MU-NLPC/Calc-aqua_rat huggingface dataset:
One fourth of a solution that was 11% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?	Choose the correct choice.
A) 24% B) 34% C) 22% D) 31% E) 8.5%

Solution: consider total solution to be 100 liters and in this case you'll have: 75*0.11+25*x=100*0.16 --> x=0.31.   Answer:31%.
Answer: D
A train crosses a platform 100 m long in 60 seconds at a speed of 45 km/hr. The time taken by the train to cross an electric pole is :  Choose the correct option.
A) 36 sec
B) 38 sec
C) 44 sec
D) 52 sec
E) None

Solution: Sol.   Speed = [45 * 5/18] m/sec = [25/2] m/sec.   Let the length of the train be x metres.   Then, x + 100 / [25/2] = 60 or x = 650 m   ∴ time taken by the trian to cross an electric pole   = [650 * 2/25= 
650 * 2/25 = 52
52 sec.   Answer 52 sec
Answer: D
David invested a certain sum of money in a bank that paid simple interest. The amount grew to $300 at the end of 2 years. He waited for another 3 years and got a final amount of $390. What was the principal amount that he invested at the beginning? Choose the correct choice from the following answers: A) $340 B) $300 C) $280 D) $260 E) $240

Solution: What shall be the rate of interest.? Does that is not required for the calculation?   Not really!   Keep in mind that the interest earned each year will be the same in Simple Interest.   At the end of 2 years, Amount = $300   At the end of 5 years, Amount = $390   This means she earned an interest of $90 in 3 years. Or $30 in each year.   We know that the interest earned each year will be the same.   Therefore she must have earned $60 in 2 years.   Hence Principal Amount = $300 - $60 = $240 Option $240300 -  60= 
300 -  60 = 240
$240 Option $240
Answer: E
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?  Choose the correct answer:
A) 166
B) 178
C) 342
D) 199
E) 112

Solution: 400*(90/100)*(95/100)= 
400*(90/100)*(95/100) = 342
342   Answer: 342
Answer: C
In a stack of boards at a lumber yard, the 13th board counting from the top of the stack is immediately below the 12th board counting from the bottom of the stack. how many boards are in the stack?  Choose one:
A) 33	B) 23	C) 25	D) 32	E) 42

Solution: 1 2 3 ....   ..............13 12 ................. 1   So the number of boards = 13+10= 
13+10 = 23
23.   Option: 23
Answer: B
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? Pick.
A) 8 B) 9 C) 7 D) 5 E) 4

Solution: 80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8nswer: 8
Answer: A
Pary spent 2⁄5 of her money on new clothes and then deposited 1⁄2 of what remained into her savings account. If she then had $21 left, how much did she have at the start?  Choose one.
A) $30 B) $35 C) $70 D) $105 E) $210

Solution: Pary spent 2⁄5 of her money on new clothes but if you see 21 is half of 3/5 money so 210 is too huge to be correct..   solution..   let the money be x..   2/5 is used...   1/2 of remaining 3/5 is put in savings account and remaining half is 21..   so 1/2 * 3/5 *x=21..   x=21*2*5/3=70..   $70
Answer: C
Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 21,870 different outfits, then for how many garments does Dave have exactly five choices?  Choose the correct choice from the following answers.
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: 21,870 = 2187*10 = 2187*5*2   Dave has exactly 5 choices for one garment.   The answer is 1.
Answer: B
Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? Pick.
A) 7	B) 6	C) 4	D) 3	E) 2

Solution: Explanation:   There are five letters in the given word.   Consider 5 blanks ....   The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.   The number of words = 3! = 6.   Answer: 6
Answer: B
A water tank is four-fifths full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
Choose the correct choice:
A) 6 B) 9 C) 10 D) 12 E) 15

Solution: The combined rate of filling/emptying the tank = 1/10 - 1/6 = -1/15   Since the rate is negative, the tank will be emptied.   A full tank would take 15 minutes to empty.   Since the tank is only four-fifths full, the time is  (4/5) * 15= 
 (4/5) * 15 = 12
12 minutes   The answer is 12.
Answer: D
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 Options:
A) 35 years  B) 40 years  C) 50 years  D) 55 years  E) None

