MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?	Answers
A) 50 m	B) 72 m	C) 80 m	D) 82 m	E) 90 m

Solution: Explanation:   Let the length of each train be x m.   Then, distance covered = 2x m.   Relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr.= 10 * 5/18 = 25/9 m/sec.   2x/36 = 25/9 => x = 50.   50 mNSWER IS 50 m
Answer: A
A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit.
Choose the correct choice from the following answers
A) 1260
B) 1200
C) 1300
D) 1500
E) 2000

Solution: Let SP be x then   (100-loss)%(1st SP) =(100+gain%):(2nd SP)   =>(95/1140 = 105/x)   x=1260   1260NSWER 1260
Answer: A
A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?  Select the correct option:
A) 90
B) 75
C) 50
D) 80
E) 60

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 400   16x = 400   x = 25.   Hence, total number of notes = 3x = 75.   Answer is 75.
Answer: B
In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 5 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?  Answers:
A) 168.	B) 80.	C) 56.	D) 64.	E) 16.

Solution: ways to select one shelf = 2   ways to select one bed = 4   ways to select one of the following: a chair or a closet = 5+3= 
5+3 = 8
8   ways to select all of them together= 2*4*8= 
2*4*8 = 64
64   64.
Answer: D
If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 315, what is the greatest possible profit that might be made in selling eight books ?
Choose the correct choice from the following answers:
A) 23267  B) 2677  C) 1800  D) 2778  E) 920

Solution: Explanation:   Least Cost Price = Rs. (200 * 8) = Rs. 1600.   Greatest Selling Price = Rs. (315 * 8) = Rs. 2520.   Required profit = Rs. (2520 - 1600) = Rs. 920.   Answer: 920) 920
Answer: E
Carol is three times Kalice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?	Choose the correct choice from the following answers
A) 6
B) 9
C) 12
D) 18
E) 24

Solution: ans B..9..   given that C=3K=2B..AND K=C-12..   substituting the values K=6,C=18 AND 9=9..
Answer: B
A coin is tossed seven times. What is the probability that there is at the least one tail?  Choose the correct choice from the following choices.
A) 127/128 B) 31/37 C) 31/18 D) 31/10 E) 31/19

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed seven times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/128; P(T) = 1 - 1/128= 127/128   127/128nswer: 127/128
Answer: A
The price of lunch for 15 people was $206.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
Choose one.
A) $11.73  B) $12.48  C) $13.80  D) $14.00  E) $15.87

Solution: Take the initial price before the gratuity is 100   The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 206 is for 115 then we have to calculate for 100   for 115 206   for 100 x   so by cross multiplication we get 115x=100*206 => x=100*206/110 by simplifying we get x as 187.27 which is the price of lunch before gratuity so the gratuity is 18.73 so   as the question ask the average price person excluding gratuity is 187.27/15=12.48 so our answer is $12.48)
Answer: B
Last year a certain bond price with a face value of 5000 yielded 9% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?  Choose the correct answer
A) 4063
B) 5325
C) 5351
D) 6000
E) 6923

Solution: Interest = 0.09*5000 = 0.065*selling price --> selling price = 0.09*5000/0.065 --> selling price = ~6,923   Answer: 6923.
Answer: E
If the remainder is 11 when positive integer n is divided by 18, what is the remainder when n is divided by 9? Choose the correct choice from the following answers.
A) 0	B) 2	C) 1	D) 3	E) 4

Solution: Assume x is quotient here,   n=18x+11 ----------(1)   and n=9x+ ?   We can also write equation (1) as:   n=(18x+9)+2.   ie 9(2x+1)+2 ie the first term is perfectly divisible by 6.   So,the remainder left is 2.   So,answer (2) is right choice.
Answer: B
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options
A) 22 B) 27 C) 12 D) 71 E) 53

Solution: Explanation:   T = 9/45 * 60= 
9/45 * 60 = 12
12   Answer: Option 12
Answer: C
The difference of 2 digit no. & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
Choose the correct option
A) 6
B) 8
C) 9
D) 10
E) 14

Solution: Let the number be xy.   Given xy – yx = 36.   This means the number is greater is than the number got on reversing the digits.   This shows that the ten’s digit x > unit digit y.   Also given ratio between digits is 1 : 2 => x = 2y   (10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.   Hence, (x + y) – (x – y) = 3y – y = 2y = 8   8
Answer: B
3 ltr of water is added with 11 ltr of a solution containing 42%of alcohol in the water. The %of alcohol in the new mixture is? Pick one
A) 23% B) 35% C) 33% D) 40% E) 45%

