MU-NLPC/Calc-aqua_rat huggingface dataset:
If f(x) = 2x+2 what is f(f(3))?
a. 18
b. 8
c. 64
d. 16  Options:
A) 8 B) 18 C) 64 D) 16 E) 26

Solution: f(3)=2*3+2= 
2*3+2 = 8
8   now put this value again in the function   f(8)=2*8+2= 
2*8+2 = 18
18   ANSWER:18
Answer: B
When a number is multiplied by 13,it will become greater to 105 by an amount with which it is lesser to105 by now. What is the number Options:  A) 12  B) 13  C) 14  D) 15  E) 16

Solution: no is 105-x, then   (105-x)*13 = 105+x   1365 -13 x =105+x   14x = 1260   x= 1260/14= 
1260/14 = 90
90   so number is  105-90= 
 105-90 = 15
15   ANSWER:15
Answer: D
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:	Select the correct option:
A) 1 : 3
B) 3 : 2
C) 3 : 4
D) 3 : 5
E) None of these

Solution: let length of trains are x and y   so speed of the trains will be x/27 and y/17 respectively.   now to cross each other time taken=23 second,   so (x+y)/((x/27)+(y/17))=23   (27*17)(x+y)/17x+27Y=23   so, ((x/y)+1)/17(x/y)+27=23/27*17   (x/y)+1=(23x/27y)+23/17   4*(x/27)=6*(y/17)   so,(x/27):(y/17)=3:2   so ratio of speed of the train will be 3:2   ANSWER:3 : 2
Answer: B
75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 30% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking? Options.
A) 25%  B) 30%  C) 50%  D) 55%  E) 75%

Solution: Let x be the number of non-smoking rooms.   Let N be the total number of rooms at the inn.   40% of non-smoking rooms have a king-sized bed.   0.4x = 0.3N   x = 0.75N   The percentage of rooms which permit smoking is 1 - 0.75 = 25%   The answer is 25%.
Answer: A
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is	Choose the most appropriate option: A) 1/2 B) 3/4 C) 3/7 D) 3/11 E) 4/7

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   1/2)
Answer: A
If y is an integer, then the least possible value of |23 - 8y| is
Choose the correct answer:
A) 5
B) 2
C) 3
D) 4
E) 1

Solution: We know that 8y is a multiple of 8, so let’s first look at the multiples of 8 closest to 23. We have “16” and “24”. Let’s subtract both of these from 23 and see which one produces the smallest result. When 2y = 16, y is 2 and when 3y = 24, y is 5. Let’s start with letting y = 4.   |23-8(2)|   |23-16|   |7| = 7   Next, let’s let y equal 3.   |23-8(3)|   |23-24|   |-1| = 1   We see that the smallest possible value of |23-8y| is 1.   Answer 1.
Answer: E
A sum of money lent out at S.I. amounts to a total of $590 after 2 years and to $815 after a further period of 5 years. What was the initial sum of money that was invested?	Pick one.
A) $490  B) $500  C) $510  D) $520  E) $530

Solution: S.I for 5 years = $815 - $590 = $225   The S.I. is $45/year   S.I. for 2 years 815 -  590= 
815 -  590 = 225
$225   The S.I. is $45/year   S.I. for 2 years= $90   Principal = $590 - $90 = $500   The answer is $500.590 -  90= 
590 -  90 = 500
$500   The answer is $500.
Answer: B
Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 18kmph. For how many minutes does the bus stop per hr Choose the correct choice from the following answers.
A) 12 min B) 11 min C) 13 min D) 20 min E) 40 min

Solution: Due to stoppages,it covers 36km less.   time taken to cover 36 km is [  36/54 *60= 
  36/54 *60 = 40
40min   Answer is 40 min.
Answer: E
It takes one machine 7 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order? Options:
A) a) 7/12  B) b) 1 1/2  C) c) 1 5/7  D) d) 3 1/2  E) e) 2 6/11

Solution: RT = W   Given:   R = 1/7 + 1/4 = 11/28   T = ?   W = 1   T = 1 / (11/28) = 28/11 = 2 6/11   Answer: e) 2 6/11
Answer: E
A train 260 m long passed a pole in 26 sec. How long will it take to pass a platform 650 m long?	Options
A) 91 sec	B) 89 sec	C) 54 sec	D) 27 sec	E) 22 sec

Solution: Speed = 260/26= 
260/26 = 10
10 m/sec.   Required time= (260 + 650)/10= 
(260 + 650)/10 = 91
91 sec.   91 secnswer: 91 sec
Answer: A
The compound ratio of 5:6, 3:2 and 4:5?	Choose the correct choice
A) 1:9  B) 1:7  C) 1:2  D) 1:1  E) 1:4