Solution: Solution   Sum of the present ages of husband, wife and child	= (27x3+3x3) years   = 90 years.   Sum of the present ages of wife and child	= (20x2+5x2) years   = 50 years.   ∴ Husband's present age	= (90 - 50)= 
(90 - 50) = 40
40 years.   Answer 40 years
Answer: B
The integer A has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of A and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?	Choose the correct choice from the following choices:
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Let A be 67 and y be a8. Then the product of A and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.   So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9= 
3+7*9 = 66
66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.   So the answer is (5).
Answer: C
A student has to obtain 30% of the total marks to pass. He got 150 marks and failed by 30 marks. The maximum marks are?	Choose one
A) 750 B) 600 C) 650 D) 550 E) 500

Solution: Let the maximum marks be x   Then, 30% of x = 150+30   30x/100 = 180   30x= 180*100= 
180*100 = 18_000
18000   x= 600   Answer is 600
Answer: B
A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 66000. What is the share of C?  Choose the correct choice
A) Rs. 15250 B) Rs. 13375 C) Rs. 16750 D) Rs. 18000 E) None of these

Solution: Explanation:   Let the investment of C be Rs. x.   The inverstment of B = Rs.(2x/3)   The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)   Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3   C's share = Rs. [(3/11) × 66000] = Rs. 18000   Answer: Option Rs. 18000
Answer: D
John makes $55 a week from his job. He earns a raise andnow makes $60 a week. What is the % increase? Choose the correct answer:	A) 16%	B) 9.66%	C) 9.09%	D) 9.98%	E) 17%

Solution: Increase = (5/55)*100 = (1/11)*100 = 9.09%.   9.09%
Answer: C
The sum of the first k positive integers is equal to k(k+1)/2. What is the sum of the integers from r to s, inclusive, where 0<r<s?
Choose the correct choice from the following answers
A) s(s+1)/2 - (r+1)(r+2)/2	B) s(s+1)/2 - r(r+1)/2	C) s(s+1)/2 - (r-1)r/2	D) (s-1)s/2 - (r+1)(r+2)/2	E) (s-1)s/2 - r(r+1)/2

Solution: Or try plug-in method: let s=4 and r=3 --> then s+r=7. Let see which option yields 7.   A. s(s+1)/2 - (r+1)(r+2)/2 = 10-10= 
10-10 = 0
0;   B. s(s+1)/2 - r(r+1)/2= 10-6= 
10-6 = 4
4;   C. s(s+1)/2 - (r-1)r/2= 10-3= 
10-3 = 7
7 --> OK;   D. (s-1)s/2 - (r+1)(r+2)/2= 6-10=-4;   E. (s-1)s/2 - r(r+1)/2 = 6-6= 
6-6 = 0
0.   Answer: s(s+1)/2 - (r-1)r/2.
Answer: C
A shopkeeper sells 200 metres of cloth for Rs. 12000 at a loss of Rs.12 per metre. Find his cost price for one metre of cloth?  Choose the correct choice from the following choices:
A) s.59 B) s.72 C) s.62 D) s.50 E) s.13

Solution: SP per metre = 12000/200   = Rs. 60 Loss per metre   = Rs. 12 CP per metre = 60 + 12   = Rs.72   Answer: s.72
Answer: B
What was the day of the week on, 20th July, 1776?  Choose the correct answer:
A) Tuesday  B) Wednesday  C) Monday  D) Saturday  E) SUNDAY

Solution: 16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)   Counting of odd days :   1600 years have 0 odd day.   100 years have 5 odd days.   75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days.   1775 years have (0 + 5 + 2)= 
(0 + 5 + 2) = 7
7 odd days= 0 odd day.   Jan Feb Mar Apr May Jun Jul   31 + 29 + 31 + 30 + 31 + 30 + 16= 
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198
198 days= (28 weeks + 6 days)   Total number of odd days = (0 + 6)= 
(0 + 6) = 6
6.   Required day was 'Saturday'.   Answer:Saturday
Answer: D
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle? Choose the correct option.
A) 6 B) 5 C) 8 D) 6 E) 3

Solution: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle   = 2∏s = 12∏ cm.   Answer: 8
Answer: C
Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 4,700 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 700 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?
Choose the correct choice from the following answers:
A) 14.0	B) 13.0	C) 12.0	D) 11.0	E) 10.0

