MU-NLPC/Calc-aqua_rat huggingface dataset:
If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 40 overs in an ideal case scenario?
Choices.
A) 1652  B) 1651  C) 1653  D) 1323  E) None

Solution: Solution:   1323   Explanation:   For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:    6 * 5 + 3= 
 6 * 5 + 3 = 33
33   But this will have to go like it only till the 39th over. In the 40th over, he can hit a six in the last ball as well as that will be the last ball of his destination.   Thus runs for the 40th over will be  6 * 6= 
 6 * 6 = 36
36.   Hence the maximum runs= 33 * 39 + 36= 
33 * 39 + 36 = 1_323
1323   Answer 1323
Answer: D
In a box of 12 pens, a total of 4 are defective. If a customer buys 3 pens selected at random from the box, what is the probability that neither pen will be defective?
Choices.
A) 1/6
B) 2/55
C) 14/55
D) 12/55
E) 3/4

Solution: Method- 1   There are 9 fine pieces of pen and 4 defective in a lot of 12 pens   i.e. Probability of first pen NOT being defective = (8/12)   i.e. Probability of Second pen NOT being defective = (7/11)   i.e. Probability of third pen NOT being defective = (6/10)   Probability of Both pen being NON-defective = (8/12)*(7/11)*(6/10) = 14/55   Answer: option 14/55
Answer: C
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2640 in all from both of them as interest. The rate of interest per annum is?	Choose the correct choice from the following options.
A) 16% B) 12% C) 74% D) 10% E) 45%

Solution: Let the rate be R% p.a. Then,   (5000 * R * 2)/100 + (3000 * R * 4)/100 = 2640   100 R + 120 R = 2640   R = 12%   Answer:12%
Answer: B
Bob finishes the first half of an exam in one-seventh the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam?
Choose the correct option:
A) 15
B) 24
C) 27
D) 36
E) 40

Solution: Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/7's the time of the second half (7/7's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem is via ratio's - first half is 1:8 and the second half is 7:8). With each eighth of an hour being 7.5 minutes (60/8), the first half of the exam would have taken 15 minutes. Correct answer is 15.
Answer: A
Of the students at a certain high school, 90 percent took a course in algebra or geometry and 18 percent took courses in both. If the percent of students who took a course in algebra was 2 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry? Pick
A) 72% B) 70% C) 65% D) 60% E) 54%

Solution: You can also just use the formula   n(A or B) = n(A) + n(B) - n(A and B)   90 = 2X + X - 18   X = 36   2X = 72   This is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 72 - 18 = 54%   Answer (54%)
Answer: E
If the sides of a triangle are 30 cm, 28 cm and 14 cm, what is its area?
Choose the correct choice from the following answers:
A) 196 cm2
B) 187 cm2
C) 178 cm2
D) 189 cm2
E) 176 cm2

Solution: The triangle with sides 30 cm, 28 cm and 14 cm is right angled, where the hypotenuse is 30 cm.   196 cm2rea of the triangle   = 1/2 * 28 * 14= 
1/2 * 28 * 14 = 196
196 cm2   196 cm2nswer: 196 cm2
Answer: A
If -4 < x < 7 and -7 < y < 3, which of the following specifies all the possible values of xy?  Answers:
A) -42 < xy < 21 B) -42 < xy < 24 C) -49 < xy < 28 D) -24 < xy < 21 E) -24 < xy < 24

Solution: The least value of xy is a bit more than 7*(-7)=-49 and the largest value of xy is a bit less than (-4)*(-7)= 
(-4)*(-7) = 28
28.   Therefore -49 < xy < 28.   Answer: -49 < xy < 28.
Answer: C
One cutting machine cuts 100 metal bars in 30 minutes.Another machine does the same job in 30 seconds.What time will it take if both machines are put on the same work ? Choose the correct choice from the following answers:
A) 25.0 seconds	B) 29.5 seconds	C) 30.0 seconds	D) 30.5 seconds	E) 30.7 seconds

