the correct answer.
Answer: (E) 1<d<7
Question: At what rate percent on simple interest will Rs.750 amount to Rs.1050 in 5 years?
(A) 8
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 300 = (750*5*R)/100
R = 8%.Answer: A
Answer: (A) 8
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 50 years now, the son's age five years back was:
(A) 15 years.
(B) 20 years.
(C) 25 years.
(D) 30 years.
(E) 35 years.
Rationale: Let the son's present age be x years. Then, (50 - x) = x
2x = 50.
x = 25.
Son's age 5 years back (25 - 5) = 20 years.
Answer: Option B
Answer: (B) 20 years.
Question: There are 5 sweets – Jumun, Kulfi, Peda, Laddu and Jilabi that I wish to eat on 5 consecutive days – Monday through Friday, one sweet a day, based on the following self imposed constraints:
1) Laddu is not eaten on Monday
2) If Jamun is eaten on Monday, then Laddu must be eaten on Friday
3) If Laddu is eaten on Tuesday, Kulfi should be eaten on Monday
4) Peda is eaten the day following the day of eating Jilabi
Based on the above, peda can be eaten on any day except?
(A) Tuesday
(B) Monday
(C) Wednesday
(D) Friday
(E) Sunday
Rationale: Peda is eaten the day following the day of eating Jilabi, So Peda can never be had on the starting day, which is Monday.
ANSWER:B
Answer: (B) Monday
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 6 : 3 : 5 : 4. If C gets Rs. 1000 more than D, what is B's share?
(A) 1500
(B) 2000
(C) 2500
(D) 2800
(E) 3000
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 3x, Rs. 5x and Rs. 4x respectively.
Then, 5x - 4x = 1000
x = 1000.
B's share = Rs. 3x = Rs. (3 x 1000) = Rs. 3000.
ANSWER :E
Answer: (E) 3000
Question: Mary jogs 9 km at a speed of 6kmph. at what speed would she need to jog during the next 1.5 hour to have an average of 9 km per hr at the entire jogging session?
(A) 12kmph
(B) 7kmph
(C) 87kmph
(D) 74kmph
(E) 78kmph
Rationale: let speed of the jogging be x kmph
total time taken=(9/6+1.5)=3 hrs
total distance covered=(9+1.5x)
9+1.5 x/3=9
9+1.5 x=27
3/2x=18
x=18*2/3=12 kmph
Answer(A)
Answer: (A) 12kmph
Question: The average (arithmetic mean) of y numbers is x. If 15 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?
(A) x/6 - 6
(B) x/6 - 5
(C) x/7 - 5
(D) x/5 - 4
(E) x/5 - 6
Rationale: (A1 + A2 + .. + Ay)/y = x
(A1 + A2 + .. + Ay + 15)/(y+1) = x - 5
=> (xy + 15)/(y+1) = x - 5
=> xy + 15 = yx -5y + x - 5
=> 20 = x - 5y
=> 5y = x - 20
=> y = x/5 - 4
Answer - D
Answer: (D) x/5 - 4
Question: A sequence of numbers is such that a1 = 11, a2 =16, and each subsequent an = an-2 + 9. Which of the following numbers is a member of the sequence?
(A) 216
(B) 246
(C) 289
(D) 299
(E) 368
Rationale: each odd term(1st , 3rd, 5th,...) of the sequence is given by 11 + 9*(something)
each even term(2nd, 4th, 6th...) of the sequence is given by 16 + 9*(something)
So if you subtract the numbers by 11 or 16 then it should be divisible by 9
216-11(=205) or 216-16(=200) are not divisible by 9
246-11(=235) or 246-16(= 240) are not divisible by 9
289-11(=278) or 289-16(=273) are not divisible by 9
299-11(=288) is divisible by 9ANSWER, 299-16(=283) are not divisible by 9
368-11(=357) or 368-16(=352) are not divisible by 9
So, Answer is D
Answer: (D) 299
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
(A) 81000
(B) 81027
(C) 81089
(D) 81027
(E) 28939
Rationale: 64000* 9/8 * 9/8
= 81000
Answer: A
Answer: (A) 81000
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
(A) 11
(B) 16
(C) 188
(D) 199
(E) 12
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer: B
Answer: (B) 16
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 28
(B) 50
(C) 99
(D) 121
(E) 81
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: B
Answer: (B) 50
Question: B @ K I 9 D Â© 5 2 T $ M 4 E J # U R 1 A Î´ K 5 W 6 % F Q 7 H P 8 Z How many such consonants are there in the above arrangement, each of which is immediately preceded by number and immediately followed by a symbol?