Solution: We have a 11 litre solution containing 42% of alcohol in the water.   => Quantity of alcohol in the solution   =11×42/ 100   Now 3 litre of water is added to the solution.   => Total quantity of the new solution = 11 + 3= 
11 + 3 = 14
14   Percentage of alcohol in the new solution=11×42/100   14   ×   100   =11×4210014×100   =11×3/100   =33%   33%
Answer: C
Which of these expressions has the greatest value? Choose the correct choice:
A) 1345211/1345215
B) 1892345/1862348
C) 1215768/1215769
D) 1532672/1532675
E) 1214651/1214651

Solution: Using elimination method on options   1892345/1862348 = 1.01610708632...   ANSWER:1892345/1862348
Answer: B
There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?  Choose the correct answer.
A) 90	B) 100	C) 110	D) 180	E) 200

Solution: Maximum points of intersection between n different circles = n*(n - 1) = 10*9= 
10*9 = 90
90   90nswer: 90
Answer: A
If 15% of A is the same as 25% of B, then A : B is :  Pick one
A) 5:3	B) 4:3	C) 7:16	D) 12:17	E) 11:13

Solution: Expl : 15% of 5:3 I= 25 % of B =155:3/100 = 25B/100 = 5/3 = 5:3   5:3nswer:5:3
Answer: A
A card is drawn from a pack of 250 card numberd 1 to 200.what is the probability that drawing a no.which is perfect cube? Select the correct option:
A) 1/40	B) 1/20	C) 1/30	D) 3/40	E) 5/40

Solution: 6^3 is 216 so only 1to 5 is a perfect cube with in 200   therefore 5c1/200c1   =1/40   1/40NSWER:1/40
Answer: A
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
Choose the correct choice from the following answers.
A) 1/455 B) 1/439 C) 1/429 D) 1/409 E) 1/420

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)   = 1/455   1/455nswer:1/455
Answer: A
Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?	Choose the correct option
A) 11. B) 12. C) 13. D) 14. E) 14.5

Solution: Price of candy before price increase= 10/1.25= 
10/1.25 = 8
8   Price of soda before price increase= 9/1.5= 
9/1.5 = 6
6   Total price= 8+6= 
8+6 = 14
14   14. is the answer
Answer: D
After decreasing 25% in the price of an article costs Rs.1500. Find the actual cost of an article?
Choose the correct choice from the following choices:	A) 1400	B) 1300	C) 1200	D) 2000	E) 1500

Solution: CP* (75/100) = 1500   CP= 20* 100 => CP = 2000   ANSWER:2000
Answer: D
850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?	Answers:
A) a) 162	B) b) 138	C) c) 60	D) d) 17	E) e) 12

Solution: Passed in english = 65%   Passed in maths = 55%   Passed in both = 40% of 55% = 2/5 * (55%) = 22%   Passed in (English + Maths - Both + Neither) 2/5 * (55 )= 
2/5 * (55 ) = 22
22%   Passed in (English + Maths - Both + Neither)= 100%   65 + 55 - 22 + Neither = 100   Neither = 100 - 98= 
100 - 98 = 2
2%= 0.02 * 850= 
0.02 * 850 = 17
17   Answer: d) 17
Answer: D
A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,00, did the manufacturer sell in 2007? Choose the correct option
A) 63,000 B) 2,000,000 C) 2,030,000 D) 204,000 E) 2,300,000

Solution: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.   97/100×2100=2037   -->2,037,000 sold in 2007. When rounded to the nearest 10,000 :   204,000   204,000
Answer: D
With # andeach representing different digits in the problem below, the difference between #and ## is 534. What is the value of?
#
-##
____
534  Choose the correct choice from the following:
A) 7
B) 8
C) 9
D) 6
E) 10

Solution: 100x   -(10x +x)   -----------   89 x= 534   x = 6   6
Answer: D
How many seconds will a train 140 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
Choose the correct choice:	A) 28 sec	B) 29 sec	C) 24 sec	D) 25 sec	E) 26 sec