Solution: 5/6 * 3/2 * 4/5= 
5/6 * 3/2 * 4/5 = 1
1/1= 
1/1 = 1
1:1   Answer: 1:1
Answer: D
A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?  Choose one
A) 22  B) 24  C) 28  D) 26  E) 29

Solution: Let the average score of 19 innings be x.   Then, 18x+98/19=x+4   The average score after 20th innings   = x + 4 = 22 + 4= 
22 + 4 = 26
26   Answer 26
Answer: D
2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?  Choose the correct choice from the following choices:  A) 400  B) 460  C) 800  D) 880  E) 900

Solution: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800   800
Answer: C
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 161?	Choose the most appropriate option
A) 2670
B) 2980
C) 3550
D) 4030
E) 4540

Solution: 100 + 102 + ... + 160 =   100*31 + (2+4+...+60) =   100*31 + 2*(1+2+...+30) =   100*31 + 2(30)(31)/2 =   100*31 + 30*31 = 130(31) = 4030   The answer is 4030.
Answer: D
Arun started a business investing Rs. 45,000. After three months. Pramod joined him with a capital of Rs.60,000. If at the end of one year, the total profit from the business is Rs.26,000, what would be Pramod's share in it?  Choose the correct answer:
A) Rs.10,000 B) Rs.14,000 C) Rs.13,000 D) Rs.16,000 E) None of these

Solution: ( arun)45000*12 : (pramod)60000*9 =>>(45*12) : (60*9) ==> (arun) 1: (pramod) 1   pramod's share is >> 26000 * 1/(1+1)= 
26000 * 1/(1+1) = 13_000
>13000   ANSWER:Rs.13,000
Answer: C
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate got  Choose the correct answer.
A) 55%
B) 56%
C) 57%
D) 58%
E) None of these

Solution: Explanation:   Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   Option 57%
Answer: C
1^23×1^23+2^8×2^8+2×123×2^8=?  Options:
A) 454621 B) 123545 C) 343566 D) 325456 E) 128513

Solution: 1+256*256+246*256   128513   128513
Answer: E
Marge has W candies, where W is an integer such that 20 < W< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
Options
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.   This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47   If she divides the candies among 6 children, she will have 1 candy remaining.   this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49   ONLY 37 is common, so candies are 37 in number..   if 37 is divided in 7 kids, remainder W= 2   2
Answer: C
If Rs.2800 yields a simple of Rs.480 in 3 Years, calculate the percentage rate?
Choose one
A) 11.6%
B) 10%
C) 14.6%
D) 12.6%
E) 13.6%

Solution: 480 = (2400*2*R)/100   R = 10%   Answer: 10%
Answer: B
The sum of two consecutive number is 97. Which is the larger number? Choices:
A) 42  B) 49  C) 44  D) 45  E) 46

Solution: Let consecutive number be x, x+1   Therefore sum of the consecutive number is x + x+1=97   2x+1=97   2x=96   x=48   Therefore larger number is x+1=49   ANSWER:49
Answer: B
The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 50,000 bacteria	Choose the correct answer
A) 10  B) 12  C) 14  D) 16  E) 18

Solution: The question basically asks how many minutes it takes for a population to increase by factor 50(50,000 / 1,000 = 50).   Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:   2^x >= 50, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^6 = 64, i.e. the population has to double 6 times.   Since it takes the population 2 minutes to double once it takes 6*2= 
6*2 = 12
12 minutes to double nine times.   Thus, solution 12= 12 is correct.
Answer: B
If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Choose the most appropriate option
A) 10	B) 18	C) 20	D) 22	E) 24

Solution: 2:3   2x + 10 : 3x + 10 = 3 : 4   4[2x + 10] = 3[3x + 10]   8x + 40 = 9x + 30   9x - 8x = 40 - 30= 
40 - 30 = 10
10   Then smallest number is= 2   2x = 20   Short cut method:   a:b = 2:3   c:d = 3:4   1.Cross multiplication with both ratios   a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1   2. If 10 is added both the number means   10 * 3= 
  10 * 3 = 30
30 and   10 * 4= 
  10 * 4 = 40
40,   Then 30 ~ 40= 10   ===> 1 -----> 10   ===> 2 -----> 20   20
Answer: C
Here are some words translated from an artificial language.
hapllesh means cloudburst
srenchoch means pinball
resbosrench means ninepin
Which word could mean "cloud nine"?  Choose the correct choice from the following options.
A) leshsrench	B) ochhapl	C) haploch	D) haplresbo	E) ochhase