Solution: Solution:H stopped 700 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 
4000/800 = 5
5hrs.   this means she reached there at 11:00.   speed difference between them is 800-500= 
800-500 = 300
300 ft/hr   so by the time H stops they have 1500 ft of distance   so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance bwn them is 1500 ft so time taken to meet= 1 hr from 11:00   means 12:00 is the answer.   12.0
Answer: C
Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio S of men to women?	Choose the correct choice.
A) 5:2	B) 5:1	C) 4:3	D) 4:1	E) 3:1

Solution: (5:2) S=184 x 5 + 170 x 2 = 1260.5:2
Answer: A
If a and b are the roots of the equation x2 - 5x + 5 = 0, then the value of a2 + b2 is: Pick:
A) 36 B) 24 C) 15 D) 6 E) 5

Solution: Sol.(b) The sum of roots = a+ b = 5   Product of roots = ab = 5   Now, a2 + b2 = (a + b)2 - 2ab = 25 - 10= 
25 - 10 = 15
15   Answer 15
Answer: C
In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1300 employees, then the no. of female employees who are computer literate ?  Choose the correct choice from the following options:
A) 546	B) 674	C) 672	D) 960	E) None

Solution: Solution: Total employees,   = 1300   Female employees, 60% of 1300.   = (60 *1300) /100= 
(60 *1300) /100 = 780
780.   Then male employees,= 520   50 % of male are computer literate,   = 260 male computer literate.   62 % of total employees are computer literate,   = (62 *1300) /100= 
(62 *1300) /100 = 806
806 computer literate.   Thus, Female computer literate= 806 - 260= 
806 - 260 = 546
546.   546nswer: Option 546
Answer: A
A 7% stock yields 10%. The market value of the stock is:  Choose the correct choice from the following answers.
A) Rs 60
B) Rs 70
C) Rs 90
D) Rs 75
E) Rs 50

Solution: Explanation:   For an income of Rs. 10, investment = Rs. 100.   For an income of Rs 7, investment =Rs.100/10 X7 =Rs 70   Market value of Rs. 100 stock = Rs. 70   Answer is Rs 70
Answer: B
How many positive integers less than 60 have a reminder 01 when divided by 3?  Pick:
A) 13
B) 14
C) 15
D) 16
E) 20

Solution: 1 also gives the remainder of 1 when divided by 3. So, there are total of 20 numbers.   Answer: 20.
Answer: E
On a ferry, there are 20 cars and 10 trucks. The cars have an average mass of 1200 kg and the trucks have an average mass of 3000 kg. What is the average mass of all 30 vehicles on the ferry?  Options:	A) 1800	B) 1900	C) 2000	D) 2100	E) 2200

Solution: The total mass of the vehicles is 20*1200+10*3000= 
20*1200+10*3000 = 54_000
54000   The average mass is   54000/30= 
  54000/30 = 1_800
1800.   The answer is 1800.
Answer: A
In a mixed college 160 students are there in one class. Out of this 160 students 1/4 students are girls. How many boys are there ?
Choose the correct option
A) A)40
B) B)60
C) C)80
D) D)120
E) E)140

Solution: Total Number of Students :160   Total Girls :   160*1/4= 
  160*1/4 = 40
40   Total Boys :  160-40= 
 160-40 = 120
120   Answer is 120
Answer: D
In how many ways can a teacher write an answer key for a mini-quiz that contains 3 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?	Choose the correct choice:
A) 88
B) 90
C) 96
D) 98
E) 102

Solution: 2 multiples-choice questions can be answered in = 4 x 4 = 16 ways   3 true-false questions can be answered in = 2x2x2 = 8 ways   But out of the 8 ways, 2 ways [(True-True-True) (False-False-False)]will contain same answers   Thus 3 true-false questions can be answered in = 2x2x2 = 6 ways   Total ways to answer the quiz = 16 x 6 = 96   Answer 96
Answer: C
Helen went to the stationers and bought things worth Euro 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? Choose the correct choice from the following choices:
A) Euro 16.70
B) Euro 15.70
C) Euro 13.70
D) Euro 18.70
E) Euro 19.70

Solution: E   Euro 19.70   Let the amount taxable purchases be Euro x.   Then, 6% of x = 30/100   x = (30/100 x 100/6) = 5.   Cost of tax free items = Euro 19.70uro [  25 - (5 + 0.30)= 
  25 - (5 + 0.30) = 19.7
Euro 19.70uro 19.70
Answer: E
Complete the series
1,-3, -7, -11, -15, -19... ...  Choices:
A) -4
B) 0
C) 3
D) -2
E) -23

