MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability W that out of the two, one is white and one is blue? Select the correct option
A) 15/56
B) 41/56
C) 13/28
D) 15/28
E) 5/14

Solution: The required probability W= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.   Ways to select 6 out of total 8 = 8C6   Ways to select 4 out of 5 white balls = 5C4   Ways to select 2 out of 3 blue balls = 3C2   Thus the required probability = (5C4*3C2)/8C6 = 15/28.   15/28 is thus the correct answer.
Answer: D
The second angle of a triangle is double the first(110). The third angle is 40 less than
the first(15). Find the first angle.
Choose the correct choice from the following options:
A) 35
B) 45
C) 55
D) 65
E) 75

Solution: First x With nothing given about the firstwemake that x   Second 2x The second is double the first,   Third x−40 The third is 40 less than the first   F +S +T =180 All three angles add to 180   (x)+(2x)+(x−40)=180 Replace F , S, and T with the labeled values.   x+2x+x−40=180 Here the parenthesis are not needed.   4x−40=180 55ombine like terms, x+2x+x   +40 +40 Add 40 to both sides   4x=220 The variable ismultiplied by 4   4 4 Divide both sides by 4   x=55 Our solution for x   First 55 Replace xwith 55 in the original list of angles   Second 2(55)=110 Our angles are 55, 110, and 15   Third (55)−40=15   correct answer 55
Answer: C
If six persons sit in a row, then the probability that three particular persons are always together is
Choose the correct answer:
A) 1/5
B) 1/8
C) 1/5
D) 1/3
E) 1/1

Solution: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5.Answer: 1/5
Answer: C
In how many ways the letters of the word MOUSE be arranged?	Choose the correct answer
A) 140	B) 150	C) 160	D) 120	E) 170

Solution: Total ways of arranging the letters = 5! = 120 ways.   120)
Answer: D
find the number, difference between number and its 3/5 is 58.  Select.
A) 140	B) 143	C) 144	D) 145	E) 146

Solution: Explanation:   Let the number = x,   Then, x-(3/5)x = 58,   => (2/5)x = 58 => 2x = 58*5,   => x = 145   Answer: Option 145
Answer: D
Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 9 hours and 16 hours after they passed each other the ratio of the speeds of the two trains was  Select
A) 2:1	B) 3:2	C) 4:3	D) 5:4	E) 1:2

Solution: Explanation:   Note : If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (b : a)   Therefore, Ratio of the speeds of two trains = = 4 : 3. Answer: 4:3
Answer: C
Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 50 kmph. For how many minutes does the bus stop per hour? Choose the most appropriate option
A) 10 min B) 15 min C) 12 min D) 8 min E) 16 min

Solution: Due to stoppages, it covers 10 km less.   Time taken to cover 10 km = (10/60 x 60) min = 10 min   10 minnswer : 10 min
Answer: A
The sum of the first 70 positive even integers is 4,970. What is the sum of the first 70 odd integers?
Pick one:
A) 4500 B) 4600 C) 4300 D) 4900 E) 5000

Solution: Sum of first n even numbers = n(n+1) =4970   Sum of first n odd numbers = n^2 = 70*70= 
70*70 = 4_900
4900 (here n=70)   Answer : 4900
Answer: D
A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 11:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?  Answers
A) 34  B) 38  C) 36  D) 40  E) 42

Solution: at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 11 strikes, there would be 10 intervals.   According to the question, the time spent in the strike and the interval is same.   At 6'o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs.   At 11'o clock, the 11 strikes and 10 intervals will take 2*(11+10)= 
2*(11+10) = 42
42 secs   42
Answer: E
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?  Choose the correct choice from the following options:  A) 10080  B) 4989600  C) 120960  D) 250035  E) None of these

Solution: In the word 'MATHEMATICS' we treat the vowels AEAI as one letter.   Thus, we have MTHMTCS (AEAI).   Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.   Number of ways of arranging these letters = 8!/(2!)(2!) = 10080.   Now, AEAI has 4 Letters in which A occurs 2 times and the rest are different.   Number of ways of arranging these letters = 4!/2! = 12.   ∴ Required number of words = (10080 * 12)= 
(10080 * 12) = 120_960
120960.   Answer is 120960
Answer: C
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/6 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?	Pick:  A) 3/10  B) 2/5  C) 1/2  D) 2/3  E) 6/5

