mathewhe/aqua_rat huggingface dataset:
Question: Trains A and B start simultaneously from stations 350 miles apart, and travel the same route toward each other on adjacent parallel tracks. If Train A and Train B travel at a constant rate of 40 miles per hour and 30 miles per hour, respectively, how many miles will Train A have traveled when the trains pass each other, to the nearest mile?
(A)  112
(B)  133
(C)  150
(D)  167
(E)  200
Rationale: Since we know the distance (350) and the combined rate (70), we plug it into the formula:
Distance = Rate * Time
350 = 70 * Time
We can solve for the time they will meet cause we added the rate of Train A and Train B together.
So the time will be 350/70 from dividing 70 on both sides to isolate Time in the equation above.
Time will be 5 hours so now you can plug that in for Train A’s distance.
Distance = Rate * Time
Distance = 40 * 5
Distance = 200 according to answer choice E.
Answer: (E)  200
Question: A single discount equivalent to the discount series of 20%, 15% and 5% is?
(A) 31.5
(B) 31.8
(C) 31.6
(D) 35.4
(E) 31.1
Rationale: 100*(80/100)*(85/100)*(95/100)
= 64.6
100 - 64.6 = 35.4
Answer:D
Answer: (D) 35.4
Question: A, B and C start a business with each investing Rs 20,000. After 5 months A withdraws Rs 5000, B withdraws Rs 4000 and C invests Rs 6000 more. At the end of the year, a total profit of Rs 69900 was recorded. Find the share of A.
(A) 20000
(B) 21500
(C) 20500
(D) 22000
(E) 21000
Rationale: A : B : C
=(20000×5+15000×7)
:(20000×5+16000×7)
:(20000×5+26000×7)
=(20×5+15×7)
:(20×5+16×7)
:(20×5+26×7)
=205:212:282
A's share =69900×205/(205+212+282)
=69900×205/699
=20500
Answer is C.
Answer: (C) 20500
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 10 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) A)7
(B) B)2
(C) C)8.9
(D) D)11.4
(E) E)3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
10/(x + 4) + 10/(x - 4) = 2
x = 11.4
Answer:D
Answer: (D) D)11.4
Question: The speeds of 3 trains in the ratio 2:6:14. The ratio between time taken by them to travel the same distance is?
(A) 6:4:3
(B) 21:7:3
(C) 4:8:9
(D) 6:5:2
(E) 4:8:7
Rationale: Ratio of time taken is = 1/2 : 1/6 : 1/14 = 21:7:3
Answer is B
Answer: (B) 21:7:3
Question: A box contains 6 pairs of shoes (12 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
(A) 1/11
(B) 1/20
(C) 1/19
(D) 1/10
(E) 1/9
Rationale: The problem with your solution is that we don't choose 1 shoe from 12, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/11as after taking one at random there are 11 shoes left and only one is the pair of the first one)=1/11
Answer: A.
Answer: (A) 1/11
Question: If the sixth day of a month is two days earlier than Wednesday, What day will it be on the 20th day of the month?
(A) Saturday
(B) Monday
(C) Sunday
(D) Wednesday
(E) Friday
Rationale: Explanation:
Given that sixth day of a month is two days earlier than Wednesday
=> Sixth day is Monday
=> 13th is Monday
=> 20th is Monday
Answer: Option B
Answer: (B) Monday
Question: One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid.
(A) 286
(B) 364
(C) 504
(D) 164
(E) 154
Rationale: As there are 12 balls along one side, it means that there are 12 layers of balls. The top most layer has 1 ball. The second layer has 3 (1+2) balls. The third layer has 6 (1+2+3) balls. The fourth layer has 10 (1+2+3+4) balls. The fifth layer has 15 (1+2+3+4+5) balls. Similarly, there are 21, 28, 36, 45, 55, 66 and 78 balls in the remaining layers.
