MU-NLPC/Calc-aqua_rat huggingface dataset:
The diameter of a wheel of cycle is 21 cm. It moves slowly along a road. How far will it go in 500 revolutions?
Choose the correct choice
A) 220  B) 330  C) 360  D) 390  E) 410

Solution: In revolution, distance that wheel covers = circumference of wheel Diameter of wheel = 21 cm   Therefore, circumference of wheel = πd   = 22/7 × 21   = 66 cm   So, in 1 revolution distance covered = 66 cm   In 500 revolution distance covered = 66 × 500 cm   = 33000 cm   = 33000/100= 
33000/100 = 330
330 m   ANSWER 330
Answer: B
A metallic sheet is of rectangular shape with dimensions 40m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m cube) is:  Choose the correct option.
A) 3220 m cube B) 4140 m cube C) 2688 m cube D) 4000 m cube E) None of these

Solution: Explanation:   l = (40 - 16)= 
(40 - 16) = 24
24 m, [because  8+8= 
 8+8 = 16
16]   b= (30 -16)= 
(30 -16) = 14
14 m,   h= 8 m.   Volume of the box = (24 x 14 x 8) m cube   = 2688 m cube.   Option 2688 m cube
Answer: C
A work can be finished in 13 days by ten women. The same work can be finished in fifteen days by ten men. The ratio between the capacity of a man and a woman is  Choose the correct choice from the following answers: A) 14:13 B) 13:15 C) 12:13 D) 13:12 E) 14:15

Solution: Work done by 10 women in 1 day = 1/13   Work done by 1 woman in 1 day = 1/(13Ã—10)   Work done by 16 men in 1 day = 1/15   Work done by 1 man in 1 day = 1/(15Ã—10)   Ratio of the capacity of a man and woman =1/(15Ã—10) : 1/(13Ã—10) = 1/15 : 1/13   = 1/15 :1/13 = 13 : 15   Answer is 13:15.
Answer: B
A 3% stock produces 10%. The market value of the stock is:  Choices:
A) Rs. 15
B) Rs. 25
C) Rs. 20
D) Rs. 30
E) Rs. 40

Solution: Let the face value of the product is Rs.100   It stock Rs.3   Market value of the stock=(3/10)*100=Rs.30   ANSWER:Rs. 30
Answer: D
In how many different ways can the letters of the word ‘ARMOUM’ be arranged?
Choose the correct choice from the following options:  A) 240  B) 260  C) 370  D) 409  E) 360

Solution: ARMOUR = 6 letter whereas R repeated twice 6! 6xSx4x3x2x1 => 360   360
Answer: E
There are 20 poles with a constant distance between each pole. A car takes 20 second to reach the 12th pole. How much will it take to reach the last pole.	Choose the correct choice from the following answers
A) 34.4543  B) 34.5455  C) 34.45128  D) 34.51288  E) 34.41222

Solution: Assuming the car starts at the first pole.   To reach the 12th pole, the car need to travel 11 poles (the first pole doesn't count, as the car is already there).   11 poles 20 seconds   1 pole (20/11) seconds   To reach the last (20th) pole, the car needs to travel 19 poles.   19 pole 19 x (20/11) seconds   = 34.5455 seconds   Answer:34.5455
Answer: B
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 10 : 5?  Options.
A) 16	B) 45	C) 277	D) 92	E) 11

Solution: Let the distances between city A to B and B to C be 10x km and 5x km respectively.   Total time taken to cover from A to C   = (10x)/40 + (5x)/60 = (30x + 10x)/120 = 40x/120 = x/3 Average speed = (10x + 5x)/(x/3) = 45 kmph.   Answer:45
Answer: B
An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?	Choose the correct choice from the following answers.
A) 4/9  B) 4/3  C) 4/2  D) 4/8  E) 4/1

Solution: 2/3 ---- 12   ? ----- 8 ==> 4/9   4/9nswer: 4/9
Answer: A
From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn Choose the correct choice from the following options:
A) 4/13
B) 1/52
C) 1/4
D) 1/5
E) None of above

Solution: Explanation:   Total number of cases = 52   Total face cards = 16 [favourable cases]   So probability = 16/52 = 4/13   4/13nswer: 4/13
Answer: A
A sells a bicycle to B at a profit of 70% and B sells it to C at a loss of 40%. Find the resultant profit or loss.  Choose the correct choice from the following answers.
A) -4% B) 2% C) -5% D) 6% E) -7%

