MU-NLPC/Calc-aqua_rat huggingface dataset:
If K is the sum of reciprocals of the consecutive integers from 23 to 28, inclusive, then K is closest in value to which of the following?	Options:	A) 1/12	B) 1/10	C) 3/14	D) 1/8	E) 1/4

Solution: 1/23 , 1/24 , 1/25 , 1/26 , 1/27 , 1/28   Hypothetically , assume all 6 Numbers to be 1/23   Hence sum of it would result in = 6/23 ( almost equals 1/4 , or slightly more than 1/4 - )   If all 6 nos were to be 1/28 ... Sum of which would result in 6/28 = 3/14 .   Hence answer should lie between 1/4 and 3/14   i.e 0.25 > 0.21   3/14
Answer: C
An Air Cooler is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
Options.
A) 18% B) 19% C) 21.2% D) 21.81% E) 22.07%

Solution: Simple interest SI = (P*R*T)/100   where P is the principal amount   R is the rate of interest   and T is time in years   the way I see it: Air Cooler on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000   For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)   thus, SI = 2000 or   2000 = (P*R*T)/100   2000 = (22,000*R*5)/(100*12)   R = (2,000*12*100)/22,000*5   R = 21.81%   Therefore answer is 21.81%
Answer: D
The average age of a committee of 12 members is 40 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
Choose the most appropriate option.
A) 38.7 years  B) 38 years  C) 36 years  D) 35 years  E) 34 years

Solution: Exp. Total age of the committee = 40*12= 
40*12 = 480
480,   Total age when a member is retired   and a new one was joined= 480-55 +39, =464   Average age of present committee = 464/12 = 38.7.   38.7 yearsnswer: 38.7 years
Answer: A
The average mark obtained by 22 candidates in an examination is 48. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
Choose the correct option:  A) 22  B) 0  C) 49  D) 58  E) 66

Solution: It is clear that 22 x 48 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 66   Answer:66
Answer: E
What is the probability of flipping a fair coin eight times and the coin landing on heads on at least two flips?
Select the correct option:
A) 61/64	B) 117/128	C) 123/128	D) 247/256	E) 253/256

Solution: The number of possible outcomes is 2^8=256.   0 heads: There is 1 way to have all tails.   1 head: There are 8 ways to have one head.   P(0 or 1 head)=9/256   P(at least 2 heads)=1 - 9/256 = 247/256   The answer is 247/256.
Answer: D
six friends go to pizza corner where there are different types of pizza available. six different flavours are there and they have to select 2 flavours from 6 flavours.In how many ways they can select? Choose the correct choice from the following answers:  A) 11  B) 12  C) 13  D) 14  E) 15 ways

Solution: 6c2 then ans is 6*5/1*2=15   ANSW15 waysR:15 ways
Answer: E
A radio station has to choose five days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any five of the seven weekdays can be chosen. How many different five-day combinations of the seven weekdays can be constructed? Choose the correct choice:
A) 9	B) 15	C) 21	D) 56	E) 35

Solution: Pick 5 days out of 7.. 7215 = = 21   Answer : 21
Answer: C
14 men can complete a piece of work in 22 days. In how many days can 18 men complete that piece of work?  Select:	A) 23 days	B) 26 days	C) 17 days	D) 29 days	E) 20 days

Solution: 17 days   17 days   14 * 22 = 18 * x => x = 17 days
Answer: C
If the complement of a certain angle is four times the measure of that certain angle, then what is the measure of that certain angle? Choose the most appropriate option:
A) 45°  B) 30°  C) 22.5°  D) 18°  E) 15°

Solution: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.   The original angle is x, so the complement is 4x, and together, these add up to 90 degrees.   x + 4x = 90   5x = 90   x = 18°   Answer = (18°)
Answer: D
Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 1.5. Which of the following operations would decrease the standard deviation of Set J?  Choose the correct answer:	A) Multiply each term by e/d	B) Divide each term by b/c	C) Multiply each term by −1	D) Divide each term by a/e	E) Multiply each term by c/e

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   Divide each term by a/e
Answer: D
The measurement of a rectangular box with lid is 25cmx6cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
Choose the correct choice from the following choices.
A) 288 B) 48 C) 36 D) 864 E) 964

