MU-NLPC/Calc-aqua_rat huggingface dataset:
You cook a pot of beef stew for you and your roommate. Normally it lasts 7 days between the two of you. If 3 guests are now staying with you and your roommate, how many days will the beef stew now last if everyone eats it?
Choose the correct option:
A) 2.8
B) 1
C) 3.5
D) 14
E) 1.6

Solution: First set up a ratio with all the relevant values and also the unknown variable:   2*7 = 5*x   Now solve by multiplying 2 by 7 and then dividing that product by 5:    2*7= 
 2*7 = 14
14   14/5= x   x = 2.8   The value of x represents the amount of days a bot of beef stew will last for 5 total people.   2.8nswer: 2.8
Answer: A
a;b = 8: 10, b:c = 7: 9, a:b:c = ?  Choose one
A) 56 : 70: 80 B) 56 : 70: 70 C) 56 : 70: 60 D) 56 : 70: 95 E) 56 : 70: 90

Solution: a;b = 8: 10   b:c = 7: 9   a:b:c =56 : 70: 90   Answer : 56 : 70: 90
Answer: E
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
Pick one:
A) 2999 B) 2777 C) 1000 D) 297 E) 2781

Solution: X * (110/100) * (95/100) = 1045   X * (11/10) * (1/100) = 11   X = 1000   Answer:1000
Answer: C
The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?	Select the correct option.
A) 5	B) 4	C) 6	D) 8	E) 3

Solution: 65*(90/100)*((100-x)/100) = 56.16   x = 4%.Answer:4
Answer: B
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word GUAVA could be arranged to create a five-letter code? Choose the correct choice from the following:
A) 5!  B) 5! − (3! + 2!)  C) 5! − 2!  D) 5!/2!  E) 6!/(3! × 2!)

Solution: GUAVA - five letters can be arranged in 5! ways   since 'A' repeats 2 times , we need to divide the 5! ways by 2! to adjust repetition.   5!/(2!)   Ans. 5!/2!) 5!/(2!)
Answer: D
A sum of money place at compound interest doubles itself in 10 years. In how many years will it amount to eight times itself?	Choose one.
A) 10 years B) 20 years C) 30 years D) 40 years E) 50 years

Solution: 100 ---- 200 ---- 10   400 ---- 10   800 ---- 10   ------   30 years   Answer: 30 years
Answer: C
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:	Choose the correct choice from the following: A) Rs. 3500 B) Rs. 3750 C) Rs. 3840 D) Rs. 3900 E) None

Solution: EXPLANATION   Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.   Then, 10x = 4y or y = 5b/2 x   15x + 2y = 4000   15x + 2 x 5/2 x= 4000   20x = 4000   x = 200.   So, y = 172 = 500.   Hence, the cost of 12 chairs and 3 tables = 12x + 3y   = Rs. (2400 + 1500)   = Rs. 3900.   Answer Rs. 3900
Answer: D
The ratio between the number of sheep and the number of horses at the Stewart farm is 6 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?	Answers:
A) 18 B) 28 C) 48 D) 56 E) 60

Solution: Let the number of sheeps and horses be 4x and 7x.   Now total number of horses = total consumption of horse food/consumption per horse = 12880/230= 
12880/230 = 56
56, which is equal to 7x.=> x = 8   Sheeps =6x = 6*8= 
6*8 = 48
48.   Hence 48.
Answer: C
Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum? Choose the correct choice
A) 20	B) 21	C) 25	D) 27	E) 29

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.12000. A's share is?
Choose the correct choice from the following options.
A) 2999	B) 2778	C) 6000	D) 2889	E) 4000

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 12000= 
1/3 * 12000 = 4_000
4000   Answer:4000
Answer: E
Ravi invested certain amount for two rates of simple interests at 6% p.a. and 7% p.a. What is the ratio of Ravi's investments if the interests from those investments are equal?  Choose the correct choice from the following answers
A) 7:7 B) 7:4 C) 7:1 D) 7:6 E) 7:8

Solution: Let x be the investment of Ravi in 6% and y be in 7%   x(6)(n)/100 = y(7)(n)/100   => x/y = 7/6   x : y = 7:6   Answer: 7:6
Answer: D
The food in a camp lasts for 30 men for 40 days. If ten more men join, how many days will the food last?
Choose the correct answer.
A) 80 days	B) 30 days	C) 65 days	D) 16 days	E) 15 days

