MU-NLPC/Calc-aqua_rat huggingface dataset:
A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.52 if each film contains 36 photos?
Choose the correct choice from the following answers: A) 4 films and 10 photos B) 5 films and 6 photos C) 5 films and 14 photos D) 6 films and 4 photos E) 6 films and 28 photos

Solution: 1st photo = 0.55   Subsequent = 0.55*0.6= 
0.55*0.6 = 0.33
0.33   Price of 1 full film=0.55+0.33*35= 
0.55+0.33*35 = 12.1
12.1   Price of 4 full film= 12.1*4= 
12.1*4 = 48.4
48.4   52.52-48.4=4.18   4.18=0.55+0.33x   x=11   52.58--->4 full films and  1+11= 
 1+11 = 12
12 photos   4 films and 10 photosnswer: 4 films and 10 photos
Answer: A
In a simultaneous throw of a pair of dice, find the probability of getting a total more than 7	Choose the most appropriate option
A) 1/2 B) 7/12 C) 5/13 D) 5/12 E) 6/17

Solution: Total number of cases = 6*6= 
6*6 = 36
36   Favourable cases= [(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,4),(5,6),(5,3),(5,5),(6,2),(6,3),(6,4),(6,5),(6,6)] = 15   So Probability = 15/36 = 5/12   Answer is 5/12
Answer: D
A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Choose the correct option:
A) Rs. 1090	B) Rs. 1160	C) Rs. 1190	D) Rs. 1202	E) Rs. 1204

Solution: since,c.p=1400   loss%=(c.p-s.p)/c.p*100   15=(1400-s.p)/1400*100   so,after solving answer=1190.   ANSWER:Rs. 1190
Answer: C
total dinning bill of 8 people was $139.00 and 10% tip divided the bill evenly ?what is the bill amount each person shared .  Choose the correct answer.
A) 11.84 B) 12.84 C) 23.84 D) 19.11 E) 10.12

Solution: dinner bill of 8 person = 139 + 10% tip   so,   10% of 139 = (139*10)/100= 
(139*10)/100 = 139/10 = around 13.9
13.9   So, the actual total amount= 139+13.9= 
139+13.9 = 152.9
$ 152.9   so per head bill= 152.9/8 = $ 19.11   ANSWER:19.11
Answer: D
The number of arrangements that can be made with the letters of the word JOHNNIE so that the vowels occupy the even places? Options:  A) A)122  B) B)134  C) C)144  D) D)156  E) E)176

Solution: Explanation:   The word JOHNNIE has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 6= 
 24 * 6 = 144
144.   144
Answer: C
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 8?	Choose one:	A) 1	B) 3	C) 5	D) 4	E) 6

Solution: You should consider the worst case scenario: if you pick numbers 0, 1, 2,3 and 4 then no two numbers out of these 5 add up to 8.   Now, the next, 6th number whatever it'll be (5,6,7,8 or 9) will guarantee that two number WILL add up to 8. So, 6 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 8   Answer: 6
Answer: E
In what proportion must wheat at Rs. 15 per kg. be mixed with wheat at Rs. 18 per kg. So that the mixture will be worth Rs. 17 per kg. ? Choose the correct choice from the following answers:
A) 1 : 9 B) 1 : 3 C) 1 : 2 D) 1 : 1 E) 1 : 8

Solution: Explanation:   Wheat/Rs. 15 per kg.   Wheat/Rs. 18 per kg.   For the mixture to be worth Rs. 17 per kg. The ratio should be:   (18 – 17) : (17 – 15)   1 : 2   ANSWER:1 : 2
Answer: C
What is the remainder of R=3^19 when divided by 10? Choose the correct choice
A) 0
B) 1
C) 5
D) 7
E) 9

Solution: I looked for patterns:   ^2 - units digit 9   ^3 - units digit 7   ^4 - units digit 1   ^5 - units digit 3   hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9   and we can then see:   ^16 - units digit 1, or   ^18 - units digit 9   and ^19 - units digit 7   therefore, R=when divided by 10, the remainder must be 7.7
Answer: D
In Set T, the average (arithmetic mean) equals the median R. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above. Choose the correct choice from the following choices:
A) I only	B) I and II	C) II and III	D) I, II, and III	E) IV only

Solution: This is a very good 'trap question'.   Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR   Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3   If you think that only in 'consecutive integers' the average is equal to the median R you might fall for 'D'.   Ans: IV only
Answer: E
How many cubes of 3cm edge can be cut out of a cube of 18cm edge	Select the correct option
A) 36 B) 232 C) 216 D) 484 E) None of these

Solution: Explanation:   number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216   Answer: 216
Answer: C
20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 10:40 in the morning? Choose the correct choice:	A) 32.	B) 36.	C) 42.	D) 46.	E) 60.

