MU-NLPC/Calc-aqua_rat huggingface dataset:
Antony has s pairs of shoes, which is 1/2 as many as Steve and thrice as many as Stephen. In terms of s, how many pairs of shoes do the three of them have combined?	Pick.
A) 14/3*s B) 10/3*s C) 4s D) 5s E) 11/3*s

Solution: == s +2s + s/3 ==> 3s + 1/3 s = 10/3*s   Ans .10/3*s
Answer: B
The greatest number of four digits which is divisible by 16,24,40 and 72 is:	Choose the correct choice from the following answers
A) 9020  B) 9400  C) 9360  D) 9600  E) 9740

Solution: Greatest number of 4-digits is 9999.   L.C.M. of 16, 24, 40 and 72 is 720.   On dividing 9999 by 720, the remainder is 639.   Required number  (9999 - 639)= 
 (9999 - 639) = 9_360
9360.   Answer: Option 9360
Answer: C
A man can row 4 kmph in still water. When the river is running at 1.8 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options
A) 7.13
B) 6.19
C) 4.12
D) 3.19
E) 4.21

Solution: M = 4   S = 1.8   DS = 5.8   US = 2.2   x/5.8 + x/2.2 = 1   x = 1.59   D = 1.59 * 2 = 3.19   Answer: 6.19
Answer: B
John started a business investing Rs. 70,000. Rose joined him after six months with an amount of Rs.1,05,000 and Mary joined them with Rs. 1.4lakhs after another 6 months. The amount of profit earnedshould be distributedin what ratio among John, Rose and Mary respectively, 3years after John started the business? Pick one
A) 10 : 11 : 13  B) 9 : 15 : 16  C) 12 : 15 : 16  D) 14 : 15 : 18  E) 12 : 15 : 20

Solution: John : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16   12 : 15 : 16
Answer: C
A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?  Choose the correct choice from the following:  A) 176 km  B) 224 km  C) 168 km  D) 197 km  E) 258 km

Solution: Let the total distance be x km.   Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10   15x = 168 * 20 => x   = 224 km.   Answer: 224 km
Answer: B
In how many ways can 4 arts and 4 science students be arranged in a row so that the arts and the science students are placed alternately?	Choose the correct choice from the following options:
A) 288	B) 185	C) 326	D) 576	E) 360*120

Solution: The four art students can be arranged in those 4 A-slots in 4! = 24 ways.   The four science students can be arranged in those 4 S-slots in 4! = 24 ways.   Total arrangements = 24*24= 
24*24 = 576
576   Answer=(576)
Answer: D
The variables a and b are non-zero integers V. If a = 2b^3/c, what happens to c when a is halved and b is doubled?	Pick one
A) c is not changed.  B) c is halved.  C) c is doubled.  D) c is multiplied by 4.  E) c is multiplied by 16.

Solution: a = 2b^3/c   c = 2b^3/a   when a is halved and b is doubled   c =2(2b)^3/(a/2)   c=16*2b^3/a   Ans. c is multiplied by 16. c is multiplied by 16.
Answer: E
The residents of the town R participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of town R, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?	Choose the correct choice from the following choices
A) - 30 B) - 20 C) - 18 D) - 12 E) - 6

Solution: (21-6*2)<number of hours that Pat watched television last week <(21-6*1)   =9<P<15   Only option - 6 (12) satisfies this condition.
Answer: E
How many different arrangements of A, B, , D, and E are possible where A is not adjacent to B and D is not adjacent to E? Choices
A) 96	B) 48	C) 8	D) 30	E) 1

Solution: So you have A,B,,D,E   five possible ways to arrange it = 4! = 24   AB cannot be adjacents neither DE:   (AB),,D,E = 3! = 6x 2(because it can be (AB) or (BA) ) = 12   A,B,,(DE) = 3! = 6 x 2 = 12   To get rid of the double counting:   (AB),(DE) = 2! x 4 = 8   (Four possible ways to arrange it)   24 -12-12+8= 
24 -12-12+8 = 8
8 possible ways   8
Answer: C
Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 10 minutes 8 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?  Choices:
A) 3%
B) 5%
C) 8%
D) 10%
E) 12%

