MU-NLPC/Calc-aqua_rat huggingface dataset:
If John invested $ 1 at 4 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be  Choose the correct choice from the following
A) (1.5)^4
B) 4(1.5)
C) (1.05)^4
D) 1 + (0.04)^4
E) 1 + 4(0.05)

Solution: 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 $1, an R of 5% (which would 'translate' as .05) and a T of 4. We'd have....   Answer :(1.05)^4
Answer: C
If the product of 8 integers is negative, at most how many of the integers can be negative?
Options.
A) 2  B) 3  C) 4  D) 5  E) 7

Solution: The product of 8 integers is negative   Thus an odd number of integers need to be negative to have a negative product   We are asked at most how many are required.   So, the highest odd integer before 6,i.e. 7   Correct Option : 7
Answer: E
If a and b are odd integers, which of the following is an even integer? Options:	A) 2a+b	B) 3a+b	C) 4a+b	D) 2a-b	E) a-8b

Solution: If a is odd, then 3a is odd.   Then 3a+b is even.   The answer is 3a+b.
Answer: B
A man walks at a speed of 7 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?  Choose one.
A) 1 hours	B) 1 1/2 hours	C) 2 1/6 hours	D) 2 1/1 hours	E) 2 1/2 hours

Solution: Required time   = (5 1/4)/7 + (5 1/4)/7   = 1 1/2 hours.   Answer:1 1/2 hours
Answer: B
In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?	Choose the correct choice from the following answers:
A) 8200	B) 7500	C) 7000	D) 8000	E) 8400

Solution: Equal number of candidates appeared in each state.   In state A, 6% candidates got selected.   In state B, 7% candidates got selected.   Given that 80 more candidates got selected in state B than A.   Therefore, 1% of candidates appeared in each state =80   Answer: Option 8000   = 100% of candidates appeared in each state   =80×100=8000   i.e., number of candidates appeared from each state = 8000
Answer: D
If F(x, n) be the number of ways of distributing "x" toys to "n" children so that each child receives at the most 2 toys then F(4, 3) =	Choose the correct option:
A) 3
B) 4
C) 6
D) 5
E) 7

Solution: Explanation :   We have to find the number of ways in which 4 toys can be distributed to 3 children so that each child receives at the most 2 toys.There are two possible cases:Case 1: Two of them receive 2 toys each and one of them doesn’t get any toy.There are 3 possible ways to distribute the toys in this case i.e., the three possible ways of selecting the child who will not get any toy.Case 2: Two of them receive 1 toy each and one of them receives 2 toys.Again there are 3 possible ways to distribute the toys in this case i.e., the three possible ways of selecting the child who will get 2 toys.So there are a total of 6 possible ways.   Answer : 6
Answer: C
There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability E that all three secretary are assigned at least one report?	Select the correct option
A) 8/9	B) 64/81	C) 4/9	D) 16/81	E) 5/9

Solution: I got the same answer: Here's my reasoning   First Report you have 3 choices   Second Report you have 2 choices   Third Report you have 1 choice   Fourth report 3 choices again   Then total number of ways is: 3*2*1*3=3^2*2   This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.   The number of ways of ensuring at least one report goes to each secretary is 44/92 (select 2 reports out of 4 which go to the same person)*34/91 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36   Required probability E= 36/81.4/9
Answer: C
Of the 200 math majors at a certain university, 30 percent will be assigned to advanced calculus on Monday and Wednesday and the remaining 80 percent will be assigned to advanced calculus on Tuesday and Thursday. However, 40 percent of the math majors prefer Tuesday and Thursday and 60 percent prefer Monday and Wednesday. What is the lowest possible number of math majors who will NOT be assigned to the days they prefer? Answers
A) 15	B) 20	C) 30	D) 45	E) 60

Solution: 30% of students are assigned to Monday and Wednesday = 0.3*200= 
0.3*200 = 60
60   70% of students are assigned to Tuesday and Thursday= 0.7*200= 
0.7*200 = 140
140   60% of students prefer Monday and Wednesday= 0.6*200= 
0.6*200 = 120
120   40% of students prefer Tuesday and Thursday= 0.4*200= 
0.4*200 = 80
80   Since we need theleastnumber of students who will not be assigned to their preferred days, we shall fit in themaximumpossible students as per their preference:   All of the 40% of students who prefer Tuesday and Thursday can be accommodated to their preferred days, whereas only 60 out of 120 students who prefer Monday and Wednesday can be accommodated to their preferred days.   The remaining 45 students who prefer Monday and Wednesday will be allocated to Tuesday and Thursday by default, which is not their choice.   Answer is 45.
Answer: D
Frances can complete a job in 8 hours, and Joan can complete the same job in 12 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 4 p.m. to complete the job, at what time is the job finished?
Choose the correct choice from the following choices
A) 6 p.m.	B) 7 p.m.	C) 8 p.m.	D) 10 p.m.	E) 12 p.m.

