MU-NLPC/Calc-aqua_rat huggingface dataset:
350 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees  Choose one: A) 10 B) 12 C) 14 D) 16 E) 17

Solution: 26 trees have 25 gaps between them,   Required distance (350/25)= 
(350/25) = 14
14   14
Answer: C
Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel five times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?  Choose the correct choice from the following answers:	A) 4	B) 6	C) 8	D) 9	E) 12

Solution: W: the time for Wyane to do the job   S: the time for his son to do the job   We have 1/W + 1/S = 1/5 and W = 5S   Then we have 1/(5*S) + 1/S = 1/5<=> 6/(5*S) = 1/5 <=> S = 6   ANS: 6
Answer: B
Mrs. B. invested $30,000; part at 5%, and part at 8%. The total interest on the investment was $2,100. How much did she invest at each rate?  Pick:
A) x = $1,000, y = $29,000
B) x = $5,000, y = $25,000.
C) x = $10,000, y = $20,000.
D) x = $15,000, y = $15,000
E) x = $20,000, y = $10,000

Solution: 2100 = (30000-x) 5/100 + 8x/100   Solving, we get x = 20000   So, answer is 10000 & 20000   Answer = x = $10,000, y = $20,000.
Answer: C
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?	Select the correct option.
A) 289
B) 190
C) 277
D) 266
E) 255

Solution: Time taken by B run 1000 meters = (1000 * 10)/50= 
(1000 * 10)/50 = 200
200 sec.   Time taken by A= 200 - 10= 
200 - 10 = 190
190 sec.   Answer:190
Answer: B
Q=(429)^2 * 237 * (1243)^3 is thrice of ?	Choose the correct option:
A) 33605 * 31960 * (1243)^2  B) 33654 * 538219 * (1243)^2  C) 33891 * 533247 * (1243)^2  D) 34122 * 532004 * (1243)^2  E) 34606 * 534572 * (1243)^2

Solution: Q=(429)^2*237*(1243)^3 is an odd number.   Among answer choices only C is an odd number, (so thrice C also will be an odd number).   Answer: 33891 * 533247 * (1243)^2.
Answer: C
The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally? Choose the most appropriate option:	A) 22	B) 88	C) 12	D) 99	E) 14

Solution: x, 2x   (x-2):(2x-2) = 1:3   3x-6 = 2x-2   x = 4   x+2x = 3x   => 3*4= 
3*4 = 12
12   Answer: 12
Answer: C
Hydraulic press Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 5 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 5 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 5 jars?  Choices
A) m	B) n	C) m+n	D) 5n/25-mn	E) m-n

Solution: working rate p = 5/m ; working rate pq =( 1/p +1/q)* n =5 or mn/5 +n/q =5 0r n/q = 5-mn/5 = 25-mn/5   q = 5n/25-mn   m-n
Answer: E
If 6^w is a factor of (10!)^2, What is the greatest possible value of w ? Select:
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7   6= 2*3   Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice 8
Answer: D
A library has an average of 500 visitors on Sundays and 140 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :	Choose the correct option.
A) 100
B) 200
C) 300
D) 400
E) 550

Solution: Explanation:   Since the month begins with a Sunday, so there will be five Sundays in the month,   Required average = (500 * 5 + 140 * 25) / 30 = 6000/30= 
6000/30 = 200
200   Answer: 200) 200
Answer: B
What is 35% of 4/13 of 650? Pick one
A) 50	B) 60	C) 70	D) 80	E) 90

Solution: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 650, or 1/9 of 650. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.   The number 650 is a bit more than 630, so (1/9)*630 will be about 70.   Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.   The answer is 70.
Answer: C
A starts a business with $3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the
ratio 2 : 3. B's contribution in the capital is	Answers
A) 7000
B) 9000
C) 8000
D) 9900
E) 7900

Solution: Ratio in which profit is divided =2:3   Assume that 9000's contribution to the capital=b   3500×12:b×7=2:3   ⇒3500×12×3=2×b×7   ⇒b = 3500×12×3 / 2×7   =500×6×3=9000   ANSWER:9000
Answer: B
Together, Victor and Tami Vargas earn $33,280 per year. Tami earns $4,160 more per
year than Victor earns. How much do Tami earn per year? Choose the correct choice from the following options
A) $28,720 B) $8,720 C) $18,720 D) $38,720 E) $58,720