Solution: Say, the tree grows by x feet every year.   Then, 4 + 6x = (1+1/6)(4+4x)   or, x = 1/2   Answer 1/2
Answer: C
Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $620 (before payroll deductions)?
Choose the correct choice
A) 670	B) 710	C) 750	D) 790	E) 830

Solution: total pay = 40*$12.50 + $0.16*x = 620   x = 120 / 0.16= 
120 / 0.16 = 750
750   The answer is 750.
Answer: C
The three competitors in a race have to be randomly chosen from a group of four men and five women. How many different such trios contain at least one woman?	Select
A) 50 B) 60 C) 70 D) 80 E) 90

Solution: The total number of ways to choose three runners 9C3 = 84   The number of trios with only males is 4C3 = 4   The number of trios which include at least one woman is 80.   The answer is 80.
Answer: D
Find the face value of 5 in 5432100  Choices:
A) 50	B) 5	C) 50000	D) 500000	E) 5000000

Solution: Face value is the value of digit itself   face value of 5 = 5   Answer : 5
Answer: B
An analyst will recommend a combination of 2 industrial stocks, 3 transportation stocks, and 3 utility stocks. If the analyst can choose from 6 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 9 stocks are possible?	Choose the correct choice:
A) 12 B) 19 C) 60 D) 180 E) 720

Solution: 6C2 * 3C3 * 4C3 = 15*1*4= 
15*1*4 = 60
60.   Answer: 60
Answer: C
In a certain encryption pattern, HARD is coded as 1357 and SOFT is coded as 2468, What will 21448 stand for?  Choose the correct option
A) SHAFT B) SHORT C) SHOOT D) SHART E) SHAOT

Solution: on the behlaf of order like   h =1   a=3   r=5 and so on.   so 21448 is SHOOT   ANSWER:SHOOT
Answer: C
if 5x*x+14*x+k=0 having two reciprocal roots find the value of k.  Choose the correct option
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: Product of reciprocal roots =1   Product of roots of quadratic eqn ax^2+bx+c = 0 is c/a.   Hence k/5 =1   k=5   ANSW5R:5
Answer: E
A palindrome is a word or a number that reads the same forward and backward. For example, 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits 1, 2, 3, and 4, how many palindromes are possible? Choose the correct choice from the following.
A) 32 B) 64 C) 96 D) 128 E) 256

Solution: There are 4 choices for each of the first three digits.   The number of possible palindromes is 4^3=64.   The answer is 64.
Answer: B
Three pipes of same capacity can fill a tank in 8 hours. If there are only two pipes of same capacity, the tank can be filled in.	Select the correct option
A) 17
B) 13
C) 15
D) 16
E) 12

Solution: he part of the tank filled by three pipes in one hour = 1/8   => The part of the tank filled by two pipes in 1 hour = 2/3 * 1/8 = 1/12.   The tank can be filled in 12 hours.   ANSW12R 12
Answer: E
f the LCM of two integers a, b (where b> a and a>1) is a*b, then which of the following can not be true? Choose the correct choice from the following
A) Both a and b can be Prime Numbers. B) Both a and b can be consecutive integers. C) All Prime factors of a must be Prime factors of b. D) a and b do not share any Prime factors. E) a and b do not have a common factor

Solution: Say a = 2; b = 3; only option All Prime factors of a must be Prime factors of b. contradicts   All Prime factors of a must be Prime factors of b   Answer = All Prime factors of a must be Prime factors of b.
Answer: C
A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? Choose the correct option.
A) 1350 B) 1357 C) 1328 D) 1329 E) 1829

Solution: 1350rea = (l + b +2d) 2d   = (75 + 55 +2.5 * 2) 2*2.5 => 675   675 * 2 = Rs.1350   1350nswer:1350
Answer: A
A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 8 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled? Choices
A) 2.9 hrs	B) 8.9 hrs	C) 2.9 hrs	D) 7.2 hrs	E) 8 hrs

Solution: Net part filled in 1 hour = (1/4 - 1/8)   = 1/8   The cistern will be filled in 8 hrs i.e., 8 hrs.   Answer:8 hrs
Answer: E
Which of the following numbers doesn't belong to the group?
Choose the correct choice:
A) 14
B) 16
C) 20
D) 28
E) 36