Hence, the total number of balls are
= 1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78
= 364 balls
ANSWER:B
Answer: (B) 364
Question: A train travelling at a speed of 75 mph enters a tunnel 3 1/2 miles long. The train is 1/4 mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 2.5 min
(B) 3 min
(C) 3.2 min
(D) 3.5 min
(E) None
Rationale: Solution
Total distance covered	= (7/2 + 1/4) miles
= 15 / 4 miles
= (18 x 5 /18) km/hr
Time taken	= (15 / 4 x 75) hrs
= 1 /20 hrs
= (1 / 20 x 60)
= 3 min.
Answer B
Answer: (B) 3 min
Question: Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000
A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number Y of defective chips in a shipment of 60000 chips?
(A) 14
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: I agree with your solution = 20. But the question is:
There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.
The question is to find the expected number Y of defective chips, i guess it assume the minimum #, therefore it might not be 20.
Answer: (B) 20
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?
(A) 10 days
(B) 30 days
(C) 20 days
(D) 80 days
(E) 40 days
Rationale: E
40 days
Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27 = 40 days.
Answer: (E) 40 days
Question: At a monthly meeting, 3/5 of the attendees were males and 7/8 of the male attendees arrived on time. If 4/5 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
(A) 47/200
(B) 31/200
(C) 17/100
(D) 11/100
(E) 7/50
Rationale: Males who did not arrive on time are 1/8*3/5 = 3/40 of the attendees.
Females who did not arrive on time are 1/5*2/5 = 2/25 of the attendees.
The fraction of all attendees who did not arrive on time is 3/40 + 2/25 = 31/200
The answer is B.
Answer: (B) 31/200
Question: A man spends 2/5 of his salary on house rent,3/10 of his salary on food and 1/8 of his salary on conveyence.if he has Rs.1400 left with him,find his expenditure on food and conveyence.
(A) 800
(B) 900
(C) 100
(D) 700
(E) 500
Rationale: let the salary be x ,therefore house rent =2x/5,food=3x/10,conveyence=x/8.
it is given that left over salary is 1400/-
so,x-(2x/5+3x/10+x/10)=1400
by solving x=8000
expenditure on food=3200 and conveyence=1000
ANSWER:C
Answer: (C) 100
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 7200, find the total rent of the field.
(A) 37500
(B) 35500
(C) 42500
(D) 22500
(E) 32500
Rationale: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=7200 = x=(7200 x 325)/72 = 32500
Hence, total rent of the field is Rs. 32500.
Answer is E.
Answer: (E) 32500
Question: 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
(A) Friday
(B) Saturday
(C) Wednesday
(D) Sunday
(E) Monday
Rationale: Number of days from 6th March, 2004 to 5th March 2005 = 365 days
(Though Feb 2004 has 29 days as it is a leap year, it will not come in the required period)
365 days = 1 odd day
Given that 6th March, 2005 is Monday
Hence 6th March, 2004 = (Monday - 1 odd day) = Sunday
Answer: Option D
Answer: (D) Sunday
Question: Five years ago a father was thrice as old as his son. Five years hence the son will only half the age of his father. Find their present ages.
(A) 25, 25
(B) 35, 15
(C) 15, 35
(D) 15, 35
(E) 10, 40
Rationale: Explanation:
Let the present ages of father,and son be 'a' and 'b' respectively.
a - 5= 3(b-5) =>a-3 b =-10 --------(1)
a-2b =5 ------------(2) solving (1) and (2), we get b =15
Substituting b = 15 in second equation,
we get a=35
Answer: B
Answer: (B) 35, 15
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
(A) 327
(B) 340
(C) 364
(D) 499
(E) 456
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: (C) 364
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.5000, find their shares?
(A) 2000,8000
(B) 2000,4000
(C) 2000,3000
(D) 1000,3000
(E) 4000,3000
Rationale: The ratio of their profits A:B = 8:12 =2:3
Share of A in the total profit = 2/5 * 5000 = Rs.2000
Share of B in the total profit = 3/5 * 5000 = Rs.3000
Answer:C
Answer: (C) 2000,3000
Question: Rectangular tile each of size 25cm by 16cm must be laid horizontally on a rectangular floor of size 180cm by 120cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 52
(B) 54
(C) 55
(D) 65
(E) 48
Rationale: Area of tile = 25*16= 400
Area of floor = 180*120 = 21600
No of tiles = 21600/400 = 54
So, the no of tile = 54
ANSWER:B
Answer: (B) 54
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Friday, what was the expected day when both the brothers were to return home and when did Rohit Return?
