mathewhe/aqua_rat huggingface dataset:
Question: If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.
(A) 8r
(B) 4r
(C) 9r
(D) 7r
(E) 10r
Rationale: Hint: (1-cos(t))0.5 = 20.5×sin(t/2)
The answer is 8r.
Imagine the circle resting on coordinate (0,0) and moving east.
Also magine the point on the circle to start at (0,0).
Let t be the angle between the point on the circle and the center of the circle.
The position of the point on the circle, relative to t, is:
x = rt - r×sin(t)
y = r - r×cos(t)
Taking the derivatives:
dx/dt = r - r×cos(t)
dy/dt = r×sin(t)
The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.
So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.
After a few steps this integral becomes:
r×21/2 × (1-cos(t))1/2.
Using the hint:
r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi
= 2×r × (-2×cos(t/w) from 2×pi to 0)
= 8r
correct answer A
Answer: (A) 8r
Question: Seven 6 faced dice are thrown together. The probability that all the three show the same number on them is?
(A) 1/32
(B) 1/46656
(C) 1/33
(D) 1/38
(E) 1/34
Rationale: The three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways.
Hence the probability is 6/279936
= 1/46656
Answer: B
Answer: (B) 1/46656
Question: In a hostel there were 100 students. 20 students left the hostel,the average budget is increased by rupees 10. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) 2200
(B) 1660
(C) 5400
(D) 2400
(E) 1800
Rationale: Let average is x
100x + 400 = 80(x+10)
x = 20
100 * 20 + 400 = 2400
Answer:D
Answer: (D) 2400
Question: man can row upstream at 30 kmph and downstream at 40 kmph, and then find the speed of the man in still water?
(A) 30
(B) 35
(C) 40
(D) 70
(E) 45
Rationale: US = 30
DS = 40
M = (30 + 40)/2
= 35
Answer:B
Answer: (B) 35
Question: Find the odd man out
6, 13, 29, 61, 125, 253, 509
(A) 6
(B) 13
(C) 29
(D) 125
(E) 509
Rationale: 1*2+3 = 5
5*2+3 = 13
13*2+3 = 29
29*2+3 = 61
61*2+3 = 125
125*2+3 = 253
253*2+3= 509
ANSWER:A
Answer: (A) 6
Question: The equation of line a is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line a?
(A) 48
(B) 50
(C) 60
(D) 75
(E) 100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line a as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: (C) 60
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 6, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
(A) 27
(B) 22
(C) 24
(D) 26
(E) 30
Rationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes
Answer: A
Answer: (A) 27
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, (....)
(A) 27
(B) 20
(C) 22
(D) 17
(E) 26
Rationale: There are two series (8, 11, 14, 17) and (7, 12, 17) increasing by 3 and 5 respectively.
answer : D
Answer: (D) 17
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 63 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
(A) 20
(B) 10
(C) 30
(D) 50
(E) 40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+63) and number of girls were 5x
Hence, 2(5x) = x + 63
=> 10x = x + 63
=> x = 7
Number of girls in the beginning = (5x + 15) = (5×7 + 15) = 50
Answer is D.
Answer: (D) 50
Question: Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements R are possible?
(A)  30
(B)  60
(C)  90
(D)  180
(E)  540
Rationale: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements R INCLUDING the order of tasks.
could you explain the highlighted step... i'm getting 90 = 15 * 3!
suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z
one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways
X--	Y--	Z
12--	34--	56
12--	56--	34
34--	12--	56
34--	56--	12
56--	12--	34
56--	34--	12
so the answer should be 15*6 = 90
But now you can fruther decide which task you want to perform first X Y or Z..C
Answer: (C)  90
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
(A) 10
(B) 20
(C) 40
(D) 35
(E) 45
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Answer: (B) 20
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 375
(B) 400
(C) 450
(D) 350
(E) 250
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER A
Answer: (A) 375
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 288
(B) 162
(C) 878
(D) 168
(E) 122
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Answer: (B) 162
Question: If 10 crates have 96 apples each and how many apples more is required in order to make 100 apples in each crate?
(A) 5
(B) 10
(C) 40
(D) 20
(E) 0
Rationale: Each crate requires 4 apples and totally there are 10 crates so required apples = 10 * 4 = 40
Answer: C
Answer: (C) 40
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 277
(B) 267
(C) 222
(D) 160
(E) 123
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: (D) 160
Question: If the sides of a rectangle are increased by 35%, what is the percentage increase in the area?
(A) 38.25%
(B) 40.25%
(C) 82.25%
(D) 50%
(E) 65%
Rationale: If sides are a and b, after increase sides would be 1.35a and 1.35 b.
