mathewhe/aqua_rat huggingface dataset:
Question: The value of Underrot 17pi/6 + Underrot 1 is most nearly equal to which of the following integers? (Please refer to the picture below for the exact version of the question)
(A) 10
(B) 12
(C) 8
(D) 3
(E) 21
Rationale: Under root (17pi/6) ~ 9
Under root (1) = 1
Hence, 9+1 = 10 is the approx answer. A is the correct answer.
Answer: (A) 10
Question: A group of 15 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
(A) (D) nE / [15(15-n)]
(B)  (12 - n)/E
(C)  E/[12(12-n)]
(D) (A) E/(12 - n)
(E)  (12-n)E/(12n)
Rationale: total cost =E
no of people willing to participate initially =15
initial cost for each =E/15
when n people decided not to participate
Cost for each =E/15-n
A
Answer: (A) (D) nE / [15(15-n)]
Question: Two tains of equal lengths take 10 seconds and 16 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 12
(B) 14
(C) 16
(D) 12.3
(E) 18
Rationale: Sol.
Speed of the first train = [120 / 10] m/sec = 12 m/sec.
Speed of the second train = [120 / 16] m/sec = 7.5 m/sec.
Relative speed = (12 + 7.5) = m/sec = 19.5 m/sec.
∴ Required time = (120 + 120) / 19.5 secc = 12.3 sec.
Answer D
Answer: (D) 12.3
Question: The price of a cycle is reduced by 25 % The new price is reduced by a further 20 %. The 2 reductions together are equal to a single reduction of
(A) 25%
(B) 38%
(C) 40%
(D) 52%
(E) 28%
Rationale: Let the original price of the cycle be 100. After the first reduction the price will be 75.
This new price is then reduced by 20% = 0.8 x 75 = 60
60 represents a reduction of 40 percent on the original.
C
Answer: (C) 40%
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?
(A) 12 minutes
(B) 17 min
(C) 19 min
(D) 11 min
(E) 16 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B
= 6 - 1 = 5 rounds per hour.
Time taken to complete one round at this speed
= 1/5 hr
= 12 min.
Answer: A
Answer: (A) 12 minutes
Question: A palindrome is a number that reads the same forward and backward, such as 171. How many even, 6-digit numbers are palindromes?
(A) 405
(B) 450
(C) 400
(D) 900
(E) 2500
Rationale: First recognize you only need to consider the first three digits (because the second three are just the first three flipped)
There are 900 possibilities for the first three digits of a 6 digit number, 100-999 inclusive. Everything starting with a 2,4,6,8 will be even, which is 4/9ths of the combinations.
4/9*900 = 400
ANSWER:C
Answer: (C) 400
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) 2 : 3
(B) 4 : 3
(C) 6 : 7
(D) 9 : 16
(E) None
Rationale: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √16 : √9
= 4 : 3.
Answer B
Answer: (B) 4 : 3
Question: Two stations AA and BB are 110 km apart on a straight line. One train starts from AA at 7 am and travel towards BB at 20 km/hr speed. Another train starts from BB at 8 am and travel towards AA at 25 km/hr speed. At what time will they meet?
(A) 9 am
(B) 10 am
(C) 11 am
(D) 12 am
(E) None of these
Rationale: In 1 hour (7 am to 8 am) train from station A travels 20 km distance and reaches to C, (say).
A ----------------- C ---------------B
7 am --------------------------------- 8 am
AC = 20 km, CB = 90 km
Distance travelled in 1 hour = 20 km
Remaining distance =110âˆ’20 = 90 km
Time=Distance/Speed
90/20+25=2 hours
So, time = 8 am + 2 am = 10 am
Answer : B
Answer: (B) 10 am
Question: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $3,600. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
(A) 850
(B) 1,100
(C) 1,800
(D) 2,550
(E) 3,400
Rationale: Assume the cost of the least sized (26 Inch) TV = x
Cost of 28 inches TV = x + 200
Cost of 30 inches TV = x + 400
Cost of 32 inches TV = x + 600
Total cost = 4x + 1200 = 3600
Therefore x = 2400/4 = 600
Price of 28inch + 30 inch = 800 + 1000 = 1800
Option C
Answer: (C) 1,800
Question: The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 10 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?