Solution: d=6, r=2;   Volume of the largest sphere= 4/3πr3   = 4/3 *π*3*3*3= 36πcm3 ANSWER:36
Answer: C
A river 2m deep and 45 m wide is flowing at the rate of 5 kmph the amount of water that runs into the sea per minute is?  Choose the correct answer.
A) 4500 M3
B) 4580 M3
C) 7500 M3
D) 4900 M3
E) 4700 M3

Solution: Explanation:   (5000 * 2 * 45)/60= 
(5000 * 2 * 45)/60 = 7_500
7500 M3   Answer: Option 7500 M3
Answer: C
A train passes a train coming from opposite direction, speed 32 kmph in 25 sec. If the speed of the train is 40 km/hr. What is the length of train?	Choose the correct answer:
A) 300
B) 400
C) 500
D) 350
E) 200

Solution: Speed = (40+32) * 5/18 = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Length of the train= 25 * 20= 
25 * 20 = 500
500 m.   Answer: 500
Answer: C
A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 104 pounds?  Choices:
A) 8	B) 7	C) 16	D) 10	E) none of the above

Solution: Ans is 10:   39 pounds --> 6 days   104 pounds --> x days   x = 104*6/39= 
104*6/39 = 16
16   the animal has already consumed food in 6 days so the the number of days   for it's total consumption be 104 pounds is   16-6= 
  16-6 = 10
10
Answer: D
A motorcyclist goes from Nagpur to Pune, a distance of 500 kms at an average of 100 kmph speed. Another man starts from Nagpur by car 3 Â½ hours after the first, and reaches Pune Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?  Select the correct option:  A) 1:2  B) 1:7  C) 3:5  D) 1:5  E) 1:1

Solution: T = 500/100 = 10 h   T = 10 - 4= 
10 - 4 = 6
6   Time Ratio= 10:6 = 5:3   Speed Ratio = 3:5   Answer: 3:5
Answer: C
A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? Options
A) 18:11 B) 2:3 C) 3:2 D) 11:9 E) 11:10

Solution: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.   A : B   8000*18 : (8000*6) + (4000*12)   144000 : 96000   A:B = 3:2   ANSWER:3:2
Answer: C
If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of grass ? Choose the correct choice from the following options
A) Green
B) BLUE
C) PINK
D) ORANCE
E) BLACK

Solution: Explanation:   Pink → Orange   Orange → Blue   Blue → Red   Red → Green   Green → Black   Black → White   The color of grass is 'Green' but in coding language, 'Green' is called 'Black'.   ANSWBLACKR: BLACK
Answer: E
If 4XZ + YW = 10 and XW + YZ = 20, what is the value of the expression (2X + Y)(2Z + W)?
Choose the correct choice from the following choices
A) 9.	B) 12.	C) 15.	D) 50.	E) 18.

Solution: (2x+y)*(2z+w) = 10+2(20) =50   Answer : 50.
Answer: D
Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.86. How much was lent at 5%?	Choose the correct option:
A) 228  B) 299  C) 400  D) 500  E) 188

Solution: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 85   5x/100 + 90 â€“ 6x/100 = 86   x/100 = 4   => x = 400   Answer:400
Answer: C
A cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
Pick one:
A) 28
B) 32
C) 36
D) 40
E) 44

Solution: Area of the wet surface = [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 4 x 1.25) + 4 x 4]   = 36   The answer is 36.
Answer: C
Hal bought walnuts at 5 for $1 and apples at 4 for $1.He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?
Choose the correct choice from the following.
A) 50	B) 45	C) 60	D) 80	E) 55