Solution: Let the total work be 24 units.   Frances can complete 3 units/hr   Joan can complete 2 units/hr   Work done by Frances in 6 hours is 18 units ; work left for Joan is 6 units ( 24 - 18)   Time required by Jones to complete the remaining work will be   6/2= 
  6/2 = 3
> 3 hours   Given Jones starts at 4PM , so she would complete the work at 7 PM   Answer will be (7 p.m.)
Answer: B
Amar takes as much time in running 15 meters as a car takes in covering 40 meters. What will be the distance covered by Amar during the time the car covers 1.9 km?	Choose the correct choice from the following answers
A) 700 m
B) 720 m
C) 712 m
D) 600 m
E) 640 m

Solution: Distance covered by Amar   = 15/40 (1.9km)   = 3/8(1900) = 712 m   Answer: 712 m
Answer: C
Ms. Mary sold two properties, X and Y, for $25,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ? Options
A) $2100 B) $2222 C) $2320 D) $2083.33 E) $2183.33

Solution: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...   Total %Loss = (Common Gain% or Loss%/10)^2   Hence Here Loss% = (20/10)^2 = 4%   which means he recovered only 96% of his investment which amount to a total revenue = 25000 + 25000= 
25000 + 25000 = 50_000
50000   i.e. 96% of cost= 40000   therefore, 4% of cost (Loss) = $2083.33   Answer: $2083.33
Answer: D
The ratio of the selling prices of three articles is 5:6:9 and the ratio of their cost prices is 4:5:8 respectively. What is the ratio of their respective percentages of profit, if the profit on the first and the last articles is the same?  Answers:
A) 4:5:6  B) 10:8:5  C) 5:6:9  D) 7:6:9  E) Cannot be determined

Solution: Given that the selling prices of three articles,   S.P1 =5X, S.P2 =6X, S.P3 =9X,   And their cost prices are C.P1 =4Y, C.P 2 =5Y, C.P3 =8Y   Given that , S.P1 –C.P1 =S.P2 –C.P2, 5X-4Y =9X-8Y, X =Y,   Their profit percentages are, p1 =(5-4)/4*100= 
(5-4)/4*100 = 25
25% ,   p2= (6-5)/5*100= 
(6-5)/5*100 = 20
20%, p3= (9-8)/8*100 = 12 1/2 %   Ratio of the percentages is 25:20:12 1/2 = 10:8:5   ANSWER:10:8:5
Answer: B
42 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?  Choose one.
A) 10  B) 16  C) 13  D) 14  E) 19

Solution: Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons 30 : 42 :: 12 : x   Working hours/day 6 : 5   30 x 6 x x = 42 x 5 x 12   x = (42 x 5 x 12)/(30 x 6)   x = 14   ANSWER 14
Answer: D
What is the remainder when 8^1 + 8^2 + 8^3 +...+ 8^9 is divided by 8?
Choose the correct choice from the following options:	A) 4	B) 0	C) 2	D) 5	E) None of the above

Solution: Notice that in the brackets we have the sum of 9 even multiples of 8, which yields remainder of 0 upon division by 8.   Answer : 0
Answer: B
A circular logo is enlarged to fit the lid of a jar. The new diameter is 40 per cent larger than the original. By what percentage has the area of the logo increased? Select the correct option.
A) 50
B) 96
C) 100
D) 125
E) 250

Solution: Let old diameter be 4 , so radius is 2   Old area = 4π   New diameter is 5.6 , so radius is 2.8   New area = 7.84π   Increase in area is 3.84π   % increase in area = 3.84/4*100   So, % increase is 96%   Answer will be (96)
Answer: B
In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/6 . If the probability that a number 12 or larger is drawn is 1/3 , what is the probability that a number less than or equal to 20 is drawn?	Pick.
A) 1/18  B) 1/6  C) 1/3  D) 1/2  E) 5/6

Solution: You can simply use sets concept in this question. The formula   Total = n(A) + n(B) - n(A and B) is applicable here too.   Set 1: Number 12 or larger   Set 2: Number 20 or smaller   1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)   1/3 + P(Set 2) - 1/6 = 1   P(Set 2) = 5/6   Answer (5/6)
Answer: E
Ron begins reading a book at 2: 30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6: 00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page? Choices:
A) 7: 00 p.m. B) 7: 30 p.m. C) 10: 45 p.m. D) 11: 30 p.m. E) 11: 45 p.m.