Solution: You are asked to find two unknown amounts. Victor’s earnings: x   Represent the amounts using algebra. Tami’s earnings: x 4,160   Write an equation showing that the sum of the   two amounts is $33,280. Solve the equation. x x 4,160 33,280   Combine like terms. 2x 4,160 33,280   Subtract 4,160 from both sides of the equation. 2x 4,160 4,160 33,280 4,160   2x 29,120   Divide both sides by 2.   x 14,560   Now go back to the beginning, when you first wrote the amounts in algebraic language. Since   x represents Victor’s earnings, you know that Victor earns $14,560 per year. Tami’s earnings are   represented by x+4,160. Add: 14,560+4,160=18,720. Tami earns $18,720 per year.   Answer: Victor earns $14,560, and Tami earns $18,720.   correct answer $18,720
Answer: C
A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 7% dividend at the end of the year,then how much does he get ?  Choose the correct choice:
A) Rs. 500  B) Rs. 840  C) Rs. 650  D) Rs. 720  E) None

Solution: Solution   Number of shares = (14400/120)= 
(14400/120) = 120
120.   Face value= Rs. (100x120 ) = Rs. 12000.   Annual income = Rs.(7/100x12000) = Rs. 840.   Answer Rs. 840
Answer: B
A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?	Choose the most appropriate option.
A) 277 B) 277 C) 120 D) 882 E) 272

Solution: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.   Length of the train = 20 * 6= 
20 * 6 = 120
120 m.   Answer: 120
Answer: C
Four dice are thrown simultaneously. Find the probability that all of them show the same face.
Choose one:  A) 1/216  B) 1/215  C) 5/300  D) 1/415  E) 1/500

Solution: Total no of elementary events = 6^4   n(S) = 6^4   x={(1,1,1,1)(2,2,2,2).....(6,6,6,6)}   n(X)=6   n(X)/n(S) =6/6^4   =1/216   1/216NSWER 1/216
Answer: A
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam?
Answers
A) 1/4	B) 12/47	C) 1/3	D) 5/12	E) 20/47

Solution: Let the total work be 60 units. Pual does   60/3= 
  60/3 = 20
20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12)= 
(20 + 15 + 12) = 47
47 units per hr. So the time taken to finish the work= 60/47 hrs.   adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work   R>( 60/47 *12)/60 =12/47   Answer 12/47
Answer: B
If five numbers are randomly selected without replacement from set {1, 2, 3, 4, 5}, what is the probability that the numbers are selected in ascending order?
Choose the correct option:
A) 1/256
B) 1/120
C) 1/480
D) 1/240
E) 1/50

Solution: The total number of ways to arrange 5 numbers is 5! = 120.   There is only one way to arrange the numbers in ascending order.   P(ascending order) = 1/120   The answer is 1/120.
Answer: B
The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.	Choose the correct choice from the following answers
A) 25years
B) 45years
C) 12years
D) 6years
E) 16years

Solution: Total age of 39 persons = (39 x 15) years   = 585 years.   Average age of 40 persons= 15 yrs 3 months   = 61/4 years.   Total age of 40 persons = (_(61/4 )x 40) years= 610 years.   :. Age of the teacher = (610 - 585)= 
(610 - 585) = 25
25 years.   25yearsns: 25years
Answer: A
In the first 10 overs of a cricket game, the run rate was only 3.6. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?	Choices.
A) 6.25	B) 6.5	C) 6.15	D) 7	E) 8

Solution: 10 overs - run rate = 3.6   runs scored in first 10 overs = 36   remaining overs 40   total runs to be scored= 282   32 runs already scored 282-36= 
282-36 = 246
246   246 runs to be scored in 40 overs   let required runrate be x   40*x=246   x=246/40= 
246/40 = 123/20 = around 6.15
6.15   the required runrate is 6.15   ANSWER:6.15
Answer: C
John has $1,600 at the beginning of his trip, after spending money, he still has exactly $600 less than he spent on the trip. How much money does John still have? Choose the correct choice:  A) $200  B) $400  C) $600  D) $800  E) $500

Solution: Suppose total money spent = x   Not spend (Money he still has)= x-600   x+x-600 = 1600   x= 1100   Money not spend= 1100-600= 
1100-600 = 500
500   Answer : $500
Answer: E
Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 48 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
Choose the correct option
A) 5  B) 7  C) 8  D) 9  E) 6