Solution: one man can consume the same food in 30*40= 
30*40 = 1_200
1200 days.   10 more men join, the total number of men= 40   The number of days the food will last = 1200/40= 
1200/40 = 30
30 days.   Answer:30 days
Answer: B
The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan? Select the correct option:
A) 25 years B) 30 years C) 36 years D) Cannot be determined E) None of these

Solution: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.   Then, (1/3 * 5x)/(1/2 * 6x) = 5/9   15 = 15   Thus, Shaan's age cannot be determined.   ANSWER:Cannot be determined
Answer: D
Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?	Choices:
A) 1261	B) 1268	C) 1269	D) 1265	E) 1263

Solution: 1261 = 8000(21/20)3   = 9261   = 8000   ---------   1261   1261nswer:1261
Answer: A
Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 38 percent ryegrass, what percent of the weight of this mixture is X ?	Select
A) 10%	B) 33.33 %	C) 40%	D) 86.66%	E) 66.66 %

Solution: ---------------->Ryegrass   X-------------->	40%   Y-------------->	25%   M(mixture)---->38%   0.4X + (M-X)0.25 = 0.38M   0.15X = 0.13M   X = 0.8666M   X = 86.66% of M   86.66%
Answer: D
A bag is filled with pennies and nickels in the ratio of 10 to 5. There are 60 nickles in the bag, how many coins are there in that bag?
Choose the correct choice
A) 40
B) 180
C) 65
D) 70
E) 80

Solution: A ratio of pennies to nickels of10 to 5 means that we can write the number of pennies and nickels in the form   number of pennies = 10x and number of nickels = 5x   But we know the number of nickels, 60. Hence   5x = 60   Solve for x   x = 12   The total number of coins is given by   10x + 5x = 15x  10  + 5= 
 10  + 5 = 15
15x= 15 × 12 = 180   Answer : 180
Answer: B
A cheetah runs m miles in n hours. How many miles will it run in x hours at the same rate?  Choose the correct choice from the following answers.
A) mnx  B) m⁄n  C) mx⁄n  D) mx  E) mn⁄x

Solution: Given Speed = m/n   To Find distance in x hours with same speed   Distance = speed * time   Distance = m/n*x = mx/n   Answer mx⁄n
Answer: C
A tree of height 36m is on one edge of a road broke at a certain height. It fell in such a way that the top of the tree touches the other edge of the road. If the breadth of the road is 12m, then what is the height at which the tree broke? Choose the correct choice from the following answers:
A) 16  B) 17  C) 18  D) 19  E) 20

Solution: Let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree.   From the diagram, (36−x)2=x2+122(36−x)2=x2+122   ⇒1296−72x+x2=x2+144⇒1296−72x+x2=x2+144   ⇒72x=1296−144⇒72x=1296−144   ⇒x=16   16nswer:16
Answer: A
What percent of a day is 7 hours?	Choose the correct option:
A) 29.2%
B) 12.5%
C) 13%
D) 11.3%
E) None of these

Solution: Explanation :   Solution: required percentage = (7/100 * 24) = 29.2%   29.2%nswer : 29.2%
Answer: A
A two digit number when 18 added becomes another two digit number with reversed digits. How many such two digit numbers are possible?  Options.
A) 2	B) 3	C) 7	D) 8	E) 9

Solution: Explanation:   Let the two digit number be 'ab' and the number formed after adding 18 to it is 'ba'   So ab + 18 = ba   ⇒⇒ (10a + b) + 18 = 10b + a   ⇒⇒ 18 = 9b – 9a   ⇒⇒ 2 = b – a   So we know that ab, ba both are two digit numbers so a, b ≠≠ 0.   Also when b = 9, a = 7; b = 8, a = 6; b = 7, a = 5; b = 6, a = 4; b = 5, a = 3; b = 4, a = 2; b = 3, a = 1   Total 7 combinations are possible.   7orrect Option: 7
Answer: C
78 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?  Choose the correct choice from the following choices.
A) 10
B) 13
C) 26
D) 15
E) 16

Solution: Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons	30	:	78	:: 12 : x   Working hours/day	6	:	5   30 x 6 x x = 78 x 5 x 12   x =	(78 x 5 x 12)/(30 x 6)   x = 26.   ANSWER:26
Answer: C
For every $30 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as  Choose the correct choice.
A) 1 : 4 : 400 B) 1 : 4 : 100 C) 1:4:600 D) 100 : 4 : 1 E) 400 : 4 : 1

Solution: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 150 dollar of B   therefore 4 dollar M = 600 dollar of B also 1 dollar Y   Y:M:B = 1:4:600   = 1:4:600   1:4:600
Answer: C
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 80?
Choose one
A) 24	B) 26	C) 20	D) 22	E) 18