(A) None
(B) One
(C) Two
(D) Three
(E) More than three
Rationale: Explanation:
Number Consonant Symbol
Such combinations are:
9 D Â© : 2 T $
ANSWER IS C
Answer: (C) Two
Question: A bat is bought for Rs.400 and sold at a gain of 25% find its selling price?
(A) s.460/-
(B) s.480/-
(C) s.500/-
(D) s.520/-
(E) s.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 500 (125 * 4 = 500)
Selling price = Rs.500/-
Option 'C'
Answer: (C) s.500/-
Question: The average age of father and his two sons is 27 Years. Five years ago, the average age of the two sons was 12 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
(A) 45
(B) 46
(C) 47
(D) 48
(E) 49
Rationale: The total present age of father and two sons is 3S27 = 81 yrs
The total present age of sons is (12+5) X 2 = 34Years
so, present age of father is 81 – 34 = 47 yrs
Answer C
Answer: (C) 47
Question: The sector of a circle has radius of 21 cm and central angle 150o. Find its perimeter?
(A) 91.5
(B) 91.4
(C) 97
(D) 91.3
(E) 91.1
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (150/360 * 2 * 22/7 * 21) + 2(21)
= 55 + 42 = 97 cm
Answer:C
Answer: (C) 97
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.
(A) 20
(B) 40 rs
(C) 50
(D) 60
(E) 90
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B
Answer: (B) 40 rs
Question: A man bought a horse and a carriage for Rs. 3000. He sold the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse.
(A) 2200
(B) 1800
(C) 1200
(D) 1000
(E) 1500
Rationale: Let the C.P of the horse be Rs. X, Then, C.P of the carriage = Rs.(3000- x).
20% of x - 10% of ( 3000-x ) =2% of 3000 = 60,
x/5 - ( 3000-x )/10 = 60, 3x - 3000 = 600, 3x =3600, x = 1200.
Hence, C.P of the horse = Rs. 1200
ANSWER:C
Answer: (C) 1200
Question: A is twice as good a workman as B and they took 10 days together to do the work B alone can do it in.
(A) 17 days
(B) 12 days
(C) 30 days
(D) 25 days
(E) 27 days
Rationale: WC = 2:1
2x + x = 1/10
x = 1/30 => 30 days
ANSWER:C
Answer: (C) 30 days
Question: Amit, Raju and Ram agree to pay their total electricity bill in the proportion 3 : 4 : 5. Amit pays first day's bill of Rs. 50, Raju pays second day's bill of Rs. 55 and Ram pays third day's bill of Rs. 75. How much amount should Amit pay to settle the accounts?
(A) Rs. 15.25
(B) Rs. 17
(C) Rs. 12
(D) Rs. 5
(E) NONE OF THE ABOVE
Rationale: EXPLANATION:
Total bill paid by Amit, Raju and Ram = ( 50 + 55 +75 ) = Rs. 180
Let amount paid by Amit, Raju and Ram be Rs. 3x, 4x and 5x respectively.
Therefore, (3x + 4x + 5x ) = 180
12x = 180
x = 15
Therefore, amount paid by,
Amit = Rs. 45
Raju = Rs. 60
Ram = Rs. 75
But actually as given in the question, Amit pays Rs. 50, Raju pays Rs. 55 and Ram pays Rs. 80. Hence, Amit pays Rs. 5 less than the actual amount to be paid. Hence he needs to pay Rs. 5 to Raju settle the amount.
ANSWER IS D
Answer: (D) Rs. 5
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is
(A) 45 kg
(B) 55 kg
(C) 75 kg
(D) 15 kg
(E) 35 kg
Rationale: Weight of the teacher = (35.4 x 25 - 35 x 24) kg
= 45 kg.
Answer: A
Answer: (A) 45 kg
Question: In covering a distance of 90 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
(A) 5 km/h
(B) 8 km/h
(C) 10 km/h
(D) 15 km/h
(E) 20 km/h
Rationale: Let A's speed be X km/hr.
Then, 90/x - 90/2x = 3
45/x = 3
x = 15 km/hr.
Answer : D
Answer: (D) 15 km/h
Question: Find the total number of prime factors in the expression (4)^11 x (7)^3 x (11)^2
(A) 26
(B) 22
(C) 25
(D) 27
(E) 29
Rationale: (4)^11x (7)^3 x (11)^2
= (2 x 2)^11 x (7)^3 x (11)^2
= 2^11 x 2^11 x7^3x 11^2
= 2^22 x 7^3 x11^2
Total number of prime factors = (22 +3+ 2) = 27.