Solution: By guess it is clear that the time taken will be less than 30 seconds and very near to it. Therefore, answer 29.5 seconds will be correct. Answer-29.5 seconds
Answer: B
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 sec. What is the length of the fast train? Choose the correct answer:
A) 38 7/6 m	B) 38 7/4 m	C) 38 8/9 m	D) 38 7/9 m	E) 38 7/7 m

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 7 = 350/9 = 38 8/9 m.Answer:38 8/9 m
Answer: C
Sum of two numbers is 15. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be? Answers: A) 6, 9 B) 10, 5 C) 7, 8 D) 9, 6 E) 1,5

Solution: Explanation:   x + y = 15   2x – 3y = 5   x = 10 y = 5   ANSWER IS 10, 5
Answer: B
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 10 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal Choose the correct answer:
A) 7  B) 9  C) 10  D) 11  E) 12

Solution: Since (ii) holds for every real number x, it will remain valid if we replace x with   -x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 10 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 10-3= 
10-3 = 7
7. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 7
Answer: A
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Choose the most appropriate option.
A) 20/7	B) 20/5	C) 20/9	D) 20/21	E) 20/8

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18 = 7*5= 
7*5 = 35
35 mps.   The time required= d/s = 100/35 = 20/7 sec.   20/7nswer:20/7:
Answer: A
At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $110. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola? Choose the correct answer:
A) $1
B) $27
C) $31
D) $41
E) It cannot be determined

Solution: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:   3B+7S+C=110   4B+10S+C=164.5   Subtracting the first equation from the second gives us B+3S=54.5   Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=11. In any case, there is no necessity to know each item's price, just the sum.   $1nswer: $1
Answer: A
A discount electronics store normally sells all merchandise at a discount of 5 percent to 45 percent off the suggested retail price. If, during a special sale, an additional 2 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $400 before any discount?  Choose the correct choice from the following choices:
A) $215.00  B) $200.00  C) $215.80  D) $182.00  E) $215.60

Solution: Original price : 400$   Max first discount = -45%   Thus : 400âˆ—(1âˆ’45/100)=220   Second discount on the discounted price = -2%   Thus : 220âˆ—(1âˆ’2/100)=215.60   Answer $215.60
Answer: E
On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 370 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?	Choose the correct choice from the following choices
A) 237
B) 287
C) 197
D) 740
E) 720

Solution: Explanation:   Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.   2x/(x - 370) = 2 + 2(extra)   => 2x - 740 = x => x = 740.   Answer: 740
Answer: D
Coconuts were purchased at 150 per hundred and sold at 2 per coconut. If 2000 coconuts were sold, what was the total profit made?  Choices
A) 500
B) 1000
C) 1500
D) 2000
E) None of these

Solution: C.P. for one coconut = 150⁄100 = 3⁄2   S.P. for one coconut = 2   Profit on one coconut = 2 - 3⁄2 = 1⁄2   ∴ Profit on 2000 coconut = 1⁄2 × 2000 = 1000   Answer 1000
Answer: B
In a division sum, the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:	Choose the correct answer.
A) 53  B) 58  C) 51  D) 60  E) 62

Solution: Diver = (4*3)+2= 
(4*3)+2 = 14
14   4* Quotient= 14   Quotient = 3.5   Dividend = (Divisor * Quotient) + Remainder   Dividend = ( 14 * 3.5) + 4= 
( 14 * 3.5) + 4 = 53
53   53
Answer: A
85 kg of a mixture containing milk and water in the ratio 27:7. How much more water is to be added to get a new mixture containing milk and water in the ratio 3:1?	Choose the correct choice from the following:
A) 10kg  B) 7kg  C) 5kg  D) 9kg  E) 3kg

Solution: Milk in 85kg of mix = 85*27/34 = 135/2 kg   Water in it= 85-135/2 = 35/2 kg   Let x kg of water be added to it.   (135/2)/(35/2 + x) = 3/1   x=5kg   Answer is 5kg
Answer: C
A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5.5, what is the number of items must be sold monthly for the factory to cover its cost exactly?	Pick one.
A) 9,000	B) 15,000	C) 18,000	D) 22,500	E) 27,000

