MU-NLPC/Calc-aqua_rat huggingface dataset:
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 220 kilometers? Answers
A) 4.5 B) 5.5 C) 6.5 D) 7.5 E) 8.5

Solution: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 220 kilometers?   220 ÷ 40 = 5.5 × 1 gallon = 5.5 gallons   correct answer 5.5
Answer: B
How many times the keys of a typewriter have to be pressed in order to write first 400 counting numbers? Options
A) 2388	B) 1092	C) 2788	D) 1192	E) 1901

Solution: Explanation:   1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   Answer: 1092
Answer: B
If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, what was the concentration of the original solution?  Choose one
A) 19.3%
B) 17%
C) 16.67%
D) 15.5%
E) 12.5%

Solution: Let X be the quantity of non-vinegar in the strong vinegar solution   Thus vinegar quantity will be 12 - X   When 50 ounces of water were added the percentage of vinegar becomes 3%, thus (12 - X)/62 = 3/100   From this equation X = 10.14   Answer (12-10.14)/12 = 15.5%   ANSWER:15.5%
Answer: D
The cost price of a radio is Rs.1800 and it was sold for Rs.1430, find the loss %?	Pick one.
A) 18%
B) 20.5%
C) 30%
D) 45%
E) 12%

Solution: 1800 ---- 370   100 ---- ? => 20.5%   Answer:20.5%
Answer: B
Two diesel trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
Select:  A) 10 sec  B) 30 sec  C) 40 sec  D) 20 s  E) 50 sec

Solution: D   Relative speed = (42 + 30) * 5/18 = 4 * 5= 
4 * 5 = 20
20 mps.   Distance covered in passing each other= 120 + 280= 
120 + 280 = 400
400 m.   The time required= d/s = 400/20= 
400/20 = 20
20 sec.
Answer: D
If watches bought at prices ranging from Rs 200 to Rs 350 are sold at prices ranging from Rs 300 to Rs 425. What is the greatest possible profit that might be made in selling eight watches?	Choose the correct choice from the following:	A) Rs 900	B) Rs 800	C) Rs 1,800	D) Rs 2,800	E) None of these

Solution: Profit would be maximum if watches are brought for Rs 200 and sold for Rs 425   Profit = Rs (425 - 200)= 
(425 - 200) = 225
Rs 225   Profit of 8 watches= Rs 225 x 8 = Rs 1,800   ANSWER:Rs 800
Answer: B
A box is being assembled to fit 3 different toys. There are 10 stuffed animals, 5 cars and 6 science kits to chose from. How many different toy boxes are possible?  Choose the correct choice from the following options
A) 31	B) 21	C) 300	D) 25	E) 50

Solution: 10 x 5 x 6 = 300   Answer: 300
Answer: C
9873 + x = 13800, then x is ?	Answers:
A) 3327 B) 3237 C) 3927 D) 2337 E) None of these

Solution: Answer   x = 13800 - 9873= 
13800 - 9873 = 3_927
3927   Option: 3927
Answer: C
If two sides of a triangle are 10 and 8, which of the following could be the area of triangle?
1. 35
2. 48
3. 56  Choices:
A) a) 1 only
B) b) 1 and 2 only
C) c) 1 and 3 only
D) d) 2 and 3 only
E) e) 1, 2 and 3 only

Solution: when two sides of a triangle are known , the maximum area occurs when the angle between those two sides is 90.   lets say base = 12 , height =8 (angle = 90)   maximum area = (1/2)*12*8= 
(1/2)*12*8 = 48
48 ( this is the same maximum area even when base is 8 and height is 12).   if we fix the base and keep lowering the angle, it will result in a lower height . hence the resulting area will always be < 48.   C,D and E are ruled out.   1 and 3 are possible areas as their areas are less than 48.   Hence the answer is c) 1 and 3 only.
Answer: C
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
Answers.
A) 144	B) 125	C) 130	D) 160	E) 158