Solution: Let's start with the concrete information:   He buys everything for $19.50 and earns $3 after selling so he sells everything for $22.50 (= 2250 cents).   He sells each item for 5/20 = 25 cents so in all he sells   2250/25= 
  2250/25 = 90
90 items   60ost of each walnut= 1/5= 
1/5 = 1/5 = around 0.2
$.2= 20 cents   60ost of each apple = 1/4= 
1/4 = 1/4 = around 0.25
$.25= 25 cents   Now we have one equation to solve:   20*w + 25*(90 - w) = 1950 (w is the number of walnuts he buys)   4w + 5(90 - w) = 390   w = 60   Answer (60)
Answer: C
A cubical tank is filled with water to a level of 1 foot. If the water in the tank occupies 16 cubic feet, to what fraction of its capacity is the tank filled with water?  Select the correct option
A) 1/2 B) 1/3 C) 1/4 D) 1/5 E) 1/6

Solution: The volume of water in the tank is H*L*B = 16 cubic feet.   Since H = 1, then L*B = 16 and L = B = 4.   Since the tank is cubical, the capacity of the tank is   4*4*4= 
  4*4*4 = 64
64.   The ratio of the water in the tank to the capacity is 16/64= 1/4   The answer is 1/4.
Answer: C
A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 10% below the cost price of the claimed weight.
Select:
A) 19.81%
B) 20%
C) 37.5%
D) 23.75%
E) 37.5%

Solution: There is a one step calculation method too. It requires more thought but is faster.   The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.   While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.   But he also sells at 10% less   (1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)   11/10 * 5/4 * 9/10 = (1 + p%)   profit % = 23.75%   23.75%
Answer: D
Find the area of a parallelogram with base 24 cm and height 16 cm? Choose the most appropriate option.
A) 297 cm2 B) 384 cm2 C) 672 cm2 D) 267 cm2 E) 286 cm2

Solution: Area of a parallelogram   = base * height   = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: 384 cm2
Answer: B
How many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 5 percent sugar solution?
Choose the correct choice
A) 20  B) 25  C) 30  D) 32  E) 35

Solution: Let x be the amount that needs to be evaporated.   0.02(50) = 0.05(50-x)   0.05x = 2.5 - 1= 
2.5 - 1 = 1.5
1.5/0.05= 
1.5/0.05 = 30
30 liters   The answer is 30.
Answer: C
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.2 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is: Choose the correct option:	A) 2:5	B) 2:3	C) 2:4	D) 1:1	E) 2:9

Solution: Let the ratio be k : 1. Then,   k * 16.2 + 1 * 15.4 = (k + 1) * 15.8   = (16.2 - 15.8)k = (15.8 - 15.4)   = k = 0.4/0.4= 
0.4/0.4 = 1
1/1= 
1/1 = 1
1/1 : 1= 1:1.   Answer:1:1
Answer: D
A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is. Choose the most appropriate option:
A) 200 m	B) 150 m	C) 148 m	D) 140 m	E) None of these

Solution: Explanation:   Let the triangle and parallelogram have common base b,   let the 200 mltitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then   200 mrea of triangle =1/2∗b∗h1   200 mrea of rectangle =b∗h2   200 ms per question 1/2∗b∗h1=b∗h2   1/2∗b∗h1=b∗100   h1=100∗2=200m   Option 200 m
Answer: A
In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 6,000 have been vaccinated against both, how many have been vaccinated only against rubella?	Choose the correct option.
A) 2,5000  B) 7,500  C) 12,000  D) 15,000  E) 17,500

Solution: Use a single variable as far as possible.   Number vaccinated only against mumps = x   Number vaccinated against both = 2x = 6000 (so x = 3000)   Then, number vaccinated against mumps (including both) = x + 2x = 3x   Number vaccinated against rubella = 2*3= 
2*3 = 6
6x   Then, number vaccinated against only rubella= 6x - 2x = 4x 6  - 2= 
6  - 2 = 4
4x= 4*3000 = 12,000   Answer (12,000)
Answer: C
Each of the following equations R has at least one solution EXCEPT	Pick:
A) R=–2^n = (–2)^-n  B) R=2^-n = (–2)^n  C) 2^n = (–2)^-n  D) (–2)^n = –2^n  E) (–2)^-n = –2^-n

Solution: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.   Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.   In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.   If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: A
AT + CD = AAA, where AT and CD are two-digit numbers and AAA is a three digit number; A, T, C, and D are distinct positive integers. In the addition problem above, what is the value of C?	Options:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined

