MU-NLPC/Calc-aqua_rat huggingface dataset:
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is?  Answers:
A) 16%
B) 12%
C) 74%
D) 10%
E) 45%

Solution: Let the rate be R% p.a. Then,   (5000 * R * 2)/100 + (3000 * R * 4)/100 = 2200   100 R + 120 R = 2200   R = 10%   Answer:10%
Answer: D
A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 280 dollars, and, in a third, loses 20. In the end he finds he has gained 120 dollars, by the three together. How much did he gain or lose bv the first ?  Choices
A) 80	B) -140	C) 140	D) 120	E) None

Solution: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.   Let x = the sum required.   Then according to the statement x + 280 - 20 = 120   And x = -140.   Answer -140
Answer: B
Five bells begin to toll together and toll respectively at intervals of 6, 5, 7, 10 and 12 seconds. How many times will they toll together in one hour excluding the one at the start ?	Select: A) 7 times B) 8 times C) 9 times D) 11 times E) 12 times

Solution: Explanation:   L.C.M. of 6, 5, 7, 10 and 12 is 420.   So, the bells will toll together after every 420 seconds i.e. 7 minutes.   Now, 7 x 8 = 56 and 7 x 9 = 63.   Thus, in 1-hour (or 60 minutes), the bells will toll together 8 times, excluding the one at the start.   Answer: 8 times
Answer: B
Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years? Choose the most appropriate option:
A) 198
B) 400
C) 268
D) 267
E) 256

Solution: 441   = P(21/20)2   P = 400   Answer:400
Answer: B
Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 3. Which of the following operations would decrease the standard deviation of Set J?  Choices
A) Multiply each term by e/d
B) Divide each term by b/c
C) Multiply each term by −1/2
D) Divide each term by d/e
E) Multiply each term by c/e

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   Multiply each term by −1/2
Answer: C
The population of a town is 7900. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
Choose one.
A) 9750  B) 8000  C) 8500  D) 9500  E) 10000

Solution: Formula :   ( 9750fter =100 denominator   9750go = 100 numerator)   7900 Ã— 100/90 Ã— 100/90 = 9753   9750)
Answer: A
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 9 sec. What is the length of the fast train? Options.
A) 27 7/6 B) 27 C) 27 7/2 D) 50 E) 27 7/1

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 9= 
50/9 * 9 = 50
50 m   Answer:50
Answer: D
When 0.252525...........is converted into a fraction, then find the result.	Choose the correct choice from the following
A) 25/99  B) 25/90  C) 25/999  D) 25/9999  E) None

Solution: Answer   0.252525 ..... = 0.25= 25/99   Correct Option: 25/99
Answer: A
To apply for the position of photographer at a local magazine, a photographer needs to include three or four photos in an envelope accompanying the application. If the photographer has pre-selected seven photos representative of her work, how many choices does she have to provide the photos for the magazine?
Choose the correct choice from the following options:  A) 54  B) 60  C) 64  D) 70  E) 75

Solution: 7C3 + 7C4 = 35 + 35= 
35 + 35 = 70
70   The answer is 70.
Answer: D
A can do a work in 7 days and B in 12 days. If they work on it together then in how many days required to complete the work?
Choose the correct choice from the following answers
A) 83/19	B) 84/19	C) 81/19	D) 77/19	E) 87/19

Solution: Person ( A ) ( 84/19 ) ( A+84/19 )   Time - ( 7 ) ( 12 ) (84/19)   Rate - ( 12 ) ( 7 ) ( 19 )   Work - (84) ( 84 ) ( 84 )   therefore A+84/19 requires (84/19) days to complete entire work   = 84/19   Answer is 84/19
Answer: B
Pat will walk from intersection A to intersection B along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from A to B can Pat take that have the minimum possible length? Pick one:
A) 6
B) 8
C) 10
D) 14
E) 16

Solution: Consider this a as coordinate plane with A as origin and B as (2,3).   The shortest possible way is when you go take either right or up. (lefts and downs make repetitions and thus non shortest paths)   now, to get to (2,3) form (0,0) you need min 5 steps.   so you have to choose all the paths such that you have 2 steps out of 5 along x axis and getting to 3 of y axis.   The number of ways = 5C2 =10   (or alternately all paths that have 3 steps along y and takes you to 2 of x. .. 5C3 = 10)   Can you explicate your combinatorial method a bit more. For example, If I add another Avenue, eg, Avenue D, and another street, Street 5, I will have to go 3 steps right and 4 steps up to get to point C.   In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.   So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/3!2!=10.   Answer: 10.
Answer: C
A person can row upstream 2 kmph and downstream 8 kmph. Find the rate of the stream and person rate in still water.	Choose the correct option:
A) 1,5
B) 2,5
C) 5,5
D) 3,5
E) 5,1