Solution: Let the slower pipe alone fill the tank in x min.   Then, faster pipe will fill it in x/3 min.   1/x + 3/x = 1/36   4/x = 1/36 => x = 144 min   144NSWER 144
Answer: A
The greatest number by which the product of three consecutive multiples of 3 is always Pick.
A) 54 B) 81 C) 162 D) 243 E) None of these

Solution: Explanation:   3*6*9= 
3*6*9 = 162
162   Option 162
Answer: C
A car left town A towards town B driving at a speed of V = 32 km/hr. After 3 hours on the road the driver stopped for 15 min in town C. Because of a closed road he had to change his route, making the trip 28 km longer. He increased his speed to V = 40 km/hr but still he was 30 min late. Find:
a) The distance the car has covered.
b) The time that took it to get from C to B.
Choose the correct choice from the following answers.
A) 223
B) 277
C) 116
D) 268
E) 281

Solution: From the statement of the problem we don't know if the 15 min stop in town C was planned or it was unexpected. So we have to consider both cases.   1st case. The stop was planned. Let us consider only the trip from C to B, and let xx be the number of hours the driver spent on this trip.   Then the distance from C to B is S=40⋅xS=40⋅x km. If the driver could use the initial route, it would take him x−3060=x−12x−3060=x−12 hours to drive from C to B. The distance from C to B according to the initially itinerary was (x−12)⋅32(x−12)⋅32 km, and this distance is 2828 km shorter than 40⋅x40⋅x km. Then we have the equation   (x−1/2)⋅32+28=40x(x−1/2)⋅32+28=40x   32x−16+28=40x32x−16+28=40x   −8x=−12−8x=−12   8x=128x=12   x=128x=128   x=148=112=13060=x=148=112=13060= 1 hr 30 min.   So, the car covered the distance between C and B in 1 hour and 30 min.   The distance from A to B is 3⋅32+128⋅40=96+60=1563⋅32+128⋅40=96+60= 
96+60 = 156
156 km.   2nd case. The driver did not plan the stop at C. Suppose it took xx hours for him to get from C to B. Then the distance is S=40⋅xS=40⋅x km. It took x−3060−1560=x−4560=x−34x−3060−1560=x−4560=x−34 h to drive from C to B. The distance from C to B is 32(x−34)32(x−34) km, which is 2828 km shorter than 40⋅x40⋅x, i.e.   32(x−34)+28=40x32(x−34)+28=40x   32x−24+28=40x32x−24+28=40x   4=8x4=8x   x=12hr⋅x=30min.x=12hr⋅x=30min. Then the time of the trip from C to B was 30 min. The distance covered equals 3⋅32+12⋅40=96+20= 
96+20 = 116
116km3⋅32+12⋅40=96+20= 
96+20 = 116
116km.   Answer:116
Answer: C
The number of new words that can be formed by rearranging the letters of the word 'REDUCTION' is ?
Choose the correct choice from the following answers
A) 362879	B) 362889	C) 120	D) 5040	E) 5039

Solution: Number of words which can be formed   = 9! - 1 = 362880 - 1= 
362880 - 1 = 362_879
362879   362879nswer:362879
Answer: A
The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?  Choose the correct answer
A) 12
B) 16
C) 18
D) 20
E) 24

Solution: This is an A.P. in which a = 6, d = 6 and Sn = 1800   Then,	n	[2a + (n - 1)d] = 1800   2   n	[2 x 6 + (n - 1) x 6] = 1800   2   3n (n + 1) = 1800   n(n + 1) = 600   n2 + n - 600 = 0   n2 + 25n - 24n - 600 = 0   n(n + 25) - 24(n + 25) = 0   (n + 25)(n - 24) = 0   n = 24   Number of terms = 24.   24)
Answer: E
For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is? Select the correct option:
A) between 2 and 20	B) between 10 and 20	C) between 20 and 30	D) between 30 and 40	E) greater than 40