Solution: D = 140 + 150= 
140 + 150 = 290
290   S= 36 * 5/18= 
36 * 5/18 = 10
10 mps   T= 290/10= 
290/10 = 29
29 sec   29 sec
Answer: B
A student finds the average of nine positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say pq for qp. Due to this, the average becomes 1 less than the previous one. What was the difference of the two digits p and q?	Options:	A) 8	B) 6	C) 1	D) 4	E) 2

Solution: Explanation :   Let the original number be pq i.e., (10p + q).   After interchanging the digits, the new number becomes qp i.e., (10q + p).   The question states that the average of 9 numbers has become 1 less than the original average.   Therefore, the sum of the original 9 numbers will be 9*1 more than the sum of the 9 numbers with the digits interchanged.   i.e., 10p + q = 10q + p + 9= 
+ 9 = 9
> 9a - 9b= 9   => a - b = 1.   Answer : 1
Answer: C
If x is 12 percent greater than 70, then x =  Pick one
A) 78.4
B) 91.0
C) 88.0
D) 70.4
E) 71.2

Solution: 12% of 70 = (70*0.11) = 8.4   12% greater than 70 = 70 + 8.4= 
70 + 8.4 = 78.4
78.4   78.4nswer is clearly 78.4.
Answer: A
3 years ago, the avg age of a family of 5 individuals was 17. A kid have been born the avg age of family is an exact today? What is the age of the kid?  Choose the correct choice.
A) 2 years	B) 5 years	C) 6 years	D) 4 years	E) 7 years

Solution: 2 years   2 years   Current age of 5 individuals is,   =5 x 17 + 3 x 5 = 100 years   2 yearslso, current ages of 5 persons + 2 yearsge of the kid   = 6 x 17 = 102 years   Therefore, 2 yearsge of the Kid = 102 – 100 = 2 years.
Answer: A
select the no. which is different from series
13,16,19,22,24,28  Choose the most appropriate option
A) 24
B) 28
C) 19
D) 13
E) 22

Solution: 13. 16. 19. 22. 24. 28   every step it increase by 3 but from 22 it should 25 but it is 24so,24 is different   answer 24
Answer: A
The moon revolves around the earth at a speed of approximately 1.05 kilometers per second. This approximate speed is how many kilometers per hour?	Pick one.
A) 60 B) 61.2 C) 62.5 D) 3,780 E) 3,672

Solution: moon revolves around the earth at a speed of 1.02kilometers per second.   one hour equal to 60 minutes.   one minute equals to 60 seconds. so one hour equals to 3600seconds.   so one hour, speed= 1.05*3600= 
1.05*3600 = 3_780
3780kilometers per hour.   Option 3,780 is correct
Answer: D
In what time will a train 150 metres long cross an electric pole, if its speed be 122 km/hr?  Choose the correct choice from the following answers
A) 2.42  B) 6.42  C) 5.42  D) 4.42  E) 3.42

Solution: Solution   Speed	= (122 x 5 /18) m/sec   = 33.88m / sec   Time taken	= (150 /33.88) sec   = 4.42 sec.   Answer 4.42
Answer: D
Find the average of all numbers between 4 and 41 which are divisible by 5	Pick:
A) 22.5
B) 20
C) 25
D) 30
E) 35

Solution: Explanation:   22.5verage=(5+10+15+20+25+30+35+40)/8=180/8= 
180/8 = 45/2 = around 22.5
22.5   22.5nswer: Option 22.5
Answer: A
A and B began business with Rs.2000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B.	Pick one.
A) 240 B) 288 C) 277 D) 455 E) 361

Solution: (2*8 + 1*4):(4*8 + 5*4)   5:13   13/18 * 630= 
13/18 * 630 = 455
455   Answer: 455
Answer: D
A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?	Choose one
A) 1/36
B) 5/36
C) 10/36
D) 15/36
E) 20/36

Solution: First off, we want to find the probability of rolling a pair of any number. There are six   pairs and a total of 36 different ways to roll a pair of dices: 6/36 = 1/6.   Next, we want to account for the third die - it cannot be the same as the first two,   so it can be any of five numbers out of 6: 5/6.   Therefore probability is 5/6 x 1/6 = 5/36.   It is tempting here to think that we have solved the problem. But if we read carefully, the   question does not say that the first two dice have to be the same and the third die has   to be different.   the question says a gambler rolls 3 dice. So the first two do not have to be pairs.   As long as 2 of the 3 dice are pairs and the last die is a different number. To find the   number of way this can occur, we use combinations formula: 3!/2!1! = 3.   We multiply this to the numerator to give us 3 x 5/36 = 15/36.   ANSWER:15/36
Answer: D
Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 5 days?	Choose the correct choice from the following options.
A) 3
B) 5
C) 6
D) 9
E) 12