Solution: Hapl means cloud; lesh means burst; srench means pin; och means ball; and resbo means nine. Leshsrench (choice a) doesn't contain any of the words needed for cloud nine. We know that och means ball, so that rules out choices b and c. When you combine hapl (cloud) with resbo (nine), you get the correct answer   Answer:haplresbo
Answer: D
N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N? Choose one
A) 23	B) 28	C) 4	D) 1	E) 25

Solution: If the remainder is same in each case and remainder is not given, H4F of the differences of the numbers is the required greatest number    6905 - 1305= 
 6905 - 1305 = 5_600
5600   6905 - 4665= 
6905 - 4665 = 2_240
2240   4665 - 1305= 
4665 - 1305 = 3_360
3360   Hence, the greatest number which divides 1305, 4665 and 6905 and gives the same remainder, N= H4F of 5600, 2240, 3360   = 1120   Sum of digits in N   = Sum of digits in 1120   = 1 + 1 + 2 + 0= 
1 + 1 + 2 + 0 = 4
4   Answer is 4
Answer: C
If A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in either mean or the median being modified.
A) A is replaced by J
B) A and H are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and D are removed
Choose the correct answer
A) 1) A and B
B) 2) A and E
C) 3) A,B,E
D) 4) All of them
E) 5) None of them

Solution: Here answer will be (C).   There are 10 equidistant numbers on the number line.   Mean and median will be the average of middle two numbers.   If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. Other changes will affect the mean and median.   Answer: 3) A,B,E
Answer: C
The perimeter of an isosceles right triangle is 10 + 10 sq rt 2. What is the length of the hypotenuse of the triangle?	Choose the correct choice.
A) 5  B) 6  C) 7.07  D) 8  E) 9

Solution: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 =10 + 10 Sqrt2 or,   a. ( 2+ sqrt2) = 10(1 + sqrt2), a= 10*(1+sqrt2)/2+sqrt2 =10*2.414/3.414 =0.707*10= 
0.707*10 = 7.07
7.07   7.07
Answer: C
The relationship between quantities m and n is expressed by the equation 10m = 5(n - 42). If the difference between the two chosen values of n is 30, what is the difference in the corresponding values of m?	Pick one:
A) 30/11
B) 42/11
C) 60/11
D) 150/11
E) 15

Solution: Another Simple way   10m=5(n-42)   Assume n = 42 to make one side equal to 0   then 10m=0   and m = 0   Repeat it by assuming n as 42+30 i.e 72   10m= 5(72-42)   10m=150   m=150/10= 
150/10 = 15
15 - 0= 
15 - 0 = 15
15   Answer : 15
Answer: E
A women walking at 5 Kmph reaches her office 8 minutes late. If she walks at 9 Kmph, she reaches there 8 minutes earlier. How far is the office from her house? Choose the correct choice:
A) 2 1/5 Km
B) 3 Km
C) 4 1/3 Km
D) 5 Km
E) 5 1/3 Km

Solution: Formula = S1*S2/S2-S1 * T1+T2/60   = 5*9/2 * 16/60   = 45/2 * 16/60   = 3 Km   3 Km)
Answer: B
On a map, 3.5 inches represent 35 miles. How many miles approximately is the distance if you measured 127 centimeters assuming that 1-inch is 2.54 centimeters?	Choose the correct choice from the following choices:
A) 515	B) 500	C) 525	D) 530	E) 535

Solution: 1 inch = 2.54 cm   3.5 inch = 2.54 * 3.5 cm   8.89 cm = 35 miles   127 cms = 35/8.89*127= 
35/8.89*127 = 500
500 miles   Answer : 500
Answer: B
A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
Choose the correct choice from the following answers
A) 22 1/7 kmph  B) 22 2/2 kmph  C) 22 1/4 kmph  D) 22 1/2 kmph  E) 42 1/2 kmph

Solution: 100 --- 10 22 1/2 kmphS = 10   ? ---- 1   75 ---- 15 US = 5   ? ----- 1 S = (10 - 5)/2   = 2 2 1/2 kmph   Answer:22 1/2 kmph
Answer: D
Tough and Tricky questions: Exponents.
If 3^m3^m2^m = 9^n, then m/n = Pick
A) 1/3  B) 2/3  C) 1  D) 3/2  E) 3

Solution: I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!   What I did was to test powers of 3 that would lead to 9.   So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n   What I did was test 3 raised to the power of 2 like this:   3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2/3.2/3
Answer: B
The tax on a commodity is diminished by 30% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?  Answers:
A) 12%
B) 14%
C) 16%
D) 20%
E) 23%