Solution: SOL:   Lets consider h(100):   => 2*4*6*8.........*98*100   => (2*1) * (2 * 2) * (2 * 3) * (2 * 4)............ * (2 * 49) * (2 * 50)   => (2^50) * (1*2*3*4........*49*50)   => h(100) = (2^50) * (50!)   We can thus conclude that h(100) is divisible by every number from 1 to 50. Thus all the prime numbers between 1 and 50 are prime factors of h(100).   But when 1 is added [h(100) + 1] is no more divisible by any of these prime numbers. Thus the smallest prime factor of [h(100) + 1] would have to be a number greater than 50;   ANSWgreater than 40R:greater than 40
Answer: E
If a person throw 2 dice simultaneously then find the probability of the sum of dots is a prime number?	Select:  A) 5/12  B) 6/13  C) 8/17  D) 9/11  E) 3/5

Solution: If 2 dies are thrown E = event of getting a prime number = 15   total number of possible out comes = 36   probability = 15/36 = 5/12   5/12nswer is 5/12
Answer: A
A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?	Answers.
A) 228
B) 267
C) 800
D) 297
E) 127

Solution: 25 = E/(1000 - E) * 100   1000 - E = 4E   1000 = 5E => E = 200   1000 - 200= 
1000 - 200 = 800
800   Answer: 800
Answer: C
Find k if 64 ÷ k = 4. Choose the correct option
A) 8
B) 16
C) 24
D) 36
E) 40

Solution: Since 64 ÷ k = 4 and 64 ÷ 16 = 4, then   k = 16   correct answer 16
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 42 inch from the base of the mountain. How many km is he from the base of the mountain?
Options
A) 14.83  B) 14.81  C) 14.8  D) 14.82  E) 18.3

Solution: 18.3xplanation:   Since 312 inch = 136 km   So 1 inch = 136/312 km   So 42 inch = (136 Ã— 42)/ 312 = 18.3 km   Answer: 18.3
Answer: E
How many keystrokes are needed to type numbers from 1 to 1000 on a standard keyboard? Select the correct option:  A) 2893  B) 3000  C) 5213  D) 5642  E) None of these

Solution: Explanation :   While typing numbers from 1 to 1000, we have 9 single digit numbers from 1 to 9. Each of them requires one keystroke. That is 9 key strokes.   There are 90 two-digit numbers, from 10 to 99. Each of these numbers requires 2 keystrokes. Therefore, one requires 180 keystrokes to type the 2 digit numbers.   There are 900 three-digit numbers, from 100 to 999. Each of these numbers requires 3 keystrokes. Therefore, one requires 2700 keystrokes to type these 3 digit numbers.   And,1000 is a four-digit number which requires 4 keystrokes.   Hence, total  9+180+2700+4= 
 9+180+2700+4 = 2_893
2893 keystrokes is required.   2893nswer : 2893
Answer: A
A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 10 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave?
Choose the correct answer.
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: The fraction of work completed in two days is 2/5 + 2/10 + 2/30 = 20/30   The fraction of work remaining is 1 - 20/30 = 10/30   The number of days required for Z is 10 days.   The answer is 10.
Answer: E
By selling 50 meters of cloth. I gain the selling price of 10 meters. Find the gain percent? Choose the correct choice from the following answers:
A) 42 7/7%  B) 42 5/8%  C) 42 6/4%  D) 42 6/8%  E) 25%

Solution: SP = CP + g   50 SP = 50 CP + 10 SP   40 SP = 50 CP   40 --- 10 CP gain   100 --- ? => 25%   Answer: 25%
Answer: E
A hiker walked for 3 days. She walked 18 miles on the first day, walking 6 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk? Choose the correct choice from the following:  A) 24  B) 44  C) 53  D) 60  E) 62