Solution: selling price - Cost price = 3 so per unit profit =3   cost to recover =45000   no of items required = 45000/3= 
45000/3 = 15_000
15000   Ans 15,000
Answer: B
The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 60 percent, then the value of T decreases by what percent? Answers
A) 25%  B) 33 ¹/₃%  C) 50%  D) 66 ²/₃%  E) 75%

Solution: We can assign numbers:   lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)   Now increasing S by 50% gives S=4, K remains constant, so T = 2 (6/2=3)   decrease in T= 1, percent decrease in T = (1/4)*100= 
(1/4)*100 = 25
25%   25%nswer 25%
Answer: A
The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct choice:
A) 10 m	B) 16 m	C) 245 m	D) 19 m	E) 225 m

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (150 + x)/30   = 25/2 => 2(150 + x) = 750 => x   = 225 m.   Answer: 225 m
Answer: E
A, B and C rents a pasture for Rs.899. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay? Options
A) 270  B) 279  C) 267  D) 255  E) 552

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 899= 
9/29 * 899 = 279
279   Answer: 279
Answer: B
In a hotel we can order two types of varieties, but we can make 5 more varieties in home. One can choose the four varieties with two from hotel as must. Find how many ways one can order.  Choices:	A) 14	B) 10	C) 56	D) 28	E) 29

Solution: 2c2*5c2=10ways   ANSWER:10
Answer: B
The denominator of a fraction is 1 less than twice the numerator. If the numerator and denominator are both increased by 1, the fraction becomes 3/5. Find the fraction?	Choices.
A) 2/3  B) 3/5  C) 4/7  D) 5/9  E) None of these

Solution: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.   d = 2n - 1   (n + 1)/(d + 1) = 3/5   5n + 5 = 3d + 3   5n + 5 = 3(2n - 1) + 3 => n = 5   d = 2n - 1 => d = 9   Hence the fraction is : 5/9   ANSWER:5/9
Answer: D
The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
Select.
A) Rs.12000  B) Rs.14200  C) Rs.17520  D) Rs.13500  E) Rs.14500

Solution: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]   P = 13500   ANSWER:Rs.13500
Answer: D
All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 153 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A? Choose the correct choice
A) 1289
B) 1198
C) 281
D) 1224
E) 282

Solution: Explanation:   B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.   Quantity of water in B = 8k - 5k = 3k.   Quantity of water in container C 8  - 5= 
8  - 5 = 3
3k.   Quantity of water in container C= 8k - 3k = 5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 153 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 153 8  - 3= 
8  - 3 = 5
5k   Container: A B C   Quantity of water: 8k 3k 5k   It is given that if 153 liters was transferred from container C to container B, then both the containers would have equal quantities of water.   5k - 153= 3k + 153 => 2k = 306 => k = 153   The initial quantity of water in A = 8k = 8 * 153= 
8 * 153 = 1_224
1224 liters.   Answer: Option 1224
Answer: D
Consider the following sets:
L = {3, 4, 5, 5, 6, 7},
M = {2, 2, 2, 8, 8, 8},
N = {15, 15, 15, 15, 15, 15},
Rank those three sets from least standard deviation to greatest standard deviation.	Choose the correct choice from the following
A) L, M, N  B) M, L, N  C) M, N, L  D) N, L, M  E) N, M, L

Solution: Now we have to compare the standard deviations of Set L and Set M. In Set L, the mean is clearly 5: two of the entries equal 5, so they have a deviation from the mean of zero, and no entry is more than two units from the mean. By contrast, in Set M, the mean is also 5, and here, every number is 3 units away from the mean, so the standard deviation of M is 3. No number in Set L is as much as 3 units away from the mean, so whatever the standard deviation of L is, it absolutely must be less than 3. That means, Set L has the second largest standard deviation, and Set M has the largest of the three. N, L, M in increasing order. Answer = N, L, M.
Answer: D
If two boys starting from same point, walking in the opposite directions with 4km/hr and 2km/hr as average speeds respectively. Then the distance between them after 6 hours is?
Choose the correct choice from the following choices.
A) 32
B) 33
C) 34
D) 35
E) 36