Answer is D.
Answer: (D) 27
Question: The price of precious stone is directly proportional to square of its weight. what will be the loss incurred if a stone weighing 28gm and costing 28,000 breaks into two pieces whose weights are in the ratio 15:13?
(A) 13958.58
(B) 13928.58
(C) 14000
(D) 13562.42
(E) None of these
Rationale: Explanation :
Let price = p,weight = w.
p=k w^2 ---------eq(1) [here k is a constant taken]
As it is given dat price is directly proportional to weight
given w = 28,p = 28000
So from eq(1),k=1000/28
Now the broken pieces are 15gm nd 13gm
By putting the values of w and k in eq(1) we get
p1=8035.71(for w=15)
p2=6035.71(for w=13)
Total cost for broken pieces = (8035.71+6035.71) = 14071.42
So the loss=(28000-14071.42)
=13928.58
Answer : B
Answer: (B) 13928.58
Question: If taxi fares were $1.00 for the first 1/5 mile and $0.30 for each 1/5 mile there after, then the taxi fare for a 3-mile ride was
(A) $1.56
(B) $2.40
(C) $3.80
(D) $5.20
(E) $2.80
Rationale: In 3 miles , initial 1/5 mile charge is $1
rest of the distance = 3 - (1/5) = 14/5
rest of the distance charge = 14(0.3) = $4.2 (as the charge is 0.3 for every 1/5 mile)
=> total charge for 3 miles = 1+4.2 =5.2
Answer is D.
Answer: (D) $5.20
Question: The average expenditure of a labourer for 5 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is
(A) 69.5
(B) 71.2
(C) 60.4
(D) 62.1
(E) 72.1
Rationale: Income of 6 months = (5 × 85) – debt
= 425 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 695
Average monthly income = 695 ÷ 10 = 69.5
Answer A
Answer: (A) 69.5
Question: Tom divided $360 among his six children for them to use for Christmas gifts. His daughter Kate
added $20 to her portion, then used the money to buy 16 gifts that each cost the same amount.
What was the price of each of Kate’s gifts?
(A) $5
(B) $10
(C) $15
(D) $20
(E) $25
Rationale: $360 ÷ 6 = $60 for each child
$60 + $20 = $80 Kate’s money
$80 ÷ 16 = $5 cost of each gift
correct answer A
Answer: (A) $5
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 30 percent of the pack would be outfielder cards?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 30% of toatal Ocards
12-X<.3*12
X<12-3.6
X<8.4
X=8
Ans E
Answer: (E) 8
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 2 months and 7 months respectively. What was the ratio of their investments?
(A) 10:12:14
(B) 12:24:28
(C) 20:22:12
(D) 5:49:16
(E) None of these
Rationale: Explanation :
Ratio in which A,B and C shared the profit = 5 : 7 : 8
Assume that the ratio of their investment = a:b:c
Then 14a : 2b : 7c = 5 : 7 : 8
Good to go, we got the equation. Now it's a matter of time to find a, b and c
14a/2b = 5/7
=> 98a = 10b
=> b = 98a/10 = 49a/5 ---(1)
14a/7c =5/8
=> 2a/c =5/8
=> 16a = 5c
=> c = 16a/5 ---(2)
a : b : c = a : 49a/5 : 16a/5 = 1 : 49/20 : 16/5 = 5 : 49 : 16. Answer : Option D
Answer: (D) 5:49:16
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the R odds that x^2+y^2>1?
(A) 1. pi/4
(B) 2. R=pi/16
(C) 3. R=1-pi/4
(D) 4. 1-pi/16
(E) 5.4-pi
Rationale: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Answer: (C) 3. R=1-pi/4
Question: Sandy walked 20 meters towards south. Then Sandy turned to her left and walked 25 meters. She then turned to her left and walked 20 meters. She then turned to her right and walked 30 meters. What distance is she from the starting point and in which direction?
(A) 35 m East
(B) 35 m North
(C) 30 m West
(D) 45 m West
(E) 55 m East
Rationale: The net distance is 25 + 30 = 55 meters to the east.
The answer is E.
Answer: (E) 55 m East
Question: In an examination 35% of the students passed and 546 failed. How many students appeared for the examination?