Solution: In the above series clearly we know we can get the next term by subtract 4 from the previous term so the answer is Option -23) -23
Answer: E
Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/3, what percent of the total number of the remaining employees would then be clerical?  Choose the correct choice from the following choices
A) 25% B) 22.2% C) 20% D) 12.5% E) 11.1%

Solution: Let's see, the way I did it was   1/3 are clerical out of 3600 so 1200 are clerical   1200 reduced by 1/3 is 1200*1/3   so it reduced 400 people , so there is 800 clerical people left   but since 400 people left, it also reduced from the total of 3600 so there are 3200 people total   since 800 clerical left / 3200 people total   you get (25%) 25%
Answer: A
If x and y are odd integers, which of the following must always be a non-integer	Answers
A) xy
B) y/x
C) x/y
D) -x^2y
E) xy/4

Solution: as X and Y are odd, multiplication of x and y would result in odd integer   (Odd Integer)/2 will always be non integer   xy/4
Answer: E
A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 250. Find the total worth of the stock?
Choose one
A) 12500	B) 20000	C) 20289	D) 20027	E) 20026

Solution: Let the total worth of the stock be Rs. x.   The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50   The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50   Total SP = 11x/50 + 38x/50 = 49x/50   Overall loss = x - 49x/50 = x/50   x/50 = 250 => x = 12500   12500nswer: 12500
Answer: A
What is the minimum number of square marbles required to tile a floor of length 3 metres 39 cm and width 1 metres 13 cm?  Select the correct option:
A) 176  B) 187  C) 540  D) 748  E) 3

Solution: The marbles used to tile the floor are square marbles.   Therefore, the length of the marble=width of the marble.the length of the marble=width of the marble.   As we have to use whole number of marbles, the side of the square should a factor of both 3 m 39 cm and 1m 13. And it should be the highest factor of 3 m 39 cm and 1m 13.   3 m 39 cm = 339 cm and 1 m 13 cm = 113 cm.   The HCF of 339 and 113 = 113.   Hence, the side of the square is 113.   The number of such square marbles required,   =339×113/113×113   =3 marbles   Option(3)
Answer: E
complete the numerical series with the correct number
5+3+3=151527
9+2+4=183652
8+6+5=484082
5+4+6=203046
9+5+4= ? Choose the correct choice:
A) 453676  B) 454586  C) 454585  D) 454386  E) 444586

Solution: 9+5+4= 453676   453676nswer : 453676
Answer: A
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference X between the highest and the lowest incentive received by the 5 salesmen in the month? Select:  A) $4000  B) $5000  C) $9000  D) $11,000  E) $13,000

Solution: Break down the question in to steps:   Step #1: incentives received by 5 salesmen -->abcde   Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de   Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000   Step #4: What is the difference between the highest and the lowest incentive:   - The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.   - The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.   - Therefore the first two numbers( ab) must equal 4, 000   - There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b   if a = 1,000 b = 3,000 --> difference X between the highest and the lowest incentive = 12,000 - 1,000 =11, 000   no other options for a or b to fit the criteria   Final List:1,0003,0007,00012,00012,000   Answer $11,000
Answer: D
The rates of simple interest in two banks A and B are in the ratio 5 : 4. A person wants to deposit his total savings in two banks in such a way that he received equal half-yearly interest from both. He should deposit the savings in banks A and B in the ratio. Choose the correct choice from the following options.
A) 2 : 5 B) 4 : 5 C) 5 : 2 D) 5 : 4 E) None of these

Solution: Let the savings be X and Y and the rates of simple interest be 5x and 4x respectively.   Then, X × 5x × 1⁄2 × 1⁄100 = Y × 4x × 1⁄2 × 1⁄100 or X⁄Y = 4⁄5   i.e., X : Y = 4 : 5.   Answer 4 : 5
Answer: B
Revenues were recorded for Store A and Store B over a period of three months. In the first month, Store A's revenues were $60,000 higher than Store B's revenues. In the second month, Store A's revenues were $9,000 higher than Store B's revenues. If Store A's average (arithmetic mean) monthly revenue for the three months was $4,000 greater than Store B's average monthly revenue, then Store B's revenue in the third month was how much greater than Store A's revenue? Choose the correct option:  A) $14,000  B) $15,000  C) $42,000  D) $46,000  E) $57,000