Percentage increase in area = (1.35a*1.35b - ab) *100/ab = 82.25
Answer : C
Answer: (C) 82.25%
Question: The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 100 kg
(B) 102.5 kg
(C) 85 kg
(D) Data inadequate
(E) None of these
Rationale: Explanation:
Total weight increased = (10 x 3.5) kg = 35 kg.
Weight of new person = (65 + 35) kg = 100 kg.
Answer: A
Answer: (A) 100 kg
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
(A) 1/7
(B) 2/7
(C) 1/3
(D) 7/12
(E) 2/3
Rationale: Same amount of water made bigger jar 1/6 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/6+1/6=2/6= 1/3 full.
Answer: C.
Answer: (C) 1/3
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?
(A) 60
(B) 80
(C) 40
(D) 120
(E) 160
Rationale: Explanatory Answer
Let the original number be x.
Let A be the value obtained when x is increased by 12.5%.
Therefore, A = x + 12.5% of x
Let B be the value obtained when x is decreased by 25%.
Therefore, B = x - 25% of x
The question states that A - B = 30
i.e., x + 12.5% of x - (x - 25% of x) = 30
x + 12.5% of x - x + 25% of x = 30
37.5% of x = 30
x = 30/37.5*100 = 80
The correct choice is (B)
Answer: (B) 80
Question: A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction?
(A) 8%
(B) 10%
(C) 2%
(D) 5%
(E) 6%
Rationale: Actual price = 100+10 = $110
Saving = 10/110 * 100 = 100/11 =10% approximately
Answer is B
Answer: (B) 10%
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?
(A) 2 meters
(B) 6 meters
(C) 5 meters
(D) 3 meters
(E) 7 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 72,000 m : C is the circumference
C = 3 meters
correct answer D
Answer: (D) 3 meters
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
(A) 159
(B) 194
(C) 205
(D) 209
(E) None of these
Rationale: We may have 1 boy and 3 girls or 2 boys and 2 girls or 3 boys and 1 girl or 4 boys
Required number of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + 6C4
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + 6C2
= (6 x 4) +[(6x5)/(2x1) x (4x3)/(2x1)] + [(6x5x4)/(3x2x1)) x 4] +[(6x5)/(2x1)]
= 24 + 90 + 80 + 15 = 209
Answer D.
Answer: (D) 209
Question: 1/2-[(2/5*5/32)+1]+9/16=
(A) 29/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Rationale: 1/2 - [(2/5*5/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: (E) 0
Question: A man sold two chairs at Rs. 1,200 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is:
(A) 1% loss
(B) 2% loss
(C) 4% loss
(D) 15 gain
(E) NOne
Rationale: Solution: In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut:
Loss on total deal,
= (Common loss or gain percentage /10)2 = (20/10)2
= 4%
Alternatively, It can be also calculated through Graphic Change Method: This can be given by,
100==20% gain ==>120==20% loss==>96.
Loss = 4% (As 100 became 96).
Answer: Option C
Answer: (C) 4% loss
Question: If - 5 < x < 7 and y < - 9, then the lowest possible value for (-xy) is
(A) between 60 and 70
(B) between 0 and 60
(C) 0
(D) between 0 and -70
(E) none of these
Rationale: If - 5 < x < 7 and y < - 9,
Say y = -100 (y<-9)
x = 6
So -xy =600 which is more than 70.
Answer is E.
Answer: (E) none of these
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 277
(B) 276
(C) 800
(D) 271
(E) 255
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Answer: (C) 800
Question: C and D start a business with Rs.4000 and Rs.10000 respectively. Hoe should they share their profits at the end of one year?
(A) 5:2
(B) 2:5
(C) 5:3
(D) 3:5
(E) 2:3
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by C and D =
4000 : 10000 => 2:5 .
Answer:B
Answer: (B) 2:5
Question: What is the area inscribed by the lines y = 10, x = 1, y = 3x+1 on an xy-coordinate plane?
(A) a) 1
(B) b) 2
(C) c) 3
(D) d) 6
(E) e) 12
Rationale: First, let's graph the lines y = 10 and x = 1
At this point, we need to find the points where the line y = 3x+1 INTERSECTS the other two lines.
For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 3x+1 to get y = 3(1)+1 = 4
Perfect, when x = 1, y = 5, so one point of intersection is (1,4)
For the horizontal line, we know that y = 10, so we'll PLUG y = 10 into the equation y = 3x+1 to get 10 = 3x+1. Solve to get: x = 3
So, when y = 10, x = 3, so one point of intersection is (3,10)
Now add these points to our graph and sketch the line y = 3x+1
At this point, we can see that we have the following triangle.