(A) A)540
(B) B)400
(C) C)700
(D) D)650
(E) E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 546
65x/100 = 546
x = 546*100/65 = 840
Answer is E
Answer: (E) E)840
Question: X divided by Y equals 7.28 what is a possible remainder?
(A) 20
(B) 21
(C) 5
(D) 6
(E) 9
Rationale: With the decimal being 28/100, the simplest form is 7/25. If the divisor is a multiple of 25, the remainder must be a multiple of 7. The only number that is so is 21. Answer B.
Answer: (B) 21
Question: Annika hikes at a constant rate of 12 minutes per kilometer. She has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes. If Annika continues east, then turns around and retraces her path to reach the start of the trail in exactly 51 minutes, for how many kilometers total did she hike east?
(A) 3.625
(B) 3
(C) 4.5
(D) 4
(E) 3.5
Rationale: Set up two R x T =D cases.
1. 1/12 km/ min x T = 2.75
from which T= 33 mins.
We know total journey time now is 51 +33 =84.
The rate is the same ie 1/12km/min.
set up second R x T =D case.
1/12 km/min x 84 = 7 km
Now the total journey would be halved as distance would be same in each direction. 7/2 =3.5
E.
Answer: (E) 3.5
Question: An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?
(A)  1
(B)  5
(C)  11
(D)  15
(E)  17
Rationale: The number should be a possible factor of 85 so choices C and D are out
out of other possible choices it says that number of patients detected increased 85 %
if we take 1 for plugging in then the number obtained before increase is not a integer same is the case with 5
so correct option - E
Answer: (E)  17
Question: A car going at 10 miles per hour set out on an 80-mile trip at 9:00 A.M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A.M.?
(A)  45
(B)  20
(C)  53
(D)  55
(E)  60
Rationale: Let Car A = car that starts at 9 AM
Car B = car that starts at 9:10 AM
Time for which car A travels at speed of 10 m per hour = 1.5 hours
Distance travelled by Car A = 10 *1.5 =15 miles
Since Car B catches up Car A at 10:30 , time = 80 mins = 4/3 hour
Speed of Car B = 15/(4/3) = 20 miles per hour
Answer B
Answer: (B)  20
Question: Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A man rows to a place at a distance of 4664 km and comes back to the starting point. The total time taken by him is:
(A) 784 hours
(B) 794 hours
(C) 780 hours
(D) 684 hours
(E) 884 hours
Rationale: Speed downstream = (12 + 1.2) = 13.2 kmph
Speed upstream = (12 - 1.2) = 10.8 kmph
Total time taken=4664/13.2+4664/10.8 = 353 + 431 = 784 hours
ANSWER:A
Answer: (A) 784 hours
Question: If the average marks of three batches of 70, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
(A) 53.33
(B) 54.28
(C) 55
(D) 57
(E) None
Rationale: Sol.
Required average = [70x50 + 60x55 + 45x60 / 70 + 60 + 45]
= [3500 + 3300 + 2700 / 175]
= 9500 / 175 = 54.28.
Answer B
Answer: (B) 54.28
Question: You have 10 users plugged into a hub running 10Mbps half-duplex. There is a server connected to the switch running 10Mbps half-duplex as well. How much bandwidth does each host have to the server?
(A) 22
(B) 377
(C) 26
(D) 10
(E) 88
Rationale: Explanation:
Each device has 10 Mbps	to the server.
Answer: Option D
Answer: (D) 10
Question: 70% of the employees in a multinational corporation have VCD players, 83 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
(A) (a) 15%
(B) (b) 5%
(C) (c) 10%
(D) (d) 18%
(E) (e) 25%
Rationale: so 30% employees don't have VCD devices.
17% employees don't have MO
20% employees don't have ACs
15% employees don't have WM
Summ of employees that don't have some device = 30%+17%+20%+15% = 82% < 100%
So definitely at least 18% employees have 4 devices.
ans: D
Answer: (D) (d) 18%
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 3 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 287
(C) 289
(D) 270
(E) 360
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 3 = 360
Answer: E
Answer: (E) 360
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 171
(B) 150
(C) 278
(D) 266
(E) 256
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x
= 150 m.
Answer:B
Answer: (B) 150
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 14.8 sec
(C) 10.6 sec
(D) 10.8 sec
(E) 20.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5
= 10.8 sec.