Solution: Explanation:   Please remember,   If a is rate downstream and b is rate upstream   Rate of current = 1/2(a-b)   Rate in still water = 1/2(a+b)   => Rate of current = 1/2(8-2) = 3 kmph   => Rate in still water = 1/2(8+2) = 5 kmph   Option 3,5
Answer: D
Which of the following points is symmetric with y=x at (4,5)? Options.
A) (-2,-1) B) (-2,1) C) (2,1) D) (-1,-2) E) (5,4)

Solution: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.   (4,5) would become (5,4).   Answer ((5,4)).
Answer: E
In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 55, what is the least possible difference between n and m.
Choices: A) a.1 B) b.3 C) c.4 D) d.7 E) e.9

Solution: 2n+5m=55   try with n=5 and m=8 the equation will be satisfied   2(5)+5(9)=55   so difference between M and N is 4,   Answer c.4
Answer: C
Hendrix works 20 days a month at d dollars per day for m months out of the year. Which of the following represents his 5 year pay?
Select.
A) m/(20d*5)	B) 100md	C) 50md/6	D) 20d/5m	E) 20d/5

Solution: Total income of Amber in a year = d*20*m dollars. Now 5 year income = Total*5= d*20*m *5 = 100md Answer is 100md
Answer: B
On January 1, 2010, Dave invests 70% of his retirement savings in Antarctic largecap stocks, 20% in Antarctic midcaps, and 10% in Antarctic smallcaps. In 2010, largecaps rise 5%, midcaps rise 10%, and smallcaps rise 15% in the Antarctic stock market; however, in 2011, largecaps fall 10% and midcaps fall 20%, while smallcaps rise x% in Antarctica. If, on January 1, 2012, Dave has the same total amount of retirement savings as he did two years before, then x is between	Choose the correct choice from the following options
A) 10 and 20	B) 20 and 30	C) 30 and 40	D) 40 and 50	E) 50 and 60

Solution: Here are the starting values:   L = $7,000   M = $2,000   S = $1,000   Apply the first year’s changes, so that you have these numbers on 1/1/2011:   Newer L = $7,000 + 5% = $7,350   Newer M = $2,000 + 10% = $2,200   Newer S = $1,000 + 15% = $1,150   Now apply the second year’s changes to L and M:   Newest L = $7,350 – 10% = $7,350 – $735 = $6,615   Newest M = $2,200 – 20% = $2,200 – $440 = $1,760   Add these to get $8,375. So the newest S must be $10,000 (the target final total of Dave’s retirement savings) minus $8,375, or $1,625.   The dollar change in S from 1/1/11 to 1/1/12 is $1,625 – $1,150 = $475. So the question is this: what percent change does $475 represent, from a starting point of $1,150? Since $1,150 is a nasty divisor, switch to benchmarks:   10% of $1,150 = $115.   So 20% is just double that, or $230.   And 40% is double that, or $460.   Since $475 is just slightly larger than $460 (but not enough to get you to 50%, which would be $460 + $115), x must be between 40 and 50.   Intuitively, it should make sense that you’d need a much bigger positive percent change in the smallest investment (S) to make up for even a moderate downturn in the larger investments (L and M), so if you were completely stuck for time and needed to guess in a hurry, you should favor C/D/E over A or B.   The correct answer is 40 and 50.
Answer: D
A plane was originally flying at an altitude of x feet when it ascended 2,000 feet and then descended 5,000 feet. If the plane's altitude after these two changes was 1/2 its original altitude, then the solution of which of the following equations gives the plane's original altitude, in feet ?	Pick one
A) x + 2000 = 1/3*(x - 3000)
B) 1/3*(x - 3000) = x
C) x - 3000 = 1/2*x
D) x - 7000 = 1/3*x
E) x - 3000 = 1/3*x

Solution: Plane's original altitude = x   Plane's new altitude after ascending 2000 ft = x+2000   Plane's new altitude after descending 5000 ft from previous altitude = x+2000-5000 = x-3000   So, after two changes plane is at 1/2 its original altitude => x-3000 = x/2   Answer (x - 3000 = 1/2*x)
Answer: C
If a light flashes every 6 seconds, how many times will it flash in 2/5 of an hour?  Choose the correct choice:  A) 181  B) 211  C) 241  D) 271  E) 301