The base has length 2 and the height is 6
Area = (1/2)(base)(height)
= (1/2)(2)(6)
= 6
Answer:
D
Answer: (D) d) 6
Question: The perimeters of two squares are 40 cm and 28 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
(A) 22 cm
(B) 28.4 cm
(C) 26 cm
(D) 28 cm
(E) 29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 28/4 = 7 cm
Area of third Square = 10*10 - 7*7
= 51 cm
So side of third square = 7.1 [because area of square = side*side]
Perimeter = 4*Side = 4*7.1 = 28.4 cm
Answer: Option B
Answer: (B) 28.4 cm
Question: One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 2,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
(A) $ 5,000
(B) $ 6,000
(C) $ 8,000
(D) $ 10,000
(E) $ 12,000
Rationale: This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
D
Answer: (D) $ 10,000
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) 21.6
(B) 21.69
(C) 21.66
(D) 21.64
(E) 21.61
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 = Rs.21.60.Answer:A
Answer: (A) 21.6
Question: The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 5 years ago ? (RBI Assistant 2015)
(A) 24
(B) 18
(C) 12
(D) 16
(E) 13
Rationale: Let the present age of Viju be 7x years and that of Aju be 2x years.
Then, 4 years from now
7x + 4 / 2x + 4 = 5 / 2
or 4x = 12
or x = 3
Viju present age = 7 * 3 = 21 years
Viju age 5 years ago = 21 - 5 = 16 years
answer :D
Answer: (D) 16
Question: In his room, Dumbo has three trousers. One of them is black, the second is blue, and the third is brown. In his room, he also has four shirts. One of them is black and the other 3 are white. He opens his room in the dark and picks out one shirt and one trouser pair without examining the colour. What is the likelihood that neither the shirt nor the trouser is black?
(A) 1/12
(B) 1/6
(C) 1/2
(D) 1/4
(E) 1/3
Rationale: Probability that trouser is not black = 2/3
Probability that shirt is not black = 3/4
Required probability = 2/3 x 3/4 = 1/2
ANSWER:C
Answer: (C) 1/2
Question: If y exceeds x by 20%, then x is less than y by?
(A) 16 2/7%
(B) 16 7/3%
(C) 16 2/3%
(D) 16 2/6%
(E) 16 1/3%
Rationale: X=100	y=120
120------20
100-------? => 16 2/3%
Answer: C
Answer: (C) 16 2/3%
Question: From 6 positive numbers and 6 negative numbers, how many groups C of 4 numbers, yielding a positive product, can be formed?
(A) 720
(B) 625
(C) 30
(D) 960
(E) 255
Rationale: Potential combinations of 4 numbers that will yield positive product
++++ 4C6
---- 4C6
++-- 2C6*2C6
4C6 + 4C6 + 2C6*2C6
C=15 +15 + 15*15 = 255.E
Answer: (E) 255
Question: What is the 9th digit to the right of the decimal point in the decimal equivalent of 48/11?
(A) 3
(B) 5
(C) 6
(D) 4
(E) 2
Rationale: 48/11 = 4.3636....
36 is non-terminating repeating decimal.
The 9th digit to the right of decimal point will be 3.
Answer A
Answer: (A) 3
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6800 ?
(A) 4966
(B) 6791
(C) 2877
(D) 2676
(E) 1881
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6800 x 6) - 34009]
= Rs. (40800 - 34009)
= Rs. 6791
Answer: B
Answer: (B) 6791
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.4400, what will be the difference between Q and R's share?
(A) 2788
(B) 5500
(C) 7282
(D) 2782
(E) 2729
Rationale: 4 --- 4400
5 --- ? => 5500
Answer:B
Answer: (B) 5500
Question: The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 2333
(B) 2777
(C) 1200
(D) 1987
(E) 1671
Rationale: P --- 10 ---- 600
P --- 5 ----- 300
3P --- 5 ----- 900
------
=> 1200
Answer:C
Answer: (C) 1200
Question: Mike invested $2000 in fund A and $1000 in fund B. Over the next Three years, the money in Fund A earned a total interest of 18 percent for the three years combined and the money in fund B earned 30 percent annual interest compounded annually. Three years after Mike made these investments. Mike's investment in fund A was worth how much more than his investment in fund B?
(A) 1. $160
(B) 2. $150
(C) 3. $200
(D) 4. $183
(E) 5. $163
Rationale: interest on fund A will be 360. rate of interest will be 6% per annum simple interest as 18% is for 3 year. this will make investment A 2360 at the end of 3rd year.
interest on fund B will be 1197 on 30% interest compounded annually. This will make investment B 2197 at the end of 3rd year.