Solution: Since AT and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.   So, A=1 and we have 1T+CD=111   Now, C can not be less than 9, because no two-digit integer with first digit 1 (1T<20) can be added to two-digit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1T<111).   Hence C=9.   Answer: 9.
Answer: D
The labeled price of a table is Rs. 8,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?  Answers
A) Rs. 5758 B) Rs. 6195 C) Rs. 6608 D) Rs. 7200 E) None of these

Solution: Explanation:   Labeled price = Rs. 8,000   By giving 5% discount on labeled price, the selling price is   = 95 / 100 * 8000 = Rs. 7600   By earning 15% profit on the selling of price Rs. 7600 the cost price is   = 100 / 115 * 7600= Rs. 6608   Therefore, approximate cost is 6608   ANSWER Rs. 6608
Answer: C
An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?  Choose the correct option:
A) Rs. 72 B) Rs. 90 C) Rs. 66 D) Rs. 96 E) None of these

Solution: Let CP = Rs. 100x   SP = Rs. 120x   MP = 120x/80 * 100 = Rs. 150x   D = Rs. 150x - Rs. 120x = Rs. 30x   D - P = 30x - 20x = Rs. 6, 10x = Rs. 6   120x = 120/10 * 6 = Rs. 72   Rs. 72NSWER:Rs. 72
Answer: A
A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?	Pick.
A) 170
B) 180
C) 190
D) 120
E) 130

Solution: Length of the train be ‘X’   X + 120/15 = X + 180/18   6X + 720 = 5X + 900   X = 180m   Answer: Option 180
Answer: B
The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 12 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
Select the correct option: A) $223 B) $225 C) $224 D) $213 E) $215

Solution: Final price = (1+12/100) * Original Price   = 1.12 * Original Price   From options given only 224 is divisible by 1.12 as it is stated OP is whole dollar amount.   Hence $224
Answer: C
If the sides of a square are multiplied by 10, the area of the original square is how many times as large as the area of the resultant square? Choices:
A) 1%	B) 10%	C) 100%	D) 500%	E) 1000%

Solution: Let x be the original length of one side.   Then the original area is x^2.   The new square has sides of length 10x, so the area is 100x^2.   The area of the original square is 1/100 = 1% times the area of the new square.   The answer is 1%.
Answer: A
Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 9/49, what is the probability that the next one she draws will be pink? Answers:
A) 1/49  B) 4/7  C) 3/7  D) 16/49  E) 40/49

Solution: The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 9/49 = (3/7) * (3/7)   Therefore probability that the next one she draws is pink = 4/7   Option (4/7)
Answer: B
In a race, the odds in favour of cars P, Q, R, S are 1 : 3, 1 : 4, 1 : 5 and 1 : 6 respectively. Find the probability that one of them wins the race.  Choose one:
A) 9/17
B) 114/121
C) 319/420
D) 27/111
E) 37/111

Solution: P(P) = 1/4, P(Q) = 1/5, P(R) = 1/6 and P(S) = 1/7.   All the events are mutually exclusive and hence,   the required probability:   = P(P) + P(Q) + P(R) + P(S)   = 1/4 + 1/5 + 1/6 + 1/7   = 319/420   ANSWER:319/420
Answer: C
At a game of billiards, A can give B 15 points in 60 & A can give C 20 points in 60. How many points can B give C in a game of 90?	Select:
A) 30 points	B) 20 points	C) 10 points	D) 5 points	E) 0 points

Solution: 10 points   ANSWER:10 points
Answer: C
A person walks at a speed of 4 km/hr and runs at a speed of 8 km/hr. How many hours will the person require to cover a distance of 20 km, if the person completes half of the distance by walking and the other half by running?	Choose the correct option
A) 2.75 B) 3.25 C) 3.75 D) 4.25 E) 4.75

Solution: time = 10/4 + 10/8 = 30/8= 
30/8 = 15/4 = around 3.75
3.75 hours   The answer is 3.75.
Answer: C
If a man's rate with the current is 15 km/hr and the rate of the current is 11⁄2 km/hr, then his rate against the current is	Choose the correct choice from the following options
A) 12 km/hr
B) 22 km/hr
C) 23 km/hr
D) 28 km/hr
E) 13 km/hr

