MU-NLPC/Calc-aqua_rat huggingface dataset:
After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?  Pick one
A) 2992 B) 2882 C) 1200 D) 2999 E) 2123

Solution: 1200P* (76/100) = 912   1200P1200 * (76/100)= 
1200 * (76/100) = 912
912   1200P= 12 * 100= 
12 * 100 = 1_200
> 1200P= 1200   Answer: 1200
Answer: C
Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?  Answers:
A) 3 9/16 hrs  B) 3 9/19 hrs  C) 3 9/17 hrs  D) 3 3/17 hrs  E) 4 9/17 hrs

Solution: Net part filled in 1 hour = 1/5 + 1/6 - 1/12   = 17/60   The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.   Answer:3 9/17 hrs
Answer: C
A basket has 7 apples and 5 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is  Answers:
A) 45/99
B) 43/99
C) 42/99
D) 49/99
E) 52/99

Solution: Total fruits = 12Since there must be at least two apples,(742/993 * 542/991)/1242/994 + 742/994/1242/994 = 42/99.Answer:42/99
Answer: C
What is the product of all the prime factors of 21?
Options.
A) 20	B) 21	C) 18	D) 17	E) 16

Solution: factors : 1,3,7,21   3*7= 
3*7 = 21
21   Answer : 21
Answer: B
In the Land of Oz only one or two-letter words are used. The local language has 67 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?	Select:
A) 65  B) 66  C) 67  D) 131  E) 134

Solution: The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...   The number of 1 letter words (X) that can be made from 67 letters is 67;   The number of 2 letter words (XX) that can be made from 67 letters is 67*67, since each X can take 67 values.   Total: 67+67*67.   Similarly:   The number of 1 letter words (X) that can be made from 66 letters is 66;   The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.   Total: 66+66*66.   The difference is (67+67*67)-(66+66*66)= 
(67+67*67)-(66+66*66) = 134
134.   Answer: 134.
Answer: E
Two whales are moving in the same direction at 18 mps and 15 mps. The faster whale crosses the slow whale in 15 seconds. What is the length of the slower whale in meters? Select the correct option: A) 45 m B) 56 m C) 39 m D) 33 m E) 62 m

Solution: Relative speed = (18 - 15)= 
(18 - 15) = 3
3 mps.   Distance covered in 15 sec= 15 * 3= 
15 * 3 = 45
45 m.   The length of the faster train= 45 m.   45 mnswer: 45 m
Answer: A
Little Krish had $200.50. He spent $35.25 on sweets and gave to his two friends $25.20 each. How much money was left?
Choose one:
A) $220.85
B) $214.85
C) $ 114.85
D) $314.85
E) $104.85

Solution: Krish spent and gave to his two friends a total of   35.25 + 25.20 + 25.20= 
35.25 + 25.20 + 25.20 = 85.65
$85.65   Money left    200.50 - 85.65= 
 200.50 - 85.65 = 114.85
$114.85   correct answer is $ 114.85) $ 114.85
Answer: C
The salary of A, B, C, D, E is Rs. 9000, Rs. 5000, Rs. 11000, Rs. 7000, Rs. 9000 per month respectively, then the average salary of A, B, C, D, and E per month is
Choose the correct option.
A) Rs. 7000  B) Rs. 8200  C) Rs. 8500  D) Rs. 9000  E) None

Solution: Answer   Average salary   = 9000 + 5000 + 11000 + 7000 + 9000 / 5   = Rs. 8200   Correct Option: Rs. 8200
Answer: B
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 14 cm	Choose the correct option.
A) 178 cm2 B) 179 cm2 C) 266 cm2 D) 167 cm2 E) 197 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (14)   = 266 cm2   Answer: 266 cm2
Answer: C
Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?	Choose one.
A) 338 B) 77 C) 298 D) 540 E) 882

Solution: A+B+C = 1170   4A = 3B = 2C = x   A:B:C = 1/4:1/3:1/2 = 3:4:6   6/13 * 1170 = Rs.540   Answer: 540
Answer: D
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 correct choice from the following answers:	A) 14 kmph	B) 11 kmph.	C) 51 kmph.	D) 61 kmph.	E) 71 kmph.