(A) 1/6
(B) 1/3
(C) 2/3
(D) 5/6
(E) 17/18
Rationale: priyalr
6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.
the view of the window of 10 rows is blocked. two wings, therefore 20 window seats are blocked.
Total window seats = 60
Total blocked window seats = 20
Total unblocked seats = 40
We know that a window seat was given, therefore probability for not window seat is 40/60 =2/3
ANS C
Answer: (C) 2/3
Question: what is the smallest integer that is multiple of 6,7 and 20
(A) 141
(B) 180
(C) 130
(D) 122
(E) 420
Rationale: Correct Answer :E
It is the lcm of 6,7 and 20 which is 420
Answer: (E) 420
Question: The owner of a furniture shop charges his customer 25% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table?
(A) 620
(B) 400
(C) 45
(D) 500
(E) 800
Rationale: CP = SP * (100/(100 + profit%))
= 1000(100/125) = Rs. 800.
Answer: E
Answer: (E) 800
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81 : 121
(B) 9 : 11
(C) 729 : 1331
(D) 27 : 121
(E) None of these
Rationale: Ratio of the sides = ³√729 : ³√1331 = 9 : 11
Ratio of surface areas = 92 : 112 = 81 : 121
ANSWER:A
Answer: (A) 81 : 121
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is?
(A) 153600
(B) 155600
(C) 156600
(D) 157000
(E) 158000
Rationale: Perimeter = Distance covered in 8 min. = 12000	x 8	m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m^2.
A)
Answer: (A) 153600
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 216° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 60%
Rationale: ANSWER: E
216° divided by 360° equals 0.6, therefore the sector is equal to 60% of the total
Answer: (E) 60%
Question: A car traveled 300 meters from point A to point B at a speed of 6 meter per second. Then it took the same route and came back to point A at a speed of 2 meter per second. What is its average speed?
(A) 2m/s
(B) 3m/s
(C) 4m/s
(D) 5m/s
(E) 6m/s
Rationale: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)
2X6X2/8= 3. 'B' is the answer.
Answer: (B) 3m/s
Question: The U.S. Defense Department has decided that the Pentagon is an obsolete building and that it must be replaced with an upgraded version: the Hexagon. The Secretary of Defense wants a building that is exactly 70 feet high and 200 feet on a side, and that has a hexagonal bull's-eye cutout in the center (somewhat like the current one) that is 25 feet on a side. What will be the volume of the new building in cubic feet?
(A) 3,937,500 cubic feet
(B) 15,750 cubic feet
(C) 11550√3 cubic feet
(D) 7,160,947 cubic feet
(E) 3,937,500√3 cubic feet
Rationale: Volume of the Hexagon with side 200 and height 70 = Area * height
= 6*(sqrt(3)/4)(200^2)(70)
Volume of the center bull's eye that is similar in shape of a hexagon but side 25
= 6 * (sqrt(3)/4)(25^2)*70
Volume of the building = 6*(sqrt(3)/4)(200^2)(70) - 6 * (sqrt(3)/4)(25^2)*70=7,160,947
Answer is D
Answer: (D) 7,160,947 cubic feet
Question: An outlet pipe empties a tank which is full in 10 hours. If the inlet pipe is kept open, which lets water in at the rate of 16 litres/min then outlet pipe would take 8 hours longer. Find the capacity of the tank.
(A) 8600 litres
(B) 200 litres
(C) 21600 litres
(D) 11200 litres
(E) 13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 16 litres/min, or 16*60 = 960 liters/hour;
Net outflow rate when both pipes operate would be x-960 liters/hour.
Capacity of the tank = x*10 hours = (x-960)*(10+8) hours
10x=(x-960)*18 --> x=2160 --> capacity = 10x = 21600 liters.
Answer: C.
Answer: (C) 21600 litres
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is?
(A) 15
(B) 18
(C) 20
(D) 25
(E) 26
Rationale: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
C)
Answer: (C) 20
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 56 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
(A) 52
(B) 54
(C) 56
(D) 58
(E) 60
Rationale: Annie earned 40x + 16(2x) = 72x
Let H be the number of hours that Harry worked.