Solution: M gains 50-30= 
50-30 = 20
20 pages per hour on R   at 6pm R has read 105 pages and M is  105+5= 
 105+5 = 110
110 pages behind him   time=110/20= 
110/20 = 11/2 = around 5.5
5.5 hours   they are on the same page at 11:30pm   11: 30 p.m.
Answer: D
A boat travels 80 km downstream in 8 hours and 60 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.	Pick one
A) 7.5 km/hr, 2.5 km/hr B) 5 km/hr, 4 km/hr C) 1 km/hr, 6 km/hr D) 2 km/hr, 1 km/hr E) 4 km/hr, 1 km/hr

Solution: Downstream speed=80km/8hrs   =10kmph   upstream speed80  /8= 
80  /8 = 10
10kmph   upstream speed=60km/12hrs   =5kmph   speed of boat60  /12= 
60  /12 = 5
5kmph   speed of boat=avg of downstream and upstream speeds   speed of boat=(10+5)/2= 
(10+5)/2 = 15/2 = around 7.5
7.5kmph.   current speed=half of the difference of downstream and upstream speeds   currend speed=(10-5)/2= 
(10-5)/2 = 5/2 = around 2.5
2.5kmph   ans is 7.5km/hr, 2.5km/hr   7.5 km/hr, 2.5 km/hrNSWER:7.5 km/hr, 2.5 km/hr
Answer: A
Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
Choose the correct choice from the following answers: A) 287 B) 132 C) 156 D) 158 E) 267

Solution: 2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   88 * 1 1/2= Rs.132   Answer: 132
Answer: B
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3? Pick one.
A) 37
B) 42
C) 49
D) 52
E) 53

Solution: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).   In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.   i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0   or −27+36+21+12=k−27+36+21+12=k   or k=k= 42   42
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train. Choose the correct option
A) 150 meter	B) 286 meter	C) 186 meter	D) 288 meter	E) 265 meter

Solution: Speed = 60*(5/18) m/sec   = 50/3 m/sec   Length of Train (Distance)   = Speed * Time     (50/3) * 9= 
  (50/3) * 9 = 150
150 meter   150 meternswer:150 meter
Answer: A
Which of the following equations is NOT equivalent to 4c^2 = d^2 - 9 ?
Pick:
A) 4c^2 + 9 = d^2
B) 4c^2 - d^2 = -9
C) 4c^2= (d + 3)(d - 3)
D) 2c = d - 3
E) c^2 = (d^2-9)/4

Solution: 4c^2 = d^2 - 9   The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.   Looking at Answer D, we have....   2c = d - 3   While you COULD take the square root of both sides of the original equation, it's important to note that the square root of d^2 - 9 is NOT (d-3).   d^2 - 9 can be factored into (d-3)(d+3), but neither of these parentheses is the square root of d^2 - 9.   You can see the proof when you square either of the two parentheses:   (d-3)^2 = d^2 - 6c+ 9   (d+3)^2 = d^2 + 6c + 9   Thus, 2c = d - 3 is NOT equivalent to the prompt.
Answer: D
Virat buys an old car for Rs. 50000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 60000, his gain percent is:
Choose the correct choice from the following choices
A) 3 (4/7) % B) 11 (1/9) % C) 12 (2/3) % D) 12% E) None of these

Solution: Explanation:   C.P. = Rs. (50000 + 4000) = Rs. 54000   S.P. = Rs. 60000.   Gain% = ( (6000 / 54000) * 100 ) % = 11 (1/9)%   ANSWER 11 (1/9) %
Answer: B
A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. what is the rate of interest ?  Choose the correct choice from the following options.
A) 3 %  B) 4 %  C) 5 %  D) 6 %  E) 7 %

Solution: Solution   S.I= Rs.(15500-12500) =Rs.3000   Rate=(100*3000/12500*4)% =6%   Answer 6 %
Answer: D
How much is 85% of 40 is greater than 4/5 of 25?  Choose the correct option:
A) 22
B) 14
C) 88
D) 12
E) 66

