MU-NLPC/Calc-aqua_rat huggingface dataset:
An investor bought two shares of stock, which he sold for $36 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
Choose the most appropriate option:
A) a profit of $5 B) a profit of $3 C) a loss of $3 D) a loss of $5 E) neither a profit nor a loss

Solution: The cost of the first stock was 36/1.2= 
36/1.2 = 30
30, so the profit from it is 6.   The cost of the second stock was 36/0.8= 
36/0.8 = 45
45, so loss from it is 9.   Overall the loss is $3.   The answer is a loss of $3.
Answer: C
An engineer undertakes a project to build a road 15 km long in 300 days and employs 35 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
Pick:  A) a. 43  B) b. 53  C) c. 55  D) d. 68  E) e. 60

Solution: 35 workers working already   Let x be the total men required to finish the task in next 200 days   2.5 km done hence remaining is 12.5 km   Also, work has to be completed in next 200 days (300 - 100 = 200)   We know that, proportion of men to distance is direct proportion   and, proportion of men to days is inverse proportion   Hence, X = (35 * 12.5 * 100) / (2.5 * 200)   thus, X = 87.5 that is approximately 88   Thus, more men needed to finish the task = 88-35= 
88-35 = 53
53   hence Answer is b. 53
Answer: B
In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
Select
A) 33  B) 787  C) 18  D) 10  E) 87

Solution: Convert kmph to mps. 36 kmph = 36 * 5/18= 
36 * 5/18 = 10
10 mps.   The distance to be covered is equal to the length of the train.   Required time t= d/s = 100/10= 
100/10 = 10
10 sec.   Answer:10
Answer: D
What is the probability that a 4 person committee chosen at random from a group consisting of 3 men, 7 women, and 5 children contains exactly 1 woman?	Answers:
A) 56/195 B) 77/832 C) 11/77 D) 308/1411 E) 22/832

Solution: Total possible selections = 4 out of 15 group members = 15C4   Favorable selections = 1 out of 7 women and 3 out of 8 (= 3 men + 5 children) = 7C1 * 8C3   Thus the required probability = 7C1*8C3 / 15C4 = 56/195. Thus 56/195 is the correct answer.
Answer: A
What decimal fraction is 90 ml of a litre ?
Choose the correct choice from the following:
A) .9  B) .009  C) .09  D) 0.09  E) None of these

Solution: Answer   Required fraction = 90/1000   = 9/100= 
9/100 = 9/100 = around 0.09
.09   .09orrect Option: .09
Answer: C
The graphs of the two equations y = a x 2 + b x + c and y = A x 2 + B x + C, such that a and A have different signs and that the quantities b 2 - 4 a c and B 2 - 4 A C are both negative,
Choose the correct choice from the following: A) intersect at two points B) intersect at one point C) do not intersect D) none of the above E) Cannot be determined

Solution: Solution   Since a and A have different signs the graphs of the two equations are parabolas opening in diffent directions: If one opens up the other opens down. Also since b 2 - 4 a c and B 2 - 4 A C are both negative, none of the parabola cuts the x axis. This means that each one of these parabolas is either above the x axis or below the x axis and therefore do not intersect.   Answer do not intersect
Answer: C
A train running at the speed of 60 km/hr crosses a pole in 3 seconds. Find the length of the train.  Choose the correct choice from the following answers
A) 60	B) 50	C) 75	D) 100	E) 120

Solution: :   Speed = 60*(5/18) m/sec = 50/3 m/sec   Length of Train (Distance) = Speed * Time     (50/3) * 3= 
  (50/3) * 3 = 50
50 meter   Answer:50
Answer: B
Steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 100 mph. What is his average speed of travel for the entire journey?	Pick:
A) 60 mph
B) 56.67 mph
C) 53.33 mph
D) 64 mph
E) 76 mph

Solution: Answer   Average speed of travel = Total distance travelled/Total time taken   Total distance traveled by Steve = Distance covered in the first 2 hours + distance covered in the next 3 hours.   Distance covered in the first 2 hours = speed * time = 40 * 2= 
40 * 2 = 80
80 miles.   Distance covered in the next 3 hours= speed * time = 100 * 3= 
100 * 3 = 300
300 miles.   Therefore, total distance covered= 80 + 300= 
80 + 300 = 380
380 miles.   Total time taken= 2 + 3= 
2 + 3 = 5
5 hours.   Hence, average speed= Total distance travelled/Total time taken=380/5= 
380/5 = 76
76 miles per hour.   Choice 76 mph
Answer: E
A man can row downstream at 26 kmph and upstream at 22 kmph. Find the speed of the man in still water and the speed of stream respectively?	Answers:  A) 24, 2  B) 12, 6  C) 15, 3  D) 14, 4  E) None of these