(A) Wednesday, Sunday
(B) Thursday, Monday
(C) Monday, Friday
(D) Monday, Friday
(E) none
Rationale: Rajat returned on Friday -i.e. 3 days earlier
so actual day to return home is Monday.
Rohit returned after days so Friday
ANSWER:C
Answer: (C) Monday, Friday
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.55%, what fraction of the products was checked by worker y?
(A) 1/3
(B) 1/4
(C) 1/5
(D) 1/6
(E) 1/8
Rationale: x: 0.5% is 0.05%-points from 0.55%.
y: 0.8% is 0.25%-points from 0.55%.
Therefore the ratio of products checked by y:x is 1:5.
Thus, worker y checked 1/6 of the products.
The answer is D.
Answer: (D) 1/6
Question: The difference between the ages of two persons is 20 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the younger person is?
(A) 30
(B) 35
(C) 25
(D) 28
(E) 32
Rationale: Let their ages be x years and (x+20) years
Then, (x+20) - 15 = 2(x-15)
x +5 = 2x-30
x = 35
Answer is B
Answer: (B) 35
Question: 20-5*4^2+15 = ?
(A) 287
(B) -13
(C) -45
(D) 13
(E) None
Rationale: 20-5*4^2+15
= 20-5*16+15
=20-48+15=-45..
C
Answer: (C) -45
Question: A car rental company charges for mileage as follows: 3 dollars per mile for the first n miles and 4 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
(A) 5d-n
(B) 6d-n
(C) 7d-n
(D) 8d-n
(E) 4d-n
Rationale: Total Distance in miles = d
Millage Charge = 3n + (d-n) 4
3n --> For the first n Miles
(d-n)4--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 4 .
If we solve the equation , We will get 4d-n
Answer : E
Answer: (E) 4d-n
Question: In an examination series, which consists of 5 exams, Arvind scored an average of 60 marks in
the first 3 exams and an average of 70 in the last 4 exams, what is the average score of
Arvind for the first and last two exams if his average scores of all the five exams are 65?
(A) 31
(B) 32
(C) 63
(D) 64
(E) 65
Rationale: let a,b,c,d,e be the five exams
(a+b+c+d+e)/5=65
a+b+c+d+e=325
first 3 exams avg is (a+b+c)/3=60
a+b+c=180
d+e=325-180=145
avg of last 4 exams is (b+c+d+e)/4=70
b+c+d+e=280
a=325-280=45
avg of first and last two exams are(a+d+e)/3=(45+145)/3=(190)/3=63.33
ANSWER:C
Answer: (C) 63
Question: A bakery has 6 employees. It pays annual salaries of $15,000 to each of 2 employees, $17,000 to 1 employee, and $18,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
(A) $16,200
(B) $16,500
(C) $16,800
(D) $17,000
(E) $17,400
Rationale: average = 2(15000)+(17000)+3(18000) / 6 = $16,833
The answer is C.
Answer: (C) $16,800
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 9.30 a.m
(B) 10 a.m
(C) 10.40 a.m
(D) 11 a.m
(E) 11.40 am
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
answer B
Answer: (B) 10 a.m
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
(A) 87 min
(B) 82 min
(C) 86 min
(D) 47 min
(E) 72 min
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D
Answer: (D) 47 min
Question: The greatest number by which the product of three consecutive multiples of 4 is always
(A) 384
(B) 81
(C) 162
(D) 243
(E) None of these
Rationale: Explanation:
4*8*12 = 384
Option A
Answer: (A) 384
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 23 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
(A) 42
(B) 48
(C) 56
(D) 64
(E) 72
Rationale: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.23(800) = 256
The answer is C.