Solution: (85/100) * 40 – (4/5) * 25   = 14   Answer: 14
Answer: B
On a map the distance between two mountains is 312 inches. The actual distance between the mountains is 136 km. Ram is camped at a location that on the map is 28 inch from the base of the mountain. How many km is he from the base of the mountain?
Pick one:	A) 14.83	B) 12.2	C) 14.8	D) 14.82	E) 14.12

Solution: Explanation:   Since 312 inch = 136 km   So 1 inch = 136/312 km   So 28 inch = (136 Ã— 28)/ 312 = 12.2 km   Answer: 12.2
Answer: B
A certain family has 3 sons: Richard is 6 years older than David, and David is 8 years older than Scott. If in 8 years, Richard will be twice as old as Scott, then how old was David 7 years ago?
Answers
A) 8  B) 10  C) 12  D) 14  E) 7

Solution: Let's say   Age of Richard is "R"   Age of David is "D"   Age of Scott is "S"   Now   Richard is 6 years older than David,   i.e. R = D +6   David is 8 years older than Scott   i.e. D = S +8   If in 8 years, Richard will be twice as old as Scott   i.e. R+8 = 2x(S+8)   i.e. R+8 = 2S + 16   i.e. R = 2S+8   But R = D+6 = (S+8)+6 = S+14   therefore, 2S + 8 = S +14   i.e. S = 6   i.e. R = 20   i.e. D = 14   Now,   how old was David 7 years ago?   i.e. D-7 = 14-7= 
14-7 = 7
7 years   ANSW7R:7
Answer: E
A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 25 miles per gallon, and from Town B to Town C, the car averaged 30 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C? Choose one:  A) 24  B) 25  C) 23  D) 22  E) 26.5

Solution: step 1) took LCM of 25 and 30.. came as 150.   step 2) 150 distance between B to C... do 150/30 hence 5 gallons used   step 3) twice distance.. hence 150*2= 300... do as above.. 300/25= 12 gallons used   step 4) total gallons.. 5+12= 17 gallons   step ) total miles= 150+300= 
150+300 = 450
450 miles   hence.. average of whole journey= 450/17 which comes to 26.5   Answer : 26.5
Answer: E
Five bells ring together and ring at intervals of 2, 6, 8, 12 and 15 seconds respectively. How many times will they ring together in 60 minutes?	Choices
A) 34
B) 33
C) 32
D) 31
E) 30

Solution: Explanation:   LCM of 2, 6, 8, 12 and 15 is 120   120 second = 2 minutes   Six bells rings in 2 min intervals   Therefore, Number of times they ring together in 60 min = 1 + (60/2)= 
1 + (60/2) = 31
31   Answer: Option 31
Answer: D
Submarine M and Submarine N are equipped with sonar devices that can operate within a 5,000 yard range. Submarine M remains in place while Submarine N moves 4,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West  Pick:
A) I only B) II only C) I and III only D) III only E) II,III only

Solution: It's evident if we make a diagram for the Movement of N respect to M.   From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.   Thus it can only move north or west or anything in that curve.   Answer : I and III only
Answer: C
In a group of 100 cars, 37 cars do not have air conditioning. If at least 41 cars have racing stripes, what is the greatest number of cars that could have air conditioning but not racing stripes? Choose the correct choice from the following answers:
A) 45
B) 47
C) 59
D) 51
E) 53

Solution: Lets assume AC=63(includesonly AC carsandcars with AC and racing stripes)   lets assume RS(racing stripes)>=41(includescars with AC and racing stripesandonly racing stripes).   Now since we want to maximize(only AC) we have to see to it thatcars with AC and racing stripesis minimal(assume 0) But since RS>=41.. we have to assign atleast 4 tocars with AC and racing stripes.   Hence AC=63-4= 
63-4 = 59
59.   The answer is
Answer: C
The difference between simple and compound interest on Rs. 1700 for one year at 10% per annum reckoned half-yearly is? Choose the most appropriate option:  A) 8.25  B) 4.25  C) 9.25  D) 3.25  E) 2.25

Solution: S.I. = (1700 * 10 * 1)/100 = Rs. 170   C.I. = [1700 * (1 + 5/100)2 - 1700]   = Rs. 174.25 Difference = (174.25 - 174)   = Rs.4.25.   Answer:4.25
Answer: B
Lines y=√5·x+1 and y=2√5·x−1 intersect at what height above the x axis?
Options:
A) 3  B) √5  C) 3√5  D) 0  E) 5√5