Solution: Explanation:   Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 26 --- (1)   and x - y = 22 --- (2)   From (1) & (2) 2x = 48 => x = 24, y = 2.   24, 2nswer: Option 24, 2
Answer: A
Two dogsled teams raced across a 400-mile course in Alaska. Team A finished the course in 4 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour? Choose the correct choice from the following answers
A) 12	B) 15	C) 18	D) 20	E) 25

Solution: Let v be team B's average speed.   Time = Distance/Rate and the time difference was 4 hours.   400/v - 400/(v+5)= 4   400v + 2000 - 400v = 4(v)(v+5)   500 = (v)(v+5)   (20)(25) = (v)(v+5)   v = 20 mph   The answer is 20.
Answer: D
If 10! - 2*(5!)^2 is divisible by 10^n, what is the greatest value of n?	Select the correct option:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: =10∗9∗8∗7∗6∗5!−2∗5!∗5∗4∗3∗2∗1   =5!∗10∗3∗8(125)   =5∗(2∗2)∗3∗2∗(5∗2)∗24∗5∗5∗5   =5∗2∗5∗2∗5∗2∗5∗2∗24∗5∗3   =10^4∗2^4∗5∗3   =10^4∗5∗2∗12∗3   =10^5∗36   Answer: 5
Answer: E
The tens digit of a two-digit number is two more than its unit digit. The two-digit number is 7 times the sum of the digits. Find the units digits?	Choose the correct choice from the following answers:
A) 1 B) 2 digits C) 3 D) 4 E) 5

Solution: Let the two-digit number be 10a + b   a = b + 2 --- (1)   10a + b = 7(a + b) => a = 2b   Substituting a =   2b in equation (1), we get   2b = b + 2 => b = 2   Hence the units digit is: 2.   ANSWER:2 digits
Answer: B
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?	Choose the most appropriate option
A) 9 a.m	B) 10 a.m	C) 10.30 a.m	D) 11 a.m	E) 9 a.m

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer:10 a.m
Answer: B
A rower whose speed is 2.5 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 0.5 km/hr. What is the rower's average speed (in km/hr) for the total journey?
Choose the correct option.
A) 2.2	B) 2.3	C) 2.4	D) 2.5	E) 2.6

Solution: time upstream = d / 2   time downstream = d / 3   total time = d/2 + d/3 = 5d/6   average speed = 2d / (5d/6) = 2.4 km/hr   The answer is 2.4.2  / (5 /6)= 
2  / (5 /6) = 12/5 = around 2.4
2.4 km/hr   The answer is 2.4.
Answer: C
A train 150 m long crosses a platform 120 m long in 10 sec; find the speed of the train?
Choose the correct answer.
A) 87 kmph  B) 65 kmph  C) 97 kmph  D) 16 kmph  E) 18 kmph

Solution: D = 150 + 120= 
150 + 120 = 270
270   T= 10   S = 270/10 * 18/5 = 97 kmph   Answer:97 kmph
Answer: C
Let the function p(n) represent the product of the first n prime numbers, where n > 0. If x = p(n) + 1, which of the following must be true?
(i) x is always odd
(ii) x is always prime
(iii) x is never the square of an integer	Choose the correct answer.
A) ii only B) iii only C) i and ii only D) i and iii only E) ii and iii only

Solution: If n=2 then 2X3+1=7   if n=3 then 2*3*5= 
2*3*5 = 30
30+1= 
30+1 = 31
31 the answer will always be odd b/c 2 is a prime and the product will always be an even plus 1   If you try n=4 then you get   2*3*5*7= 
  2*3*5*7 = 210
210 which is not a prime   ANSWER:i and iii only
Answer: D
Find the value of 3+2.(8-3)  Pick.
A) 25	B) 13	C) 17	D) 24	E) 19

Solution: 3+2.(8-3)   =3+2(5), =3+2*5, =3+10, =13 , Correct answer : (24)
Answer: D
A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey? Select:	A) 20	B) 30	C) 43	D) 24	E) 80

Solution: Ans.(D)   Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 6 From, fundamental principle, total number of ways of performing the journey = 4 x 6 = 24 ways
Answer: D
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and B quits 15 days before the project is completed, in how many days total will the project be completed?	Select the correct option
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: A's rate is 1/20 of the project per day.   B's rate is 1/30 of the project per day.   The combined rate is 1/12 of the project per day.   In the last 15 days, A can do 3/4 of the project.   Thus A and B must complete 1/4 of the project, which takes 3 days.   The total number of days is  3 + 15= 
 3 + 15 = 18
18.   The answer is 18.
Answer: D
Of 30 applicants for a job, 10 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?  Choices: A) 14 B) 13 C) 9 D) 7 E) 5