Solution: All of the numbers are multiples of 2. But only one is not a multiple of 4: 14.   14nswer: 14
Answer: A
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 10,290,000, how many red beads were removed?  Choose the correct option.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: 10,290,000   = 2^4 * 5^4 * 1029   = 2^4 * 3 * 5^4 * 343   = 2^4 * 3 * 5^4 * 7^3   The answer is 3.
Answer: B
By selling an article at Rs.700, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?	Pick one:
A) s.600	B) s.480	C) s.500	D) s.450	E) s.420

Solution: SP = 700   Profit = 25%   CP = (SP)*[100/(100+P)]   = 700 * [100/125]   = 560   Loss 700 *  100/125= 
700 *  100/125 = 560
560   Loss= 25% = 25% of 560 = Rs.140   SP = CP - Loss = 560 - 140 = Rs.420   ANSWs.420R:s.420
Answer: E
If the area of circle is 706 sq cm then its circumference?	Select the correct option:
A) 21  B) 88  C) 66  D) 94  E) 90

Solution: 22/7 r2 = 706 => r = 15   2 * 22/7 * 15 = 94   Answer: 94
Answer: D
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 54 seconds. What is the length of each train (in meters)?
Options:  A) 45  B) 55  C) 65  D) 75  E) 85

Solution: The relative speed = 46 - 36= 
46 - 36 = 10
10 km/hr= 10 * 5/18 = 25/9 m/s   In 54 seconds, the relative difference in distance traveled is  54 * 25/9= 
 54 * 25/9 = 150
150 meters   This distance is twice the length of each train.   The length of each train is  150/2= 
 150/2 = 75
75 meters   The answer is 75.
Answer: D
Which of the following fractions is greater than 3/4 and less than 5/6?
1. 3/4 2. 5/6 3. 1/2 4. 2/3 5. 4/5 6. 9/10	Choose the correct answer: A) 4/5 B) 1/2 C) 9/10 D) 5/6 E) 2/3

Solution: 3/4= 
3/4 = 3/4 = around 0.75
0.75, 5/6= 0.833, 1/2= 0.5, 2/3= 0.66, 4/5= 0.8, 9/10= 0.9.   Clearly, 0.8 lies between 0.75 and 0.833.   Therefore, 4/5 lies between 3/4 and 5/6.   4/5nswer is 4/5.
Answer: A
Find the sum of prime numbers lying between 58 and 72?  Choose the correct choice from the following answers: A) 198 B) 258 C) 252 D) 272 E) None

Solution: Solution   Required sum	= 59 + 61 + 67 + 71)   = 258.   Answer 258
Answer: B
If a and b are different positive integers and a + b = ab(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b	Choose the correct choice from the following options:
A) I only	B) II only	C) III only	D) I and II	E) I and III

Solution: Number picking might not be the best way to solve MUST BE TRUE questions.   The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).   As forCOULD BE TRUEquestions:   The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.   I only
Answer: A
A car travels uphill at 30 km/hr and downhill at 50 km/hr. It goes 100 km uphill and 50 km downhill. Find the average speed of the car? Pick one
A) 32kmph B) 33kmph C) 34kmph D) 35kmph E) 36kmph

Solution: avg speed=total distance/total time.   total distance traveled=100+50= 
100+50 = 150
150km;   time taken for uphill journey=100/30=10/3;   time taken for down hill journey=50/50=5/5;   avg speed=150/(10/3+5/5)=35kmph   ANSWER:35kmph
Answer: D
A circle passes through two adjacent vertices of a square and is tangent to one side of the
square. If the side length of the square is 2, what is the radius of the circle? Choose the correct choice from the following.
A) 3/2	B) 4 /3	C) 5 /4	D) 6 /5	E) None of these

Solution: Let A and B be the vertices through which the circle passes. LetM be the midpoint   of the line segment AB. The center C of the circle is on the line joining M to the midpoint of   the opposite side, which is also on the circle (see diagram below). Let r be the radius of the   circle. The length of the line segment joiningM to C is r-(2r-2) = 2-r as shown below.   Then 12+(2-r)2 = r2 by the Pythagorean Theorem. This gives 1+4-4r+r2 = r2, which   simplifies to 5- r = 0, so r = 5/4   correct answer 5 /4
Answer: C
n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 1800, then what is the smallest possible value of n?  Choose one:
A) 8 B) 10 C) 12 D) 15 E) 18

