MU-NLPC/Calc-aqua_rat huggingface dataset:
40% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?  Select: A) 30% B) 40% C) 50% D) 60% E) 70%

Solution: To maximize the percentage of companies offering both, let's assume that all 40% of companies which offer wireless internet also offer snacks.   The answer is 40%.
Answer: B
The ratio between v and y is 7/9; v and y are increased by 4, what is the ratio between the new values of v and y?	Choose the correct choice from the following answers
A) 7/9	B) 14/9	C) 7/18	D) 11/13	E) It Cannot Be Determined

Solution: Ratio = 7k/9k = 7/9, 14/18, etc.   v and y are increased by 4 --> (7k + 4)/(9k + 4)   New ratio can be 11/13, 18/22, etc.   Answer: It Cannot Be Determined
Answer: E
The product of two numbers is 276 and the sum of their squares is 289. The sum of the number is?
Options.
A) A)29  B) B)25  C) C)27  D) D)31  E) E)35

Solution: Let the numbers be x and y.   Then, xy = 276 and x2 + y2 = 289.   (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 276) = 841   x + y = 29.   Option 29
Answer: A
When a train travels at a speed of 100kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
Choose the correct choice from the following options:  A) 15km  B) 50km  C) 60km  D) 85km  E) 95km

Solution: Let x be the time reached with the speed 100km/h   50km/h ----> x+15   Distance is equal so   100(km/h)× xhr = 50(km/h) × (x+15) hr   So   100 x = 50x + 750   So the would be in km   15kmnd x = 15   15kmNSWER:15km
Answer: A
There are 13 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl & 2 boys are selected ?	Choose the correct choice from the following answers:	A) 120	B) 480	C) 780	D) 720	E) 800

Solution: n(s) = sample space = 237803 = 1771   E = event that 1 girl and 2 boys are selected   n(E) = we have to select 2 boys from 13 and 1 girl from 10   = 137802 * 107801   = 780   Ans - 780
Answer: C
Find the value of 3 + 2 • (8 – 3)
Select the correct option:
A) (a) 25	B) (b) 13	C) (c) 17	D) (d) 24	E) (e) 15

Solution: 3 + 2 • (8 – 3)   = 3 + 2 (5)   = 3 + 2 × 5   = 3 + 10= 
3 + 10 = 13
13   Answer: ((d) 24)
Answer: D
Which of the following are square numbers ? Choices:
A) 14	B) 12	C) 20	D) 64	E) 99

Solution: Clearly 64 = 8^2 is a square numbers. Ans : 64
Answer: D
An engine moves at the speed of 60 kmph without any coaches attached to it.Speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached.When 9 coaches are attached speed decreases to 48 kmph.What will be the speed of train when 25 coaches are attached. Choose the correct choice from the following choices.
A) 35
B) 28
C) 40
D) 44
E) 42

Solution: 1.   No. of coaches =9   sqr root=3   speed decreases by 12   12=k*3   k=4   No. of coaches=25   swr root=5   decrease=5*4= 
5*4 = 20
20   New speed=60-20= 
60-20 = 40
40   40
Answer: C
A dirt cake consists entirely of chocolate and vanilla pudding, Gummy Worms, and crushed Oreo's. If the ratio of both the Oreo's and gummy worms were doubled in a serving, , what is the ratio of the pudding to the rest of the dish? Choose the most appropriate option
A) 4: 5  B) 2: 7  C) 3: 8  D) 4: 1  E) Not enough information given

Solution: This answer is too simple to put such a long answer to, the option you want to choose is Not enough information given.
Answer: E
By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
Choose the correct choice from the following answers:
A) 33 1/3%  B) 33 1/8%  C) 33 6/3%  D) 36 1/3%  E) 31 1/3%

Solution: Let the CP of each pen be Rs. 1.   CP of 99 pens = Rs. 99   Profit = Cost of 33 pens = Rs. 33   Profit% = 33/99 * 100 = 33 1/3%   33 1/3%nswer: 33 1/3%
Answer: A
A milkman sells his milk at CP but he mixes it withwater and thereby gains 25%. What is the % of water in the mixture?  Pick one.
A) 10% B) 15% C) 20% D) 30% E) 40%