Harry earned 30x + 1.5x(H-30) = 72x
(1.5x)(H) = 87x
H = 58 hours
The answer is D.
Answer: (D) 58
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 153 different possible selections of the 2 members, how many members does the club have?
(A) 20
(B) 27
(C) 40
(D) 18
(E) 95
Rationale: I have done this problem by substituting numbers
We have n!/2!(n-2)! =153
or n(n-1)/2 = 153 or n^2 -n =306 or (n-18) (n+17)=0
n=18 satisfies the equation
D
Answer: (D) 18
Question: Working at constant rate, pump X pumped out half of the water in a flooded basement in 3 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?
(A) a. 20
(B) b. 12
(C) c. 14
(D) d. 18
(E) e. 24
Rationale: rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
20 hours
A
Answer: (A) a. 20
Question: An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
(A) 72
(B) 88
(C) 266
(D) 16
(E) 19
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
Answer: A
Answer: (A) 72
Question: If a copier makes 6 copies every 3 seconds, then continues at this rate, how many minutes will it take to make 6,000 copies?
(A) 55
(B) 60
(C) 50
(D) 65
(E) 70
Rationale: 6 copies 3 seconds
6000 copies = (6000*3)/6 seconds
= 3000/60 minutes
= 50 minutes
Answer : C
Answer: (C) 50
Question: Firm A's revenues are described by the equation Ra = 17.12x and its costs by Ca = 12.87x + 2400.
Firm B's revenues are described by the equation Rb = 13.27x and its costs by Cb = 8.77x + 1500.
(x denotes the quantity of sales).
If A's volume of sales increases from 1000 to 2000 over the same period that B's volume increases from 2000 to 3000, the percent increase in profits for the firm with the biggest dollar increase in profits is
(A) 20%
(B) 30%
(C) 60%
(D) 50%
(E) 33%
Rationale: Because you need the % increase in profit.
The increase in profit = 4.5 * 1000 (increase in the units from 2000 to 3000)
The original profit = 4.5*2000 - 1500 (initially 2000 units were sold)
% increase = (4.5 * 1000)/(4.5*2000 - 1500) * 100 =60%
ANSWER:C
Answer: (C) 60%
Question: A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
(A) 11 hrs
(B) 8 hrs 45 min
(C) 7 hrs 45 min
(D) 9 hrs 20 min
(E) 10 hrs 25 min
Rationale: Explanation:
Solution 1Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back.
Therefore,
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back =5 hours 45 min
Hence, the time he would take to walk both ways
=5 hours 45 min + 2 hours
=7 hours 45 min
ANSWER IS C
Answer: (C) 7 hrs 45 min
Question: The average of six numbers is 3.95. The average of two of them is 3.5, while the average of the other two is 3.85. What is the average of the remaining two numbers?
(A) 4.5
(B) 4.6
(C) 4.7
(D) 4.8
(E) 4.9
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.5 × 2) + (3.85 × 2)]
= 23.70 – (7.0 + 7.7)
= 23.70 – 14.7 = 9.00
∴ Required average = (9.0⁄2) = 4.5
Answer A
Answer: (A) 4.5
Question: In a certain sequence the term an is given by the formula:
an=an−1+2n−1 for all integer n>1. If a7=49, what is a1?
(A) −1
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: an=an−1+2n−1an=an−1+2n−1....
as we can see that each subsequent term is 2n-1 greater than previous..
so we can straightway find a7a7=(2*1-1)+(2*2-1)+(2*3-1)+(2*4-1)+(2*5-1)+(2*6-1)+(2*7-1)+a1a1=3+5+7+9+11+13+a1a1
a7a7=49=48+a1a1..
or a1a1=1
ans C
Answer: (C) 1
Question: 50% of the apartments in a certain building have windows and hardwood floors. 25% of the apartments without windows have hardwood floors. If 40% of the apartments do not have hardwood floors, what percent of the apartments with windows have hardwood floors?