Solution: 1800=2^3*3^2*5^2   5^2 means that n must be at least 10. That is, We need 5 and 10.   The answer is 10.
Answer: B
One hour after Yolanda started walking from X to Y, a distance of 80 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 8 miles per hour and Bobâs was 9 miles per hour, how many miles had Bob walked when they met?
Select the correct option.
A) 38.07 B) 40 C) 42 D) 39 E) 40.07

Solution: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 8(t + 1) miles. These distances must sum to 80 miles, so 9t + 8(t + 1) = 80, which may be solved for t as follows   9t + 8(t + 1) = 80   9t + 8t + 8 = 80   17t = 72   T = 4.23 (hours)   Therefore, Bob had walked 9t = 9(4.23) = 38.07 miles when they met. The best answer is 38.07.
Answer: A
Timothy leaves home for school, riding his bicycle at a rate of 9 miles per hour. Fifteen minutes after he leaves, his mother sees Timothy’s math homework lying on his bed and immediately leaves home to bring it to him. If his mother drives at 33 miles per hour, how far (in terms of miles) must she drive before she reaches Timothy?
I think is a 700 level problem but I tag it as 600/700, let me know. Either way I hope in an explanationThanks
Choose the correct choice from the following options:  A) 1/3  B) 3  C) 27/8  D) 9  E) 12

Solution: In 15 mins, Timothy travels=9/4 miles.   Now, let his mother takes x hours to reach him, traveling at 31mph.   So, 33x=9x+9/4   x=3/32 hrs.   Thus, the distance traveled by his mother to reach= 36*3/32=27/8 miles. Ans 27/8
Answer: C
There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?	Choose the correct choice from the following answers:
A) 20  B) 30  C) 50  D) 60 peacocks  E) 80

Solution: Explanation:   Let x and y be the number of deer and peacocks in the zoo respectively. Then,   x + y = 80 ...(i) and   4x + 2y = 200 or 2x + y = 100 ...(ii)   Solving (i) and (ii), we get) x = 20, y = 60.   Answer: 60 peacocks
Answer: D
What is the two-digit number? I. Sum of the digits is 7. II. Difference between the number and the number obtained by interchanging the digits is 9. III. Digit in the ten's place is bigger than the digit in the unit's place by 1.
Choose the correct option
A) I and II
B) II and III
C) I and III
D) I and II as well as I and III
E) All

Solution: Explanation:   Let the tens and units digit be x and y respectively.   I. x + y = 7.   II. (10x + y) - (10y + x) = 9 x - y = 1.   III. x - y = 1.   Thus, I and II as well as I and III give the answer.   Correct answer is (I and II as well as I and III).
Answer: D
Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 3000 Km?	Select the correct option:
A) 100. B) 25. C) 30. D) 150. E) 50.

Solution: Total distance= 150.istance travelled by A +150.istance travelled by car B   150.istance= speed*time   150.istance of A= 3x * 6   150.istance of B= x*2   (3x * 6) + (x*2) = 3000   x= 150 KM/hr   150. is the answer
Answer: D
Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?  Choose the correct answer:
A) 1/4	B) 3/4	C) 4/7	D) 4/11	E) 5/7

Solution: Total number of cases = 6*6= 
6*6 = 36
36   Favourable cases= [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27   So Probability = 27/36 = 3/4   3/4)
Answer: B
55th word of SHUVANK in dictionary??
Choose the correct choice from the following answers.
A) AHSNKUV B) AHNKSVU C) AHNKUSV D) AHNKUVS E) AHNKUVV

Solution: First of all write letters in the alphabetical order : A,H,K,N,S,U,V   Then we fix the in order AHK_ _ _ _=> we get 4! means 24 words.   After Next letter in alphabetical order is AHN_ _ _ _=> we get 4! means 24 words   Now we get total 48 words.. Then   In order to Next word is AHSK_ _ _ => Filling this we can fill in 3! Ways means 6.   Now we get total 54 words then next Word is AHSNKUVHSNKUV   AHSNKUVNSWER:AHSNKUV
Answer: A
If the price of a book is first decreased by 25% and then increased by 20%, then the decrease in the price will be? Choose the correct choice from the following options:
A) 20%
B) 10%
C) 25%
D) 18%
E) 30%