Solution: The resultant profit or loss = 70 - 40 - (70*40)/100 = +2= 
+2 = 2
2%   Answer is 2%
Answer: B
Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 15 members of this sequence?
Select the correct option.
A) 618  B) 900  C) 788  D) 928  E) 1022

Solution: I would split them up like this.   23 28 33 and so on (8 terms)....the 8th term = 23+7*5= 
23+7*5 = 58
58   27 32 37 and so on (7 terms)......the 7th term= 27+6*5= 
27+6*5 = 57
57   Since the distance between any two numbers is the same we can use arithmetics   first+last/2 times no of numbers= the sum   (23+58)/2 * 8= 
(23+58)/2 * 8 = 324
324   (27+57)/2 * 7= 
(27+57)/2 * 7 = 294
294= 618   618
Answer: A
An empty pool being filled with water at a constant rate takes 5 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
Choose the correct choice:
A) 5 hr 30 min
B) 5 hr 20 min
C) 4 hr 48 min
D) 3 hr 20 min
E) 2 hr 40 min

Solution: (3/5) of a pool/ 5 hours = 3/25 (the rate)   (3 pools/25 hours) = (2/5* pool)/ x hours   Cross multiply 3x = (2/5) 25   x = 3 1/3   1/3 of an hour = 20 minutes   3 hr 20 min
Answer: D
7^8 is equal to which of the following? Choices:	A) 5,764,787	B) 5,764,788	C) 5,764,799	D) 5,764,800	E) 5,764,801

Solution: Units digit spotting can be fun   Cyclicity of 7 to the power of anything   7^1= 7   7^2= 9   7^3= 3   7^4= 1   7^5= 7   --- pattern formed --   So the cycle of this is 4. The fifth power will start the cycle again. Therefore, 7 to the power of 8 will give a units digit of 1. Answer 5,764,801
Answer: E
If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?	Choose the correct choice from the following:	A) 4/5	B) 3/5	C) 3/10	D) 1/5	E) 1/10

Solution: 100%-(15%+10%+55%)=20% remains for other allocations --> 20% 100 -(15 +10 +55 )= 
100 -(15 +10 +55 ) = 20
20% remains for other allocations --> 20% = 20/100   --  20= 
  --  20 = 20
20/100= 1/5.   Answer: 1/5.
Answer: D
A can finish a work in 8 days and B can do same work in half the time taken by A. then working together, what part of same work they can finish in a day?
Select the correct option
A) 3/5 B) 3/6 C) 3/7 D) 3/8 E) None of these

Solution: Explanation:   Please note in this question, we need to answer part of work for a day rather than complete work. It was worth mentioning here because many do mistake at this point in hurry to solve the question   So lets solve now,   A's 1 day work = 1/8   B's 1 day work = 1/4 [because B take half the time than A]   (A+B)'s one day work =   (1/8+1/4)=3/8   So in one day 3/8 work will be done   Answer: 3/8
Answer: D
A pharmaceutical company received $2 million in royalties on the first $15 million in sales of generic equivalent of one of its products and then $6 million in royalties on the next $72 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $15 million in sales to the next $72 million in sales?  Choose the correct choice from the following.
A) 25%  B) 30%  C) 32.5%  D) 37.5%  E) 40%

Solution: change in ratio of royalties to sales = 2/15 -6/72 = 1/20   % decrease = (1/20)/(2/15) *100= 
(1/20)/(2/15) *100 = 75/2 = around 37.5
37.5%   Answer: 37.5%)
Answer: D
The workforce of Company X is 60% female. The company hired 22 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?  Choose the correct option: A) 160 B) 220 C) 264 D) 360 E) 420

Solution: Let's xx be total quantity of employees   0.6x=females before adding men   0.55(x+22)=females after adding men   as quantity of women doesn't change we can make an equation:   0.6x=0.55(x+22)   0.05x=12.1   x=242 - this is quantity of employees before adding 22 men   So after adding it will be 264   Answer is 264
Answer: C
If each side of the square is increased by 25% find the percentage change in its area? Options.
A) 89.45%
B) 56.25%
C) 89.98%
D) 54.48%
E) 45.0%