Solution: Explanation: If six computers require 15 days to process the data, thats   a total of 90 computer-days the product of 6 and 15. If you change the number   of computers or the number of days, 90 will have to remain the product, whether   that means 90 days of one computer or one day with 90 computers.   In 5 days, the number of computers is:   5c = 90   c = 18   18 computers is 12 more than the 6 that it took to do the job in 15 days, so   the correct choice is (12).
Answer: E
In a business, three friends X,Y and Z shared the profit in the ratio 5:7:8. X invested his amount for 14 months, Y for 8 months and Z for 7 months respectively. Find the ratio of their investments?  Options.
A) 19:49:64	B) 20:49:64	C) 20:49:65	D) 20:50:64	E) None

Solution: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively Then, 14x : 8y : 7z = 5 : 7 : 8 Now, 14x/8y = 5/7 => y = (49/20)x 14x/7z = 5/8 => z = (16/5)x => x : y : z = x : (49/20)x : (16/5)x => x : y : z = 20 : 49 : 64   Answer 20:49:64
Answer: B
In Town X, 90 percent of the population are employed, and 20 percent of the population are employed males. What percent of the employed people in Town X are females? Choose the correct choice from the following choices:
A) 16%  B) 66%  C) 77%  D) 88%  E) 52%

Solution: Total employed people 90%, out of which 20 are employed males, hence 70% are employed females.   (employed females)/(total employed people)=70/90=7/9=77%   Answer: 77%.
Answer: C
The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?  Choose one.
A) 12
B) 14
C) 16
D) 18
E) 20

Solution: Explanation:   63 + 83 + 103 = a3 => a = 12   12)
Answer: A
A certain mixture of nuts consists of 5 parts almonds to 1 parts walnuts, by weight. What is the number of pounds of almonds in 140 pounds of the mixture ?
Choose the correct choice from the following answers.
A) 116 B) 84 C) 40 D) 28 E) 20

Solution: 116lmonds : Walnuts = 5 : 1   Total mixture has 6 parts   In a 140 pound mixture, 116lmonds are 5/6 (total mixture)   = 5/6 * 140 = 116 pounds   116nswer (116)
Answer: A
In a can, there is a mixture of milk and water in the ratio 8 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 12 : 5. Find the capacity of the can?  Choose the most appropriate option
A) 40	B) 18.4	C) 48	D) 50	E) 56

Solution: Let the capacity of the can be T litres.   Quantity of milk in the mixture before adding milk = 8/13 (T - 8)   After adding milk, quantity of milk in the mixture = 12/17 T.   12T/17 - 8 = 8/13(T - 8)   20T = 1456 - 1088 => T = 18.4.   Answer:18.4
Answer: B
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C  Answers:  A) Rs. 300  B) Rs. 400  C) Rs. 500  D) Rs. 600  E) None of these

Solution: Explanation:   C's 1 day's work =   1/3−(1/6+1/8)   =(1/3−7/24)   =1/24   A:Rs. 400:C=1/6:1/8:1/24   =4:3:1   C′sShare=1/8∗3200=400   Option Rs. 400
Answer: B
For how many integers n is 1^n+3 = (n+3)^1? Choose the correct choice from the following.
A) None of these	B) 1	C) 2	D) 3	E) 4

Solution: If n=0   1^0+3= (0+3)^1   1^3 = 1 ; 3^1 =1 not ok   If n=1   1^1+3 =1 ; (1+3)^1=3^1=3 not OK   So, None of thesenswer : None of these
Answer: A
one men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is? Choose the correct choice from the following choices.
A) 4 days	B) 5 days	C) 6 days	D) 7 days	E) 8 days

Solution: 1M + 3W ----- 35 h   4M + 4W ------- 21 h   7M -------? d   35M + 105W = 84M +84M   21W = 49M   4 * 35 = 7 * x => x = 20 hours   20/4= 
20/4 = 5
5 days   ANSWER:5 days
Answer: B
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?	Choose the most appropriate option:	A) 887	B) 400	C) 187	D) 278	E) 191