Answer: (C) 56
Question: A shopkeeper sold an article at $1110 and gained a 20% profit. What was the cost price?
(A) $850
(B) $875
(C) $900
(D) $925
(E) $950
Rationale: Let x be the cost price.
1.2x = 1110
x = 1110/1.2 = 925
The answer is D.
Answer: (D) $925
Question: A traveller makes 3/4 of his journey by train and 2/3 of the rest by car. If he walks the remaining 12 Kms, the total distance traveled by him is
(A) 124 Kms
(B) 134 Kms
(C) 144 Kms
(D) 244 Kms
(E) None of the above
Rationale: (1-(3/4))(1-(2/3)of distance = 12 km
(1/12) of distance = 12 km
Hence distance = 144 km
ANSWER:C
Answer: (C) 144 Kms
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
(A) 35
(B) 10
(C) 40
(D) 50
(E) 55
Rationale: Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) = 90 years.
Sum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years.
Husband's present age = (90 - 50) = 40 years.
ANSWER C
Answer: (C) 40
Question: In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
(A) 7 : 2
(B) 7 : 3
(C) 7 : 5
(D) 7 : 7
(E) 7 : 9
Rationale: By the rule of alligation:
Cost of 1 kg pulses of 1st kindCost of 1 kg pulses of 2nd kind
Rs. 15	Mean Price
Rs. 16.50	Rs. 20
3.50	1.50
Required rate = 3.50 : 1.50 = 7 : 3.
Option B
Answer: (B) 7 : 3
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Sol.
Let the number be x.
Then, 3(2x +9) = 75
⇔ 2x + 9 = 25
⇔ 2x = 16
⇔ x = 8
Answer D
Answer: (D) 8
Question: A woman swims downstream 54 km and upstream 6 km taking 6 hours each time, what is the speed of the woman in still water?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 54 --- 6 DS = 9
? ---- 1
6 ---- 6 US = 1
? ---- 1 M = ?
M = (9 + 1)/2 = 5
Answer:D
Answer: (D) 5
Question: can you find the last number in the number sequence given below
10: 10 : 20 : 45 : 110 : 300 :?
(A) 870
(B) 930
(C) 540
(D) 630
(E) 730
Rationale: Correct Answer : B
? = last no * multiplication factor (increase by 0.5 every time) + sum factor (Increase by 5 every time)
10*0.5+5 = 10
10*1.0+10=20
20*1.5+15=45
45*2.0+20=300
300*3.0+30=930
Answer: (B) 930
Question: A pump can fill a tank with water in 4 hours. Because of a leak, it took 20 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 1
(B) 3
(C) 5
(D) 4
(E) 2
Rationale: P --> Pump, L ---> Leak
Pipe----------P---------L------------(P-L)--
Time---------4---------x-------------20
*
Rate---------5---------x-------------1
Work-------20---------20-----------20
Time required to empty the tank if leakage present = 20/((5) - 1)
= (20)/(4)
= 5
Ans -C
Answer: (C) 5
Question: On what sum of money will be difference between the simple interest and compound interest for 2 years at 5% p.a be equal to Rs. 25
(A) Rs.10000
(B) Rs. 20000
(C) Rs. 22000
(D) Rs. 12000
(E) Rs. 14000
Rationale: p(r/100)^2 =25 p(5/100)^2 =25=Rs.10000 Answer : A
Answer: (A) Rs.10000
Question: A chemist mixes one liter of pure water with x liters of a 40% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 40%
Concentration of salt in the mixed solution = 20%
The pure solution and the salt solution is mixed in the ratio of --> (40 - 20)/(20 - 0) = 1/1
1/x = 1/1
x = 1
Answer: D
Answer: (D) 1
Question: A boy was asked to find 7/9 of a x. But he divided the x by 7/9, Thus he got 32 more than theanswer. Find the x.
