MU-NLPC/Calc-aqua_rat huggingface dataset:
A fruit seller had some oranges. He sells 40% oranges and still has 420 oranges. How many oranges he had originally?
Options:
A) 700 B) 300 C) 200 D) 500 E) 250

Solution: sell 40% oranges and 420 oranges remaining   =>60% of oranges = 420   total oranges * 60/100 = 420   total oranges = 420*100/60= 
420*100/60 = 700
700   700NSWER 700
Answer: A
A can do a piece of work in 4 hours. B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it? Choices
A) 10 hr  B) 12 hr  C) 15 hr  D) 13 hr  E) 9 hr

Solution: A's 1 hour work = 1/4   12 hr+C 1 hour work = 1/3   A+C 1 hour work +  1= 
+  1 = 1
1/3   A+C 1 hour work = 1/2   A+12 hr+C 1 hour work  +  1= 
 +  1 = 1
1/2   A+12 hr+C 1 hour work = 1/4 + 1/3 +  1= 
+  1 = 1
1/4 + 1/3= 7/12   12 hr's 1 hour work = 7/12 - 1/2 = 1/12   12 hr alone will take 12 hours to do the work   Answer is 12 hr
Answer: B
x+(1/x) = 2 find x^2 + (1/x^2) Pick:
A) 2  B) 3.25  C) 4.25  D) 5.25  E) 6.25

Solution: squaring on both sides (x+1/x)^2=2^2   x^2+1/X^2=4-2   x^2+1/X^2=2   2NSWER:2
Answer: A
The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 70/kg. how much did a kg of coffee cost in june ?
Options: A) 70 B) 60 C) 80 D) 100 E) 120

Solution: Let the price of tea and coffee be x per kg in June.   Price of tea in July = 1.2x   Price of coffee in July = 0.8x .   In July the price of 1/2 kg (700gm) of tea and 1/2 kg (700gm) of coffee (equal quantities) = 70   1.2x(1/2) + 0.8x(1/2) = 70   => x =70   Thus proved...option 70.
Answer: A
A man's age is 125% of what it was 10 years ago, but 83 1/3%
of what it will be after 10 years. What is his present age?
Choose the correct choice from the following options.
A) 50
B) 70
C) 80
D) 55
E) 40

Solution: 125x/100 = x + 10   x = 40   present age = x + 10 =40+10= 
40+10 = 50
50   50NSWER 50
Answer: A
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 80 inches. Find b.  Choose one.
A) 8 B) 16 C) 24 D) 32 E) 48

Solution: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.   From the second premise, we know that the LCM of 12 (2^2*3) andbis 80 (2^4*5), sob=2^4 or 2^4*5 (16 or 80).   Combining 2 premises shows the answer is 16(16).
Answer: B
For an upcoming charity event, a male vocalist has agreed to sing 3 out of 8 “old songs” and 4 out of 7 “new songs.” How many ways can the singer make his selection? Choose the correct choice from the following answers:
A) 25  B) 50  C) 150  D) 147  E) 600

Solution: =8C6*7C4   =8*7/4*7*6/4   =7*7*3= 
7*7*3 = 147
147   Ans= 147
Answer: D
Kim bought a total of $4.65 worth of postage stamps in four denominations. If she bought an equal number of 10-cent and 25-cent stamps and twice as many 20-cent stamps as 5-cent stamps, what is the least number of 1-cent stamps she could have bought? Choose one:
A) 5
B) 10
C) 75
D) 90
E) 95

Solution: Let:   # of 10 and 25 cents stamps = n   # of 20 cent stamps = 2n   # of 1 cent stamps = m   Therefore:   10n + 25n + 20(2n) + m = 465 cents   75n + m = 465   Forleastnumber of 1 cents stamps, maximize 50n. Hence,   75*5 + m = 465   m = 90 i.e. 90 stamps 1 cents each   Answer: 90
Answer: D
The average earning of a person for the first four days of a week is Rs 18 and for the last four days is Rs 22. If he earns Rs 20 on the fourth day, his average earning for the whole week is?  Options.
A) Rs 18.95
B) Rs 16
C) Rs 20
D) Rs 25.71
E) None of these