Solution: C. 9   30 - 3= 
30 - 3 = 27
27   27 - 10 - 18= -9   Then 9 are in the intersection between 4 years experience and degree.   Answer 9
Answer: C
A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
Choose the correct choice:  A) 104  B) 190  C) 109  D) 278  E) 211

Solution: Explanation:   624/6= 
624/6 = 104
104 kmph   Answer:109
Answer: C
In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?  Select:
A) 160  B) 175  C) 180  D) 195  E) 172

Solution: Explanation:   Suppose the man works overtime for x hours.   Now, working hours in 4 weeks = (5 x 8 x 4) = 160.   Therefore, 160 x 2.40 + x x 3.20 = 432   => 3.20x = 432 - 384= 
432 - 384 = 48
48=> x = 15.   Hence, total hours of work = (160 + 15)= 
(160 + 15) = 175
175.   ANSWER IS 175
Answer: B
Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?  Choose the correct answer:
A) 20
B) 18
C) 23
D) 26
E) 24

Solution: (5x + 3)/(4x + 3) = 11/9   9(5x + 3) = 11(4x + 3) => x = 6   Anand's present age = 4x = 24 years.   ANSW24R 24
Answer: E
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
Options.
A) 61.5  B) 60.5  C) 63.5  D) 62.5  E) 64.5

Solution: Let capacity of 1 bucket = x   Capacity of the tank = 25x   New capacity of the bucket = 2x/5   Hence, number of buckets needed = 25x/(2x/5)=(25×5)/2=62.5   Answer is 62.5.
Answer: D
A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?	Answers
A) 1000  B) 1250  C) 1300  D) 1529.41  E) 1625

Solution: 300 gallons of water increases capacity by 30% that means   30% is 300 gallons, so 100% would be = 300*100/30= 
300*100/30 = 1_000
1000 gallons   Now 1000 +300 gallons is 85% capacity of tank.   so 100% capacity would be= 1300 *100/85= 1529.41   1529.41 is the answer
Answer: D
8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work?	Pick one
A) 5 days	B) 15 days	C) 28 days	D) 4 days	E) 7 days

Solution: Explanation:   1 man’s 1 day’s work = 1/8 × 12 = 1/96   10 men’s 1 day’s work = 1 × 10/96 = 5/48   1 woman’s 1 day’s work = 1/192   20 women’s 1 day’s work = 1/192 × 20 = 5/48   1 child’s 1 day’s work = 1/240   10 children’s 1 day’s work = 1/24   Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24   =1/4   The required No. of days = 4 days   Answer: Option 4 days
Answer: D
A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,050 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
Answers.
A) 25.0 B) 30.2 C) 35.3 D) 40.2 E) 41.4

Solution: Day 1   2t+3=21   t=9   Day 2   t+3   9+3= 
9+3 = 12
12   9r+12(r+15)=1050   r=41.4   Answer:41.4
Answer: E
On increasing the price of T.V. sets by 30%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ? Choose the correct option:
A) 4
B) 5
C) 56
D) 2
E) 7

Solution: Explanation:   Let the price be = Rs.100, and number of units sold = 100   Then, sale value = Rs.(100 × 100) = Rs.10000   New sale value = Rs.(130 × 80) = Rs.10400   Increase% = 4001000040010000 × 100 = 4%   4nswer: 4
Answer: A
A man buys a cycle for Rs. 1400 and sells it at a loss of 20%. What is the selling price of the cycle?
Choices:
A) s. 1090  B) s. 1120  C) s. 1190  D) s. 1202  E) s. 1204

Solution: since,c.p=1400   loss%=(c.p-s.p)/c.p*100   20=(1400-s.p)/1400*100   so,after solving answer=1120.   ANSWER:s. 1120
Answer: B
A five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. What is the probability that the number is divisible by 4?	Choose the correct choice
A) 1/2	B) 4/3	C) 8/9	D) 4/2	E) 1/5

Solution: In each of these cases, the five digits number can be formed using the remaining 3 digits in 3!=6 ways.   A number divisible by 4 can be formed in 6×4=24 ways.   Total number that can be formed using the digits 1, 2, 3, 4 and 5 without repetition   =5!=120   Required probability,   =24/120   =1/5   1/5
Answer: E
The average of 20, 40 and 180 is twice the average of 10, 30, and which of the following ?
Select:
A) 1)10	B) 2)30	C) 3)60	D) 4)80	E) 5)180