Solution: Bob's time = 640 secs.   His sis' time = 608 secs.   Percent increase needed = (640-608/640) * 100 = 32/640 * 100= 
32/640 * 100 = 5
5%. Ans (5%).
Answer: B
504 can be expressed as a product of primes as	Choose the most appropriate option:
A) 2 × 2 × 3 × 3 × 7 × 7
B) 2 × 3 × 3 × 3 × 7 × 7
C) 2 × 2 × 2 × 3 × 3 × 7
D) 2 × 3 × 3 × 3 × 3 × 7
E) None of these

Solution: Explanation:   It is clear that 504 = 2 × 2 × 2 × 3 × 3 × 7   Answer: Option 2 × 2 × 2 × 3 × 3 × 7
Answer: C
A train takes 18 seconds to pass completely through a station 162 m long and 15 seconds through another station 120 m long. The length of the train is :	Options:
A) 70 m
B) 80 m
C) 90 m
D) 100 m
E) None

Solution: Solution   Let the length of the train be x metres .   ∴ x+162/18 =x+120/15 =15(x+162) =18(x+120) = x=90m   Answer 90 m
Answer: C
Four-fifths of three-eighths of a number is 24. What is 250 per cent of that number? Choose the most appropriate option
A) 100 B) 160 C) 120 D) 200 E) None of these

Solution: Let the number = x.   4⁄5 × 3⁄8x = 24 or x = 24×2×5/3=80   ∴ 250 per cent of the number = 250⁄100 × 80 = 200   Answer 200
Answer: D
If x is an integer and 2.134 × 10^x is less than 2,100,000, what is the greatest possible value for x?	Choose the correct choice from the following: A) 7 B) 6 C) 5 D) 4 E) 3

Solution: If x=6   2.134 × 10^6 = 2,134,000 > 2,100,000   So, x = 5   Answer : 5
Answer: C
A can do a piece of work in 8 days which B can do in 12 days. B worked at it for 9 days. A can finish the remaining work in ?  Choose the correct option
A) 2 days
B) 5 days
C) 6 days
D) 7 days
E) 11 days

Solution: B's 9 day's work = 9 x (1/12) = 3/4   Remaining work = (1 - 3/4) = 1/4   1/4 work is done by A in = 8 x (1/4) = 2 days.   answer : 2 days
Answer: A
You enter a weight loss challenge game and manage to lose 13% of your body weight. For the final weigh in you are forced to wear clothes that add 2% to your weight. What percentage of weight loss is measured at the final weigh in?  Choose the correct choice from the following answers.
A) 13% B) 9.22% C) 11.26% D) 14% E) 12%

Solution: (100%-13%)*(100%+2%) = 0.87*1.02 = 11.26%   The weigh in records your weight loss at 11.26%!   The Answer is 11.26%
Answer: C
By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 7 p.c? Select the correct option:
A) 38028 B) 38000 C) 37200 D) 38128 E) 38982

Solution: 37200P + 37200P/8 = 45000   37200P = 40000   SP = 40000*(93/100)= 
40000*(93/100) = 37_200
37200   Answer:37200
Answer: C
What is the sum of the greatest common factor and the lowest common multiple of 48 and 72 Choose the correct choice from the following answers: A) 126 B) 184 C) 168 D) 154 E) 186

Solution: Prime factorization of 72 = 2 x 2 x 2 x 3 x 3   Prime factorization of 48 = 2 x 2 x 2 x 2 x 3   G168F = 24   L168M = 144   Sum = 168   Ans: 168
Answer: C
A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.300 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
Choose one.
A) 3750 B) 7799 C) 2500 D) 2772 E) 2912

Solution: 3750:B:C = 2/3:1/6:1/6 = 4:1:1   x * 2/100 * 2/3 = 300   B capital = 22500*1/6 = 3750.3750nswer: 3750
Answer: A
In the rectangular coordinate system, what is the area of triangle CDE with points
C=(3,7)
D=(4,4)
E=(1,1)
Choose the correct choice from the following answers:	A) 5	B) 6	C) 7	D) 6.5	E) 5.5