Solution: In 2/5 of an hour there are  24*60= 
 24*60 = 1_440
1440 seconds   The number of 6-second intervals= 1440/6= 
1440/6 = 240
240   After the first flash, there will be 240 more flashes for a total of 241.   The answer is 241.
Answer: C
Find a if (ax3 + 3x2 - 3) and (2x3 - 5x + a) when divided by (x-4) leave same rmainder?  Choose the correct choice from the following answers: A) 1 B) 3 C) 4 D) 5 E) 6

Solution: remainders are,   R1 = f(4) = a(4)3+ 3(4)2-3= 64a+45   R2 = f(4) = 2(4)3- 5(4) + a= a +108   Since R1= R2   64a +45= a+108 => 63a = 63 => a =1   1
Answer: A
A student can select one of 9 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.	Choices:
A) 22	B) 72	C) 99	D) 37	E) 108

Solution: 9C1×3C1×4C1= 9x3x4=108 ways   Answer:108
Answer: E
Find the percentage gain if a shop owner sells 18 mtr of fabric and gains Cost Price of 3 meters? Choose the correct choice from the following: A) 17.67% B) 19.67% C) 11.67% D) 16.67% E) 15.67%

Solution: Let cost of each metre be Rs. 100.   Therefore, cost price of 3m cloth = 3*100= 
3*100 = 300
300   cost price of 18m cloth= 18*100= 
18*100 = 1_800
1800   Since the trader made the CP of 3m from the sale of 18m therefore   Profit on sale of 18m= cost price of 3 m cloth = 300   Selling price of 18m = 1800+300= 
1800+300 = 2_100
2100   Profit %= 16.67%   16.67%
Answer: D
By selling a book for 260, 20% profit was earned. What is the cost price of the book?	Choices
A) A)215	B) B)216	C) C)230	D) D)235	E) E)240

Solution: SP = 120% of CP; :. CP = 260 × 100/120 = 216   Option '216'
Answer: B
We have 6 people and 4 chairs. In how many ways chairs can be occupy?
Pick:  A) 840  B) 720  C) 650  D) 914  E) 120

Solution: no. of ways they can be occupy = 6*5*4= 
6*5*4 = 120
120   Answer is 120
Answer: E
Find the third proportional to 3 and 9?
Choose the correct choice from the following options.
A) 10
B) 12
C) 27
D) 19
E) 20

Solution: Formula = Third proportional = (b × b)/a   A = 3 and B = 9   (9 x 9)/ 3 = 81/3= 
81/3 = 27
27   27
Answer: C
A die is rolled twice. What is the probability of getting a sum equal to 9? Choose the correct option:	A) 2/3	B) 2/9	C) 1/3	D) 1/9	E) 1/6

Solution: Total number of outcomes possible when a die is rolled = 6 (âˆµ any one face out of the 6 faces)   Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 Ã— 6 = 36   E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}   Hence, n(E) = 4   P(E) = n(E)/n(S)=4/36=1/9   Answer:1/9
Answer: D
In the third quarter of 2015, Atlantis Law Firm had 20 lawyers and 400 cases. In the fourth quarter of 2015, the firm had 22 lawyers and 500 cases. By approximately what percent did the ratio of lawyers to cases decrease from the third quarter to the fourth quarter.	Choose the correct choice.
A) 10.0%  B) 11.0%  C) 12.0%  D) 13.0%  E) 14.0%

Solution: 3rd quarter: lawyers/cases = 20/400 =100/2000   4th quarter: lawyers/cases = 22/500 =88/2000   ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.   So, our ratio went from 100/2000 to 88/2000   Ignoring the denominators, we went from 100 to 88   The percent change = 100(difference in values)/(original value)   = (100)(100-88)/100   = (100)(12)/100)   =12.0   Answer: 12.0%
Answer: C
q, b, and c are positive integers. If q, b, and c are assembled into the six-digit number qbcqbc, which one of the following must be a factor of qbcqbc?  Choose the correct choice from the following answers.
A) 16  B) 13  C) 5  D) 3  E) none of the above

Solution: Plug in some values and check -   qbcqbc = 123123   Not divisible by 16 and 5   let qbcqbc = 125125   Not divisible by 3   Only option (B) and (E) is left in both the cases...   Check once more to marke (13) as correct answer   let qbcqbc = 135135   Again divisible by 13   So, mark answer as (13) 13
Answer: B
In the xy-plane, the point (1, 3) is the center of a circle. The point (-2, 3) lies inside the circle and the point (1, -2) lies outside the circle. If the radius r of the circle is an integer, then r =  Choose the correct answer:
A) 6 B) 5 C) 4 D) 3 E) 2