Solution: Here Gain= 25%   error = quantity of water he mixes in the milk =x   true value = true quantity of milk = T   So the formula becomes, 25=x(T−x)×100   ⇒1=x(T−x)×4⇒T−x=4x⇒T=5x   Percentage of water in the mixture   =xT×100=x5x×100=15×100=20%   20%
Answer: C
From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 13 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?	Choose the correct choice from the following answers:
A) 38  B) 39  C) 40  D) 41  E) 42

Solution: Soln:-   13x=45 --> 87/77*x=45 --> x=45*77/87=677/17=~40.   Answer: 40.
Answer: C
A money lender lends Rs.2000 for six months at 18% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
Choose the correct choice from the following options:
A) 2228.4 B) 1978 C) 2834 D) 2827 E) 2781

Solution: 2228.4 = 2000(19/18)2   = 2228.4   2228.4nswer: 2228.4
Answer: A
Find the average of all numbers between 6 and 34 which are divisible by 5  Choose the correct choice from the following answers:
A) 15
B) 20
C) 25
D) 30
E) 35

Solution: Explanation:   Average=(10+15+20+25+305)=1005=20   Answer: Option 20
Answer: B
You buy a piece of land with an area of âˆš1600, how long is one side of the land plot?
Choose the correct choice from the following answers:
A) 28
B) 40
C) 30
D) 31
E) 32

Solution: Try filling the numbers into the answer y x y =   Find the closest to 900.   Answer 40
Answer: B
A circle is inscribed in a unit square, and a diagonal of the square is drawn. Find the total
length of the segments of the diagonal not contained within the circle.  Choose the correct choice from the following answers:
A) √4-1  B) √2-1  C) √3-1  D) √5-1  E) √6-1

Solution: The diagonal has length √2.It passes through the center of the circle, so it contains   a diameter of the circle. The length of the diagonal within the circle is therefore 1. The rest of   the diagonal outside of the circle has total length √2-1   correct answer √2-1
Answer: B
Mary charges $8.50 per hour to clean a house. If she works 20 hours, how much
does she earn in one week? Pick one.
A) $170.00 B) $110.50 C) $210.50 D) $410.50 E) $310.50

Solution: Multiply 20 hours x $8.50 =   $170.00nswer: $170.00   correct answer $170.00
Answer: A
A person purchased a TV set for Rs. 15000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?	Choose one: A) 16.58% B) 87.58% C) 46.58% D) 17.58% E) 18.58%

Solution: The total CP = Rs. 15000 + Rs. 6250 = Rs. 21250 and SP   = Rs. 31150   Profit(%) = (31150 - 21250)/21250 * 100   = 46.58%   Answer:46.58%
Answer: C
If the area of circle is 745 sq cm then its circumference?  Choose the correct choice from the following answers:
A) 11
B) 88
C) 99
D) 96.8
E) 12

Solution: 22/7 r2 = 745 => r = 15.4   2 * 22/7 * 15.4= 
2 * 22/7 * 15.4 = 96.8
96.8 Answer: 96.8
Answer: D
A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that All the four mangoes are spoiled.
Select:  A) 1/495  B) 494/495  C) 1/395  D) 394/395  E) 396/395

Solution: Out of 12,8 are good and 4 are spoiled.   Required probability = 4C4/12C4 = 1/495.   1/495NSWER:1/495
Answer: A
A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 18 days.In how many days B alone can do the work?
Pick one.
A) 5days	B) 7 days	C) 27 days	D) 9 days	E) 10 days

Solution: Explanation:   A’s 5 day work = 5*1/15=1/3   Remaining work = 1-1/3=2/3   B completes 2/3 work in 6 days   B alone can do in x days   2/3*x=18   X=27 days   Answer: Option 27 days
Answer: C
If the wages of 6 men for 15 days be Rs.2100, then find the wages of for 12 days.  Choices:
A) 2025
B) 2820
C) 2028
D) 2250
E) 2520