Solution: Use the formula of the distance formula   square root (x2-x1)^2+(y2-y1)^2   Do this for each of the sides and then the value is given as 6.
Answer: B
If the true discount on a sum due 2 years hence at 14% per annum be Rs. 168, the sum due is :  Choose the most appropriate option.
A) Rs. 768	B) Rs. 968	C) Rs. 1960	D) Rs. 2400	E) None

Solution: Solution   P.W = 100xT.D./R x T = 100x 168/14x 2 = 600.   ∴ Sum = (P.W. + TD.) = Rs. 768.   Rs. 768nswer Rs. 768
Answer: A
What is the value of 27^2 + 28^2 + 29^2 + 30^2 + 31^2 + 32^2 + 33^2 ?
Choose the correct choice
A) 6298 B) 6308 C) 6318 D) 6328 E) 6338

Solution: the method would seem to be lengthy as it is being explained but is very short actually   second would be to take advantage of proximity to 30 and a set of two numbers giving us 60 as sum..   (27^2 + 33^2) + (29^2 + 31^2) + (32^2 + 28^2)+ 30^2   (60^2-2*27*33) +(60^2-2*29*31)+ (60^2-2*28*32)+ 30^2   3*60^2+30^2-2(27*33+29*31+28*32)   3*60^2+30^2-2((30-3)*(30+3)+(30-1)*(30+1)+(30-2)*(30+2))   3*60^2+30^2-2((30^2-3^2)+(30^2-1^2)+(30^2-2^2))   3*60^2+30^2-6(30^2)+2(3^2+1^2+2^2)   we are interested only in terms where square of multiple of 10 is not involved..   2(9+1+4)=28 so the answer should be something*100+28....this gives us the answer as 6328   ANSWER:6328
Answer: D
In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (6, 0), (0, -3.5), (-6, 0)? Choose the correct choice
A) 42  B) 56  C) 88  D) 112  E) 116

Solution: 42res of rhombus= 1/2* D1 *D2   Length of 1st diagonal = 6+6= 
6+6 = 12
12   Length of 2nd diagonal= 3.5+3.5= 
3.5+3.5 = 7
7   42rea= 1/2*12*7= 
1/2*12*7 = 42
42   42 is the answer
Answer: A
In a game of 80 points; A can give B 10 points and C 15 points. Then how many points B can give C in a game of 70 ?  Choose the correct choice from the following answers: A) can give C 1 points B) can give C 4 points C) can give C 2 points D) can give C 5 points E) can give C 8 points

Solution: A: B = 80 : 70, A : C = 80 : 65.   B/C = ( B/ A * A/C) = (70/ 80 * 80 / 65) = 14/13 = 70 /65   Therefore ,In a game of 70, B can give C 5 points.   Answer is can give C 5 points.
Answer: D
Rose is thrice as good as workman as Jerry and therefore is able to finish a job in 60 days less than Jerry. if theu work together in how many days they will complete?
Choose the correct answer:  A) 21 3/4  B) 22 1/2  C) 23 4/5  D) 25 1/6  E) 27 3/5

Solution: Ratio of times taken by A and B = 1 : 3.   The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.   If difference of time is 2 days, B takes 3 days.   If difference of time is 60 days, B takes 3	x 60 = 90 days.   2   So, A takes 30 days to do the work.   A's 1 day's work =	1   30   B's 1 day's work =	1   90   (A + B)'s 1 day's work = 1	+	1 =	4	=	2   30	90	90	45   A and B together can do the work in	45	= 22	1/2 days.   2	2   22 1/2
Answer: B
In a certain company 20% of the men and 40% of the women attended the annual company picnic.If 50% of all the employees are men .What % of all the employee went to the picnic? Select the correct option.
A) 30%  B) 34%  C) 35%  D) 36%  E) 37%

Solution: total men in company 50% means total women in company 50%(assume total people in company 100%)   no of men employees attended picnic=50x(20/100)=10   no of women employees attend picnic=50x(40/100)=20   total percentage of employees attend the picnic=10+20= 
10+20 = 30
30%   30%NSWER:30%
Answer: A
TIM has 13 ten-dollar bills, 11 five-dollar bills, and 17 one-dollar bills. If TIM needs to pay exactly $128, what is the least number of bills he will need to use?  Choose one:
A) 68	B) 66	C) 565	D) 16	E) 35

