MU-NLPC/Calc-aqua_rat huggingface dataset:
Working together, Jose and Jane can complete an assigned task in 10 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 25 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose  Choose the most appropriate option.
A) 25 days
B) 30 days
C) 60 days
D) 65 days
E) 36 days

Solution: Assume:   Jose does 1 job in x days, so Jose does 1/x job in a day   Jane does 1 job in y days, so Jane does 1/y job in a day   Together, they does (x+y)/xy job in a day. This is equals to 1/20. So   (x+y)/xy = 1/10   10(x+y) = xy   Next, we're told 1 job takes 25 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.   x/2 + y/2 = 25   x+y = 50   So   xy = 500   The answer choices are:   25 days   30 days   60 days   65 days   36 days   From the answer choices, So I'll go for 25 days for Jose and 20 days for Jane.   25 daysnswer : 25 days
Answer: A
Sonalika goes 12 km towards North from a fixed point and then she goes 8 km towards South from there. In the end she goes 3 km towards east. How far and in what direction is she from her starting point?	Choose the correct choice from the following options.
A) 5km north east B) 4km north east C) 5km north west D) 6km north east E) 6km north west

Solution: she is currently at 5km north east from the starting point   5km north eastNSWER:5km north east
Answer: A
A train speeds past a pole in 15 sec and a platform 150 m long in 25 sec, its length is?
Choose the correct choice from the following
A) 50 m	B) 150 m	C) 225 m	D) 300 m	E) None of these

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 150)/25 = x/15 => x = 225 m.   ANSWER:225 m
Answer: C
Carol spends 1/4 of her savings on a stereo and 1/5 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
Choose the correct choice from the following choices:	A) 1/4	B) 2/7	C) 5/12	D) 9/20	E) 7/12

Solution: Total Savings = S   Amount spent on stereo = (1/4)S   Amount spent on television = (1-1/5)(1/4)S = (4/5)*(1/4)*S = (1/5)S   (Stereo + TV)/Total Savings = S(1/4 + 1/5)/S = 9/20   Answer: 9/20
Answer: D
there are 35 student in a school. 20 if them speek hindi 19 of them speak eng 9 of them speak both , then how many student neithe speak eng nor speak hindi  Choose the correct choice from the following answers: A) 28 B) 30 C) 32 D) 35 E) None of these

Solution: Total Number of Students = 35   No of Hindi Speaking Students (H) = 20   No of None of thesenglish Speaking Students (None of these) = 19   H intersection None of these = 9   thus H union None of these = 20 + 19 - 9= 
20 + 19 - 9 = 30
30   thus Number of student neithe speak eng nor speak hindi= 35 - 30= 
35 - 30 = 5
5   ANSWNone of theseR:None of these
Answer: E
A and B can finish a work in 7 days and 8 days respectively.if both do work one day and leave one day.and A start the work then in how much days work will finish?
Choose the most appropriate option.
A) 52/7  B) 8  C) 14/2  D) 6  E) 43/6

Solution: (A+B) work in 2 days=[1/7+1/8]=15/56   (A+B) work in 6 days=45/56   now,the turn of A,work of A in 1 day=1/7.   till now completed work=[45/56+1/7]=53/56, remaining work=[1-53/56]=3/56   now,turn of B,1/8 work B do in 1 day   so,3/56 part of work B do=[8*3/56]=3/7 days   total time taken=6+1+3/7=52/7 days   answer 52/7
Answer: A
If a man travels f miles an hour for t hours and r miles an hour for k hours, what is his average rate in miles per hour for the entire distance traveled?
Choose the correct option
A) ft + rk B) (ft + rk)/2 C) t/f + k/r D) (ft + rk)/(t + k) E) (ft + rk)/(t - k)

Solution: Average Speed = Total (ft + rk)/(t + k)istance /Total Time Taken   Total (ft + rk)/(t + k)istance travelled in t hours = ft   Total (ft + rk)/(t + k)istance travelled in s hours = rk   Total Time taken = t+k   Therefore , Average Speed = (ft+tk)/(t+k)   Answer (ft + rk)/(t + k)
Answer: D
The jogging track in a sports complex is 561 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
Choose the most appropriate option:
A) 5.29 min
B) 5.28 min
C) 4.08 min
D) 9.28 min
E) 5.988 min