(A) 10
(B) 16 2/3
(C) 40
(D) 50
(E) 83 1/3
Rationale: total apartments = 100
with windows and hardwoods = 50
without windows = 50
without windows but having hardwoods = 0.25 *50 = 12.25
12.25 + with windows and hardwoods = 60
with windows and hardwoods = 47.75
% = 47.75 / 50 > 50%
ANSWER:D
Answer: (D) 50
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 blue nor green?
(A) 3/43
(B) 5/23
(C) 6/21
(D) 7/21
(E) 8/21
Rationale: Explanation:
Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
E)
Answer: (E) 8/21
Question: When a natural number N is successively divided by 12,13,14,15. the remainders are 16,17,18,19. What will be the sum of the remainders if the order of the division is reversed?
(A) 16
(B) 19
(C) 12
(D) 11
(E) 9
Rationale: 12 13 14 15
16 17 18 19
leave the top right- most number 8
start with bottom right-most number 5
19*14+18=284
284*13+17=3709
3709*12+16=44524
this is the number required
Now, do the successive division in the reverse order
The sum of the remainders is 19
Hence, the correct option is B
Answer: (B) 19
Question: 36 identical chairs must be arranged in rows with the same number of chairs in each row. Each row must contain at least three chairs and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible?
(A) 6
(B) 9
(C) 8
(D) 7
(E) 5
Rationale: Three conditions have to be satisfied.
1. The number of students per row has to be at least 3.
2. Number of row has to be at least 3.
3. Equal number of students has to be seated in a row.
The following arrangements satisfy all 3 conditions.
Arrangement 1: 3 students to a row; 12 rows.
Arrangement 2: 4 students to a row; 9 rows.
Arrangement 3: 6 students to a row; 6 rows.
Arrangement 4: 9 students to a row; 4 rows.
Arrangement 5: 12 students to a row; 3 rows.
You will observe that the number of students in a row is a factor of 36.
So, an alternative and faster approach is to list down factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
And then start from 3 and quickly find out if the number of rows is at least 2.
Both the conditions are satisfied for the following factors : 3, 4, 6, 9, and 12. i.e., 5 arrangements.
Ans: E
Answer: (E) 5
Question: The cross-section of a water channel is a trapezium in shape. If the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross-section is 770 square meters, what is the depth of the channel (in meters)?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: 1/2 * d * (14 + 8) = 770
d = 70
The answer is C.
Answer: (C) 70
Question: What will be the difference between simple and compound interest @10% per annum on a sum of $1000 after 4 years?
(A) $48.12
(B) $52.64
(C) $64.10
(D) $72.85
(E) $60.10
Rationale: S.I. = 1000*10*4/100 = $400
C.I. = 1000 * (1 + 10/100)^4 - 1000 = $464.10
Difference = 464.10-400 = $64.10
Answer is C
Answer: (C) $64.10
Question: Two consultants can type up a report in 12.5 hours and edit it in 7.5 hours. If Mary needs 30 hours to type the report and Jim needs 12 hours to edit it alone, how many W hours will it take if Jim types the report and Mary edits it immediately after he is done?
(A) 41.4
(B) 34.1
(C) 13.4
(D) 12.4
(E) 10.8
Rationale: Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23 in theory below)--> x=150/7;
Jim needs 12 hours to edit the report--> Jim's editing rate = 1/12;
Mary and Jim can edit a report in 7.5and --> 1/y+1/12=1/7.5=2/15 (where y is the time needed for Mary to edit the report alone) --> y=20;
How many W hours will it take if Jim types the report and Mary edits it immediately after he is done--> x+y=150/7+20=~41.4
Answer: A.
Answer: (A) 41.4
Question: Ram will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
(A) 5
(B) 6
(C) 9
(D) 24
(E) 26
Rationale: Ram will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: (A) 5
Question: If w/x = 2/3 and w/y = 3/5, then (x + y)/y =
(A) 4/5
(B) 9/10
(C) 7/5
(D) 8/5
(E) 9/5
Rationale: W/X = 2/3x=>x=3/2w and W/Y = 3/5=>y=5/3w
(X+Y)/Y = (3/2w+5/3w)/(5/3x)=9/10
Correct Option: B
Answer: (B) 9/10
Question: A train 100 m long crosses a platform 125 m long in 10 sec; find the speed of the train?