Solution: An easy way to solve this question will be just to mark the points on the coordinate plane.   You'll see that the distance between the center (1, 3) and the point inside the circle (-2, 3) is 3 units   (both points are on y=3 line so the distance will simply be  1-(-2)= 
 1-(-2) = 3
3)   So the radius must be more than 3 units.   The distance between the center (1,3) and the point outside the circle (1,-2) is 5 units   (both points are on x=1 line so the distance will simply be  3-(-2)= 
 3-(-2) = 5
5)   So the radius must be less than 5 units, which implies 3 < r < 5, thus as r is an integer then r=4.   Answer: 4.
Answer: C
A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 60 days, then together ,all will finish the work in : Select the correct option
A) 13 1/3 days
B) 12 1/3 days
C) 15 days
D) 20 days
E) 30 days

Solution: C alone can finish the work in 60 days.   (A + B)can do it in 20 days   (A + B)s 1 days wok = 1/20.   As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.   Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30   (A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/60) = 1/15   All the three together will finish it in 15 days.   ANSWER:15 days
Answer: C
Ginger over the course of an average work-week wanted to see how much she spent on lunch daily. On Monday and Thursday, she spent $5.43 total. On Tuesday and Wednesday, she spent $4.54 on each day. On Friday, she spent $7.89 on lunch. What was her average daily cost?
Choose the correct answer
A) a. $3.19	B) b. $3.75	C) c. $3.90	D) d. $4.08	E) e. $4.48

Solution: On Monday and Thursday, she spent $5.43total.   On Tuesday and Wednesday, she spent $4.54on each day.   On Friday, she spent $7.89 on lunch.   The average = (5.43 + 2*4.54 + 7.89)/5 = 4.48.   Answer: e. $4.48.
Answer: E
If A = {1, 3, 5}, B = {3, 5, 6}.Find A ∪ B Choices:
A) {1,5}	B) {1,3,5,6}	C) {2,6}	D) {8,9}	E) {4,12}

Solution: A= {1,3,5}   {1,3,5,6}= {3,5,6} Therefore ,   correct answer :A ∪ {1,3,5,6} = {1, 3, 5, 6}   {1,3,5,6}
Answer: B
What is the relationship between the fractions 14/15 and 37/40.	Choose the correct choice.
A) 14/15 = 37/40 B) 14/15 < 37/40 C) 14/15 > 37/40 D) cannot bedetermined E) None

Solution: Take L14/15 > 37/40M of both 15, 40 we get 120   (14*8)/(15*8) = 112/120   (37*3)/(40*3) = 111/120   So 14/15>37/40   ANSWER:14/15 > 37/40
Answer: C
A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively? Select the correct option
A) 14, 5 B) 14, 9 C) 14, 6 D) 14, 4 E) 14, 2

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 28 => x = 14, y = 4.   Answer: 14, 4
Answer: D
The current in a river is 10 mph. A boat can travel 50 mph in still water. How far up the river can the boat travel if the round trip is to take 5 hours?
Pick.
A) 120 B) 100 C) 96 D) 85 E) 150

Solution: Upstream Speed = 50-10= 
50-10 = 40
40 mph   Downstream Speed= 50+10= 
50+10 = 60
60 mph   D/40 + D/60= 5 hours   Solving for D we get D=120   120nswer: 120
Answer: A
At 1:00, Annie starts to bicycle along a 45 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?  Choose the correct choice from the following
A) 2:00 B) 2:30 C) 3:00 D) 3:30 E) 4:00

Solution: In the first 30 minutes, Scott can travel 6 miles, so there are 39 miles left.   Together Annie and Scott can complete 26 miles.   39/26= 
39/26 = 3/2 = around 1.5
1.5, so they will meet 1.5 hours after 1:00.   The answer is 2:30.
Answer: B
Ten cards numbered 1 to 10 are placed in a box and then one card is drawn randomly. If it is known that the number on the drawn card is more than 5, what is the probability that it is an even number? Choices.
A) 1/2  B) 2/5  C) 3/5  D) 2/7  E) 3/10

Solution: There are 5 numbers higher than 5 and 3 of them are even.   The probability is 3/5.   The answer is 3/5.
Answer: C
In how many different ways can the letters of the word 'AIRPORT' be arranged in such a way that the vowels always come together? Choices:
A) A)360  B) B)720  C) C)480  D) D)5040  E) of these