Difference in investment A and investment B=2360-2197=163
answer is E.
Answer: (E) 5. $163
Question: 23, 29, 31, 37, 41, 43, (...)
(A) 53
(B) 47
(C) 48
(D) 59
(E) 45
Rationale: Explanation :
All are prime numbers in their order, starting from 23
Hence, next number is 47
Answer : Option B
Answer: (B) 47
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 10 percent on food, and 40 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A)  2.8%
(B)  3.6%
(C)  4.4%
(D)  5.2%
(E)  6.0%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=10, others=40
Tax on clothing= 2
Tax on others=3.2
Percentage= 5.2/100 =5.2%
Answer: D
Answer: (D)  5.2%
Question: If an object travels at 8 feet per second, how many feet does it travel in forty five minutes?
(A) 18000
(B) 24000
(C) 21600
(D) 18000
(E) 22000
Rationale: If an object travels at 8 feet per second it covers 8x60 feet in one minute, and 8x60x45 feet in forty five minutes.
Answer = 21600 Answer:C
Answer: (C) 21600
Question: Find the average of the first 23 natural numbers?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Average of the first 'n' natural numbers = (n + 1)/2
We get (23 + 1)/2 = 12
ANSWER:E
Answer: (E) 12
Question: A family pays $800 per year for an insurance plan that pays 80 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total which of the following?
(A) $1,000
(B) $1,200
(C) $1,400
(D) $1,800
(E) $2,200
Rationale: The family pays $800 per year for the plan, plus (100 percent minus 80 percent) or 20 percent of the first $1,000 in medical expenses, while the insurance company pays 80 percent of the first $1,000, or $800. It must pay an additional $200 to match what the family pays out. Since the $200 comes after the first $1,000 in expenses, it must represent 100 percent of additional expenses. Therefore, there must have been $1,000 plus $200 or $1,200 in medical expenses altogether.
B. $1,200
Answer: (B) $1,200
Question: A factory that employs 1000 assembly line workers pays each of these workers $5 per hour for the first 40 hours worked during a week and 1½ times that rate for hours worked in excess of 40. What was the total payroll for the assembly-line workers for a week in which 30 percent of them worked 15 hours, 50 percent worked 40 hours, and the rest worked 50 hours?
(A)  $180,000
(B)  $185,000
(C)  $190,000
(D)  $177,500
(E)  $205,000
Rationale: 30% of 1000 = 300 worked for 15 hours
Payment @ 5/hr
Total Payment = 300*15*5 = 22500
50 % of 1000 = 500 worked for 40 hours
Payment @ 5/hr
Total payment = 500*40*5 = 100000
Remaining 200 worked for 50 Hours
Payment for first 40 Hours @ 5 /hr
Payment = 200*40*5 = 40000
Payment for next 10 hr @ 7.5/hr
Payment = 200 * 10 * 7.5 = 15000
Total Payment = 22500+100000 + 40000 +15000 = 1775000
Hence , answer is D
Answer: (D)  $177,500
Question: What is the sum of all remainders obtained when the first 100 natural numbers are divided by 7?
(A) 397
(B) 401
(C) 403
(D) 405
(E) 306
Rationale: A positive integer can give only the following 9 remainders when divided by 9: 1, 2, 3, 4, 5, 6, 7, 8, and 0.
1 divided by 9 gives the remainder of 1;
2 divided by 9 gives the remainder of 2;
...
8 divided by 9 gives the remainder of 8;
9 divided by 9 gives the remainder of 0.
We'll have 11 such blocks, since 99/9=11. The last will be:
91 divided by 9 gives the remainder of 1;
92 divided by 9 gives the remainder of 2;
...
98 divided by 9 gives the remainder of 8;
99 divided by 9 gives the remainder of 0.
The last number, 100, gives the remainder of 1 when divided by 9, thus the sum of all remainders will be:
11(1+2+3+4+5+6+7+8+0)+1=306.
Answer: E.
Answer: (E) 306
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability J that the sum of the two integers will equal 9 ?
(A)  0.15
(B)  0.20
(C)  0.25
(D)  0.30
(E)  0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20. J=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: J=1*1/5.
Answer: B.
Answer: (B)  0.20
Question: Two cars cover the same distance at the speed of 40 and 24 kmps respectively. Find the distance traveled by them if the slower car takes 2 hour more than the faster car?
(A) 278
(B) 480
(C) 960
(D) 278
(E) 261
Rationale: 40(x + 2) = 24x
X = 8
60 * 8 = 480 km
Answer:B
Answer: (B) 480