Solution: Speed downstream = 15 km/hr   Rate of the current= 11⁄2 km/hr   Speed in still water = 15 - 11⁄2 = 131⁄2 km/hr   Rate against the current = 131⁄2 km/hr - 11⁄2 = 12 km/hr   12 km/hrnswer is 12 km/hr
Answer: A
What approximate value should come in place of the question mark (?) in the following equation?47.05 Ã— 8.65 â€“ 25.22 Ã— 6.4 = (28 + ?) Ã— 5  Choose the correct option
A) 28.1149  B) 24.1149  C) 21.1149  D) 22.1149  E) 31.1149

Solution: Solve using approximation   Answer 21.1149
Answer: C
A certain city with population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?	Choices.
A) 10,700	B) 10,800	C) 10,900	D) 11,000	E) 11,100

Solution: population that is 10% greater than the population of any other district..   11000.. 10% of 11000 = 1100.. so the next population will be 12100..   10*12,100 + 11000 = 132000. 11,000
Answer: D
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.162. Find the unknown rate of two blankets? Choose the correct choice from the following choices.
A) 420 B) 550 C) 490 D) 570 E) 457

Solution: 10 * 162= 
10 * 162 = 1_620
1620   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1620 – 1050= 570   Answer:570
Answer: D
If the set S is composed of the following numbers {99, 100, 100, 105, 106, 116, 123}, which of the following is largest? Choices:
A) The average (arithmetic mean) of set S
B) The median of set S
C) The mode of set S
D) The range of set S
E) The standard deviation of set S

Solution: Time consuming question...   A) 99, 100, 100, 105, 106, 116, 123 = 749 and its mean is   749/7= 
  749/7 = 107
107.   B) The list is of 7 numbers and median is 105.   C) Mode is number of repetition of a number in the list , here it is 100.   D) Range= Max value - min value = 123 -99= 
123 -99 = 24
24.   E) SD= square root of (sum of ( mean of series - number)^2 ) / n   => sq root (64+49+49+4+1+676)/7   = sq rt ( 893/7)   = sq rt ( 127) < 100   The average (arithmetic mean) of set Snswer: option The average (arithmetic mean) of set S is correct answer..
Answer: A
On thrusday mabel handled 90 transactions. anthony handled 10 % more transaction than mabel, cal handled 2/3rds of the transactions that anthony handled and jade handled 16 more transaction than cal. how much transaction did jade handled? Choose the correct option:
A) 92	B) 80	C) 72	D) 82	E) 28

Solution: Mabel handled 90 transaction, anthony 10 % more transaction the mabel. anthony = 90+90 * 10%, = 90 + 90 * 0.10 , = 90 + 9, =99, cal handled 2/3rds than anthony handled, cal = 2/3 * 99= 
2/3 * 99 = 66
66, jade handled 16 more than cal. jade= 66 + 16= 
66 + 16 = 82
82, jade handled= 82 tranasactions.   correct answer: (82)
Answer: D
Which of the following statements is equivalent to 8+2X<18−6X<23+2X8+2X<18−6X<23+2X?  Choose the correct option.
A) 4/5 < X < 2.5. B) 4/5 < X < 8/5. C) -5/8 < X < 5/4. D) 2.5 < X < 3.5. E) 5 < 8X < 12.

Solution: 8+2X<18−6X<23+2X   8<18-8x<23 (add -2x on all sides)   -10<-8x<5   10>8x>-5 (multiply by -1 on all sides)   5/4>x>-5/8   -5/8 < X < 5/4. is the answer
Answer: C
Two numbers are in ratio 4:5 and their LCM is 180. The smaller number is	Choose the correct choice from the following choices:
A) 9 B) 15 C) 36 D) 45 E) None

Solution: Solution: Let two numbers be 4x and 5x;   their LCM = 180 and HCF = x; Now,   1st number * 2nd number = LCM*HCF   Or, 4x*5x = 180*x;   Or, 20x = 180;   Or, x = 9;   then, the smaller number = 4*9= 
4*9 = 36
36.   Answer: Option 36
Answer: C