Solution: let each side of the square be a. then area =a^2   new side=125a/100=5a/4   new area=(5a/4)^2=25a^2/16   increase in area=(25a^2/16-a^2)=9a^2/16   increased %=(9a^2/16*1/a^2*100)=56.25%   Answer is(56.25%)
Answer: B
A circular mat with diameter 16 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Answers:
A) 5/12
B) 2/5
C) 1/3
D) 3/4
E) 5/6

Solution: SO we are looking for the area of the cloth over the area of the table   Area of the 1/3loth = (pi)(r)^2 which is about (3)(8)(8)   Area of the Table = (24)(24)   So the quick way to estimate is looking at the fraction like this: (3/24)(64/24)   I hope this is easy to follow, so with some simplification i get (1/8)(8/3) = (1/3) Answer is 1/3
Answer: C
A AND B CAN DO A WORK IN 12 DAYS, B AND C IN 15 DAYS, C AND A IN 20 DAYS. IF A, B AND C WORK TOGETHER, THEY WILL COMPLETE THE WORK IN: Answers
A) 5 DAYS
B) 7 5/6 DAYS
C) 10 DAYS
D) 15 2/3 DAYS
E) NONE OF THESE

Solution: (A+B)'S 1 DAY'S WORK=1/12, (B+C)'S 1 DAY'S WORK = 1/15;   (A+C)'S 1 DAY'S WORK = 1/20   ADDING, WE GET : 2(A+B+C)'S 1 DAY'S WORK =(1/12+1/15+1/20)=12/60=1/5   (A+B+C)'S 1 DAY'S WORK = 1/10   SO, A, B AND C TOGETHER CAN COMPLETE THE WORK IN 10 DAYS.   10 DAYSORRE10 DAYST OPTION: 10 DAYS
Answer: C
A student scored an average of 85 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?	Pick one
A) 86
B) 16
C) 76
D) 65
E) 26

Solution: Given M + P + C = 85 * 3= 
85 * 3 = 255
255--- (1)   M + P= 90 * 2= 
90 * 2 = 180
180 --- (2)   P + C= 70 * 2= 
70 * 2 = 140
140 --- (3)   Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.   P= (2) + (3) - (1) = 180 + 140 - 255= 
180 + 140 - 255 = 65
65   Answer:65
Answer: D
The distance from City A to City B is 30 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?	Choose the most appropriate option
A) 45  B) 88  C) 120  D) 152  E) 154

Solution: The time it takes Bob to drive to City B is 30 / 40= 
30 / 40 = 3/4 = around 0.75
0.75 hours.   Alice needs to take less than 0.25 hours for the trip.   Alice needs to exceed a constant speed of 30 /0.25= 
30 /0.25 = 120
120 miles per hour.   The answer is 120.
Answer: C
Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?	Choose the correct choice from the following choices:
A) Rs. 2100
B) Rs. 2150
C) Rs. 2200
D) Rs. 2250
E) None of these

Solution: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.   => (90%) of (110%) of x = Rs. 2178.   => (90/100)(110/100)x = 2178   => x = (2178 * 100)/(9 * 11)   => x = Rs. 2200   ANSWER:Rs. 2200
Answer: C
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 4, which of the following best approximates the circumference of circle O?	Pick one:  A) 28  B) 22  C) 20  D) 16  E) 12

Solution: Given that (1/a)+a =3   Square both sides of the equation:   We get,   [(1/a)^2 + a^2 + 2*(1/a)*a] = 9   => (1/a)^2 + a^2 + 2 = 9   => (1/a)^2 + a^2 = 7 ----------------- (1)   Diameter D = (1/a)^2 + a^2   = 7 (From (1))   So Radius = D/2 = 7/2   20ircumference = 2*Pi*r   = 2*(22/7)*(7/2)   =20   So the answer should be 20
Answer: C
The difference between simple and compound interest on Rs. 1500 for one year at 10% per annum reckoned half-yearly is?  Choose the correct answer
A) 8.0
B) 3.0
C) 9.5
D) 3.75
E) 2.15

Solution: S.I. = (1500 * 10 * 1)/100 = Rs. 150   C.I. = [1500 * (1 + 5/100)2 - 1500]   = Rs. 153.75 3.75ifference = (153.75 - 150)   = Rs.3.75   Answer:3.75
Answer: D
If -3x+2y=28 and 3x+6y=84, what is the product of x and y? Choose the correct choice from the following.
A) 264.  B) 428  C) 0  D) 462  E) 642