Solution: 4n+7 > 1   4n> -6   n > -(3/2)   n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)   From second constraint   4n+7 < 80   4n< 73   n < 18. 25   n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 18)   Combining the two   -1.5 < n<18.25   n = 1 to 18 (18 integers)   and n = -1 and 0   so 20 integers.   20 is the answer
Answer: C
Express of the following as a fraction:
42%
Choose the correct choice
A) 20/55	B) 21/50	C) 34/27	D) 17/25	E) None of them

Solution: 42% = 42/100= 21/50.   Answer is 21/50.
Answer: B
Find out the C.I on Rs.3000 at 4% p.a. compound half-yearly for 1 1/2 years	Choose the correct choice from the following options:
A) 183.62
B) 106.07
C) 106.04
D) 106.03
E) 186.01

Solution: 183.62 = 3000(51/50)3   = 3183.62   3000   -----------   183.62   183.62nswer:183.62
Answer: A
A container holds 4 quarts of milk and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts milk to 5 parts water by volume?	Choose the correct choice from the following answers:
A) 4/3	B) 5/3	C) 7/3	D) 8/3	E) 10/3

Solution: An alternate to the alligation method is the more direct/algebraic method:   Let x be the amount of water to be added.   New total amount of water = 4+x   Total amount of milk= 4   New total = 4+4+x=8+x   Final ratio required (for water) = 5/(5+3)=5/8   Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.   8/3 is thus the correct answer.
Answer: D
A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not? Choices
A) .1	B) .2	C) 3/10	D) .4	E) .5

Solution: C (3,6) - all the possible arrangements   C(2,4) is the number of ways the committe with Tom and without Mary.   P = 3/10(2,4)/(3/10 3,6) = 3/10 3/10
Answer: C
At a certain conference, 22% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 60% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance? Choose the correct choice from the following options.
A) 18.0%	B) 62.0%	C) 79.2%	D) 55.0%	E) 82.0%

Solution: Refer to the table in the attachment:   Let x= No. of members who have paid in Full   60 % members paid in full and did not register in advance = 0.6x   22 % registerd in advance and paid in full.   So if total No. of members = 100, then 22 members paid Full and registered in advance.   Hence total members who paid full amount = 0.6x + 22 =x   0.4x =22   Hence x = 55   i.e. 55 out of 100 or 55 %   Ans. 55.0%
Answer: D
Sometime after 10:00 PM a murder took place. A witness claimed that the clock must have stopped at the time of the shooting. It was later found that the postion of both the hands were the same but their positions had interchanged. Tell the time of the shooting (both actual and claimed).  Select:
A) 10:59 PM
B) 11:59 PM
C) 10:50 PM
D) 10:52 PM
E) 10:55 PM

Solution: 10:59 PMctual time of shooting = 11:54 PM   Claimed Time = 10:59 PM   10:59 PMNSWER:10:59 PM
Answer: A
The least number which must be subtracted from 670 to make it exactly divisible by 9 is:	Choose the correct choice from the following answers:
A) A)2 B) B)3 C) C)4 D) D)5 E) E)6

Solution: On dividing 670 by 9, we get remainder= 4   Therefore, required number to be subtracted= 4   Answer: 4
Answer: C
A is a positive integer. when a is divided by 4 the remainder is 3, and when divided by 9 the remainder is 1. what is the remainder if a is divided by 52? Choices.
A) Between 1 and5, inclusive B) Between 10 and15, inclusive C) 5 D) Between 8 and 12, inclusive E) Between 4 and 8, inclusive

Solution: Given the integer a   4a+3= 9a+5   Start 4a+3 -->7, 11, 15,...59,....   Of these only 55 fit the description 9a+5. The remainder when divided by 52 is 7. So answer is E).   Answer = Between 4 and 8, inclusive)
Answer: E
If x and y are numbers such that (x+8)(y-8)=0, what is the smallest possible value of x^2 + y^2
Pick: A) 4 B) 24 C) 54 D) 64 E) 94

Solution: From (x+8)(y-8)=0 it follows that either, x=-8 or y=8. Thus either x^2=64 or y^2=64.   Now, if x^2=64, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 64 + 0= 
64 + 0 = 64
64.   Similarly if y^2=64, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 64= 
0 + 64 = 64
64.   Answer: 64.
Answer: D
An article is bought for Rs.690 and sold for Rs.900, find the gain percent?
Choose the correct option
A) 33 1/8%
B) 33 8/3%
C) 33 1/3%
D) 30 10/23%
E) 32 1/3%