Solution: 128 is the total sum of money.   as we have 13 10 dollar bills so the closest we can get to 128 using the 10 dollar bills is by using 12 * 10 dollar bils   128-120= 
128-120 = 8
8   so now we need to get 8 from either 5 dollar bills or 1 dollar bills   8 - 5 (use only 1 5 dollar bill)= 3   so we can get 3 from using 3 $1 bills.   Hence 16 ( 12+1+3 )   ANSWER IS 16
Answer: D
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?  Choose the correct choice from the following choices:
A) 600 B) 882 C) 772 D) 662 E) 521

Solution: Cost price = Rs.500   profit = 20% of 500 = Rs.100   Selling price = Cost price + Profit   = 500 + 100= 
500 + 100 = 600
600   600nswer: 600
Answer: A
Professor absentminded has a very peculiar problem, in that he cannot remember numbers larger than 15. However, he tells his wife, I can remember any number up to 100 by remembering the three numbers obtained as remainders when the number is divided by 3, 5 and 7 respectively. For example (2,2,3) is 17. Professor remembers that he had (1,1,6) rupees in the purse, and he paid (2,0,6) rupees to the servant. How much money is left in the purse?
Choose the most appropriate option:
A) 56 B) 57 C) 58 D) 59 E) 60

Solution: Let the money with the professor = N   Then N = 3a +1 = 5b + 1 = 7c + 6.   Solving the above we get N = 181   (Explanation: See LCM formula 1 and 2: Click here)   When a number is divided by several numbers and we got same remainder in each case, then the general format of the number is LCM (divisors).x + remainder.   In this case 3, 5 are divisors. So N = 15x + 1. Now we will find the number which satisfies 15x + 1 and 7c + 6.   ⇒ 15x + 1 = 7c + 6 ⇒ c = 15x−5715x−57 ⇒ c = 2x+x−572x+x−57   Here x = 5 satisfies. So least number satisfies the condition is 5(15)+1 = 76.   (x = 12 also satisfies condition. So substituting in 15x + 1 we get, 181 which satisfies all the three equations but this is greater than 100)   Similarly Money given to servant = M = 3x + 2 = 5y 3  + 2= 
3  + 2 = 5
5y= 7z + 6   Solving we get M = 25.   (125 also satisfies but this is next number)   Now N - M = 56   56nswer:	56
Answer: A
Sanoop bought 8 t-shirts at an average price (arithmetic mean) of Rs.526. If Sanoop returned 4 t-shirts to the retailer, and the average price of the remaining t-shirts was Rs.505, then what is the average price, of the three returned t-shirts?	Select the correct option.
A) 560
B) 561
C) 562
D) 563
E) 547

Solution: Total price of 8 t-shirts= 8*526= 
8*526 = 4_208
4208   Total price of 5 t-shirts=4*505= 
4*505 = 2_020
2020   Total price of 4 t-shirts=4208-2020= 
4208-2020 = 2_188
2188   Average price of 3 t-shirts=2188/4= 
2188/4 = 547
547   Correct option Answer:547
Answer: E
In a group of 60 people, 35 have visited Iceland and 23 have visited Norway. If 31 people have visited both Iceland and Norway, how many people have visited neither country? Select
A) 30  B) 31  C) 32  D) 33  E) 34

Solution: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:   60= 35 + 23 - 31 + (# in Neither Group)   =33   The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.   33
Answer: D
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5565, what is the length of the plot in metres?  Choose the correct choice from the following answers
A) 333
B) 200
C) 288
D) 210
E) 1999

Solution: Let length of plot = L meters, then breadth = L - 20 meters   and perimeter = 2[L + L - 20] = [4L - 40] meters   [4L - 40] * 26.50 = 5565   [4L - 40] = 5565 / 26.50= 
5565 / 26.50 = 210
210   4L= 250   L = 250/4= 
250/4 = 125/2 = around 62.5
62.5 meters.   Answer: 210
Answer: D
A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 12 days before the completion of the work. In how many days was the work completed?  Choose the most appropriate option:
A) 13 days  B) 16 days  C) 18 days  D) 11 days  E) 38 days