Solution: 23%xplanation:   100 * 100= 
100 * 100 = 10_000
10000   70 * 110= 
70 * 110 = 7_700
7700   10000------- 2300   100 ------- ?= 23%   23%)
Answer: E
If 12 and 15 are the lengths of two sides of a triangular region, which of the following can be the length of the third side?
I. 10
II. 20
III. 30	Pick one:	A) I only	B) II only	C) I and II only	D) II and III only	E) I, II, and III

Solution: 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.   Let x be the length of the third side.   15-12 < x < 15+12   3 < x < 27   The answer is I and II only.
Answer: C
Fill in the blank with the correct number in this number series: 3, 9, 8, 7, __, 5, 18, ?  Choose the correct choice from the following
A) 6
B) 7
C) 9
D) 10
E) 13

Solution: This is a simple alternating subtraction and addition series; The first series begins with 3 and adds 5; the second begins with 9 and subtracts 2, and so on.   Answer: 13
Answer: E
The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 2 and then added to the smaller of the two original integers. Which of the following represents this operation? Choices.
A) 6t-2 B) 8t-2 C) -2 D) 3 E) -2-4t^2

Solution: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.   therefore 2* 2t + 2t-2 = 6t-2.   option 6t-2.
Answer: A
A passenger sitting near the window in a train moving at 40 km/h, noticed that it took 3 sec. for the oncoming train to pass by. What was the speed of the oncoming train if the length of the oncoming train was 66 metres?  Choose the correct answer.
A) a)39.2km/h	B) b)52km/h	C) c)56km/h	D) d)60km/h	E) e)70km/h

Solution: im getting A   3 secs to pass a 75 mts train , therefore speed = 22 meters/sec   to convert m/s to km/hrs multiply by 3.6   22*3.6= 
22*3.6 = 79.2
79.2   so its  79.2-40= 
 79.2-40 = 39.2
39.2 .   a)39.2km/h
Answer: A
A cistern 10 m long and 8 m wide contains water up to a depth of 1 m 50 cm. The total area of the wet surface is:	Select.
A) 120 m2  B) 136 m2  C) 128 m2  D) 130 m2  E) 134 m2

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (8 x 1.50 + 10 x 1.50) + 8 x 10] m2   = 134 m2.   answer :134 m2
Answer: E
What is the difference between local value & face value of 9 in the numeral 65793? Choose the correct choice from the following
A) 8453  B) 8956  C) 8991  D) 9890  E) 10000

Solution: (Local value of 9) - (Face value of 9)   = (9000 - 9)= 
(9000 - 9) = 8_991
8991   8991
Answer: C
A man covers a certain distance Win a train. If the train moved 4km/hr faster, it would take 30 min less. If it moved 2km/hr slower, it would take 20 mins more. Find the distance? Choose the correct choice from the following options.
A) 200 km	B) 50 km	C) 20 km	D) 60 km	E) 80 km

Solution: Not really. When you solve the 2 equation above, you get,   6T-4/3 = 5R/6 from simplifying equation 1   4T-2=R/2 from simplifying equation 2   You can now multiply equation 2 by 5 to get   5(4T-2=R/2 ) = 20T-10=5R/2 and then subtract this new equation from equation 1 to get T=3, followed by R=20 to give you distance W= R*T=20*3= 
20*3 = 60
60 km.60 km
Answer: D
If x and y are positive integers and x = 5y + 2, what is the remainder when x is divided by 5?  Pick:
A) 0 B) 1 C) 2 D) 3 E) 4

Solution: This question asks what IS...(the answer), so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.   We're told that X and Y are POSITIVE INTEGERS and X = 5Y + 2. We're asked for the REMAINDER when X is divided by 5.   IF....   Y = 1   X = 7   7/5 = 1 remainder 2   Final Answer:   2
Answer: C
We define that K@J is the product of j number from k in increasing order for positive integers K, J. For example, 6@4=6*7*8*9. If A=2020and B=2120, what is the value T of the ratio A/B?
Pick one:
A) 1/2 B) 1/3 C) 2/3 D) 1/4 E) 1/5

Solution: T-> A/B=20*21*……*39/21*22*….*39*40=20/40=1/2.   Therefore, the answer is 1/2.
Answer: A
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?	Choose the correct option:
A) 18 2/7%  B) 18 2/11%  C) 12 2/12%  D) 13 2/9%  E) 14 2/7%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer: 18 2/11%
Answer: B
Bradley owns b/2 video game cartridges. If Bradleyâ€™s total is one-half the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Select the correct option:
A) (16/3)b
B) (17/4)b
C) (13/8)b
D) (9/2)b
E) (7/12)b