Answer: D
Answer: (D) 10.8 sec
Question: 9,13,289,4795, 28750, 18947 which number is wrong in series
(A) 9
(B) 18947
(C) 289
(D) 4795
(E) 28750
Rationale: 28750...........
all are odd numbers expect 28750
ANSWER:E
Answer: (E) 28750
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
(A) 1 : 3
(B) 2 : 3
(C) 3 : 4
(D) 4 : 5
(E) 5 : 2
Rationale: Explanation:
By the rule of alligation:
Required ratio = 60 : 90 = 2 : 3.
ANSWER IS B
Answer: (B) 2 : 3
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
(A) Rs. 5000
(B) Rs. 6000
(C) Rs. 7000
(D) Rs. 8000
(E) Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: (E) Rs. 10000
Question: 6x − 18 = 6y
5y + 5x = 15
Which of the following is the number of solutions to the system of equations shown above?
(A) More than three
(B) Exactly three
(C) Exactly two
(D) Exactly one
(E) None
Rationale: 6x − 12 = 6y
=> 6x - 6y = 18
=> x- y =3 -- 1
5y + 5x = 15
=>x + y = 3 -- 2
From equation 1 and 2 , we get
2x = 6
=> x=3
y=0
Therefore , the given system will have Exactly one solution
D
Answer: (D) Exactly one
Question: A and B can do a work in 8 days, B and C can do the same work in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days?
(A) 7
(B) 6
(C) 5
(D) 8
(E) 9
Rationale: Let the total units of work be 48.
Units of work completed by A and B in one day = 6.
Units of work completed by B and C in one day = 4
Units of work completed by A, B, and C in one day = 8.
From the above information we get the work completed by A and C in one day is 6 units.
Therefore, the number of days taken by A and C to complete the whole work = 48/6 = 8 days.
ANSWER:D
Answer: (D) 8
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
(A) 125
(B) 150
(C) 200
(D) 250
(E) 300
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
ANSWER A
Answer: (A) 125
Question: A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 1/10, and the probability of selecting a blue paper clip is 1/2. What is the probability of selecting a silver paper clip?
(A)  5/13
(B)  1/2
(C)  4/10
(D)  3/4
(E)  11/12
Rationale: Prob of Red = 1/10
Prob of Blue = 1/2
Prob of Silver = ?
P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/10-1/2 = 4/10
Ans: C
Answer: (C)  4/10
Question: The sector of a circle has radius of 42 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 92.2 cm
(C) 28.9 cm
(D) 29.2 cm
(E) 183 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 42) + 2(42)
= 99+ 84 = 183 cm
Answer:E
Answer: (E) 183 cm
Question: A jar has 250 marbles. 46 are blue, 56 are red, 75 are green, 25 are yellow, and the remainder, purple.
What percent of the marbles are purple?
(A) 76%
(B) 24%
(C) 30%
(D) 16%
(E) 27%
Rationale: Total number of blue, red, green, and yellow marbles: 46 + 56 + 75 + 25 = 190
Percentage of marbles other than purple: 190/250 = 76%
Percenage of purple marbles: 1-.76=.24=24%
Answer is B
Answer: (B) 24%
Question: All of the citizens of a country have a three-character or four-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
(A) 36^7
(B) 37(36^3)
(C) 35(36^4)
(D) 35(36^3)
(E) 37(36^4)
Rationale: The number of possible 3-digit codes is 36^3.
The number of possible 4-digit codes is 36^4.
The total sum is 36^3 + 36^4 = 36^3(1+36) = 37(36^3)
The answer is B.
Answer: (B) 37(36^3)
Question: Find the simple interest on Rs. 64,000 at 16 2/3% per annum for 9 months.
(A) s.8500
(B) s.8000
(C) s.7500
(D) s.7000
(E) s.6500
Rationale: P = Rs.64000,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(64,000*(50/3)*(3/4)*(1/100))
= Rs.8000
Answer is B.
Answer: (B) s.8000
Question: A man two flats for $675958 each. On one he gains 15% while on the other he loses 15%. How much does he gain or lose in the whole transaction?
(A) 2%
(B) 2.25%
(C) 3.12%
(D) 4.65%
(E) 5.12%
Rationale: In such a case there is always a loss
Loss% = (15/10)^2 = 9/4 = 2.25%
Answer is B
Answer: (B) 2.25%
Question: The nth term in a certain sequence is defined for positive integer n as 1+(−1)(n(n+1)/2)^2. What is the total of the first 64 terms of this sequence?
(A) −164
(B) 0
(C) 16
(D) 32
(E) 64
Rationale: sequence goes like this 0 , 1, 0 , 1, 0 ...... 1(64th term)
sum of 64 terms = 32
ANSWER:D
Answer: (D) 32