Solution: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 12 days = 12*(1/24 + 1/30) = 9/10   Remaining work = 1/10   The number of days required for this initial work = 1 days.   The total number of days required = 12 + 1= 
12 + 1 = 13
13 days.   13 daysnswer: 13 days
Answer: A
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is? Choose the correct choice from the following choices: A) 245 B) 726 C) 566 D) 268 E) 261

Solution: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30   = 25/2 => 2(130 + x) = 750 => x   = 245 m.   245nswer: 245
Answer: A
What is the cost painting the two adjacent walls of a hall at Rs. 5 per m2 which has no windows or doors?
I.	The area of the hall is 24 sq. m.
II.	The breadth, length and height of the hall are in the ratio of 4 : 6 : 5 respectively.
III.	Area of one wall is 30 sq. m.	Choose one:
A) I only B) II only C) III only D) Either I or III E) All I, II and III are required.

Solution: EXPLANATION   From II, let l = 4x, b = 6x and h = 5x.   Then, area of the hall = (24x2) m2.   From I. Area of the hall = 24 m2.   From II and I, we get 24x2 = 24 x = 1.   l = 4 m, b = 6 and h = 5 m.   Thus, area of two adjacent walls = [(l x h) + (b x h)] m2 can be found out and so the cost of painting two adjacent walls may be found out.   Thus, III is redundant.   answer is (III only).
Answer: C
Man, woman and a boy finish work together in 6 days. Man alone takes 10 days; woman alone takes 24 days then how many days boy alone will take to do that work?
Choices.
A) 20 days	B) 30 days	C) 40 days	D) 50 days	E) 60 days

Solution: Let M, W , B be man, women, nd boy   M + W + B 's 1 day work = 1/6   M's 1 day work = 1/10   W's 1 day work = 1/24   M + W's 1 day work = 1/10 + 1/24 ==> 34/240 = 17/120   B's 1 day work = (M + W + B) - (M + W)   ==========> 1/6 - 17/120 ==> 120 - 102/720   ==========>18/720 = 1/40   So boy alone ll finish d work in 40 days   ANSWER:40 days
Answer: C
The length of the bridge, which a train 160 m long and traveling at 45 km/hr can cross in 30 sec is?	Answers:
A) 377 B) 367 C) 237 D) 215 E) 267

Solution: Speed = 45 * 5/18 = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (160 + x)/30 = 25/2   x = 215 m.   Answer: 215
Answer: D
The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 17,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China? Choices:
A) 5,476,811 kilometers squared
B) 7,500,148 kilometers squared
C) 9,843,123 kilometers squared
D) 1,878,965 kilometers squared
E) 4,787,900 kilometers squared

Solution: he difference between the areas of Russia and China is given by   17,098,242 - 9,598,094 = 7,500,148 kilometers squared   correct answer 7,500,148 kilometers squared
Answer: B
The greatest possible length which can be used to measure exactly the length 3m, 5m 30cm, 4 m is  Options:
A) 10	B) 27	C) 35	D) 87	E) 98

Solution: Explanation:   Required Length = H.C.F of 300 cm, 530 cm and 400 c   = 10 cm.   10nswer: 10) 10 cm
Answer: A
Each week, Harry is paid x dollars per hour for the first 21 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?	Pick: A) 35 B) 36 C) 37 D) 38 E) 39

Solution: 42x=21x+1.5x(H-21)   ==> 42=21+1.5(H-21)   ==> H-21 = 21/1.5= 
21/1.5 = 14
14=> H = 35   35nswer is 35
Answer: A
s is a positive integer and multiple of 2; p = 4^s, what is the remainder when p is divided by 10?  Answers.
A) 10
B) 6
C) 4
D) 0
E) It Cannot Be Determined