Solution: Total earning for the week   = Rs (4 × 18 + 4 × 22 - 20) = Rs 140   Average earning = Rs 140/7= 
140/7 = 20
Rs 20.   ANSWER:Rs 20
Answer: C
For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.25 – 6.25*?	Choose the correct choice from the following choices:
A) 1.5 B) 0.5 C) 6.25 D) 0.25 E) 6.0

Solution: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.25* =6 (the greatest positive even integer less than or equal to 6.25 is 6).   Hence, 6.25 – 6.25* = 6.25 - 6= 
6.25 - 6 = 0.25
0.25   Answer: 0.25.
Answer: D
How many consonants are present between the first and fourth vowel in the sequence of English alphabet ?	Choose the correct choice from the following.
A) 12	B) 13	C) 11	D) 10	E) None of these

Solution: Explanation:   Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z   The first and fourth vowels are A and O respectively. There are 13 letters between A and O; out of which 'E' and 'I' are vowels. Thus, there are 11 consonants between A and O.   ANSWER 11
Answer: C
A, B and C started a partnership business by investing Rs.8000, Rs.4000, Rs.2000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
Pick one:
A) 70000
B) 60000
C) 80000
D) 90000
E) 252000

Solution: A:B:C =8000:4000:2000   =4:2:1   Let total profit =p   Then pÃ—1/7=36000   p=(36000Ã—7)/1=252000   Answer is 252000.
Answer: E
P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 336 is divided among them . What is Q's share?
Choose one
A) 114 B) 128 C) 134 D) 144 E) None of these

Solution: Explanation :   The ratio of their initial investment = 1/2 : 1/3 : 1/4   = 6 : 4: 3   Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively   A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12   = (12+30) : 4*12 : 3*12   =(4+10) : 4*4 : 12   = 14 : 16 : 12   = 7 : 8 : 6   Q's share = 336 * (8/21)= 
336 * (8/21) = 128
128. Answer : Option 128
Answer: B
John and Ingrid pay 30% and 40% tax annually, respectively. If John makes $57000 and Ingrid makes $72000, what is their combined tax rate? Choose the correct choice:
A) 32%  B) 34.4%  C) 35%  D) 35.6%  E) 36.4%

Solution: (1) When 30 and 40 has equal weight or weight = 1/2, the answer would be 35.   (2) When 40 has larger weight than 30, the answer would be in between 35 and 40. Unfortunately, we have 2 answer choices D and E that fit that condition so we need to narrow down our range.   (3) Get 72000/129000 = 24/43. 24/43 is a little above 24/48 = 1/2. Thus, our answer is just a little above 35.   Answer: 35.6%
Answer: D
Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 105 km and comes back to the starting point. The total time taken by him is:	Choose the correct choice from the following answers.
A) 12 hours  B) 24 hours  C) 36 hours  D) 48 hours  E) None

Solution: Sol.   Speed upstream = 7.5 kmph; Speed downstream = 10.5 kmph.   ∴ total time taken = [105/7.5 + 105/10.5= 
105/7.5 + 105/10.5 = 24
24 hours.   Answer 24 hours
Answer: B
The parameter of a square is equal to the perimeter of a rectangle of length 14 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Choose one:	A) 23.56	B) 23.59	C) 23.55	D) 18.86	E) 23.57

Solution: Let the side of the square be a cm.   Parameter of the rectangle = 2(14 + 10) = 48 cm Parameter of the square = 48 cm   i.e. 4a = 48   A = 12   18.86iameter of the semicircle = 12cm   Circimference of the semicircle   = 1/2(âˆ)(12)   = 1/2(22/7)(12) = 264/14 = 18.86 cm to two decimal places   Answer: 18.86
Answer: D
In a lottery, there are 10 prizes and 25 blanks . A lottery is drawn at random .What is the probability of getting a prize? Pick one:
A) 1/10 B) 2/5 C) 2/7 D) 5/7 E) 10/7

Solution: Total number of prizes and blanks= 10+25= 
10+25 = 35
35   no.of prize in a lottery= 10   probability of one lottery is drawn = 10/35= 2/7   Answer is 2/7
Answer: C
There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is? Pick one
A) 90  B) 99  C) 77  D) 66  E) 221

Solution: 200*2= 
200*2 = 400
400   580   -----   180   1----2   ?----180= 90   Answer:77
Answer: C
Find the average of all the numbers between 6 and 34 which are divisible by 5? Choose the correct choice from the following answers:
A) 10  B) 20  C) 25  D) 30  E) 15