Solution: Speed in still water =1/2(14+8) kmph = 11 kmph.   Answer: 11 kmph.
Answer: B
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?	Choose the correct choice from the following answers: A) 12 B) 14 C) 15 D) 19 E) 10

Solution: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.   1/x + 1/(x - 5) = 1/(x - 9)   (2x - 5)(x - 9) = x(x - 5)   x2 - 18x + 45 = 0   (x- 15)(x - 3) = 0 => x = 15. Answer:15
Answer: C
Divide 952 to A,B,C IN 37:18:13 RATIO.CALCULATE PART OF A. Choose the correct answer:
A) 518	B) 428	C) 552	D) 526	E) 624

Solution: ADDITION OF RATIO NO. =68   P518RT OF 518=952×37/68=518   518NSWER 518
Answer: A
If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number
II. x is an odd number
III. x is a multiple of 5	Options:	A) I only	B) II only	C) III only	D) I and III	E) II and III

Solution: I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.   II. Same as above. This need not be always true.   III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)   = 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.   Therefore III only is the answer.
Answer: C
9. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is Select:
A) 41 B) 42 C) 32 D) 37 E) 39

Solution: LCM of 3, 5, 7 and 8 = 840   28523 ÷ 840 = 33 remainder = 803   Hence the least number which should be added = 840 - 803= 
840 - 803 = 37
37 Answer: Option 37
Answer: D
The contents of two vessels containing copper and tin in the ratio 2:3 and 5:7 are mixed in the ratio 3:5. The resulting mixture will have copper and tin in the ratio?  Answers:
A) 210:283 B) 312:433 C) 178:213 D) 197:283 E) 145:256

Solution: The ratio of copper and tin the new vessel= (2/5*3/8 + 5/12*5/8) : (3/5*3/8 + 7/12*5/8)   = 197/480 : 283/480 = 197:283   Answer is 197:283
Answer: D
Suraj has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13th innings?
Choose the correct option.
A) 48 B) 64 C) 36 D) 72 E) 27

Solution: To improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings.   Thus, the average after the 13th innings   = 96 - 60= 
96 - 60 = 36
36.   ANSWER:36
Answer: C
If a+b=−9, and a=30/b, what is the value of a^2+b^2? Select
A) 31
B) 21
C) 41
D) 61
E) 51

Solution: a^2 + b^2 should make you think of these formulas:   (a+b)(a+b) = a^2+b^2+2ab   We already know (a+b) = -9 and a*b = 30   (a+b)(a+b) = (-9)(-9) = a^2+b^2+2*(30)   a^2+b^2 = 81 - 60= 
81 - 60 = 21
21   Answer : 21
Answer: B
In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case.  Choose the correct choice from the following options:
A) 627  B) 528  C) 626  D) 657  E) 673

Solution: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)   = (1200)(30)(3) kg.   Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k   As the same provisions are available   => (1200)(30)(3) = (1200 + x)(25)(2.5)   x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.   Answer:528
Answer: B
The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream? Choose the correct choice from the following:
A) 10 kmph.
B) 05 kmph.
C) 18 kmph.
D) 11 kmph.
E) 12 kmph.

Solution: Speed of the boat in still water = (70+80)/2= 
(70+80)/2 = 75
75 kmph. Speed of the stream= (80-70)/2= 
(80-70)/2 = 5
5 kmph.   Answer:05 kmph.
Answer: B
To create paint with a certain shade of gray, one must combine 2.016 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray? Choose the correct choice.
A) 173.6  B) 176.4  C) 347.1  D) 694.4  E) 705.6

Solution: Since the ratio of Black to White is 2.016 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.   Now between A and B:   Black:White = 2.016:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, 173.6 fits the criteria hence should be the correct answer   173.6NSWER:173.6
Answer: A
The equation of line s is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line s?
Options: A) 48 B) 50 C) 60 D) 75 E) 100

Solution: This can be solve in two steps and without any complex calculation.   Given : equation of line s as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).   This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)   So a perpendicular from the (0,0) to hypotenuse will be the answer.   Area of triangle= 0.5*100*75=0.5*125* x   => x=60;   SO answer is 60=60
Answer: C
If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2017) = ?	Select
A) 2018	B) 2088	C) 270	D) 1881	E) 1781

Solution: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1= 
3-1 = 2
2, f(1)= 2   f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2)  ( (1)) +  (1)= 
 ( (1)) +  (1) = 2
2(1) + 3 ⇒⇒ f(2)= 5-2= 
5-2 = 3
3, f(2)= 3   f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3= 
7-3 = 4
4, f(3)= 4   ..............   f(2017) = 2018   2018ns: 2018
Answer: A
A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?	Choose the correct choice from the following answers:
A) 25600.24	B) 25600.29	C) 25600.29	D) 25600.29	E) 25600.29

Solution: 6 1/4% = 1/16   x *15/16 * 15/16 * 15/16 = 21093   x = 25600.24   25600.24nswer: 25600.24
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. In how much time will the trains cross each other?	Choose the correct option:	A) 80/9 sec	B) 80/7 sec	C) 80/6 sec	D) 89/7 sec	E) 50/7 sec

Solution: Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s   = (100 + 100 + 200)/35   = 400/35 = 80/7 sec.   Answer:80/7 sec
Answer: B
What sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?  Answers: A) 263 B) 500 C) 367 D) 368 E) 666.7