(A) 81
(B) 77
(C) 54
(D) 33
(E) 99
Rationale: D = 100 + 125 = 225
T = 10
S = 225/10 * 18/5 = 81 kmph
Answer: A
Answer: (A) 81
Question: There are 7 non-collinear points. How many triangles can be drawn by joining these points?
(A) 22
(B) 38
(C) 35
(D) 29
(E) 18
Rationale: Explanation:
A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points
The number of triangles formed = \inline {\color{Black} 7C_{3}} = 35
Answer: C) 35
Answer: (C) 35
Question: In how many different number of ways 3 boys and 2 girls can sit on a bench?
(A) 720
(B) 730
(C) 740
(D) 750
(E) 120
Rationale: npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
E
Answer: (E) 120
Question: 15, 31, 63, 127, 255, ?
(A) 513
(B) 511
(C) 523
(D) 517
(E) 527
Rationale: Each number is double of the preceding one plus 1.
Answer : B.
Answer: (B) 511
Question: The average of 20, 30 and 130 is twice the average of 10, 30, and which of the following ?
(A) 1)10
(B) 2)50
(C) 3)60
(D) 4)90
(E) 5)180
Rationale: 20 30 130 = 130+50 = 180/3 = 60
60/2 = 30
10 30 x = 40+x/3 should be smaller than 30
cross multiply 30*3-40 = 50
B
Answer: (B) 2)50
Question: The jogging track in a sports complex is 594 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 5.29 min
(B) 4.32 min
(C) 5.08 min
(D) 9.28 min
(E) 5.988 min
Rationale: Clearly, the two will meet when they are 594 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 594 m apart, they take (100/825 * 594/1000) hrs = (594/8250 * 60) min = 4.32 min.
Answer: B
Answer: (B) 4.32 min
Question: A couple decides to have 2 children. If they succeed in having 2 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 1 girl and 1 boy?
(A) 1/2
(B) 3/4
(C) 1
(D) 2
(E) 3
Rationale: Sample space = 2^2 = 4.
Favourable events = {bg}, {gb},
Probability = 2/4 = 1/2.
Ans (A).
Answer: (A) 1/2
Question: Kanul spent $3000 in buying raw materials, $2000 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
(A) $5555.555
(B) $5543.22
(C) $5568.000
(D) $5366.521
(E) $5365.66
Rationale: Let the total amount be x
then, (100-10)% of x = 3000+2000
90% of x = 5000
90x/100 = 5000
x = $50000/9
x = $5555.555
Answer is A
Answer: (A) $5555.555
Question: If a train, travelling at a speed of 180 kmph, crosses a pole in 5 sec, then the length of train is?
(A) 250 m
(B) 112 m
(C) 117 m
(D) 125 m
(E) 123 m
Rationale: A
A = 180 * 5/18 * 5 = 250 m
Answer: (A) 250 m
Question: A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 92, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
(A) 80
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 92 + 77*5x) = 260x+552x+385x = 1197x
total number of students = 15x
average = 1197x/15x = 80
A is the answer
Answer: (A) 80
Question: 4524 - ? = 2456
(A) 2058
(B) 2069
(C) 2072
(D) 2089
(E) None of these
Rationale: Explanation:
None of these
Answer: Option E
Answer: (E) None of these
Question: The average of first ten prime numbers which are odd is?
(A) 15.5
(B) 15.7
(C) 15.2
(D) 15.8
(E) 15.1
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D
Answer: (D) 15.8
Question: Matt gets a $1,300 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $400, how many sales has Matt made?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let, Average Commission = x
No. of items sold = y
Total Commission = xy
New Commission = xy+1300
New Average = (xy+1300) / (y+1) = 150+x
i.e. (xy+1300) = (y+1)* (150+x)
i.e. (xy+1300) = (xy+x+150y+150)
i.e. (1150) = (x+150y)
New Commission = 400 = 150+x
i.e. x=250
i.e. y = 6
New Sales = y+1 = 7
Answer: option D
Answer: (D) 6