(A) 60
(B) 61
(C) 62
(D) 63
(E) 65
Rationale: x/7/9 = 9x/7 = 32 + y
Actualy he should do 7x/9 = y
y = (9x/7) - 32
y = (9x - 224)/7
(9x - 224)/7 = 7x/9
81x - 2016 = 49x
81x - 49x = 2016
32x = 2016
x = 63
D
Answer: (D) 63
Question: Will must choose a 2-character computer password, consisting of 2 letter from the alphabet , in any order.From how many different passwords can Will choose?
(A) 390
(B) 2,340
(C) 4,680
(D) 1300
(E) 14,040
Rationale: 26C1*25C1 = 650.
=>650 * 2 ! = 1300.
Option E is correct answer...but OA is D.
Answer: (D) 1300
Question: If John invested $ 2 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
(A) (1.5)^4
(B) 4(1.5)
(C) (1.05)^4
(D) (2.05)^4
(E) 1 + 4(0.05)
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $2, an R of 5% (which would 'translate' as .05) and a T of 4. We'd have....
D
Answer: (D) (2.05)^4
Question: If y = x +2, Find the range of real values of y satisfying the inequalities 16x - 6 > 42 and 7x - 24 < 60"
(A) 5 < y < 14
(B) 3 < y < 12
(C) 1 < y < 10
(D) y < 10
(E) y < 12
Rationale: 16x – 6 > 42 => 16x >48 => x>3 ...(1)
And 7x – 24 < 60 = > 7x x 3 and y - 2 5 or y < 14
Combining the above range, we get, 5 < y < 14
ANSWER:A
Answer: (A) 5 < y < 14
Question: The sum of the squares of three numbers is 41, while the sum of their products taken two at a time is 20. Their sum is:
(A) 10
(B) 5
(C) 9
(D) 15
(E) None of these
Rationale: x^+y^2+z^2=138
xy+yz+zx=131
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=41+(2*20)
(x+y+z)^2=81
so x+y+z=9
ANSWER:C
Answer: (C) 9
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
(A) -33
(B) -34
(C) -46
(D) 45
(E) 46
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: (A) -33
Question: The average age of 20 men in the class is 14.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?
(A) 15.5
(B) 19.4
(C) 15.25
(D) 15.3
(E) 15.6
Rationale: Total age of 20 men = 14.6 x 20 = 292
Now, total age of 25 men = 389.
Total age of five men added later = 389 - 292 = 97.
Hence, the total average of five men = 97/5 = 19.4
ANSWER:B
Answer: (B) 19.4
Question: Whats the probability of getting 5 Sunday(my favorite day) in a 31 day month ?
(A) 3/3
(B) 2/9
(C) 6/7
(D) 1/5
(E) 3/7
Rationale: E
3/7
Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.
Answer: (E) 3/7
Question: Pipe A can fill a tank in 10 hours, pipe B in 8 hours, and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The part filled by A + B + C in 1 hour
= 1/10 + 1/8 + 1/40
= 10/40 = 1/4
All the three pipes together will fill the tank in 4 hours.
The answer is C.
Answer: (C) 4
Question: The diameter of a circle is 4/π. Find the circumference of the circle.
(A) 8
(B) 4 π
(C) 4
(D) 6
(E) 5
Rationale: circumference = 2*pi*r= 2*pi*4/pi
=> 8
A
Answer: (A) 8
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 17%
(B) 77%
(C) 44%
(D) 16%
(E) 47%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Answer: (C) 44%
Question: Set E includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First, reach to the point of getting the equation E : x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: (D) 3
Question: There are 138 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
(A) 10
(B) 11
(C) 12
(D) 16
(E) 14
Rationale: IMO 17
Take each answer choice and substract it from 135 and the divided this with 11.
D
Answer: (D) 16
Question: In a coconut grove, (x + 4) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 4) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
(A) 3
(B) 4
(C) 8
(D) 9
(E) None of the above
Rationale: (x+4)×60+x×120+(x−4)×180/(x+4)+x+(x−4)=100
⇒ 360x−480/3x = 100
⇒ 60x = 480 ⇒ x = 8
Answer C
Answer: (C) 8