Solution: Step 1: Categorize the problem   This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.   Step 2: Think like the test maker   What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlieâ€™s values in relation to Bradleyâ€™s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.   Step 3: Solve the problem   b/2 = Bradleyâ€™s total   2*b/2 = Andrewâ€™s total   1/4*b/2 = Charlieâ€™s total   Add each total   b/2 + 2*b/2+ 1/4*b/2 = b/2 + 2*b/2 + b/8 = (13/8)b   Therefore,choose (9/2)b.
Answer: D
On dividing a number by 56, we get 26 as remainder. On dividing the same number by 8, what will be the remainder ?	Choose one:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: Number=56x+26 (∵ since the number gives 26 as remainder on dividing by 56)   =(7×8×x)+(3×8)+2   Hence, if the number is divided by 8, we will get 2 as remainder.   2NSWER:2
Answer: A
Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?  Choices.
A) 20 Kmph B) 15 Kmph C) 30 Kmph D) 32 Kmph E) 34 Kmph

Solution: Total distance = 8 Km   Total time = 50 Km   Time taken to cover the distence of 3 Km = 50*2/5= 
50*2/5 = 20
20 min= 1/3 hours   Remaining distance = 8 - 3= 
8 - 3 = 5
5 Km   Required speed= 5/1/3 = 15 Kmph   15 Kmph
Answer: B
In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned? Choose the most appropriate option:
A) 3:16. B) 2:3. C) 1:3. D) 3:4. E) 2:5

Solution: Amount for Store a = 10 * 4= 
10 * 4 = 40
40   Amount for Store b= 40 * 3= 
40 * 3 = 120
120   Ratio of Total Amount Would be= 40/120 = 1:3   ANSWER:1:3.
Answer: C
Cream costs twice as much as skim milk. A certain brand of milk is 3/5 cream and 2/5 skim milk. What fraction of the cost of this brand is due to the cream? Select
A) 1/2 B) 1/3 C) 2/3 D) 3/4 E) 4/5

Solution: Let x be the cost of the skim milk in the mixture.   The cost of the cream is (3/2)*x*2 = 3x.   The total cost is x+3x = 4x and the fraction due to the cream is 3x / 4x = 3/4   The answer is 3/4.
Answer: D
What is the total number of integers between 20 and 80 (exclusive)that are divisible by 10?
Choose the correct choice from the following options
A) 5  B) 7  C) 4  D) 9  E) 3

Solution: 30,40,50,60,70   total 5   5nswer is 5
Answer: A
If the sum of the first n even positive integers is S, what is the sum of the first n positive integers, in terms of S ?	Choose the correct choice:
A) S/2 B) S C) 2S D) 2S + 2 E) 4S

Solution: S/2nswer is S/2   Given sum of 2 , 4 , 6 ....2n = S   sum of 1 2 3.....n = [sum(2 4 6....2n) ]/2 = S/2
Answer: A
Working simultaneously and independently at an identical constant rate, 5 machines of a certain type can produce a total of x units of product P in 4 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 2x units of product P in 2 days?  Choose the correct choice from the following:
A) 11  B) 13  C) 15  D) 18  E) 20

Solution: The rate of 5 machines is rate=job/time=x/4 units per day --> the rate of 1 machine 1/5*(x/4)=x/20 units per day;   Now, again as {time}*{combined rate}={job done}   then 2*(m*x/20)=2x --> m=20.   Answer: 20.
Answer: E
Exactly 36% of the numbers in set E are even multiples of 3. If 40% of the even integers in set E are not multiples of 3, what percent of the numbers in set E are not even integers?	Choose the correct option: A) 76% B) 60% C) 50% D) 40% E) 24%

Solution: Everything is correct except the red part with a typo: it should be N=0.6E --> even numbers are 60% of E --> 40% of E are not even integers.   Answer: 40%.
Answer: D
In what ratio should two varieties of sugar of Rs.18 per kg and Rs.24 kg be mixed together to get a mixture whose cost is Rs.20 per kg? Choose the correct choice from the following choices:  A) 16.59  B) 16.5  C) 16.56  D) 13.5  E) 16.51

Solution: Let the quantities of A and B mixed be 3x kg and 7x kg.   Cost of 3x kg of A = 9(3x) = Rs. 27x   Cost of 7x kg of B = 15(7x) = Rs. 105x   Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x   Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66   Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50   Answer:16.5
Answer: B