Solution: The word 'AIRPORT' has 7 different letters.   When the vowels AIO are always together, they can be supposed to form one letter.   Then, we have to arrange the letters RPRT (AIO).   Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.   The vowels (AIO) can be arranged among themselves in 3! = 6 ways.   Required number of ways = (120 x 6) = 720.   ANSWER:720
Answer: B
What is the least value of x, So that 2x5452 is divisible by 9  Choose the correct answer
A) 7 B) 8 C) 9 D) 3 E) 0

Solution: Explanation:   The sum of the digits of the number is divisible by 9.   Then the number is divisible by 9.   2 + x + 5 + 4 + 5 + 2 = 18 + x   Least value of x may be '0',   So that the total 18 + 0= 
18 + 0 = 18
18   is divisible by 9.   Answer: Option 0
Answer: E
A shopkeeper has 280 kg of apples. He sells 85% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.
Choices
A) 24% B) 25% C) 26% D) 28% E) 35%

Solution: If the total quantity was 100   Then 85 X 20% + 60 X30%= 85   This profit will remain same for any total quantity unless the % of products remains the same. Hence '35%' is the answer
Answer: E
If 5 women or 8 girls can do a work in 84 days.In how many days can 10 women and 5 girls can do the same work?	Choose the correct choice from the following choices:
A) 32
B) 33
C) 34
D) 35
E) cannot be determined

Solution: Given that 5 women is equal to 8 girls to complete work/   So,10 women=16 girls.   10 women+5 girls=16 girls+5 girls=21 girls.   8 girls can do a work in 84 days then 21 girls can do a work in (8*84)/21= 
(8*84)/21 = 32
32 days   Therefore 10 women and 5 girls can a work in 32 days.   32nswer is option 32
Answer: A
What number is obtained by adding the units digits of 734^100 and 347^83?	Choose one:
A) 7
B) 8
C) 9
D) 10
E) 11

Solution: The units digit of 734^100 is 6 because 4 raised to the power of an even integer ends in 6.   The units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.   Then   6+3= 
  6+3 = 9
9.   The answer is 9.
Answer: C
A shopkeeper give 12% additional discount on the discounted price, after giving an initial discount of 20% on the labelled price of a radio. If the final sale price of the radio is Rs.704, then what is its labelled price?
Pick one:
A) Rs.844.80	B) Rs.929.28	C) Rs.1000	D) Rs.1044.80	E) None

Solution: Solution   Let the labelled price be Rs.x.   88% of 80% of x	= 704   x=(704x100x100 /88x80)   = 1000.   Answer Rs.1000
Answer: C
Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?	Choose the correct option.
A) 1261
B) 1572
C) 1689
D) 1687
E) 2679

Solution: 1261 = 8000(21/20)3   = 9261   = 8000   ---------   1261   1261nswer: 1261
Answer: A
W and X started a business investing Rs. 30,000 and Rs. 6,000 respectively. Out of a total profit of Rs. 18,000, W’s share is :  Choose the correct choice from the following answers:  A) 14000  B) 15000  C) 16000  D) 17000  E) 18000

Solution: Ratio of their shares = 30000 : 6000 = 5 : 1.   W’s share = Rs. 18000 * 5/6   = Rs. 15000   ANSWER:15000
Answer: B
What is the smallest number which when increased by 3 is divisible by 9, 35, 25 and 21?  Choose one:
A) 1572	B) 1782	C) 1992	D) 2122	E) 2342

Solution: When increased by 3, the number must include at least 3^2*5^2*7 = 1575   The answer is 1572.
Answer: A
4 dice are thrown simultaneously on the board. Find the probability which show the same face?
Choose the correct choice from the following options:  A) 2/113  B) 3/117  C) 1/216  D) 3/111  E) 4/121

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
I sold a book at a profit of 12%. Had I sold it for $18 more, 18% would have been gained. Find the cost price?
Pick
A) $100  B) $250  C) $300  D) $200  E) $180

Solution: 118% of cost - 112% of cost = $18   6% of cost = $18   cost = 18*100/6= 
18*100/6 = 300
$300   Answer is $300
Answer: C
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Choose the most appropriate option:
A) 17.9 sec B) 11.8 sec C) 27.7 sec D) 10.8 sec E) 17.8 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 160= 
140 + 160 = 300
300 m.   Required time= 300 * 9/250 = 54/5= 
54/5 = 54/5 = around 10.8
10.8 sec.   Answer: 10.8 sec
Answer: D