Solution: Solve two equations for y   y=√5·x+1   y=2√5·x−1   Set the two equations equal to each other and solve for x   √5·x+1=2√5·x−1   2 = √5·x   2/(√5) = x   Plug x = 2/(√5) into any one of the original equations to find the y value (height above x axis) where the two lines intersect   y=√5·x+1   y=√5·(2/(√5))+1   y = 2 + 1= 
2 + 1 = 3
3   Final answer:   3) 3
Answer: A
A number when successively divided by 3,5 and 8 leaves remainders 1,4 and 7 respectively. Find the respective remainders E when the order of the divisors is reversed.	Choose one
A) 8,5,3  B) 4,2,1  C) E=3,2,1  D) E=6,4,2  E) None of above

Solution: My approach would be   Three Divisors: 3, 5, 8   Three Remain: 1, 4, 7   Start from the bottom of the last column i.e. from the third remainder:   Go up diagonally and multiply by the second divisor:  5*7= 
 5*7 = 35
35   Go down and add the second remainder:   35 + 4= 
  35 + 4 = 39
39   Go up diagonally and multiply by the first divisor:  39* 3= 
 39* 3 = 117
117   Go down and add the first remainder:  117 + 1= 
 117 + 1 = 118
118   Divide 118 by 8, 5, 3   118/8 gives quotient= 14 and remainder = 6   14/5 gives quotient = 2 and remainder = 4   2/3 gives quotient = 0 and remainder = 2   Ans is D i.e. 6,4,2
Answer: D
Of the 100 athletes at a soccer club, 40 play defense and 60 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between Choose the correct choice from the following choices
A) 10 to 20 B) 10 to 40 C) 20 to 40 D) 30 to 70 E) 40 to 70

Solution: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.   {Total} = {defense} + {midfield} - {both} + {neither}   100 = 40 + 60 - {both} + {neither}   {both} = {neither} + 0   Since the least value of {neither} is given to be 20, then the least value of {both} is   20+0= 
  20+0 = 20
20.Eliminate A and B.   Answer: 20 to 40.
Answer: C
What is the units digit of (12^3)(15^4)(31^7)?
Select the correct option
A) 0  B) 2  C) 4  D) 6  E) 8

Solution: The units digit of 12^3 is the units digit of 2^3 which is 8.   The units digit of 15^4 is the units digit of 5^4 which is 5.   The units digit of 31^7 is the units digit of 1^7 which is 1.   The units digit of 8*5*1 is 0.   The answer is 0.
Answer: A
If the sum of n terms of two series in A.P. are in the ratio (5n + 4) : (9n + 6) then find the ratio of their 13th terms.  Choices
A) 129/139 B) 129/1378 C) 129/136 D) 129/134 E) 129/131

Solution: 129/131xplanation:   Formula for sum of n terms in AP = SnSn = n2n2(2a + (n – 1)d ]   5n + 4 ⇒ 5(n – 1) + 9 ⇒ [2(92)+(n−1)5][2(92)+(n−1)5]   Common difference (d) = 5, First term (a) = 9292   Similarly   Second series given 9n + 6 ⇒⇒ 9(n – 1) + 15 ⇒ [2(152)+(n−1)9][2(152)+(n−1)9]   Common difference (d) = 9, First term (a) = 152152   So   13th term for first series is = a + 12d = 129/2   13th terms for second series is = a + 12d = 231/2   Ratio = 129/131   Answer:129/131
Answer: E
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 7720 votes were polled, then how many valid votes did B get?  Choose the correct option:
A) 1888 B) 2999 C) 2834 D) 2509 E) 2991

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 7720   32.5k = 32.5k/100k * 7720 = 2509   The number of valid votes polled in favour of B is 2834.   Answer: 250932.5 /100  * 7720= 
32.5 /100  * 7720 = 2_509
2509   The number of valid votes polled in favour of B is 2834.   Answer: 2509
Answer: D
We bought a total of 80 books at the store. Math books cost $4 and history books cost $5. The total price was $368. How many math books did we buy? Choose the correct choice from the following: A) 28 B) 32 C) 36 D) 40 E) 44

Solution: M + H = 80   H = 80 - M   4M + 5H = 368   4M + 5*(80 - M) = 368   M = 32   The answer is 32.
Answer: B
A train 90 meters long completely crosses a 270-meter long bridge in 30 seconds. What is the speed of the train in km/h?
Choose the correct answer:
A) 34.2 km/h B) 37.2 km/h C) 40.2 km/h D) 43.2 km/h E) 46.2 km/h

Solution: speed = distance / time = (90 + 270)/30 = 360/30 (m/s) * 3600/1000 = 43.2 km/h   The answer is 43.2 km/h.
Answer: D