Solution: 20 40 180 = 180+60= 
180+60 = 240
240/3= 
240/3 = 80
80.   80/2= 
80/2 = 40
40   10 30 x= 40+x/3 should be smaller than 40   cross multiply 40*3-40= 
40*3-40 = 80
80   4)80
Answer: D
A person covers a distance in 15 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.  Select:
A) 18 m/s  B) 4 m/s  C) 15 m/s  D) 10 m/s  E) 5 m/s

Solution: Explanation:   T = 15 m   Spees = 12 kmph   = 12 x 5/18 = 10/3 m/s   Let new speed be "x"   15 x (10/3) = 5x   x = 10 m/s   Answer: Option 10 m/s
Answer: D
How many diagonals does a 61-sided convex polygon have?  Options.
A) 1182
B) 1769
C) 2456
D) 3538
E) 4209

Solution: A 61-sided convex polygon has 61 vertices.   If we examine a single vertex, we can see that we can connect it with 58 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.   If each of the 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be (61)(58) = 3538   However, we must recognize that we have counted every diagonal twice.   To account for counting each diagonal twice, we must divide 3538 by 2 to get 1769.   The answer is 1769.
Answer: B
if you toss a coin two times what is the probability that it will land either heads both times or tails both times?  Choices: A) A)1/8 B) B)1/6 C) C)1/4 D) D)1/2 E) E)1

Solution: Prob to get 2 heads = 1/2*1/2 = 1/4   Prob to get 2 tails = 1/2*1/2 = 1/4   So, Prob to get eithe r 2 heads or 2 tails = 1/4+1/4 = 1/2   Answer will be 1/2.
Answer: D
A cricket bat is sold for $850, making a profit of $245. The profit percentage would be	Choose the correct answer
A) 24%	B) 25%	C) 30%	D) 36%	E) 40%

Solution: 245/(850 - 245) = 245/605 = 49/121 = 40%.   Answer: 40%.
Answer: E
Rs378 is divided among the three children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of Esha.how much the Rupee anusha get? Choose one.
A) 74	B) 84	C) 94	D) 104	E) 114

Solution: If money with Anusha=a, 84abu=b & Esha=e, then   a+b+e=378 ---(i) &   12a=8b=6e, so b=3a/2 & e=2a   Substituting these values of b & e in (i), a+(3a/2)+2a=378 , On solving, a=84   So, b=126, e=168   ANSWER:84
Answer: B
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 390 m long platform?	Choose the correct choice from the following.
A) 19 B) 27 C) 51 D) 47 E) 28

Solution: Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +390)/ 36 * 5/18   = 51 min.   Answer:51
Answer: C
A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.	Answers:
A) 100 Km B) 110 Km C) 120 Km D) 140 Km E) NONE

Solution: Explanation :   In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.   x/6 = (30+x)/8   x = 90. So distance from start after which B will catch A = 90+30= 
90+30 = 120
120km   Answer – 120 Km
Answer: C
A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 4 less, he would have made a profit of 10%. The C.P. of the article was
Choose the correct choice
A) 344  B) 600  C) 200  D) 800  E) 700

Solution: Explanation:   Let original Cost price is x   Its Selling price = (105/100) * x = 21x/20   New Cost price = (95/100) * x = 19x/20   New Selling price = (110/100 )* (19x/20 )= 209x/200   [(21x/20) - (209x/200)] = 4   => x = 800   Answer: 800) Rs 800
Answer: D
P = {105, 106, 107, 108, 109, x}
Set P above consists of 6 integers. For what value of x are the mode, the median and the average equal? Choose the most appropriate option
A) 105	B) 106	C) 107	D) 108	E) 109

Solution: Mode of a set is the number with max frequency.   Median for an even numbered set is the average of middle terms.   Average or mean is the sum of the set/No. of elements in the set.   Going from the answer choices, if we use 107 as the missing number.   The set becomes {105, 106, 107, 107, 108, 109}   Now the mode, median and mean are all same, 107   ANS (Option 107)
Answer: C
The sum of x, y coordinate values is 2490. if 6.5% of one coordinate is equal to 8.5% of the other, then the coordinate values are : Select
A) 989,1501	B) 1011,1479	C) 1401,1089	D) 1411,1079	E) None of these

Solution: Explanation :   Solution: Let the coordinates be x and y. then, 6.5% of x = 8.5% of y   => x = 85/65   y = 17/13 y   Now, x+y =249017y/13+y = 2490   => 30y/13 = 2490   => y = 2490*13/30= 
2490*13/30 = 1_079
1079.   .'. One coordinate is= y= 1079, other coordinate = 17y/13 =1411   Answer : 1411,1079
Answer: D
a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple?	Select the correct option:
A) 225	B) 228	C) 230	D) 231	E) 235