Solution: Answer: CIt may be tempting to come up with a lot of variables, one each for each month's revenue for each company. However, focus on the differences. In the first month, the difference was +60 in favor of A. (Note that we can drop the thousands since every number in the question is in terms of thousands.) In the second, the difference was +9 in favor of A. The average was +4 in favor of A. With these numbers, use the average formula to find the third month (T):   (60 + 9 + T)/3 = 4   69 + T = 12   T = -57   Since positive numbers indicate a difference in favor of A, negative numbers are in favor of B. -57 represents a $57,000 advantage in favor of Store B. Choice ($57,000) is correct.
Answer: E
81,162,49,98,25,50,56 Options:
A) 112 B) 127 C) 129 D) 128 E) 131

Solution: 81*2= 
81*2 = 162
162   49*2= 
49*2 = 98
98   25*2= 
25*2 = 50
50   56*2= 
56*2 = 112
112   112NSWER:112
Answer: A
A 2member committee comprising of one male & one female member is to be constitute out of 5 males and 3females. Among st the females. Ms.A refuses to be a member of the committee in which Mr.B is taken as the member. In how many different ways can the committee be constituted ?  Choose the correct choice from the following.
A) 12	B) 14	C) 12	D) 17	E) 20

Solution: 5C1 * 3C1 -1   = 15-1= 
15-1 = 14
14   14
Answer: B
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?	Choose the correct choice from the following answers
A) 28000
B) 29000
C) 38000
D) 40000
E) 42000

Solution: 38000P + 38000P/8 = 45000   38000P = 40000   SP = 40000*(95/100)= 
40000*(95/100) = 38_000
38000   38000
Answer: C
Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?  Choose the correct choice from the following choices
A) 2399 B) 2887 C) 3600 D) 2882 E) 2791

Solution: Explanation:   Let the beds be numbered 1 to 7.Case 1 : Suppose Anju is allotted bed number 1.   Then, Parvin cannot be allotted bed number 2.   So Parvin can be allotted a bed in 5 ways.   After alloting a bed to Parvin, the remaining 5 students can be allotted beds in 5! ways.   So, in this case the beds can be allotted in 5´5!ways = 600 ways.   Case 2 : Anju is allotted bed number 7.   Then, Parvin cannot be allotted bed number 6   As in Case 1, the beds can be allotted in 600 ways.   Case 3 : Anju is allotted one of the beds numbered 2,3,4,5 or 6.   Parvin cannot be allotted the beds on the right hand side and left hand side of Anju’s bed. For example, if Anju is allotted bed number 2, beds numbered 1 or 3 cannot be allotted to Parvin.   Therefore, Parvin can be allotted a bed in 4 ways in all these cases.   After allotting a bed to Parvin, the other 5 can be allotted a bed in 5! ways.   Therefore, in each of these cases, the beds can be allotted in 4´ 5! = 480 ways.   The beds can be allotted in (2x 600 + 5 x 480)ways = (1200 + 2400)= 
(1200 + 2400) = 3_600
3600 ways   Answer: 3600) 3600
Answer: C
A man covers a certain distance F in a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance?  Choose the correct choice from the following choices
A) 200 km
B) 50 km
C) 20 km
D) 60 km
E) 80 km

Solution: Not really. When you solve the 2 equation above, you get,   6T-4/3 = 5R/6 from simplifying equation 1   4T-2=R/2 from simplifying equation 2   You can now multiply equation 2 by 5 to get   5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance F= R*T=20*3= 
20*3 = 60
60 km.60 km
Answer: D
Find the compound interest on $50000 in 2years at 4% per annum, the interest being compounded half-yearly?
Choose the correct choice: A) $645.56 B) $4121.60 C) $954.26 D) $745.69 E) $1020.45

Solution: Principle = $50000   Rate = 2% half yearly = 4 half years   Amount = 50000*(1 + 2/100)^4 = 50000 * 51/50 * 51/50 * 51/50 * 51/50   = $54121.60   C.I. = 54121.60-50000= 
54121.60-50000 = 4_121.6
$4121.60   Answer is $4121.60
Answer: B