Solution: @ 6:30 - 2   @ 7 - 4+7 =11   @ 7:30 - 2   @ 8 - 12   @ 8:30 - 2   @ 9 - 13   @ 9:30 - 2   @ 10 - 14   @10:30 - 2   totals to 60.=60
Answer: E
Currently guavas cost 60 cents/pound. Due to a disease affecting the guava trees it is expected that next month apples will cost 250% more than they do currently. How much are guavas expected to cost next month?  Choose the correct option
A) 110 cents /pound
B) 150 cents /pound
C) 180 cents /pound
D) 200 cents /pound
E) 210 cents /pound

Solution: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).   In this case, (new cost) = 60 cents/pound + (250/100)(60 cents/pound)   = 60 cents/pound + 150 cents/pound   = 210 cents /pound   Answer : 210 cents /pound
Answer: E
A division of a company consists of four men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?  Answers
A) 2/9	B) 3/11	C) 4/15	D) 5/18	E) 6/25

Solution: Total number of ways to select 2 members = 9C2 = 36   Total number of ways to select 2 females = 5C2 = 10   P(two females) = 10/36 = 5/18   The answer is 5/18.
Answer: D
8+8  Choose one:
A) 5
B) 17
C) 16
D) 23
E) 19

Solution: 16
Answer: C
Which of the following is/are terminating decimal(s)?
I 299/(32^123)
II 189/(49^99)
III 127/(25^37)
Choices.
A) I only	B) I and III	C) II and III	D) II only	E) I, II, III

Solution: The fraction will have terminating decimal if and only if the denominator of the fraction is of the form (2^n)(5^m).   If you look at the denominators:   1) (32^123) => (2^(5*123))(5^0) => Terminating Decimal   2) (49^99) => Can't be expressed as (2^n)(5^m) => Non terminating Decimal   3) (25^37) => (2^0)(5^(2*37)) => Terminating Decimal   Hence 1 and 3 are terminating decimals => Choice [I and III]
Answer: B
Which of the following can be a perimeter w of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100  Choose the correct choice from the following choices:
A) I only
B) III only
C) II and III only
D) I, II, and III
E) Not I, II, or III

Solution: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   But how do you use the above property to solve the question?   The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: w>0.   Answer is I, II, and III.
Answer: D
Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?  Choose the correct choice from the following
A) 22	B) 30	C) 48	D) 99	E) 12

Solution: Relative speed = 90 + 30= 
90 + 30 = 120
120 km/hr.   120 * 5/18= 100/3 m/sec.   Distance covered = 500 + 500= 
500 + 500 = 1_000
1000 m.   Required time= 1000 * 3/100= 
1000 * 3/100 = 30
30 sec.   Answer: 30
Answer: B
5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is? Choose the correct option
A) 6:8
B) 6:4
C) 6:2
D) 6:5
E) 6:2

Solution: 5M + 12B ----- 4 days   7M + 6B ------- 5 days   20M + 48B = 35M + 30B   18B = 15M => 5M = 6B   M: B = 6:5   Answer: 6:5
Answer: D
What percent of a day is seven hours?  Choose the correct choice from the following answers:  A) 20.83%  B) 16x1/2%  C) 29.16%  D) 22x1/2%  E) None of these

Solution: Explanation :   Required percentage = (7/24100)%   = 29.16%.   Answer : 29.16%
Answer: C
An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 10 minutes, what part of the cistern will be emptied?	Choose the correct choice from the following:
A) 4/9  B) 4/3  C) 4/2  D) 5/9  E) 4/1

Solution: 2/3 ---- 12   ? ----- 10 ==> 5/9   Answer: 5/9
Answer: D
A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?	Answers:  A) 299  B) 375  C) 27878  D) 288  E) 212

Solution: CP1 = 100 SP1 = 120   CP2 = 80 SP2 = 80 * (125/100)= 
80 * (125/100) = 100
100   20 ----- 100   75 ----- ?=> 375.Answer: 375
Answer: B
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 9/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
Choices
A) 7/17	B) 14/31	C) 7/15	D) 17/35	E) 9/19