Solution: CP = 140*2+150*3+160*4+170*1= 
140*2+150*3+160*4+170*1 = 1_540
1540   SP= 1.5*1540= 
1.5*1540 = 2_310
2310   Total no.of kgs=2+3+4+1= 
2+3+4+1 = 10
10   SP per kg=2310/10= 
2310/10 = 231
231   ANSWER:231
Answer: D
Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12?  Choose the correct choice from the following choices.
A) 15,450
B) 18,760
C) 21,520
D) 24,360
E) 27,720

Solution: The number needs to be divisible by 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, and 2^2*3.   The lowest positive integer is 7 * 2^3 * 3^2 * 5 * 11 = 27,720   The answer is 27,720.
Answer: E
Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/5, 1/3, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third? Select.
A) 1/30n B) (n-1)/15n C) 1/5n D) (n+2)/3n E) (3n-2)/5n

Solution: 1/5 * 1/3 * (1-1/n)   = 1/15 * (n-1)/n   = (n-1)/15n   Answer - (n-1)/15n
Answer: B
In 10 years, A will be twice as old as B was 10 years ago. If A is now 5 years older than B the present age of B is Pick one.
A) 37	B) 38	C) 39	D) 35	E) 41

Solution: let present age of A be a and B be b   a+10 = 2*(b-10)   => 2b-a = 30 ......(i)   a = b+5   =>2b-b-5 = 30   b=35   so the present age of b is 35 years   ANSWER:35
Answer: D
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.  Choose the correct choice from the following answers
A) 12 sec  B) 24 sec  C) 48 sec  D) 60 sec  E) 50 sec

Solution: Relative speed =(45 + 30) km/hr   =(75 x(5/18)) m/sec   =(125/6)	m/sec.   We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.   So, distance covered = Length of the slower train.   Therefore, Distance covered = 500 m.   Therefore Required time =	(500 x6/125)= 24 sec.   Answer :24 sec
Answer: B
99,994^2 - 6^2 =  Answers.
A) 10^10 - 2 B) (10^5 – 2)^2 C) 10^4(10^5 – 2) D) 10^5(10^4 – 2) E) 10^5(10^5 – 12)

Solution: (99,994)^2 - (6)^2 = (100,000 -6)^2 - (6)^2 = (100,000)^2 - 2*6*100,000 + 6^2-6^2=(10^5)^2 - 12*(10^5) = 10^10 - 12*(10^5)=10^5(10^5 - 12) Answer 10^5(10^5 – 12)
Answer: E
Of the three numbers, second number is two times bigger than the first number and is also three times bigger than the third number. If the average of the three numbers is 44, the largest number is
Answers
A) 24  B) 36  C) 72  D) 108  E) 210

Solution: Explanation :   Let 3rd number is x. Then, second number = 3x.   First number = 3x / 2   (x + 3x + 3x/2)/3 = 44 or (x+3x+3x/2)=44*3 or 11x/2 = 44*3 or x=24.   24nswer : 24
Answer: A
Andy has 20 pairs of matched gloves. If he loses 12 individual gloves, which of the following is NOT a possible number of matched pairs he has left? Choose the correct choice
A) 9
B) 11
C) 13
D) 14
E) 15

Solution: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair   Once you understand the question, You have to choose an answer choice in seconds. Answer will be either it is minimum (A - 9) or maximum (E - 15). Eliminate B,C and D. Since 12 gloves are gone, we can ignore A and straight away choose the maximum [Here its 15 i.e E]   Since there cant be any ambigous answer it should be minimum or maximum in the listed answer choice.   Now mathematical approach for understanding:   Case1: If 12 gloves are gone the maximum probability of losing maximum gloves is 12 pairs of gloves out of 20. This means i m having 8 pairs of gloves. [Minimum number of gloves i can have is 8 pairs]   Case2: If 12 gloves are gone the maximum probability of losing minimum gloves is 12/2= 
12/2 = 6
6 means i can lose 6 glove. in this scenario i will be having 14 gloves.   Hence10 < Available Glove Pair < 15   any given time I cant possess 15 glove pair for the above mentioned scenario. And thats the answer. 15.
Answer: E
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed? Select.
A) 83.43%
B) 83.73%
C) 83.23%
D) 83.93%
E) 83.33%

Solution: Percentage of milk in the mixture formed   = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%   = 5/6 * 100% = 83.33%.   Answer:83.33%
Answer: E