Solution: Given -3x+2y=28 ---Eq 1   3x + 6y =84 -- Eq 2   Sum both eqns we get 8Y = 112 => Y = 14   Sum 2Y in eq 1 => -3X - 28 = 28.   => X = 0   Now XY = 0 * 14= 
0 * 14 = 0
0.   Option 0 is correct answer.
Answer: C
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?  Select the correct option.
A) 9:1  B) 4:7  C) 7:1  D) 2:5  E) None of these

Solution: Explanation:   Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   The required ratio of milk and water in the final mixture obtained= (8 + 10):2 = 18:2 = 9:1.   9:1NSWER IS 9:1
Answer: A
0.03 x 0.5 = ?
Answers.
A) 0.0001
B) 0.001
C) 0.015
D) 0.1
E) NONE OF THESE

Solution: Explanation:   3 x 5 = 15.   Sum of decimal places = 3   0.02 x 0.5 = 0.015   Answer- 0.015
Answer: C
A train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.	Choose the correct choice from the following
A) 45 kmph B) 50 kmph C) 55 kmph D) 60 kmph E) 70 kmph

Solution: Explanation:   Let the speed of the train be x kmph.   Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.   Therefore 100/((x+5)×5/18)=6 <=> 30 (x + 5) = 1800 <=> x = 55   Speed of the train is 55 kmph.   Answer: Option 55 kmph
Answer: C
A present value of a machine is $2000. Its value depletiation rate is 20% per annum then find the machine value before 2 years?
Select.
A) $3125
B) $2945
C) $3012
D) $2545
E) $3150

Solution: P= $2000   R = 20%   T = 2 years   Machine value before 2 years = P/[(1-R/100)^T]   =2000*5/4 * 5/4= 
2000*5/4 * 5/4 = 3_125
$3125   $3125nswer is $3125
Answer: A
Calculate the cost of p meters of rope given that the cost of m meters of said rope is q rupees? Choose the correct choice from the following choices:
A) Rs.(q*m) B) Rs.(pq/m) C) Rs.(q/m) D) Rs.(p/m) E) Rs.(p*m)

Solution: Cost of m metres = Rs. q.   Cost of 1 metre = Rs.	q/m   Cost of p metres = Rs.(q/m)* p= Rs.(pq/m)   Answer is Rs.(pq/m).
Answer: B
Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 2th shift?  Choose the correct choice from the following choices.
A) 1/27
B) 1/54
C) 1/81
D) 1/6
E) 1/216

Solution: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2   Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)   Fraction of area unpainted after SECON1/6 shift of Amit = (1/2)(2/3)(1/2)=1/6   Answer: option 1/6
Answer: D
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?	Choose one
A) 1/3	B) 1/2	C) 1/6	D) 1/8	E) 1/9

Solution: Explanation :   P(first letter is not vowel)=2/4P(second letter is not vowel)=1/3So,probability that none of letters would be vowels is =(2/4)x(1/3)=1/6   Answer : 1/6
Answer: C
If n is a positive integer and n^2 is divisible by 134, then the largest positive integer that must divide n is Choices:  A) 6  B) 12  C) 24  D) 36  E) 48

Solution: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.   Complete solution of this question is given above. Please ask if anything remains unclear.   I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.   I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.   I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true   However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true   So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?   Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.   Now, ask yourself: if n=24, is n divisible by 48? No. So, n is not always divisible by 48.   24
Answer: C
An bus covers a certain distance at a speed of 250 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?	Select the correct option:
A) 600 km/hr
B) 720 km/hr
C) 730 km/hr
D) 750 km/hr
E) 760 km/hr

Solution: Distance = (250 x 5) = 1250 km.   Speed = Distance/Time   Speed = 1250/(5/3) km/hr. [We can write 1 hours as 5/3 hours]   Required speed = 1250 x 3 km/hr = 750 km/hr.   750 km/hr
Answer: D
Angelo and Isabella are both salespersons. In any given week, Angelo makes $580 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money? Choose the correct choice from the following answers
A) 23,500  B) 24,500  C) 25,000  D) 26,500  E) 27,500

Solution: Let the weekly sales of both = x   580+(x−1000)8/100=10/100x   x = 25000   ANSWER:25,000
Answer: C
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is? Choose the correct choice from the following options:
A) 2299  B) 2779  C) 6000  D) 2878  E) 231