Solution: # of basic stereos was 2/3 of total and # of deluxe stereos was 1/3 of total, let's assume total=15, then Basic=10 and Deluxe=5.   Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 9/5 units. Total time for Basic would be  10*1= 
 10*1 = 10
10 and total time for Deluxe would be 5*9/5= 
5*9/5 = 9
9 --> total time for both of them would be 10+9= 
10+9 = 19
19 --> deluxe/total=9/19.   Answer: 9/19.
Answer: E
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
Answers
A) Rs.19,828.89 B) Rs.19,828.80 C) Rs.19,828.92 D) Rs.19,822.00 E) Rs.19,828.24

Solution: Let the sum be Rs.P   P{ [ 1 + 8/100]2 - 1 } = 2828.80   P(8/100)(2 + 8/100) = 2828.80 [a2 - b2   = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08= 
1360/0.08 = 17_000
17000 Principal + Interest= Rs. 19828.80   Answer:Rs.19,828.80
Answer: B
if 20% of a number is added to second no.,then it increase by 50%.calculate the ratio of these no.
Choose the correct choice: A) 3:2 B) 2:3 C) 5:2 D) can't be calculated E) none of these

Solution: Answer:	let no. be A and B.   (20%of A)+B=150% of B   A/5=3B/2-B=B/2;A/B=5/2,   A:B=5:2   answer 5:2
Answer: C
A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?	Choose the correct option.
A) 3:2  B) 12:5  C) 18:10  D) 18:14  E) 14:11

Solution: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.   3:2 : B   8000*18 : (8000*6) + (4000*12)   14400 : 96000   3:2:B = 3:2   3:2nswer: 3:2
Answer: A
What is his percentage profit made by Nancy if she purchased 15 dozen pencils at Rs. 20 per dozen. He sold 8 dozens at 12% profit and the remaining 7 dozens with 15% profit?  Choose the correct choice from the following answers
A) 10.08%  B) 18.08%  C) 15.08%  D) 12.08%  E) 16.08%

Solution: Explanation :   C.P of 15 dozen = Rs.(20 x 15) = Rs.300   C.P of 8 dozen = Rs. (20 x8) = Rs. 160.   C.P of 7 dozen =Rs. (20 x7) = Rs. 140   profit on 8 dozen at 12% = 12/100*160= 
12/100*160 = 96/5 = around 19.2
19.2   profit on 7 remaining dozen at 15%= 15/100*140= 
15/100*140 = 21
21   total profit= 19.2 + 21= 
19.2 + 21 = 40.2
40.2   % profit= ?/100*250 = 40.2   = 16.08%   Answer : 16.08%
Answer: E
Two employees M and N are paid a total of $616 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
Choose the correct choice from the following answers:
A) $270
B) $280
C) $290
D) $300
E) $310

Solution: 1.2N + N = 616   2.2N = 616   N = 280   The answer is $280.
Answer: B
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?	Choose the correct choice from the following answers:
A) 338
B) 279
C) 125
D) 776
E) 988

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 1/2 = Rs.125   Answer:125
Answer: C
If (4x + 7)(x + 2) = 8x^2 + x, what is a possible value of x?
Answers.
A) 12 B) -7 C) 7 D) -1 E) -14

Solution: Rearranging the given expression:   (4x + 7)(x + 2) = 8x^2 + x   i.e. 8x^2 + 15x + 14 = 8x^2 + x   i.e. 14x = -14   i.e. x = -14/14 = -1   Answer: Option -1   Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Answer: D
If a and b are positive integers, and a=3b+12, the greatest common divisor of a and b CANNOT be	Pick one:
A) 1
B) 3
C) 2
D) 5
E) 4

Solution: If b is 1, 2, 3, or 4, then GCD of a and b is 1, 2, 3, and 4 respectively. So, by POE the answer must be D.   Still: if b is a multiple of 5, then a is 12 greater than a multiple of 5, so not a multiple of 5, so both of them cannot be divisive by 5.   Answer: 5.
Answer: D
One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,00,000 as total savings, how much has he saved in Public Provident Fund ? Choose one:
A) Rs. 40,000
B) Rs. 50,000
C) Rs. 60,000
D) Rs. 90,000
E) None