Solution: She walked 18 miles on the first day, walking 6 miles per hour i.e. total time of walk on Day-1 = 18/6= 
18/6 = 3
3 Hours   Second day time of walk= 3-1= 
3-1 = 2
2 hours and Speed= 6+1= 
6+1 = 7
7 miles per hour i.e. Distance walked on second day= 2*7= 
2*7 = 14
14 miles   Third day time of walk= 3 hours and Speed = 7 miles per hour i.e. Distance walked on second day = 3*7= 
3*7 = 21
21 miles   Total Distance travelled on three days= 18+14+21= 
18+14+21 = 53
53   Answer: Option 53
Answer: C
Paul professes to sell his goods at the cost price but he made use of 375 grams instead of a kg, what is the gain percent?
Choose the correct choice.
A) 24 2/3% B) 25 2/3% C) 26 2/3% D) 27 2/3% E) 28 2/3%

Solution: 375 --- 100   100 --- ? => 26 2/3%   Answer:26 2/3%
Answer: C
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?  Pick one.
A) 2356
B) 3465
C) 4232
D) 4225
E) 5184

Solution: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184   432 12 x 62   5184
Answer: E
There are 2 sections A and B in a class, consisting of 26 and 34 students respectively. If the average weight of section A is 50kg and that of section B is 30kg, Find the average of the whole class?	Choose the correct choice from the following answers.
A) 35.29kg
B) 37.25kg
C) 42.45kg
D) 38.66kg
E) 29.78kg

Solution: Total weight of 26+34 students = 26*50 + 34*30= 
26*50 + 34*30 = 2_320
2320   Average weight of the class is= 2320/60 = 38.66 kg   Answer is 38.66kg
Answer: D
Angela has 14 pairs of matched socks. If she loses 7 individual socks, which of the following is NOT a possible number of matched pairs she has left?
Choose the correct answer
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: I think if Angela loses 7 individual socks,then she is bound to have lost minimum of 3 pairs and 1 individual sock,in this way she is left with only 10 pairs of socks (14-(3+1)).   Hence,11 cannot be the answer as maximum is 10.   Hence, option (11)
Answer: D
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 200 revolutions. How many revolutions does the second wheel make in covering d feet?
Choices:
A) 200x/y B) 200y - x C) 200x - y D) 200y/x E) 200x

Solution: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)   Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)   Revolutions = distance/circumference   So, from equation (1)   200 = d/(x*pi)   d = 200 * x * pi ---------- (3)   From equation (2)   Revolutions = d/(y*pi) = (200 * x * pi) / (y*pi) = 200x/y   200x/ynswer (200x/y)
Answer: A
Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 8 hours to paint a wall with dimensions a and c. He takes 4 hours to paint a wall with dimensions b and c and 12 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 3, then what is the volume of the room?
Select the correct option:
A) 4.5 cubic meters B) 2.4 cubic meters C) 3.0 cubic meters D) 3.6 cubic meters E) It can’t be determined.

Solution: Time to paint each wall as given in problem:   4.5 cubic metersC = 8 hours   BC = 4 hours   4.5 cubic metersB = 12 hours   Since he works at constant rate and it takes him twice as long to paint 4.5 cubic metersC compared to BC   4.5 cubic metersC=2BC   Plug in 3 for 4.5 cubic meters and you find that B=1.5   Since painting 4.5 cubic metersB takes 3 times as long compared to BC,   4.5 cubic metersB=3BC   Plug in 6 for 4.5 cubic meters and 3 for B and you find that C=1   4.5 cubic meters*B*C=3*1.5*1= 
3*1.5*1 = 4.5
4.5 cubic meters   4.5 cubic metersnswer: 4.5 cubic meters
Answer: A
Choose the missing terms out of the given alternatives.
DKY, FJW, HIU, JHS, ? Choose the correct choice from the following answers:
A) LGQ
B) KGR
C) LFQ
D) KFR
E) MED

Solution: A   LGQ   The first letters are alternate. The second letter of moves one step backward to obtain the second letter of the successive term. The third letter moves two steps backward to obtain the third letter of the subsequent term.
Answer: A
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 12 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?	Choose the correct choice from the following answers:
A) 30
B) 45
C) 60
D) 90
E) 120