Solution: Average = (10+15+20+25+30) 5 = 100/5= 
100/5 = 20
20   Answer is 20
Answer: B
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 K of the work will be done by Adam?  Choose the correct choice:
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   K>( 60/47 *12)/60 =12/47   Answer 12/47
Answer: B
A, B and C can independently complete a piece of work in 8,12 and 6 days respectively. A and B work together for 4 days and leave. How long will C take to finish the remaining work?	Choices.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: A and B work together for 4 days and completed 4*(1/8 +1/12) =5/6 work.   Balance 1/6 work will be completed by C in one day.   1NSWER:1
Answer: A
z is a positive integer and multiple of 2; w = 4^z, what is the remainder when w is divided by 10? Choose the correct answer:
A) 10	B) 6	C) 4	D) 0	E) It Cannot Be Determined

Solution: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:   4/10 is 0 with a remainder of 4   14/10 is 1 with a remainder of 4   5/10 is 0 with a remainder of 5   105/10 is 10 with a remainder of 5   It is also essential to remember that the z is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, z must be a positive even integer.   With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?   The units digit of 4 raised to an integer follows a specific repeating pattern:   4^1 = 4   4^2 = 16   4^3 = 64   4^4 = 256   4^(odd number) --> units digit of 4   4^(even number) --> units digit of 6   There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.   Since z must be an even integer, the units digit of w=4^z will always be 6. Consequently, the remainder when w=4^z is divided by 10 will always be 6.   In case this is too theoretical, consider the following examples:   z=2 --> w=4^z=16 --> w/10 = 1 with a remainder of 6   z=4 --> w=4^z=256 -->w/10 = 25 with a remainder of 6   z=6 --> w=4^z=4096 --> w/10 = 409 with a remainder of 6   z=8 --> w=4^z=65536 --> w/10 = 6553 with a remainder of 6   Answer: 6.
Answer: B
A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 370 m long platform?
Select:
A) 37 min  B) 55 min  C) 47 min  D) 67 min  E) 49 min

Solution: E   49 min   Let the length of the train be x m.   When a train crosses an electric pole, the distance covered is its own length.   So, x = 12 * 36 * 5 /18= 
12 * 36 * 5 /18 = 120
120 m.   Time taken to cross the platform= (120 +370)/ 36 * 5/18 = 49 min.
Answer: E
In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 2009 were what percent of the profits in 2008? Pick one
A) 96%  B) 105%  C) 120%  D) 124.2%  E) 138%

Solution: x = profits   r= revenue   x/r = 0,1   x= 10   r=100   2009:   r=80   x/80 = 0,12 = 12/100   x= 80*12/100= 
80*12/100 = 48/5 = around 9.6
9.6   9.6/10= 
9.6/10 = 0.96
0.96= 96%, 96%nswer 96%
Answer: A
The value of ((x – y)³ + (y - z)³ + (z – x)³)/(15 (x – y) (y – z) (z – x))
is equal to :	Options:
A) 0
B) 1/12
C) 1
D) 1/5
E) 1/3

Solution: Since (x – y) + (y – z) + (z – x) = 0,   so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).   (3 (x – y) (y – z) (z – x))/(15(x – y) (y – z) (z – x)) = 1/5.   ANSWER:1/5
Answer: D
A crate of apples contains 1 bruised apple for every 20 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
Choices:
A) 270  B) 360  C) 480  D) 600  E) 320

Solution: as given 3 out of every 4 bruised apple is not fit to sell   or, 75% of the bruised apples are not fit to sell.   as per the question 12 are not fit to sell   or,   0.75x=12   x=1200/75= 
1200/75 = 16
16   thus total number of bruised apples=16   total number of apples =20*16= 
20*16 = 320
320   Answer: 320
Answer: E
If x = y+3+4.5x and y = x+33, what is the value of x/y ? Choose the correct option
A) -6/5. B) -8/25 C) 1/4. D) 5/6. E) 1.5.