Solution: Clearly, the two will meet when they are 561 m apart.   To be (4.5 + 3.75)= 
(4.5 + 3.75) = 8.25
8.25 km apart, they take 1 hour.   To be 561 m apart, they take (100/825 * 561/1000) hrs= (561/8250 * 60)= 
(561/8250 * 60) = 102/25 = around 4.08
4.08 min.   Answer: 4.08 min
Answer: C
I. j; k; m; n; p
II. j - 10; m; m; m; p + 15
III. j + 2; k + 1; m; n - 1; p - 2
If j, k, m, n, and p are consecutive positive integers such that j < k < m < n < p, the data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation T in which of the following? Options:
A) I, III, II
B) II, I, III
C) II, III, I
D) III, I, II
E) III, II, I

Solution: Range of 1st Set = (p-j)   Range of 2nd Set = P+15 - j +10 = (p-j) +25   Range of 3rd Set = P -2 - j - 2 = (p-j) - 4   R2 > R1 > R3 ==> SD2 > SD1 > SD3   Since,T= Higher the Range -> More Dispersion in the Set -> More Standard Deviation.II, I, III
Answer: B
If 6!/3^x is an integer, what is the greatest possible value of x?  Choose the most appropriate option
A) 2	B) 4	C) 5	D) 6	E) 7

Solution: 6 - 2*3   3 - 1*3   Hence max of 3^2 is allowed. IMO 2.
Answer: A
A certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 4 of 7 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?	Options.
A) 42	B) 70	C) 175	D) 165	E) 315

Solution: 51751*71754 = 5*35= 
5*35 = 175
175   the answer is (175)
Answer: C
A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 1.25 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 30 worth of diesel fuel?
Choices
A) 20 seconds  B) 1 minute  C) 1 minute 20 seconds  D) 20 minutes  E) 1 hour 20 minutes

Solution: 2 gal / 5 sec   $1.25 / gal   $30/$1.25 = 24 gal   2 gal / 5 sec with 24 gal   30/ 1.25= 
  30/ 1.25 = 24
24 gal   2 gal / 5 sec with 24 gal= 60 sec   B. 1 minute
Answer: B
In how many ways can the letters of the word LITTER be arranged in a row so that the vowels appear in alphabetic order? Choose the correct choice from the following options.
A) 390
B) 400
C) 440
D) 360
E) 460

Solution: TWO letters can be arranged in 2! ways.   only one combination EI is required.   6 letters can be arranged in 6! ways.   thus 6!/ 2! * 1 = 360   360
Answer: D
what is the remainder when 9614241 is divided by 99 Choose the correct answer
A) 50  B) 65  C) 45  D) 54  E) 60

Solution: 9614241 / 99   9614241 / 9*11   1068249 / 11 => rem = 6   we have cancelled it by 9   reqd remainder = 9*6= 
9*6 = 54
54   ANSWER:54
Answer: D
Alfred buys an old scooter for $4700 and spends $800 on its repairs. If he sells the scooter for $6400, his gain percent is?
Choose the most appropriate option:
A) 5.45%	B) 16.36%	C) 7%	D) 8.12%	E) 10%

Solution: C.P. = 4700+800= 
4700+800 = 5_500
$5500   S.P.= $6400   Gain = 6400-5500= 
6400-5500 = 900
$900   Gain%= 900/5500 * 100 = 16.36%   Answer is 16.36%
Answer: B
n a series of numbers , the next number is formed by adding 1 to the sum of the previous numbers, and the 10th number is 1280. Then what is the first number in the series? (series will be like this x , x+1, (x+(x+1))+1,....... )  Select the correct option:  A) 2  B) 4  C) 5  D) 7  E) 9