Solution: 690 ---- 210   100 ---- ? => 30 10/23%   Answer:30 10/23%
Answer: D
In a certain game there are 6 steps, referred to as step 1, step 2, and so on with the final step being step 6. The steps are played one after the other. In each step a score of 1, 2,or 3 is obtained. Mary played the game, getting at least one score of each of 1, 2, and 3, and never getting the same score in consecutive steps. What is the greatest possible score that Mary could have gotten?	Choose the correct choice from the following options:
A) 7
B) 8
C) 5
D) 9
E) 5

Solution: There are two conditions:   1. Mary got at least one score of each of 1, 2, and 3.   2. She never got the same score in consecutive steps.   Taking that into account, the greatest possible score that Angel could have gotten is  3 + 1 + 3 + 2= 
 3 + 1 + 3 + 2 = 9
9.   Answer: 9.
Answer: D
A can do a work in 15 days and B in 20 days. If they work on it together then in how many days required to complete the work?  Choose the correct option
A) 300/31  B) 300/35  C) 300/21  D) 300/15  E) 300/20

Solution: Person ( A ) ( 300/35 ) ( A+300/35 )   Time - ( 15 ) ( 20 ) (300/35)   Rate - ( 20 ) ( 15 ) ( 35 )   Work -(300) (300) (300)   therefore A+300/35 requires (300/35) days to complete entire work   = 300/35   Answer is 300/35
Answer: B
Which of the following is closer to (4!+3!)-(4!-3!)?
Choose one:	A) 6	B) 8	C) 10	D) 12	E) 14

Solution: 4!+3!)-(4!-3!)=24+6-24+6= 
24+6-24+6 = 12
12   Answer: 12
Answer: D
If an examination 63% of the candidates in English,65% passed in Mathematics, and 27% failed in both subjects.What is the pass percentage? Choose one.
A) 55%	B) 60%	C) 65%	D) 75%	E) None.

Solution: Fail in English=100-63= 
100-63 = 37
37%   Fail in maths=100-65= 
100-65 = 35
35%   so pass %= 100-(37+35-27)= 
100-(37+35-27) = 55
55%   55%NSWER:55%
Answer: A
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?  Choices.
A) Rs. 4991  B) Rs. 5991  C) Rs. 6001  D) Rs. 6991  E) None of these

Solution: Explanation:   Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.   Required sale = Rs. [ (6500 x 6) - 34009 ]   = Rs. (39000 - 34009)   = Rs. 4991.   Rs. 4991NSWER IS Rs. 4991
Answer: A
A's 5th birthday is on 12th which is a (say) Monday of a leap year. What willbe the day on their 6th birthday?	Answers:
A) sunday B) monday C) tuesday D) wednesday E) thursday

Solution: If 5th Birthday is on or before Feb 29, then 6th Birthday is on Wednesday.   If 5th Birthday is after Feb 29, then 6th Birthday is on Tuesday.   ANSWER:tuesday
Answer: C
A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 9 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
Choices:  A) 3  B) 9  C) 15  D) 21  E) 30

Solution: Let the duration, in minutes, for which the company charges the same under plan A and plan B be t minutes.   Then under plan A the cost would be $0.6+0.06(t-9) and under plan B the cost would be $0.08t. We want these amount to be equal: 0.6+0.06(t-9)=0.08t --> 60+6(t-9)=8t --> t=3.   3nswer: 3.
Answer: A
Wayne goes to a fruits vendor to purchase mangoes and oranges. The cost of 4 mangoes is $10, and the cost of 5 oranges is $10. If Wayne buys fruits worth $31, he has purchased at least how many mangoes?
Pick one:
A) 1
B) 2
C) 6
D) 8
E) 13

Solution: Cost of each mango = $10 / 4 = $2.50.   Cost of each orange = $10 / 5= 
10 / 5 = 2
$2.   Let number of mangoes be m, and number of oranges be o.   Then 2.5m + 2o= 31   => 5m + 4o = 62   => 5m = 62 - 4o   To find minimum m, we need to maximize o, and ensure that (62 - 4o) is divisible by 5.   o = 3, m = (62 - (4)3) / 5 = 10.   o = 8, m = (62 - (4)8) / 5 = 6.   o = 13, m = (62 - (4)13) / 5 = 2.   More than this, m will go -ve. So, Wayne has to purchase at least 2 mangoes.   Answer: 2
Answer: B
For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 276 books with me to gift her.
Can you calculate, on which day is our anniversary? Choose the correct choice from the following choices:
A) 31	B) 28	C) 23	D) 33	E) 25