Solution: 70 = (P*3*7/2)/100   P = 666.7   Answer: 666.7
Answer: E
A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey? Choose the correct option
A) 20
B) 34
C) 35
D) 46
E) 50

Solution: Ans.(A)   Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: A
The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: Pick.
A) 9000	B) 9400	C) 9600 is greatest number	D) 9670	E) 9800

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 15, 25, 40 and 75 is 600.   On dividing 9999 by 600, the remainder is 399.   Required number  (9999 - 399)= 
 (9999 - 399) = 9_600
9600. Answer: Option 9600 is greatest number
Answer: C
How many 4-digit positive integers are there in which all 4 digits are even? Choices:
A) 625	B) 600	C) 500	D) 400	E) 256

Solution: Positive integers - 2,4,6,8,0   Let the integers of a four digit positive number be AB500D   A can take four values (2,4,6,8)   B can take five values (0,2,4,6,8)   500 can take five values (0,2,4,6,8)   D can take five values (0,2,4,6,8)   The total is 5*5*5*4   The answer according to me is 500   ANSWER:500
Answer: C
The sum of two consecutive integers is 41. Find the numbers.	Pick one.
A) 17, 18  B) 7, 8  C) 5, 6  D) 20,21  E) 8, 9

Solution: n + (n + 1) = 41   2n + 1 = 41   2n = 40   n = 20   Answer: 20,21
Answer: D
A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 30 paise per sq. metre  Choose the correct choice from the following answers:
A) s255
B) s780
C) s880
D) s480
E) s980

Solution: area of the plot=110m*65m=7150sq.m   area of plot excluding gravel110 *65= 
110 *65 = 7_150
7150sq.m   area of plot excluding gravel=105m*60m=6300sq.m   area of gravel 105 *60= 
105 *60 = 6_300
6300sq.m   area of gravel=7150sq.m-6300sq.m =850sq.m   cost of building it = 850sq.m*30   = 25500p   in Rs =25500/100= 
25500/100 = 255
Rs255   s255NSWER:s255
Answer: A
For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 45 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?	Choose the correct choice from the following: A) 22% B) 24% C) 25% D) 29% E) 28%

Solution: Total sales =800   Comission = (20/100)*500+ (45/100)*300   =100 + 135= 
100 + 135 = 235
235   %Comission=(235/800)*100=29.4~ 29%   Answer is 29%
Answer: D
A meeting has to be conducted with 5 employees.Find the number of ways in which the employees may be selected from among 8 employees,if 2 employees will not attend the meeting together.	Choose the correct option:
A) 1.35  B) 2.91  C) 3.12  D) 4.126  E) 5.36

Solution: 8 employees, but two of them cannot attend the meeting together.   We can split it into two cases.   1. Meeting without these two employees in it. That would mean selecting 5, from the remaining 6 which is 6C5 = 6   2. Meeting with one of the two employees. select 1 employees from two, and then select 4 from the remaining 6, which is 2C1 X 6C4 = 15.   So, answer is   30 + 6= 
  30 + 6 = 36
36.   Answer : 5.36
Answer: E
Vijay bought 160 shirts at the rate of Rs. 235 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Select the correct option:	A) Rs. 297	B) Rs. 270	C) Rs. 277.5	D) Rs. 285	E) None of these

Solution: Total CP per shirt = 235 + 1400/160 + 1.75 + 320/160 = Rs. 247.5   SP = CP[(100 + profit%)/100]   = 247.5 * [(100 + 20)/100] = Rs. 297.   Rs. 297NSWER:Rs. 297
Answer: A
A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is :  Pick:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: Sol.   Let the total distance be 3x km.   Then, x/3 + x/4 + x/5 = 47/60 ⇔ 47x/60 = 47/60 ⇔ x = 1.   ∴ total distance = (3*1)= 
(3*1) = 3
3km.   Answer 3
Answer: C
What least value should be replaced by * in 2631*4 so the number become divisible by 3
Select:  A) 3  B) 4  C) 5  D) 2  E) 7

Solution: Explanation:   Trick: Number is divisible by 3, if sum of all digits is divisible by 3, so (2+6+3+1+*+4) = 16+* should be divisible by 9,   16+2 will be divisible by 2,   so that least number is 2.   Answer: Option 2
Answer: D
In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 11,000, how many purple chips were selected?  Choose one:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 11,000 = 1*5^3*8*11   The factor of 8 must come from the purple point value, so there is 1 purple chip.   The answer is 1.
Answer: A
Which of the following CANNOT be the median T of the four consecutive positive integers w, x, y, and z, where w < x < y < z ? Choose the correct option
A) (w+x)/2 - 1 B) (w+z)/2 C) (x+y)/2 D) (y+z)/2 -1 E) (w+x+y+z)/4