Solution: Answer: Option B   Sol.   The given series is x, x + 1, 2x + 2, 4x + 4 ......   If you observe the pattern here, the coefficient of x + 1 is in the powers of 2. So 4th term has a power of 2, 5th term has a power of 3... 10th term has a power of 8. So tenth term would be 2828(x + 1)   = 256(x+1).   Given 256(x+1) = 1280   x = 4.   Answer:4
Answer: B
Josh spends a total of $5.50 buying N items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then N may be which of the following?  Choices.
A) 99 B) 100 C) 101 D) 109 E) 140

Solution: Let x be the number of single bubblegums and y be the number of bubblegum pack.   then   5x+50y=550   or x+10y=110   or x=110-10y   Now,   let y=0, then x= 110 and N=x+y or N=0+110= 
0+110 = 110
110.   let y=1, then x=100 and N=100+1= 
100+1 = 101
101 (given in the options)   let y=2, then x= 90 and N=92   the value will further decrease and hence we do not need to calculate anymore values.   ANSWER:- 101
Answer: C
Alice deposited Rs 2 million in bank at 4 % simple interest per year. After 10 year how many Rs she will get from bank?	Select:
A) 75000 B) 90000 C) 10000 D) 80000 E) 60000

Solution: i = (200000*10*4)/100= 
(200000*10*4)/100 = 80_000
80000   Answer: 80000
Answer: D
By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent . Answers:
A) 96%
B) 48%
C) 50%
D) 36%
E) 45%

Solution: (SP of 33m)-(CP of 33m)=Gain=SP of 11m   SP of 22m = CP of 33m   Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.   Gain%=[(11/22)*100= 
(11/22)*100 = 50
50%   Ans: 50%
Answer: C
There are many numbers that can be expressed as the sum of three squares in three different ways.
Can you find out the smallest of such number?
Options.
A) 55  B) 54  C) 49  D) 50  E) 51

Solution: 54   54   7^2 + 2^2 + 1^1   6^2 + 3^2 + 3^2   2^2 + 5^2 + 5^2
Answer: B
The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday? Choose the correct choice.
A) 22	B) 679	C) 62	D) 34	E) 12

Solution: M + Tu + W + Th = 4 * 48= 
4 * 48 = 192
192   Tu + W + Th + F= 4 * 46= 
4 * 46 = 184
184   M= 42   Tu + W + Th = 192 -42= 
192 -42 = 150
150   F= 184 – 150 = 34.Answer: 34
Answer: D
Working alone, A can complete a certain kind of job in 10 hours. A and D, working together at their respective rates, can complete one of these jobs in 5 hours. In how many hours can D, working alone, complete one of these jobs? Pick one:  A) 9  B) 10  C) 11  D) 12  E) 13

Solution: Let total time taken by D to complete the job = D   total time taken by A to complete the job = 10   Work done by A in an hour   1/A = 1/10   Working together A and D can complete the job in 5 hours   1/A + 1/D = 1/5   =>1/D = 1/5 - 1/A   = 1/5 - 1/10   = 1/10   => D = 10 hours   Answer 10
Answer: B
Susan, Tim,and Kim need to be seated in 3 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Choose the correct answer
A) A)6 B) B)120 C) C)80 D) D)240 E) E)60

Solution: Total number of arrangements = 3! = 6   In exactly half, Susan will be to the left of Tim, which gives us 3 arrangements   Option (6)
Answer: A
Two cyclist start from the same places in opposite directions. One is going towards north at 18kmph and the other is going towards south 20kmph. What time will they take to be 76km apart?
Choose the correct answer:
A) 1 1/4 hours	B) 2 1/3 hours	C) 4hours	D) 3 3/4 hours	E) 2 hours

Solution: To be (18+20) km apart, they take 1 hour   To be 76 km apart, they take   1/38 * 76= 
  1/38 * 76 = 2
2 hrs   Answer is 2 hours
Answer: E
Calculate the L.C.M of 4/9, 5/ 7, 9/13, 7/15 is :	Choose the correct choice:
A) 1230 B) 1290 C) 1260 D) 1240 E) 2260