Solution: One way of approaching this question is by Relative speed method   1. Speed/ Rate of Donovan = Distance/ time => 400/48 =>50/6   2. Speed/ Rate of Michael = Distance/ time => 400/40= 
400/40 = 10
> 10   Relative Speed between them= 10 - 50/6 => 10/6 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)   In order to pass Donovan-   Distance to be covered = 400, Relative Rate = 10/6   Total Time taken by Micheal to surpass Donovan = Distance / rate => 400*6/10 => 2400/10= 
2400/10 = 240
> 240   No. of laps taken by Michael= Total time / Michael's rate => 240/40= 
240/40 = 6
> 6   Hence correct answer is 6 Laps.   6
Answer: E
A cab driver 5days income was $25, $50, $60, $65 , $70. Then his average income is?
Pick one:
A) A)$58	B) B)$54	C) C)$65	D) D)$48	E) E)$62

Solution: avg = sum of observations/number of observations   avg income=(25+50+60+65+70)/5= 
(25+50+60+65+70)/5 = 54
54   Answer is $54
Answer: B
If a committee of 3 people is to be selected from among 7 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? Choose one:
A) 20 B) 40 C) 50 D) 180 E) 280

Solution: You now have your Committee of 3 people. But you've selected them in an order, when order doesn't matter.   Selection #1 = Jack   Selection #2 = Susan   Selection #3 = Mary   Assume this is a good committee where Jack is not married to Susan or Mary and Susan and Mary are not married. The above committee will be the same as the following committee:   Selection #1 = Susan   Selection #2 = Mary   Selection #3 = Jack   To account for the fact that the order does not matter, we must divide out the number of ways a single committee can be the same members but in different order. 3 places = 3!, 3*2*1 = 6.   14*12*10 / 6= 
14*12*10 / 6 = 280
280. Answer 280.
Answer: E
What is the remainder when 14,456 × 15,657 × 16,788 is divided by 10? Select the correct option.
A) 6	B) 8	C) 4	D) 3	E) 2

Solution: Only the unit's digit of the product will decide the remainder when divided by 10.   Hence, 6*7*8= will give units digit as 6   So, whatever be the number, if it ends in 6, the remainder after dividing with 10 will be 6.   Option6
Answer: A
In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,6). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?  Choose the correct answer:
A) 1/5
B) 1/3
C) 1/2
D) 2/3
E) 4/5

Solution: The area of the right triangle is (1/2)*4*6= 
(1/2)*4*6 = 12
12.   Only the points (a,b) below the line y=x satisfy a - b > 0.   The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.   P(a - b > 0) = 8/12 = 2/3   The answer is 2/3.
Answer: D
Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest? Pick one:
A) 5:1	B) 5:7	C) 5:2	D) 5:8	E) 5:2

Solution: Let the amount lent at 4% be Rs. x   Amount lent at 10% is Rs. (6000 - x)   Total interest for one year on the two sums lent   = 4/100 x + 10/100 (6000 - x) = 600 - 3x/100   => 600 - 3/100 x = 450 => x = 2500   Amount lent at 10% = 3500   Required ratio = 5:7   Answer:5:7
Answer: B
The smallest number which when diminished by 8, is divisible 8, 16, 24, 32 and 40 is: Choose one.
A) 1008 B) 1015 C) 488 D) 490 E) 590

Solution: Required number = (L.C.M. of 8, 16, 24, 32, 40) + 8   = 480 + 8= 
480 + 8 = 488
488   Answer: Option 488
Answer: C
A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 72.25, the number of the member is the group is: Select:
A) 57  B) 67  C) 77  D) 85  E) 97

Solution: Explanation:   Money collected = (72.25 x 100) paise = 7225 paise.   ∴ Number of members = √(7225) = 85.   Answer: 85
Answer: D
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is	Choose the correct choice from the following choices.
A) 25/42  B) 25/47  C) 25/32  D) 25/48  E) 25/41

Solution: :   Total fruits = 9   Since there must be at least two apples,   = 25/42.   25/42nswer: 25/42
Answer: A
How many words can be formed by using all letters of the word ‘BIHAR’ ?  Choose the correct choice from the following choices.
A) 110
B) 120
C) 130
D) 140
E) None