Solution: (1) x = y + 3 + 4.5x   Substitute y for y = x + 33 (Eq. we are given)   x = x + 33 + 3 + 4.5x   Combine like terms   x = 5.5x +36 --> -4.5x = 36 --> x = -8   (2) y = x + 18   Substitute x for x = -8   y = (-8) + 33= 
(-8) + 33 = 25
25   (3) x/y= ?   Substitute x and y we found above   x/y = (-8) / (25) =-8/25   My answer: -8/25
Answer: B
Working alone at its constant rate, machine K took 3 hours to produce 1/6 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?  Choose the correct choice from the following options:
A) 8  B) 12  C) 16  D) 24  E) 30

Solution: Machine K works at a rate of 1/18 of the units per hour.   The rate of K + M together is 5/6 * 1/6 = 5/36 of the units per hour.   The rate of machine M is 5/36 - 1/18 = 1/12.   It would have taken machine M a total time of 12 hours.   The answer is 12.
Answer: B
If y ≠ 3 and 2b/y is a prime integer greater than 2, which of the following must be true?
I. b = y
II. y = 1
III. b and y are prime integers.	Answers.
A) None B) I only C) II only D) III only E) I and II

Solution: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.   So we should try to make the listed statements not true for some b and y (which satisfy y≠3 and 2b/y=prime>2).   I. b = y --> not necessarily true: b=3 and y=2 (2b/y=3=prime>2);   II. y=1 --> not necessarily true: b=3 and y=2 (2b/y=3=prime>2);   III. b and y are prime integers --> not necessarily true: b=10 and y=4 (2b/y=5=prime>2).   Nonenswer: None.
Answer: A
Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set?  Options.
A) 573 B) 608 C) 613 D) 616 E) 621

Solution: The set S = {5, 13, 21, 29, ..................... }   1st Number = 8 * 0 + 5= 
8 * 0 + 5 = 5
5   2nd Number= 8 * 1 + 5= 
8 * 1 + 5 = 13
13   3rd Number= 8 * 2 + 5= 
8 * 2 + 5 = 21
21   72th Number= 8 * (72-1) + 5= 
8 * (72-1) + 5 = 573
573   573nswer= 573
Answer: A
what is the compound interest on rs:80,000 for 4 months at the rate of 5% per annum Choose the most appropriate option.
A) 1341.69 B) 1342.69 C) 1343.69 D) 1344.69 E) 1345.69

Solution: it is monthly compound   rate=5/12% per month   80000*(1+5/1200)^4-80000=1341.69   1341.69NSWER:1341.69
Answer: A
The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?	Select.
A) m  B) m  C) m  D) m  E) m

Solution: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X   = 245 m.   Answer:m
Answer: C
What is the least number that should be added to 1077, so the sum of the number is divisible by 23?	Select:
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: (1077 / 23) gives a remainder 19 so we need to add 4.   The answer is 4.
Answer: D
Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 500x is the cube of a positive integer?
Choose the correct answer:
A) 2
B) 3
C) 5
D) 10
E) 15

Solution: We want to know the smallest x that will make 500x a CUBE of some number. Let's call that number y.   Let's first figure out what we're working with. The prime factorization of 500 can be visualized:   ...........500   ......../.......\   ......50.......10   ...../..\....../...\   ...25...2...2.....5   .../..\   ..5....5   So, we have 5 * 5 * 5 * 2 * 2 that can be multiplied together to get 500. Now we need to figure out what we need to make 450 * x into a cube of y (y^3=500*x).   We have two 5s, two 3s, and one 2. To arrange these numbers in identical sets (2,5), we need at least one more 2. Each of these numbers will give us the value of y (2*5=10), which, multiplied by itself three times, gives us 500 * x.   Looking at the factors we need to complete the sets, we get x= 2. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.   Therefore, we can go with answer choice A.   If time permits, we can do a sanity check. We calculated that y should be 2 * 5, or 10. 10 * 10 * 10 = 1000. 2lso, 500 * 2 = 1000.
Answer: A
Profits in the partnership of Bess, Bill and Bob are shared in the ratio 1 : 2 : 3. If Bill's share of the profits is $300, what is Bob's share?  Choose the most appropriate option:
A) $150
B) $900
C) $600
D) $450
E) None