Solution: Required L.C.M =L.C.M. of 4, 5, 9, 7/H.C.F. of 9, 7, 13, 15 =1260/1= 
1260/1 = 1_260
1260   Answer is 1260
Answer: C
If x=2y=4z, what is y-z, in terms of x?
Select.
A) 2x
B) x/2
C) x/4
D) 3x/5
E) 3x/7

Solution: x=2y=4z   x/4 = z   and y = x/2   y-z = x/2 - x/4 = x/4   Answer is x/4
Answer: C
In a garden, 26 trees are planted at equal distances along a yard 700 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees? Select the correct option.
A) 10  B) 28  C) 12  D) 14  E) 16

Solution: 26 trees have 25 gaps between them.   Length of each gap = 700/25= 
700/25 = 28
28   i.e., distance between two consecutive trees= 28   Answer is 28.
Answer: B
In a tree, 2/5 of the birds are robins while the rest are bluejays. If 1/3 of the robins are female and 2/3 of the bluejays are female, what fraction of the birds in the tree are male?
Choose the correct answer:	A) 3/5	B) 4/15	C) 7/15	D) 8/15	E) 17/30

Solution: The fraction of birds that are male robins is (2/3)(2/5)=4/15.   The fraction of birds that are male bluejays is (1/3)(3/5)=1/5.   The total fraction of male birds is 4/15 + 1/5 = 7/15.   The answer is 7/15.
Answer: C
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?  Choices
A) 19 kmph B) 18 kmph C) 14 kmph D) 13 kmph E) 17 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph.   Answer: 14 kmph
Answer: C
For each month of a given year except December, a worker earned the same monthly salary and donated one-tenth of that salary to charity. In December, the worker earned N times his usual monthly salary and donated one-fifth of his earnings to charity. If the worker's charitable contributions totaled one-nineth of his earnings for the entire year, what is the value of N?  Choose one
A) 8/5 B) 5/2 C) 3 D) 11/3 E) 22

Solution: Let monthly salary for each of the 11 months except December was x, then   11x*1/10 + Nx*1/5 = 1/9(11x + Nx);   11/10 + N/5 = 1/9(11 + N)=>   11+2N/10 = 11+N/9=>66+12N=110+10N =>2N=44   N = 22   Answer: 22
Answer: E
Zoe is interested in dividing her high school trophies into boxes so they can be put away in storage. Unfortunately, they do not divide equally. It turns out that in order for the boxes to each have an equal number of trophies, Zoe won't need one of the boxes and will have to add two of her college trophies to the last box. Which of the following can describe the number of initial high school trophies and the initial number of boxes (in the order trophies, boxes)? Choose the correct choice from the following choices
A) 26; 8.	B) 50; 7.	C) 27; 4.	D) 25; 3.	E) 45; 10.

Solution: Option 26; 8..) Initially 26 trophies, increased to 28 trophies; and initially 8 boxes decreased to 7 boxes:    28 / 7= 
 28 / 7 = 4
4 trophies per box.
Answer: A
Two trains are traveling on a collision course. If train A is traveling at a speed of 350 mph and train B is traveling 28% slower, how much time will it take the trains to collide if the initial distance between the two is 2408 miles?
Choose the correct answer:
A) Two hours and 30 minutes.
B) One hour and 10 minutes.
C) Two hours and 25 minutes.
D) Three hours and 15 minutes.
E) Four hours and 0 minutes.

Solution: Answer is E. Four hours and 0 minutes.   Since they are racing towards each other, the speed is accumulative, ie. 350 mph + 350*0.72 = 602 (0.72 because the second train is 28% slower)   So time before collision is total distance / total speed = 2408/602= 
2408/602 = 4
4 hours and 0 mins
Answer: E
Running 3/4th of his usual rate, a man is 15min late. Find his usual time in hours ?
Answers:
A) 2/3 hrs
B) 3/4 hrs
C) 1/3 hrs
D) 1/4 hrs
E) 1 hr