Solution: Whole trip = distance by foot + distance by bus + distance by car   x = 1/5x + 2/3x + 12   x - 13/15x = 12   2/15x = 12 => so x = (15/2)*12= 
(15/2)*12 = 90
90Km   Answer 90
Answer: D
If 5 and 7 are prime numbers, which of the following CANNOT be the sum of 5 and 7?
Choose the correct choice from the following answers:
A) 12 B) 13 C) 24 D) 36 E) 48

Solution: Ans :13
Answer: B
In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:  Choose the most appropriate option.
A) 12 km/hr  B) 11 km/hr  C) 10 km/hr  D) 8 km/hr  E) None of these

Solution: Explanation :   Let speed of the boat in still water = a and speed of the stream = b   Then   a + b = 14   a - b = 8   Adding these two equations, we get 2a = 22   => a = 11   ie, speed of boat in still water = 11 km/hr. Answer : Option 11 km/hr
Answer: B
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12200 after a year?	Choices
A) 3660 B) 3637 C) 3630 D) 3631 E) 3635

Solution: 6300:4200:10500   3:2:5   3/10 * 12200= 
3/10 * 12200 = 3_660
3660   3660nswer: 3660
Answer: A
If p is an odd integer and q is an even integer, which of the following must be an even integer?
Choose the correct choice from the following.
A) 1+2p+2q^2
B) p+3q
C) 2p+q
D) 2p+q-1
E) 3p-q+2

Solution: p is odd; for this assume p=1   q is even; for this assume q = 2   1+(2*1)+2(2^2) = 11 Odd    1+(3*2)= 
 1+(3*2) = 7
7 Odd    (2*1)+2= 
 (2*1)+2 = 4
4 Even     (2*1)+2-1= 
  (2*1)+2-1 = 3
3 Odd    (3*1)-2+2= 
 (3*1)-2+2 = 3
3 Odd   Answer:2p+q
Answer: C
A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone?
Choose the correct choice from the following options:
A) 1 1/9 days
B) 1 1/2 days
C) 1 3/2 days
D) 1 2/2 days
E) 1 5/2 days

Solution: 3/20 * 2 + (2 + x)/5 = 1   x = 1 1/2 days   Answer: 1 1/2 days
Answer: B
The ratio between the number of sheep and the number of horses at the Stewar farm is 6 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??
Choose the correct choice:
A) 18 B) 28 C) 32 D) 48 E) 58

Solution: et no of sheep and horses are 6k and 7k   no of horses= 12880/230= 
12880/230 = 56
56   now 7K=56 and k=8   no of sheep=(6*8)= 
(6*8) = 48
48   ANSWER:48
Answer: D
A worker earns $20 on the first day and spends $15 on the second day. The worker earns $20 on the third day and spends $15 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $100? Choose the correct answer:
A) 30	B) 33	C) 35	D) 38	E) 40

Solution: Every two days, the net total is $5.   After 32 days, the worker will have $80.   On day 33, the worker will receive $20 for a net total of $100.   The answer is 33.
Answer: B
Lorna invests $9000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate?
Choose the correct choice from the following answers:  A) $160  B) $1,600  C) $2,200  D) $4,400  E) $1,800

Solution: We have that 'x' invested at 6%   We also have that '9000-x' invested at 11%   Now then 580/9000 is approx 10%   Therefore, -4x+9000-x=0   5x=9000   x=1800 approximately. Probably higher   Only $1,800 matches
Answer: E
Kamal started a business investing Rs.9000. After five months, Sameer joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be the shares of sameer in the profit?
Pick.
A) Rs.1883.78 B) Rs.2380 C) Rs.3690 D) Rs.3864 E) none

Solution: Solution   Kamal : Sameer	=(9000×12):(8000 ×7)   = 108 : 56   = 27 : 14.   Sameer's share	= Rs.(6970 ×14/41)   =Rs.2380.   Answer Rs.2380
Answer: B
Mixture D is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture D, how many kilograms of mixture D must be added to make a 70% material B in the new mixture?
Choose the correct choice from the following.
A) A)6 B) B)7 C) C)8 D) D)9 E) E)10