Solution: Let the original price be $100   New final price = 120% of (75% of $100)   = 120/100 * 75/100 *100= 
120/100 * 75/100 *100 = 90
$90   Decrease is 10%   Answer is 10%
Answer: B
A person covers a distance in 21 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.  Choose the correct choice
A) 18 m/s
B) 4 m/s
C) 14 m/s
D) 10 m/s
E) 5 m/s

Solution: Explanation:   T = 21 m   Spees = 12 kmph   = 12 x 5/18 = 10/3 m/s   Let new speed be "x"   21 x (10/3) = 5x   x = 14 m/s   Answer: Option 14 m/s
Answer: C
Barbara has 10 shirts and 8 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?	Choose the correct choice:
A) 41  B) 66  C) 36  D) 70  E) 74

Solution: Total no of combinations available is= 10 shirts X 8 pants = 80   Eliminate the 2shirts X 3 pants combo = 6 which gives.......>> 80-6= 
80-6 = 74
74   ANSWER: 70
Answer: D
A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 960gm. for a kg.His gain is …%.
Choices.
A) 4.16%
B) 5.36%
C) 4.26%
D) 6.26%
E) 7.26%

Solution: His percentage gain is 100*40/960 as he is gaining 40 units for his purchase of 960 units.   so 4.16%.   4.16%NSWER:4.16%
Answer: A
The average age of a group of persons going for picnic is 16 years. Twelve new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is  Choose the correct answer:  A) 5  B) 10  C) 12  D) 40  E) 50

Solution: Solution   Let the initial number of persons be x. Then   16x + 12 x 15 = 15.5(x+20)   = 0.5x = 6   x = 12.   Answer 12
Answer: C
What percent is 36 paisa's of 12 rupees? Choices
A) 2 %
B) 3 %
C) 4 %
D) 5 %
E) 6 %

Solution: 12 Rupees = 1200 paisa's   36/1200 × 100 = 3/12   12/3 = 3 %   3 %
Answer: B
9C2 + 9C3 +10C4=? Answers:  A) 300  B) 330  C) 360  D) 390  E) 410

Solution: 36+84+210= 
36+84+210 = 330
330   ANSWER:330
Answer: B
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?	Choose the correct choice from the following answers:
A) 10
B) 15
C) 17
D) 24
E) 26

Solution: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways   4: Or 4p = — 4:- 4X3X2X1- 24 ways   24
Answer: D
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?  Choose the correct option:  A) 60.5  B) 35.5  C) 25.5  D) 62  E) 62.5

Solution: Let the capacity of 1 bucket = x.   Then, the capacity of tank = 25x.   New capacity of bucket =(2/5)x   Required number of buckets =	25x/(2x/5)   = 25x * 5/2x   =125/2= 
125/2 = 125/2 = around 62.5
62.5   Answer is 62.5.
Answer: E
In 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each, how many pumps will raise 2030 tons of water in 12 days of 11 hrs each?
Choose the correct option
A) 12	B) 15	C) 18	D) 21	E) 22

Solution: Explanation:   pumps work time   12 1218 99   x 2030 132   => 1218/(912*99) = 2020/(x × 132)   => x = 15 pumps   Answer: Option 15
Answer: B
In the City 45% of the population lived in the East at the Beginning of the Year and the rest of the City lived in the West. During the Same Year, the population of City grew by 5.0%. If the population in the West grew by 2.5%, by how much did the population grow in the remaining side?
Choose the correct choice from the following answers.
A) 5.9%
B) 2.5%
C) 5.0%
D) 8.2%
E) 7.5%

Solution: Ratio of population in City = 7.5%ast:West :: 45%:45% = 1:1   Mean growth = 5%   West Growth: 2.5%   7.5%ast Growth = ??   7.5%ast-------------Average--------------West   ? __(1n)_____5.0%_____(1n)_____2.5%   Since:   2.5+1n=5   n=2.5   Therefore:   7.5%ast=5+1n   7.5%ast=5+2.5   That is the population grew in 7.5%ast Side of the town is 7.5%
Answer: E