Solution: Using the properties of consecutive positive integers we could right away eliminate B,C and E.   (B) - The average of first and last terms is the median   (C) - For even number of integers, the median is the average of middle terms   (E) - The average is equal to median if the integers are consecutive   Remaining answer choices are A and D.   For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median T.   (w+x)/2 - 1nswer ((w+x)/2 - 1)
Answer: A
39! is divided by 41 then what is the remainder?	Choose the correct choice from the following choices:
A) 1	B) 2	C) 4	D) 6	E) 7

Solution: Substituting p = 41 in the wilson's theorem, we get   40!+141=0   40×39!+141=0   −1×39!41=−1   Cancelling -1 on both sides,   39!41=1   1
Answer: A
Rajeshâ€™s school bus is facing North when reaches his school. After starting from Rajeshâ€™s house, it turning twice and then left before reaching the school. What direction the bus facing when it left the bus stop in front of Rajeshâ€™s house?
Options
A) East  B) North  C) South  D) West  E) East-West

Solution: West   ANSWER West
Answer: D
Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
Choose the correct choice from the following answers:
A) 2400 B) 277 C) 2789 D) 2669 E) 2123

Solution: First persons investment = x   Second persons investment = x + 1000   Third persons investments = x + 2000   x + x + 1000 + x + 2000 = 9000   3x = 6000   x = 2000   Ratio = 2000 : 3000 : 4000   2:3:4   4/9 * 54000 = 2400.2400nswer: 2400
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. In how much time will the trains cross each other?	Choose the correct choice:
A) 80/9  B) 80/7  C) 80/2  D) 80/1  E) 80/3

Solution: Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/35 = 80/7 sec.   Answer: 80/7
Answer: B
In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate? Choose the correct choice from the following
A) Cannot be determined B) 43 C) 3 D) 6 E) 10

Solution: Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position.   Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points.
Answer: A
A trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?
Pick: A) 118 B) 88 C) 90 D) 42 E) 22

Solution: SP of 1m of cloth = 8925/85 = Rs. 125   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 125 - Rs. 7 = Rs. 118   118nswer:118
Answer: A
Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 20% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
Select the correct option.
A) 17% less than N  B) 25% less than N  C) equal to N  D) 20% greater than N  E) 25% greater than

Solution: Correct answer is (A).   This year, the price of a tree is price1=P/N.   If this price increases by 20% it becomes price2=P/N*1.20   Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.20) i.e. N/1.20 i.e. .83*
Answer: A
f, b, and c are positive integers. If f, b, and c are assembled into the six-digit number fbcfbc, which one of the following must be a factor of fbcfbc?	Choose the correct answer: A) 16 B) 13 C) 5 D) 3 E) none of the above

Solution: Plug in some values and check -   fbcfbc = 123123   Not divisible by 16 and 5   let fbcfbc = 125125   Not divisible by 3   Only option (B) and (E) is left in both the cases...   Check once more to marke (13) as correct answer   let fbcfbc = 135135   Again divisible by 13   So, mark answer as (13) 13
Answer: B
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.70 per glass on the first day, what was the price per glass on the second day?
Choose the correct choice from the following answers
A) $0.15	B) $0.20	C) $0.30	D) $0.40	E) $0.46

Solution: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;   On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;   So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.   We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.   Say the price of the glass of the orangeade on the second day was $x then 2*0.7=3*x --> x=$0.46.   Answer: $0.46.
Answer: E
If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability E that N is divisible by 3?
Choices:
A) 1/3 B) ¼ C) 9/25 D) 5/16 E) 0

Solution: Prime digits are: 2, 3, 5, 7   Total number of 2 digit #s with both digits prime are:   4*4= 
  4*4 = 16
16   out of these numbers divisible by 3= 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.   => prob = 5/16.   Ans D. Took me 3:20 mins.
Answer: D
In a certain school, the ratio of boys to girls is 5 to 17. If there are 72 more girls than boys, how many boys are there?  Choose the correct option:
A) 27 B) 36 C) 45 D) 72 E) 108

Solution: The ratio of b to G is 5:13 and the other data point is G are more than boys by 72...   Looking at the ratio we can say that the 12(17-5) extra parts caused this diff of 72. so 1 part corresponds to 72/8= 
72/8 = 9
9 and so   5 parts correspond to 12*9= 
12*9 = 108
108.   108
Answer: E
A certain collage has total of 450 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?  Choose the correct option
A) 130
B) 80
C) 75
D) 60
E) 50

Solution: Answer is A.   Six majors are as follows: a + b + c + d + e + f   Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20   4 of the majors have 300 seniors: a + b + c +d = 300   There are a total of 450 seniors.   So e + f = 150. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 130.   130
Answer: A