Solution: Solution   The word BIHAR contains 5 different letters.   Required number of words = 5P5 = 5 ! = (5 x 4 x 3 x 2 x 1) = 120   Answer 120
Answer: B
A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 4 : 1 ? Choose the correct answer:  A) 6 months  B) 3 months  C) 2 months  D) 8 months  E) 9 months

Solution: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 4. or x = (85000 * 12) / (42500 * 4)= 
(85000 * 12) / (42500 * 4) = 6
6.   So, B joined for 6 months.   6 monthsnswer: 6 months
Answer: A
What will come in place of the x in the following Number series? 46080, 3840, 384, 48, 8, 2, x
Choose the correct choice from the following options.
A) 1 B) 3 C) 5 D) 6 E) 7

Solution: 46080 /12= 
46080 /12 = 3_840
3840   3840 /10= 
3840 /10 = 384
384   384 /8= 
384 /8 = 48
48   48 /6= 
48 /6 = 8
8   8/4= 
8/4 = 2
2   2 /2= 
2 /2 = 1
1   1
Answer: A
A, B and C rents a pasture for Rs.928. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?	Select the correct option:
A) 270
B) 289
C) 288
D) 255
E) 552

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 928= 
9/29 * 928 = 288
288   Answer: 288
Answer: C
What is the difference between the place values of two sevens in the numeral 54707429 ?  Choose the correct choice from the following answers:	A) 699990	B) 693000	C) 99980	D) 699930	E) None of these

Solution: Explanation:   Required Difference   = 700000 - 7000= 
700000 - 7000 = 693_000
693000   Answer is 693000
Answer: B
In an election between two candidates first candidate got 65% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
Select the correct option:
A) 7000 votes
B) 8000 votes
C) 9000 votes
D) 9800 votes
E) 9900 votes

Solution: Total = 100 %,   First person got 65%   second person got remaining 35 % of votes.   than 35 % = 2800   35% = 35Ã—80 = 2800   100% =100Ã—80 =8000 votes   8000 votes
Answer: B
What is the sum of the 1st 5 prime numbers greater than 20?
Choose the correct answer:
A) 121	B) 151	C) 168	D) 164	E) 161

Solution: Required sum = (23 + 29 + 31 + 37 + 41)= 
(23 + 29 + 31 + 37 + 41) = 161
161   Note: 1 is not a prime number   Answer 161
Answer: E
Jason flips a coin three times. What is the probability W that the coin will land on the same side in all three tosses? Choose the correct choice from the following: A) 1/16 B) 1/8 C) 1/4 D) 1/3 E) 1/2

Solution: Total outcome is 2^3=8   Favorable cases HHH or TTT   Therefore, probability W is 2/8 or 1/4.1/4
Answer: C
From 5 positive numbers and 7 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?  Choose the correct choice from the following:
A) 720 B) 625 C) 250 D) 960 E) 355

Solution: The number of ways to choose 4 positive numbers is 5C4 = 5.   The number of ways to choose 4 negative numbers is 7C4 = 35.   The number of ways to choose 2 positive and 2 negative is 5C2*7C2 = 10*21= 
10*21 = 210
210.   The total number of groups is 5+35+210= 
5+35+210 = 250
250.   The answer is 250.
Answer: C
A squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . How many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference?  Select:
A) 10 feet
B) 8 feet
C) 13 feet
D) 15 feet
E) 18 feet

Solution: total circuit=16/4= 
16/4 = 4
4   total feet squirrel travels=4*2= 
4*2 = 8
8 feet   ANSWER:8 feet
Answer: B
Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 36 marks in that test. Find the pass mark in the first test? Choose the correct choice from the following:  A) 277  B) 266  C) 111  D) 121  E) 224

Solution: Let the maximum mark in each test be M.   The candidate failed by 36 marks in the second test.   pass mark in the second test = 216 + 36= 
216 + 36 = 252
252   45/100 M= 252   Pass mark in the first test = 40/100 M = 40/45 * 252= 
40/45 * 252 = 224
224.   Answer:224
Answer: E
Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 14 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	Choose the correct option
A) 11  B) 444  C) 420  D) 287  E) 221

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 14 + 21= 
14 + 21 = 35
35   T= 12   D = 35 * 12= 
35 * 12 = 420
420   Answer:420
Answer: C
How many of the positive factors of 56 , 96 and how many common factors are there in numbers?  Choose the correct choice from the following answers:
A) 2 B) 4 C) 3 D) 5 E) 1