Solution: EXPLANATION   Let savings in N.S.C and P.P.F. be Rs. x and Rs. (100000 – x) respectively. Then,   1/3x=1/2(100000-x)   => x/3 + x/2 = 50000   => 5x/6 = 50000   => x= 50000 x 6 /5= 60000   Savings in Public Provident Fund = Rs. (100000 – 60000) = Rs. 40000   Rs. 40,000nswer Rs. 40,000
Answer: A
John and Amanda stand at opposite ends of a straight road and start running towards each other at the same moment. Their rates are randomly selected in advance so that John runs at a constant rate of 2, 3, 4, 5, or 6 miles per hour and Amanda runs at a constant rate of 3, 4, 5, 6, or 7 miles per hour. What is the probability that John has traveled farther than Amanda by the time they meet? Choose the correct option:
A) 1/3 B) 2/5 C) 3/5 D) 4/25 E) 6/25

Solution: John will run farther if he runs at 6 mph and Amanda runs at 5 mph, 4 mph, or 3 mph.   In this case, P(John runs farther) = 1/5 * 3/5 = 3/25   John will run farther if he runs at 5 mph and Amanda runs at 4 mph or 3 mph.   In this case, P(John runs farther) = 1/5 * 2/5 = 2/25   John will run farther if he runs at 4 mph and Amanda runs at 3 mph.   In this case, P(John runs farther) = 1/5 * 1/5 = 1/25   Overall, P(John runs farther) = 3/25 + 2/25 + 1/25 = 6/25   The answer is 6/25.
Answer: E
Calculate the sum of first 19 natural numbers.	Choose the correct choice.
A) 190  B) 120  C) 150  D) 199  E) 110

Solution: Solution   We know that(1+2+3+.....+19)	= n(n+1)/2   Therefore (1+2+3+....+19)	=(19×20 / 2)   = 190.   190nswer 190
Answer: A
The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 60 per cent. The two reductions together are equal to a single reduction of
Choose the correct choice from the following options:  A) 45%  B) 70%  C) 35%  D) 32.5%  E) 30%

Solution: Price = p   initially price reduced by 25% which means new price is 3/4P   Now on this new price further 60percent is reduced which means the new price is merely 40percent of 3/4P   ==> (3/4)x(2/5)P = 6/20P is the new price after both deduction which is 30percent of the original value P. This implies this entire series of deduction is worth having discounted 70% of P. So answer is 70% = 70%
Answer: B
A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $96, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)	Choose the correct choice from the following options.
A) 81 B) 84 C) 85 D) 88 E) 90

Solution: LET C= CHAIR ; T =TA84LE   2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T   IC +1T =96 OR 1/7T + 1T =96 THEREFORE T= 96*7/8= 
96*7/8 = 84
84   84
Answer: B
The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 900 feet squared, what is the difference between the length and the width of the roof? Pick one
A) 38.	B) 40.	C) 42.	D) 44.	E) 45.

Solution: Let the width= x   x*4x=900   x^2= 225   x= 15   Length= 4*15= 
4*15 = 60
60   difference= 60-15= 
60-15 = 45
45   45. is the answer
Answer: E
5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job?  Pick: A) 8 B) 9 C) 6 D) 2 E) 1

Solution: Explanation:   Solution: It is given that 5/8th of the work is completed in 10 days.   => Remaining work = 3/8th of total   Applying unitary method:   Total work will be completed in  10 * 8 / 5= 
 10 * 8 / 5 = 16
> It takes 16 days to complete total work=> Hence, remaining work days = 16 - 10= 
16 - 10 = 6
6 days   ANSWER:6
Answer: C
Which is the least number that must be subtracted from 1828 so that the remainder when divided by 8, 12, 16 is 4? Answers
A) 0	B) 4	C) 8	D) 6	E) 2

Solution: First we need to figure out what numbers are exactly divisible by 8,12,16. This will be the set {LCM,LCMx2,LCMx3,...}   LCM(8,12,16) = 48 = 48   number is to be subtracted is 0   The largest such number less than or equal to 1828 is 48*38+4   0
Answer: A
Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5y + 3 = 0? Choose the most appropriate option:
A) + 5y - 2 = 0	B) + 5y + 2 = 0	C) - 5y + 2 = 0	D) - 5y - 2 = 0	E) of these