Solution: Can be done with weighted avg method.   if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil .   D1=20(initial mix.)   Avg. is what we need..ie 70% of material B means 30% of oil   D2=36(36% of 10 kg mix)   w1/w2=(D2-Avg)/(Avg-D1)   (36-30)/(30-20)   6/10   means for every 10 kg of new mix. we need 6 kg of mix D   6ns 6
Answer: A
How many three-digit numbers are there such that all three digits are different and the first digit and last digit is not zero? Choices: A) 576 B) 648 C) 720 D) 729 E) 810

Solution: All three digits are different and first digit is not zero.   So first digit can be filled in 8 ways.   And, second digit can be filled in 9 ways.   And, third digit can be filled in 8 ways.   Total ways = 8*9*8= 
8*9*8 = 576
576   Hence option (576).
Answer: A
If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price?
Choices:
A) $1740  B) $1560  C) $1500  D) $1800  E) $1600

Solution: C   $1500   Let the cost price of an article be $ x.   (19% of x) - (12% of x) = 105   19x/100 - 12x/100 = 105 => 7x = 105 * 100   => x = 1500   $1500ost price = $1500
Answer: C
On flipping 2 coins together what is the outcomes for at least two heads? Choose the correct choice from the following answers:
A) {HH}
B) {TT}
C) {HT}
D) {TH}
E) None

Solution: Sample space, S = {HH, TH, TH, TT}   Favorable outcomes for at least two heads   = favorable outcomes for exactly two heads and favorable outcomes for more than two heads   = {HH}   {HH}
Answer: A
In a class of 300 students, 100 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?	Choose the correct option
A) 80%  B) 70%  C) 67%  D) 20%  E) 10%

Solution: No of students study french= 300- No of students study spanish = 300-100= 
300-100 = 200
200   % of the students study french but not spanish= (200/300)*100 % = 67 %   Answer : 67%
Answer: C
If two sides of a triangle have lengths 3 and 5, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19  Choose one
A) None	B) I only	C) II only	D) II and III only	E) I, II, and III

Solution: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   Therefore:   (5-3) < {third side} < (5+3).   2 < {third side} < 8.   Perimeter = {third side} + 3 + 5 = {third side} + 8.   10 < {perimeter} < 16.   Answer: II only.
Answer: C
An investment yields an interest payment of $225 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
Pick
A) $30,000	B) $30,400	C) $31,300	D) $32,500	E) $35,100

Solution: Let the principal amount = P   Simple annual interest = 9%   Simple monthly interest = (9/12) = (3/4)%   (3/4)*(P/100) = 225   =>P = (225 *4 * 10^2 )/3   = 75*4*10^2   = 300 * 10^2=30000   $30,000nswer $30,000
Answer: A
A contractor completed five-ninths of a job before a second contractor completed an additional one-third. What fraction of the job is left undone?  Choose the correct choice from the following options
A) one-ninth	B) two-thirds	C) four-ninths	D) eight-ninths	E) none

Solution: Ans is A   Fraction of Job completed = 5/9 + 1/3 = 5/9 + 3/9 = 8/9 Fraction left undone = 1 - 8/9 = 9/9 - 8/9 = 1/9 i.e. one-ninth
Answer: A
A girl swims downstream 63 km and upstream 28 km taking 72 hours each time; what is the speed of the current?  Choose the correct choice from the following answers:
A) 0.5  B) 1.5  C) 2.1  D) 2.5  E) 5.2

Solution: 63 --- 7 2.5S = 9   ? ---- 1   28 ----7 US = 4   ? ---- 1 S = ?   S = (9 - 4)/2= 
(9 - 4)/2 = 5/2 = around 2.5
2.5   Answer: 2.5
Answer: D
Veena ranks 73rd from the top in a class of 182. What is her rank from the bottom if 35 students have failed the examination?
Choose the correct option.
A) 88	B) 108	C) 110	D) 75	E) 93

Solution: total student=182   failed=35   paasd student=182-35=160   from bottom her rank is=147-73+1= 
147-73+1 = 75
75   ANSWER:75
Answer: D