Solution: Explanation:   Walking at 3/4th of usual rate implies that time taken would be 4/3th of the usual time. In other words, the time taken is 1/3rd more than his usual time   so 1/3rd of the usual time = 15min   or usual time = 3 x 15 = 45min = 45/60 hrs = 3/4 hrs.   ANSWER IS 3/4 hrs
Answer: B
The ages of two persons differ by 32 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively	Answers:
A) 20,20 B) 46,14 C) 25,15 D) 30,10 E) None of these

Solution: Explanation:   Let their ages be x and (x + 32) years.   5 (x - 5) = (x + 32 - 5) or 4x = 52 or x = 14.   Their present ages are 46 years and 14 years   Option 46,14
Answer: B
A saleswoman makes a 5% commission on the selling price for each products she sells. If she sells 250 products and makes $750 in commission, what was the selling price of each product?	Answers
A) 30
B) 60
C) 90
D) 120
E) 300

Solution: Commission per one product: 750/250= 
750/250 = 3
3   3= 5% of the selling price   3 = 0.05x   x = 60   Answer is 60.
Answer: B
What is the least number which when divided by 5, 6, 9 and 18 leaves remainder 4 in each care?
Choose one.
A) 30
B) 44
C) 36
D) 56
E) 94

Solution: 94xplanation:   LCM of 5, 6, 9 and 18 is 90   Required number = 90 + 4= 
90 + 4 = 94
94   Answer: Option 94
Answer: E
If it takes 30 construction workers 70 days to build a skyscraper, how long would it take 50 workers?  Choose the correct choice from the following answers
A) 52 days	B) 47 days	C) 42 days	D) 37 days	E) 32 days

Solution: 30 * 70 = 50 * x   x = 42   Answer: 42 days
Answer: C
Sides of a rectangular park are in the ratio 3: 2 and its area is 5766 sq m, the cost of fencing it at 50 ps per meter is?  Answers:	A) 287	B) 1287	C) 125	D) 155	E) 271

Solution: 3x * 2x = 5766 => x = 31   2(93 + 62) = 310 m   310 * 1/2 = Rs.155   Answer: 155
Answer: D
If toaster X costs 10 percent more than toaster Y costs, which of the following COULD be true?
I. Toaster Y costs $10 less than toaster X costs
II. Toaster X costs $20 more than toaster Y costs
III. Toaster Y costs 10 percent less than toaster X costs
Select the correct option:
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

Solution: 1. In case p=100 , Toaster X = 110   Toaster Y = 100   1 could be true .   2. In case p=200 ,   Toaster X = 220   Toaster Y = 200   2 could be true .   3. Never true .   Toaster Y will be (1/11)x100 percent lesser i.e 9.09 percent   Answer I and II only.
Answer: B
If x < 12, then it must be true that... Choose the correct answer.
A) -x < -12	B) -x - 2 < 14	C) -x + 2 < -10	D) x + 2 < 10	E) x - 4 < 15

Solution: A. -x < -12 --> x>12. Not true.   B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.   C. -x + 2 < -10 --> x>12. Not true.   D. x + 2 < 10 --> x<8. Not true, consider x=10.   E. x - 4 < 15 --> x<19. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.   Answer: x - 4 < 15.
Answer: E
Two trains are running in opposite directions with the same speed. If the length of each train is 420 m and they cross each other in 12 sec, then the speed of each train is?  Choose the correct choice from the following options
A) 11  B) 26  C) 126  D) 99  E) 27

Solution: Let the speed of each train be x m/sec.   Then, relative speed of the two trains = 2x m/sec.   So, 2x = (420 + 420)/12 => x = 35   Speed of each train = 10 m/sec.   = 35 * 18/5= 
35 * 18/5 = 126
126 km/hr.   Answer: 126
Answer: C
Six high school boys gather at the gym for a modified game of basketball involving three teams. Three teams of 2 people each will be created. How many ways are there to create these 3 teams?	Select.
A) 15  B) 30  C) 42  D) 90  E) 108