Solution: C   23rd day   1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23= 
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 = 276
276   Thus our anniversary falls on the 23rd day of the month.   You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: C
How many even number in the range between 6 to 100 inclusive are not divisible by 3
Choose the correct option.
A) 15	B) 30	C) 32	D) 33	E) 46

Solution: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)   For 2,   6,8,10,12,14...100   using AP formula, we can say 100 = 10 + (n-1) *2   or n=48.   For 6,   6,12,18,...96   using AP formula, we can say 96 = 12 + (n-1) *6   or n=16.   Hence, only divisible by 2 but not 3 = 48-16= 
48-16 = 32
32. hence, Answer 32
Answer: C
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?  Choose the correct choice from the following answers.
A) 10
B) 9
C) 12
D) 20
E) 18

Solution: Due to stoppages, it covers 9 km less.   Time taken to cover 9 km = (9/54 * 60)= 
(9/54 * 60) = 10
10 min   10nswer 10)10 mins.
Answer: A
A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?  Choose the correct choice from the following options.
A) 187 ways	B) 600 ways	C) 568 ways	D) 178 ways	E) 876 ways

Solution: Two men, three women and one child can be selected in ⁴C₂ * ⁶C₃ * ⁵C₁ ways   = (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5= 
(4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5 = 600
600 ways.   Answer: 600 ways
Answer: B
A man has Rs. 512 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Choose the correct choice from the following answers
A) 90  B) 94  C) 96  D) 97  E) 99

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 512   16x = 512   x = 32.   Hence, total number of notes = 3x = 96.   96
Answer: C
A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 5 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?	Pick.
A) 48pi/x B) 75x C) 48x D) 240x E) x/75

Solution: Revolutions - circumference of the rim.   => 20pi*X*60 = 5pi*Revolutions   => 4/1 *X *60 = Revolutions => 240X - Option 240x
Answer: D
Set #1 = {A, B, C, D}
Set #2 = {K, L, M, N, O, P}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?	Choose the most appropriate option:
A) 1/6 B) 1/3 C) 3/8 D) 2/3 E) 5/6

Solution: So Not a vowel in Set-1 : 3/4   And not a vowel in Ser-2:5/6   Now,   3/4∗5/6=5/8   This is for not a vowel.   Then for at least one vowel will be = 1−5/8=3/8   Answer will be 3/8.
Answer: C
John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?  Select.
A) 30 ml  B) 40 ml  C) 70 ml  D) 90 ml  E) 100 ml

Solution: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)   concentration of water in pure water= 1 ...(2)   Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3   => concentration of water in mixture2 =310   By rule of alligation,   concentration of water in mixture1 (29)   concentration of water in pure water (1)   Mean concentration   (310)   1−310=710   310−29=790   => Quantity of mixture1 : Quantity of water   =710:790=110:190=1:19   Given that Quantity of mixture1 = 630 ml   => 630 : Quantity of water =1:19   => Quantity of water =630×19=70 ml   70 ml
Answer: C
What is the lowest positive integer that is divisible by each of the odd integers between 13 and 19, inclusive? Choices:
A) 3×17×19×21 B) 13*15*17*19 C) 7×15×17×19 D) 7×15×19×21 E) 15×17×19×21

Solution: We should find the LCM of 13,15 = 3*5, 17, 19--> LCM = 3*5*13*17*19 = 13*15*17*19.   Answer: 13*15*17*19
Answer: B
Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 1:2 and 6:4 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
Choose the correct option:
A) 1:1  B) 2:1  C) 3:1  D) 5:1  E) 6:1

Solution: Vessel 1:1 = 300 gallons --> milk = 100, water = 200;   Vessel B = 500 gallons --> milk = 300, water = 200;   Vessel 1:1 + B = 800 gallons --> milk = 400, water 400   The ratio =400/400 --> 1:1   1:1nswer: 1:1
Answer: A
A can finish a work in 24 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Select the correct option
A) 6  B) 5  C) 5.5  D) 7  E) 8

Solution: B's 10 day's work = ( 1 x 10 ) = 2 .   15 3   Remaining work = ( 1 - 2 ) = 1 .   3 3   Now, 1 work is done by A in 1 day.   24   Therefore 1 work is done by A in ( 24 x 1 ) = 8 days.   8
Answer: E