Solution: factors of 56- 1, 2, 4, 7, 8, 14, 28, 56   factors of 96- 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96   3omparing both, we have three common factors of 56 and 96- 1,2,4   Answer(3)
Answer: C
Two airplanes take off from one airfield at noon. One flies due east at 204 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?	Select.
A) 166  B) 408  C) 400  D) 483  E) 566

Solution: B   In two hours:   the plane flying East will be 408 miles away from airport.   the other plane will be 566 miles away from airport.   566/408 = ~1.4 = ~sqrt(2)   This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 408 miles apart.408
Answer: B
What is the smallest five digit number that is divisible by 15, 36, 40, and 54?
Options:  A) 10400  B) 10800  C) 11200  D) 11600  E) 12000

Solution: 15 = 3 * 5   36 = 2^2 * 3^2   40 = 2^3 * 5   54 = 2 * 3^3   LCM = 2^3 * 3^3 * 5 = 1080   The smallest five-digit number that is a multiple of 1080 is 10*1080 = 10,800   The answer is 10800.
Answer: B
Karen places a bet with Tom that she will beat Tom in a car race by 4 miles even if Karen starts 4 minutes late. Assuming that Karen drives at an average speed of 60 mph and Tom drives at an average speed of 45 mph, how many E miles will Tom drive before Karen wins the bet?
Choose the correct choice from the following options:
A) 15
B) 18
C) 21
D) 24
E) 27

Solution: Let K and T be the speeds of Karen and Tom respectively.   t be the time that Karen will travel ----> t+4/60 will be the total time Tom will travel by the time the distance between Karen and Tom is 4 miles.   Thus, per the question , K(t) - T(t+4/60) = 4 ---> t = 7/15 hours   Thus the distance traveled by Tom when Karen is 4 miles ahead of him E: T*(t+4/60) = 45 (7/15+4/60) = 24 miles. 24 is the correct answer.
Answer: D
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is a + 2?	Choose the correct choice from the following options.
A) a - 5  B) a  C) a - 1  D) a - 3  E) a + 1

Solution: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2   And 1st integer= 3rd integer- 4   let's say 3rd integer = n and 4th integer = n+2   2n+2/2= a+2   n= a+1   1st integer= a+1-4= a-3   a - 3 is the answer
Answer: D
The ratio of radius of a circle and the side of a square is 2 : 3. Find the ratio of their areas:  Choose the most appropriate option:  A) 2 : 1  B) 4 : 9  C) 8 : 77  D) 4 : 121  E) None

Solution: radius/side = 2/3   â‡’ area of circle/area of square= 4/9   Answer: 4 : 9
Answer: B
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.7, what is the probability that Malachi will return home at the end of the day on the following Monday?
Choose the most appropriate option:
A) 0.063
B) 0.128
C) 0.488
D) 0.512
E) 0.64

Solution: Re-phrasing the question:   What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain   Probablity of rain = 0.7   Therefore, probability of no rain = 0.3   0.3*0.3*0.7= 
0.3*0.3*0.7 = 0.063
0.063   Hence 0.063
Answer: A
Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?  Choose the correct choice:
A) 120  B) 116  C) 108  D) 107  E) 72

Solution: # of three-digit integers greater than 600 is 399 (999-600);   Numbers with all distinct digits:   4*9*8= 
  4*9*8 = 288
288. First digit can take 4 values: 6, 7, 8 or 9, second digit can take 9 values (10 minus the one we used for the first digit) and third digit can tale 8 values (10 minus 2 digits we've already used for the first two digits);   Numbers greater than 600 which have all alike digits: 4 (666, 777, 888, 999);   {Total}-{all distinct}-{all alike}={two alike, one different} --> 399-288-4=107.   Answer: 107. --  399-288-4= 
 --  399-288-4 = 107
107.   Answer: 107.
Answer: D
How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?	Choose the correct choice from the following answers
A) 287  B) 288  C) 500  D) 277  E) 121

Solution: Let length of tunnel is x meter   Distance = 800+x meter   Time = 1 minute = 60 seconds   Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s   Distance = Speed*Time   800+x = (65/3) * 60   800+x = 20 * 65= 
20 * 65 = 1_300
1300   x= 1300 - 800= 
1300 - 800 = 500
500 meters   Answer: 500
Answer: C