Solution: To put it in a different way:   Say 6 boys are a,b,c,d,e,f and we need to form 3 teams say t1,t2,t3   With a : a,b a,c a,d a,e a,f --->5   With b : b,c b,d b,e b,f --->4   With c : c,d c,e c,f --->3   With d : d,e d,f --->2   With e : e,f --->1   With f : --- --->0   Hence Total is 5+4+3+2+1+0= 
5+4+3+2+1+0 = 15
15.   15NSWER:15
Answer: A
A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?	Pick one:
A) 13	B) 59	C) 35	D) 37	E) 38

Solution: Let the original number be 'a'   Let the divisor be 'd'   Let the quotient of the division of aa by dd be 'x'   Therefore, we can write the relation as a/d=xa/d=x and the remainder is 24.   i.e., a=dx+24   When twice the original number is divided by d,2a is divided by d.   We know that a=dx+24. Therefore, 2a=2dx+48   The problem states that (2dx+48)/dleaves a remainder of 11.   2dx is perfectly divisible by dd and will therefore, not leave a remainder.   The remainder of 11 was obtained by dividing 48 by d.   When 48 is divided by 37, the remainder that one will obtain is 11.   Hence, the divisor is 37.   Option (37)
Answer: D
The average age of 20 men in the class is 15.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?  Pick one.
A) 15.5	B) 15.4	C) 15.25	D) 15.3	E) 15.6

Solution: Total age of 20 men = 15.6 x 20 = 312   Now, total age of 25 men = 389.   Total age of five men added later = 389 - 312= 
389 - 312 = 77
77.   Hence, the total average of five men= 77/5= 
77/5 = 77/5 = around 15.4
15.4   ANSWER:15.4
Answer: B
A train 605 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?  Options.
A) 51  B) 64  C) 11  D) 22  E) 33

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [605 * 3/55= 
605 * 3/55 = 33
33 sec   Answer: 33
Answer: E
Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 16^a and y = 9^b, which of the following is a possible units digit of xy?	Choose the correct choice from the following choices
A) 1
B) 6
C) 5
D) 7
E) 8

Solution: Only Units digit of X and Y contribute to the Units digit of XY.   Finding all values ofXfor positive values ofa   When,   a=1; X=16   a=2; X=256   a=3; X=4096........ Units digit repeat in a cycle of 6,6,6,6......   Similarly, Finding all values ofYfor positive values ofb   When,   b=1; Y=9   b=2; Y= 81   b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....   So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y   When X=6 and Y=9: Units digit of XY = 4   When X=6 and Y=1: Units digit of XY = 6   When X=6 and Y=9: Units digit of XY = 4   When X=6 and Y=1: Units digit of XY = 6   Only two possibilities for Units digit of XY i.e. 4 and 6.   Only 6 is given in answer choices, therefore answer is 6
Answer: B
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:	Select the correct option:
A) 101
B) 107
C) 111
D) 185
E) 196

Solution: Let the numbers be 37a and 37b.   Then, 37a x 37b = 4107   ab = 3.   Now, co-primes with product 3 are (1, 3).   So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111).   Greater number = 111.   Answer: Option 111
Answer: C
A man takes 3 hours 45 minutes to row a boat 20 km downstream of a river and 2 hours 30 minutes to cover a distance of 3 km upstream. Find the speed of the current.
Pick one:
A) 1 km/hr B) 2 km/hr C) 3 km/hr D) 4 km/hr E) None of these

Solution: Explanation:   First of all, we know that   speed of current = 1/2(speed downstream - speed upstream) [important]   So we need to calculate speed downstream and speed upstream first.   Speed = Distance / Time [important]   Speed upstream =(20/3 3/4)km/hr   =16/3km/hr   Speed Downstream = (3/2 1/2)km/hr   =6/5km/hr   So speed of current = 1/2(16/3−6/5)   =2km/hr   Option 2 km/hr
Answer: B
A sells a bicycle to B at a profit of 60% and B sells it to C at a loss of 40%. Find the resultant profit or loss. Choices:
A) -4%	B) 5%	C) -5%	D) 6%	E) -7%

Solution: The resultant profit or loss = 60 - 40 - (60*40)/100 = -4%   loss = 4%   -4%nswer is -4%
Answer: A