Solution: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24   A's wages : B's wages : C's wages   1/6 : 1/8 : 1/24 = 4:3:1   C's share = 1/8 * 3200 = Rs. 400   Answer:400
Answer: B
One woman and one man can build a wall together in one hour, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them two hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?  Answers:
A) 5/7
B) 6/7
C) 10/7
D) 12/7
E) 22/7

Solution: Solution:Let work done by man, women and girl per hour be m,w,g respectively.   Then, m+w = 1/1-->(1) , w + 2g = 1/1-->(2) and m + g =1/2-->(3).   No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g   From (1) and (2), m=2g and from (3) g=1/6,m=1/3 and w=2/3.   So, n = 1/(7/6) = 6/7   Option, 6/7
Answer: B
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution? Choose the most appropriate option:
A) 12:8  B) 8:16  C) 9:16  D) 8 :12  E) 16:9

Solution: Water:soap = 3:2   Soap:Salt=12:8   => For 12 soap, salt = 8   => For 2 Soap, salt = (8/12)*2 = 16/12=4/3   So, water:soap:salt = 3:2:4/3 = 9:6:4   After open container, water:soap:salt = 2.25:6:4   So, water:salt = 2.25:4 = 9:16   ANSWER:9:16
Answer: C
Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
Pick
A) Rs.932	B) Rs.132	C) Rs.108	D) Rs.109	E) Rs.131

Solution: 2 * 22/7 * 14= 
2 * 22/7 * 14 = 88
88   88 * 1 1/2= Rs.132   Answer: Rs.132
Answer: B
A = {2,0, 1, -3, 6, -8}
B = {-1, 2, -4, 7,-6,20}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?  Answers: A) 1/4 B) 1/3 C) 5/12 D) 4/9 E) 1/2

Solution: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:   P(positive, positive) = 3/6*3/6 = 9/36;   P(negative, negative) = 2/6*3/6 = 6/36.   P = 9/36 + 6/36   = 15/36   = 5/12.   Answer: 5/12.
Answer: C
When a=x+(3/x) and b=x-(3/x), (2^a^2)/(2^b^2)=?  Choose the correct option.
A) 2	B) 4	C) 8	D) 16	E) 4096

Solution: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=6/x and a+b=2x, 2^(a-b)(a+b)=2^(6/x)(2x)=2^12=4096   Therefore, the answer is 4096
Answer: E
A person travels equal distances with speeds of 5 km/hr, 6 km/hr and 7 km/hr and takes a total time of 47 minutes. The total distance is?	Choose the correct choice from the following: A) 5 km B) 3 km C) 7 km D) 9 km E) 2 km

Solution: Let the total distance be 3x km.   Then, x/5 + x/6 + x/7 = 27/53   27x/53 = 47/60 => x = 1.54   Total distance = 3 * 1.54 = 4.61 km.   5 kmnswer:5 km
Answer: A
The arithmetic mean of set G is zero. If H = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of G consisting of all those elements in G which are more than two but less than three standard deviations away from the arithmetic mean of G, what could be equal to the standard deviation of G?
Choose the most appropriate option:
A) 0.54 B) 0.77 C) 0.82 D) 0.97 E) 1.62

Solution: This is a fairly straightforward question that can be solved quickly by just applying the options   We are provided with Mean, m= 0   and H = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of S   H consists of all those elements in G that are more than 2 but less than 3 GDs away from the arithmetic mean of G   If an element is 1 GD away from the mean, we can write it as either m + GD or m - GD   Similarly, if an element is 2 GDs away from the mean, we can write it as either m + 2*GD or m - 2*GD   So, if these elements lie within 2 and 3GDs of mean, m=0   we can find which one of these values of GD satisfies each value within H   Only GD = 0.77 does   Answer : 0.77
Answer: B
A girl walking at the rate of 9 Km per hour crosses a square field diagonally in 12 seconds. The area of the field is:
Select the correct option:
A) 430 Sq.m	B) 425 Sq.m	C) 450 Sq.m	D) 475 Sq.m	E) 350 Sq.m

Solution: Distance covered in (9×1000)/(3600) × 12 = 30 m   Diagonal of squarre field = 30 m.   area of square field = 30(power)2/2   = 900/2= 
900/2 = 450
450 Sq.m   Answer is 450 Sq.m.
Answer: C