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18000= 
1/3 * 18000 = 6_000
6000.Answer: 6000
Answer: C
A train 140 m long crosses a platform 160 m long in 16 sec; find the speed of the train?	Choose the correct choice from the following answers:
A) 87 kmph
B) 65 kmph
C) 68 kmph
D) 16 kmph
E) 18 kmph

Solution: D = 140 + 160= 
140 + 160 = 300
300   T= 16   S = 300/16 * 18/5= 
300/16 * 18/5 = 135/2 = around 67.5
67.5 kmph   Answer:68 kmph
Answer: C
There are 10 solid colored balls in a box, including 1 Green and 1 Yellow. If 3 of the balls in the box are chosen at random, without replacement, what is the probability that the 3 balls chosen will include the Green ball but not the yellow ball.
Choose the correct option: A) 1/6 B) 7/30 C) 1/4 D) 3/10 E) 4/15

Solution: But we ARE told that there is is only 1 green ball and only 1 yellow ball in the box, becausethere are 10 solid colored balls in a box,including 1 Green and 1 Yellowmeans exactly that. How else?   Would it make ANY sense if there were for example 2 green balls and we were told thatthere are 10 solid colored balls in a box,including 1 Green and 1 Yellow?   Hmm.. yeah, that does make sense. I'm a non-native English speaker so I tend to over-analyze simple things. In this case, since the wordonlywas missing i.e. there are 10 solid colored balls in a box, includingexactly/only1 Green and 1 Yellow . 7/30ut yeah, in retrospect this is a Quant question not a Verbal SCThanks for the explanation answer is 7/30
Answer: B
Four friends, Patricia, Melyssa, Tania, and Cassandra, are pooling their money to buy a $1100 item. Patricia has twice as much money as Melyssa. Tania has $10 more than Patricia. Cassandra has 20% more than Tania. If they put all their money together and spend the $1100, they will have $32 left. How much money does Patricia have?  Select the correct option:
A) $200  B) $420  C) $300  D) $315  E) $280

Solution: P= 2M ; T= P+10 ; $300= 1.2(T)   P+M+T+$300-1100=32   P+0.5P+P+10+1.2(P+10) = 1132   P+0.5P+P+10+1.2P+12=1132   P+0.5P+P+1.2P+22=1132   P+0.5P+P+1.2P=1110   3.7P=1110   P=300   Answer:$300
Answer: C
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?	Choose the most appropriate option: A) 18 B) 20 C) 22 D) 25 E) 26

Solution: 2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then smallest number is= 2   2x = 20   18
Answer: A
Simplify : 5793405 x 9999	Answers:	A) 57928256595	B) 59278256595	C) 57928262559	D) 59722422582	E) None of them

Solution: 5793405x9999=5793405(10000-1)=57934050000-5793405= 
57934050000-5793405 = 57_928_256_595
57928256595.   57928256595nswer is 57928256595
Answer: A
A bakery has 6 employees. It pays annual salaries of $16,000 to each of 2 employees, $18,000 to 1 employee, and $19,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
Choose one:
A) $17,200 B) $17,500 C) $17,800 D) $18,000 E) $18,400

Solution: average = 2(16000)+(18000)+3(19000) / 6 = $17,833   The answer is $17,800.
Answer: C
In the first week of last month, Company X realized an average wholesale profit of $5712 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit? Answers.
A) $3 B) $4 C) $7 D) $13 E) $51

Solution: The key operator that everyone seems to have missed is the average. The average profit of $5304 per day is equivalent to a total profit of $39984 for the whole week.   Therefore, the difference between sale price and cost per unit is equal to $39984, which is divisible by all of the answer choices, except for 13.   So, $13 is the answer.
Answer: D
If a and b are different positive integers and a + b = b(a + b), then which of the following must be true?
I. a = 1
II. b < a
III. b = 1	Select the correct option
A) I only B) II only C) III only D) II and III E) I and III

Solution: b has to equal a squared, and that only works if b is 1. There are no positive integers less than 1, soII and III are correct.   Answer : II and III
Answer: D
A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 1:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet? Choose the most appropriate option:	A) 10.18 p.m	B) 10.29 p.m	C) 8.30 p.m	D) 10.38 p.m	E) 10.32 p.m

Solution: D = 70 * 1 ½ = 105 km   RS = 85 – 70 = 15   T = 105/15= 
105/15 = 7
7 h     1.30 + 7= 
  1.30 + 7 = 8.3
8.30 p.m.   Answer:8.30 p.m
Answer: C