Solution: 36xplanation:   Total distance = Distance traveled by person A+ Distance traveled by person B   = (4Ã— 6) + (2Ã— 6)   = 24+ 12= 
24+ 12 = 36
36 Km   Answer:36
Answer: E
What number has a 5:1 ratio to the number 9?
Select the correct option:
A) 45	B) 50	C) 88	D) 52	E) 12

Solution: 5:1 = x: 9   x = 45   45nswer: 45
Answer: A
Find the odd man out. 362, 482, 551, 263, 344, 284
Pick.
A) 362  B) 482  C) 551  D) 344  E) None of these

Solution: Explanation :   In all numbers except 344, the product of first and third digits is the middle digit. Answer : Option 344
Answer: D
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 650 resolutions?  Choose the correct choice from the following choices.
A) 724 m B) 704 m C) 915.2 m D) 278 m E) 927 m

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 650 resolutions.   = 650 * 2 * 22/7 * 22.4= 
650 * 2 * 22/7 * 22.4 = 91_520
91520 cm= 915.2 m   Answer:915.2 m
Answer: C
A certain sum of money doubles itself in 10 years in how much many years will it trible itself at the same rate? Choose the correct choice from the following answers
A) 20
B) 15
C) 17
D) 18
E) 25

Solution: 100 ---- 100 --- 10   100 --- 10   --------------   300 ---- 20 years   20NSWER 20
Answer: A
During a sale of 20% on everything in a store, a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 10 candies. The store still makes a profit of 12% on this sale. What is the mark up percentage on each candy?	Pick.
A) 100%  B) 80%  C) 75%  D) 66+2/3%  E) 55%

Solution: Hi Akhil, I can share the way I solved it..   Let's say Marked price = M   So, there's a discount of 20% on M So, new S.P. = 80% of M   Now, the child convinces the owner to sell 20 candies for the price of 14 candies .   Let's say each candy after discount is 1$. So, S.P. of 20 candies = 20$. THe child bought it for 14 $ So, he got a discount of  6/20 *100= 
 6/20 *100 = 30
30%   So, the latest S.P.= 70% of 80% of M = 0.7* 0.8 M   Now, we are given that the shopkeeper still makes a profit of 12%. So we have ,   0.7 * 0.8 * M = 1.12 C.P   So, we get, M= 2 C.P.   i.e. Marked price was kept 100% above C.P.   80%
Answer: B
The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:  Choose the most appropriate option:	A) 18	B) 19	C) 20	D) 21	E) 46

Solution: l2 + b2 = 41.   Also, lb = 20.   (l + b)2 = (l2 + b2) + 2lb = 41 + 40= 
41 + 40 = 81
81   (l + b)= 9.   Perimeter = 2(l + b) = 18 cm.   18nswer:18
Answer: A
The triplicate ratio of 3:5 is? Choose the correct choice:
A) 27:125  B) 1:62  C) 1:34  D) 3:64  E) 5:64

Solution: 3^3: 5^3 = 27:125   27:125NSWER:27:125
Answer: A
A bag marked at $80 is sold for $68. The rate of discount is?  Choose the correct option:  A) 10%  B) 15%  C) 20%  D) 25%  E) 30%

Solution: Rate of discount = 12/80 * 100= 
12/80 * 100 = 15
15%   Answer is 15%
Answer: B
A certain sum of money at simple interest amounted Rs.780 in 5 years at 4% per annum, find the sum? Select:
A) 337
B) 268
C) 198
D) 650
E) 168

Solution: 780 = P [1 + (5*4)/100]   P = 650'   Answer:650
Answer: D
In a certain game of shooting the points in each round for the first,second,third and fourth position were 10,5,2,1 . No other points were given. Daniel participated in several rounds in the competition and the product of his score was 1000. In How many Rounds did he participate?  Pick one:
A) 100 B) 50 C) Cannot be determined D) 105 E) 25

Solution: Correct answer is C because we are given that there won't be any points awarded for rounds other than 1st four position.   Thus, it may happen that he played 150 rounds out of only 70 rounds were there in which he was awarded some points.
Answer: C
A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Choose one:
A) 150 m B) 240 m C) 260 m D) 280 m E) 380 m