Solution: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:   4/10 is 0 with a remainder of 4   14/10 is 1 with a remainder of 4   5/10 is 0 with a remainder of 5   105/10 is 10 with a remainder of 5   It is also essential to remember that the s is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, s must be a positive even integer.   With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?   The units digit of 4 raised to an integer follows a specific repeating pattern:   4^1 = 4   4^2 = 16   4^3 = 64   4^4 = 256   4^(odd number) --> units digit of 4   4^(even number) --> units digit of 6   There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.   Since s must be an even integer, the units digit of p=4^s will always be 6. Consequently, the remainder when p=4^s is divided by 10 will always be 6.   In case this is too theoretical, consider the following examples:   s=2 --> p=4^z=16 --> s/10 = 1 with a remainder of 6   s=4 --> p=4^z=256 --> s/10 = 25 with a remainder of 6   s=6 --> p=4^z=4096 --> s/10 = 409 with a remainder of 6   s=8 --> p=4^z=65536 --> s/10 = 6553 with a remainder of 6   Answer: 6.
Answer: B
If a survey shows that 28 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
Pick:
A) 56%  B) 64%  C) 72%  D) 82%  E) 86%

Solution: Those who support = 28.   % of those who don't support it is (200-28)/ 200 = 86%   Answer 86%
Answer: E
A company consists of 5 senior and 3 junior staff officers. If a committee is created with 2 senior and 2 junior staff officers, in how many ways can the committee be formed? Choose the correct answer.
A) 12  B) 30  C) 45  D) 80  E) 200

Solution: Choose 2 senior from 5 senior and choose 2 junior from 3 junior:   5C2 * 3C2 = 10*3= 
10*3 = 30
30   Ans: 30
Answer: B
A briefcase has a number-lock system containing a combination of 3 digits (Each digit can be of numbers 0 to 8). If the correct combination is unknown, how much maximum time would be required to open the bag if each “trial” of combination takes 3 seconds? Select the correct option:
A) 36.45 minutes
B) 36.47 minutes
C) 36.41 minutes
D) 36.42 minutes
E) 36.65 minutes

Solution: Explanation:   Maximum number of trials required = 9 * 9 * 9= 
9 * 9 * 9 = 729
729. Since for each combination trial, 3 seconds are required to open the briefcase is given as   3 * 729= 
  3 * 729 = 2_187
2187 seconds= 36.45 minutes.   36.45 minutesNSWER: 36.45 minutes
Answer: A
Shyam walks 5 km towards East and then turns left and walks 6 km. Again he turns right and walks 9 km. Finally he turns to his right and walks 6 km. How far is he from the starting point? Choose the correct choice from the following choices
A) 26 km
B) 21 km
C) 14 km
D) 9 km
E) 19 km

Solution: he is 14 km towards East from starting point.   ANSWER:14 km
Answer: C
Lalasa, Bhavani and Geetha has bought items of Rs. 4000, Rs. 12000 and Rs. 6000 respectively. Addition to it, Bhavani has spent Rs. 2000 to buy sunglasses. The difference between the money spent by A and C is? Pick:  A) 800  B) 650  C) 450  D) 400  E) 680

Solution: Ratio of cost of items bought by Lalasa, Bhavani and Geetha is 4000 : 10000 : 6000 = 2 : 5 : 3   And also given that, additional items bought by Bhavani is Rs. 2000   => 5 parts out of 10 parts is Rs. 2000   Now, required difference is 3 - 2= 
3 - 2 = 1
1 part   Required difference= 1/5 (2000) = Rs. 400.Answer: 400
Answer: D
The probability that A speaks truth is 4/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact? Options.
A) 19/35  B) 19/37  C) 19/39  D) 19/33  E) 19/31

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 4/5 * 4/7 + 1/5 * 3/7   = 19/35   19/35nswer:19/35
Answer: A
1/(2-√3)=?  Answers:
A) 9+4√5
B) 9-4√5
C) 9+2√5
D) 2+√3
E) 4+9√5

Solution: This question requires us to rationalize (fix) the denominator.   For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044   Given: 1/(2-√3)   Multiply top and bottom by the CONJUGATE of 2-√3, which is 2+√3   So, 1/(9-4√5) = (1)(9+4√5)/(9-4√5)(9+4√5)   2+√3
Answer: D