Solution: Ans is D   Given profit ratio, $900ess : $900ill : $900ob = 1 : 2 : 3 To make $900ill's portion $300, multiply by $150 => $900ess : $900ill : $900ob = $150 : $300 : $450 => $900ob's share = $450
Answer: B
A, B and C enter into a partnership and theirs shares are in the ratio 1/2 : 1/3 : 1/4. After two months, A withdraws half of his capital and after 10 months, a profit of Rs.378 is divided among them. What is B’s share?  Choices
A) Rs.129	B) Rs.144	C) Rs.156	D) Rs.168	E) Rs.178

Solution: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.   Let their initial investments be 6x, 2x and 3x respectively.   A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.   Therefore, B’s share = Rs. 378 * 8/21   = Rs.144.   ANSWER:Rs.144
Answer: B
A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent  Choose the most appropriate option
A) 3488  B) 7789  C) 5400  D) 2887  E) 1881

Solution: Explanation:   Interest for 1 year is the same whether it's simple interest or the compound interest.   Now interest of third year = 8575 - 7350= 
8575 - 7350 = 1_225
1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest= 1225   if 100 is the principal interest =(1225/7350) * 100 = 50/3 %   When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100   Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %   Therefore amount after 2 years = 100 + 325/9 = 1225/9   If 1225/9 is the amount principal =100   if 7350 is the amount principal =(900/1225)*7350= 
(900/1225)*7350 = 5_400
5400   So sum= 5400; Rate = 50/3 %   Answer: 5400) 5400
Answer: C
Look at this series: 3, 1, (1/3), (1/9),... What number should come next?	Choose the correct choice from the following options
A) 1/27
B) 1/18
C) 1/61
D) 2/27
E) None

Solution: Explanation: This is a simple division series; each number is divisible by 3 of the previous number. In other terms to say, the number is divisible by 3 successively to get the next result.   9/3= 
9/3 = 3
3   3/3= 
3/3 = 1
1   1/3= 1/3   (1/3)/3 = 1/9   (1/9)/3 = 1/27 and so on.   1/27nswer: Option 1/27
Answer: A
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches? Choose one.
A) 10
B) 36
C) 38
D) 40
E) 42

Solution: Let Length and Breadth of photograph be L and B respectively.   Perimeter is given by 2*(L+b) -----(1)   10ccording to the question:   (L+2)(B+2) = m ----(2)   and   (L+6)(B+6) = m + 52 ---------> (L+6)(B+6) - 52 = m ------(3)   Equating (2) and (3)   (L+2)(B+2) = (L+6)(B+6) - 52   LB + 2L + 2B + 4 = LB + 6L + 6B + 36 -52   Simplify   4L + 4B = 20 ------> 2(L+B) = 10 (Check eq (1))   10nswer is 10
Answer: A
8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 15th and the 20th terms?  Choose one:	A) 324	B) 335	C) 346	D) 357	E) 379

Solution: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.   Thus, 11n – 3 describes the values in the sequence where n is the number of the term.   The 15th term is 15 × 11 – 3 = 162   The 20th term is 20 × 11 – 3 = 220 – 3 = 217.   The sum of these two values is 376   The correct answer is choice (379).
Answer: E
Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are
Select the correct option: A) 12, 24, 30 B) 12, 24, 38 C) 12, 24, 362 D) 12, 24, 36 E) 12, 24, 321

Solution: Explanation:   Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12   \inline \fn_jvn \therefore The numbers are 12, 24, 36   Answer: 12, 24, 36) 12, 24, 36
Answer: D
How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?	Choose the correct choice from the following options
A) 376	B) 377	C) 236	D) 228	E) 212

Solution: The smallest number in the series is 1000, a 4-digit number.   The largest number in the series is 4000, the only 4-digit number to start with 4.   The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.   The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.   Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.   Including 4000, there will be 376 such numbers.   376nswer: 376
Answer: A
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is  Choose the correct choice from the following choices
A) 7/19	B) 7/18	C) 7/12	D) 7/19	E) 7/15

Solution: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = 7C2/`5C2 + 8C2/15C2   = 7/15   Answer: 7/15
Answer: E
According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 10 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?  Options:
A) 25 B) 30 C) 50 D) 67 E) 100

Solution: Orange juice concentrate: water::1:3   total quantity of orange juice = 200*6= 
200*6 = 1_200
1200 oz   so Orange juice concentrate: water :: 300 oz:900 oz   no. of 10 oz can= 300 oz/10 oz = 30   Answer 30, 30 cans
Answer: B