Solution: The quadratic equation whose roots are reciprocal of 2x2 + 5y + 3 = 0 can be obtained by replacing y by 1/y.   Hence, 2(1/y)2 + 5(1/y) + 3 = 0   => 3x2 + 5y + 2 = 0   ANSWER:+ 5y + 2 = 0
Answer: B
Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 60. No two digits of h are identical. How many different numbers are possible values of h?  Select:
A) 20	B) 22	C) 24	D) 30	E) 36

Solution: Answer = 24 = 24   Let number =abcd   Given that a*b*c*d = 60   a,b,c,d can be 1,2,3,10   Number of ways = 4*3*2= 
4*3*2 = 24
24
Answer: C
Average age of total 80 students from three classes, V, VI and VII, is 13 years. Average age of 30 students of class V is 11 1/2 years. If average age of another 30 students of class VI is 12 1/2 years, what is the average aage of rest of 20 students of class VIII ?  Select the correct option: A) 13 1/2 years B) 14 1/2 years C) 15 years D) 16 years E) 5 years

Solution: Explanation :   Sum of ages of 80 students = 80 x 13 = 1040   Sum of ages of 30 students of class V = 30 x 11.5 = 345   Sum of ages of 30 students of class VI = 30 x 12.5 = 375   ∴ Total age of 20 students of class VII = 1040 - 345 - 375= 
1040 - 345 - 375 = 320
320   ∴ Average age= 320/20= 
320/20 = 16
16 years.   Answer : Option 16 years
Answer: D
A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 19 seconds. What is the length of the platform in meters?
Choose one:  A) 220 meters  B) 360 meters  C) 420 meters  D) 600 meters  E) Cannot be determined

Solution: Speed of the train in metres/sec = 72000/3600= 
72000/3600 = 20
20   Distance travelled by train to cross the platform= 30 * 20= 
30 * 20 = 600
600= Length of train + Length of platform   Distance travelled by train to cross the man = 19 * 20= 
19 * 20 = 380
380= Length of train   Length of platform = 600 - 380= 
600 - 380 = 220
220   220 metersnswer: 220 meters
Answer: A
If W is the set of all the integers between 35 and 64, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Options:
A) 18	B) 19	C) 61	D) 31	E) 11

Solution: Official Solution:   Number of multiples of 3   Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 63, the smallest is 36): 63 - 36 = 27   Step 2. Divide by 3: 27 / 3 = 9   Step 3. Add 1: 9 + 1 = 10.   So there are 10 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.   Number of multiples of 2   Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 64, the smallest is 36): 64 - 36 = 28   Step 2. Divide by 2: 28 / 2 = 14   Step 3. Add 1: 14 + 1 = 15.   So there are 15 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.   Add the 10 multiples of 3 and the 15 multiples of 2: 10+15=25.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take   10+15= 
  10+15 = 25
25. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:   Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 60 - 30= 30   Step 2. Divide by 6: 30 / 6 = 5   Step 3. Add 1: 5 + 1 = 6.   So there are 6 multiples of 6 within the range: we counted 6 numbers twice.   Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:   = 10+15 - 6   = 25 - 6= 
25 - 6 = 19
19   Therefore, the final number of multiples of 2, 3 or 6 is 19.   Hence, this is the correct answer. (19)
Answer: B
An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 40 meters. How many times did the ball bounce?  Choose the correct choice from the following:  A) 2  B) 6  C) 7  D) 8  E) 9

Solution: Division of total distance travelled will be 16+16+8   2ns:2
Answer: A
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?	Select the correct option:
A) 3 hr
B) 2 hr
C) 1 hr
D) 4 hr
E) 5 hr

Solution: 600/x - 600/(x + 1/2) = 200   x(2x + 1) = 3 2x2 + x - 3  (2  + 1)= 
 (2  + 1) = 3
3 2x2 + x - 3= 0   (2x + 3)(x - 1) = 0   x = 1 hr.   ANSWER 1 hr
Answer: C
There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?  Choose one:
A) 14  B) 16  C) 21  D) 25  E) 27

Solution: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   Similarly, if 3 of the boxes have green balls, there will be 4 options.   If 4 boxes have green balls, there will be 3 options.   If 5 boxes have green balls, then there will be 2 options.   If all 6 boxes have green balls, then there will be just 1 options.   Total number of options = 6 + 5 + 4 + 3 + 2 + 1= 
6 + 5 + 4 + 3 + 2 + 1 = 21
21   21
Answer: C