Solution: Speed = 54 x 5/18 = 15 m/s   Length of the train = (15 x 20)m = 300 m.   Let the length of the platform be x metres.   Then, (x + 300)/30 = 15   --> x + 300 = 450   x = 150m.   150 mnswer : 150 m.
Answer: A
In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,10). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?
Choose the correct option
A) 1/5	B) 1/3	C) 1/2	D) 2/3	E) 2/5

Solution: The area of the right triangle is (1/2)*4*10= 
(1/2)*4*10 = 20
20.   Only the points (a,b) below the line y=x satisfy a - b > 0.   The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.   P(a - b > 0) = 8/20 = 2/5   The answer is 2/5.
Answer: E
Baby Isabel plays with blocks. Each block is 4.5 inches tall. She has a collection of 33 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?	Select:
A) 67.19"
B) 90.9"
C) 106.34"
D) 120.5"
E) 148.5"

Solution: 4.5"*33=148.5". Answer is 148.5".4.5 *33= 
4.5 *33 = 148.5
148.5". Answer is 148.5".
Answer: E
P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 130 days, in how many days can R alone complete the remaining work?
Choices.
A) 50 days  B) 83.6 days  C) 100 days  D) 150 days  E) 80 days

Solution: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days   Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days   P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 380 days   P works for 60 days--> 60/200 work done => 30%   Q works for 130 days--> 130/250 work done => 52%   22% work left ... R alone will take 22% * 380 = 83.6 days   Answer is (83.6 days)
Answer: B
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 54° of the circle, what percentage of MegaTek employees are in manufacturing?  Select the correct option:
A) 15% B) 25% C) 30% D) 35% E) 72%

Solution: 15%NSWER:15% 54° divided by 360° equals 0.15, therefore the sector is equal to 15% of the total
Answer: A
What will come in place of the x in the following Number series? 18, 22, X, 46 ,78, 142  Choose the correct choice:
A) 35
B) 56
C) 30
D) 87
E) 98

Solution: (30)   The pattern is +4, +8, +16, +32, +64   So the missing term is = 30
Answer: C
Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets Q did Irwin score?  Choose the correct choice from the following.
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: First thing I noticed was that all these numbers are prime...   Prime factorization gives the following   Step 1:2*1210   Step 2:2*11*110   Step 4:2*11*11*10   Step 5:2*11*11*2*5   So he scored Q= 2 11-point baskets in my opinion.   Answer 2
Answer: C
A batsman scored 80 runs which included 2 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets?
Choose the correct option.
A) 45% B) 500/11 C) 75% D) 55% E) 35%

Solution: Explanation :   Number of runs made by running,   =>80−(2×4+2×6).   =>80−20   =>60   Hence, the required percentage is:-   =>60/80*100= 
60/80*100 = 75
>75%   Answer : 75%
Answer: C
The simple Interest on a certain sum of money at the rate of 4% p.a. for 5 years is Rs. 1680. At what rate of interest the same amount of interest can be received on the same sum after 4 years ? Choose the most appropriate option.
A) 5%	B) 6%	C) 7%	D) 8%	E) 9%

Solution: S.I. = 1680, R = 4% T = 5 years   Principal = (100 *1680)/ (5*4)= 
(100 *1680)/ (5*4) = 8_400
8400   So P= 8400   Rate = (100 *1680)/ (8400 * 4)= 
(100 *1680)/ (8400 * 4) = 5
5%   5%NSWER:5%
Answer: A
If x-y=8, which of the following must be true?
I. If x is negative, y must be negative
II. If x is positive, y must be positive
III. Both x and y are positive Choose one:  A) I only  B) II only  C) III only  D) I and II  E) II and III

Solution: The best way to approach such questions is to plug in values for x and y   Given: x-y=8   III. Both x and y are positive:   Let x=10 and y=2   x-y=8   But,   Let x=6 and y=-2   x-y=8   Therefore, NOT TRUE   II. If x is positive, y must be positive   Let x=10 and y=2   x-y=8   But,   Let x = 6 and y=-2   x-y=8   Therefore, NOT TRUE   I. If x is negative, y must be negative   If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!   Therefore, TRUE   I onlyns: 'I only'
Answer: A