Solution: Let the required wages be Rs. x.   More men, More wages	(Direct Proportion)   Less days, Less wages	(Direct Proportion)   Men 6: 9 : :2100:x   Days 15:12   Therefore (6 x 15 x x)=(9 x 12 x 2100) = x=(9 x 12 x 2100)/(6 x 15)=2520   Hence the required wages are Rs. 2520.   Answer is 2520.
Answer: E
Some persons can do a piece of work in 24 days. Two times the number of these people will do half of that work in?	Options
A) 3 B) 4 C) 5 D) 6 E) 8

Solution: 24/ (2 * 2)= 
24/ (2 * 2) = 6
6 days   Answer:6
Answer: D
Set J consists of the terms {a, b, c, d, e}, where e > d > c > b > a > 0.5. Which of the following operations would decrease the standard deviation of Set J?
Pick.
A) Multiply each term by e/d B) Divide each term by b/c C) Multiply each term by −1 D) Divide each term by d/e E) Multiply each term by a/e

Solution: CONCEPT: Standard Deviation is Defined as Average Deviation of Terms in the set from the Mean value of the set. i.e.   1) It depends on the separation between the successive terms of the set   2) If a Constant Value is Added/Subtracted in every terms of set then the Separation between successive terms does NOT change Hence S.D. remains Constant   3) If a Constant Value is Multiplied in every terms then the Separation between succesive terms gets multiplied by the constant Hence S.D. remains gets multiplied by same Number   Multiply each term by a/e
Answer: E
Right now, the ratio between the ages of Karthik and Prasath is 4:3. After 6 years, Karthik’s age will be 26 years. What is the age of Prasath right now?  Choices:
A) 15 years
B) 35 years
C) 25 years
D) 45 years
E) 55 years

Solution: A   15 years   If the current ages of Karthikh and Prasath be 4A years and 3A years correspondingly.   Then, 415 years + 6 = 26   415 years = 20   15 years = 5   Prasath’s age = 315 years = 15 years.
Answer: A
The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?  Choices:
A) 288
B) 240
C) 288
D) 277
E) 211

Solution: 4a = 68 => a = 17   172 – 82 = 152   1/2 * 16 * 30= 
1/2 * 16 * 30 = 240
240.Answer: 240
Answer: B
On a weekend, 4 friends went skiing and evenly split the cost of their cabin. If the amount paid by each person was an integer, which of the following could not have been the cost of the cabin? Choose the correct choice:
A) $448 B) $492 C) $614 D) $548 E) $356

Solution: Each of the seven persons evenly splitting the cost is an integer amount, therefore check the divisibility by 4 for all answer choices.   448/4= 
448/4 = 112
112   492/4= 
492/4 = 123
123   614/4= 
614/4 = 307/2 = around 153.5
153.50   548/4= 
548/4 = 137
137   356/4= 
356/4 = 89
89   C is not an integer amount.   Answer:$614
Answer: C
The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
Choose the correct option
A) 18	B) 16	C) 26	D) 17	E) 11

Solution: Explanation:   1500 ---- 270   100 ---- ? => 18%   18nswer:18
Answer: A
In a 160 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
Choose the correct choice from the following choices:
A) 22 seconds B) 12 seconds C) 13 seconds D) 18 seconds E) 28 seconds

Solution: B runs 56 m in 7 sec.   => B runs 160 m in 7/56*160= 
7/56*160 = 20
20 seconds   Since A beats B by 7 seconds, A runs 160 m in (20-7)= 
(20-7) = 13
13 seconds   Hence, A's time over the course= 13 seconds   ANSWER:13 seconds
Answer: C
Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?  Choose the correct answer: A) 20% B) 25% C) 40% D) 15% E) None of these

Solution: Explanation :   Assume that the merchant while purchasing, purchases 120cm at Rs120 , that is 1cm at Rs1.   He sells 80 cm at Rs 120.   While the original CP = Rs 80 for 80 cm.   20% discount on 120 = 24,   So, actual SP = 120-24= 
120-24 = 96
96   Profit= 96-80= 
96-80 = 16
16   P%= (P/CP) x 100 = (16/80) x 100 = 20%.   20%nswer : 20%
Answer: A
Three coins are tossed in the air and two of the coins land with heads face upwards. What are the chances on the next toss of the coins that atleast two of the coins will land with heads face upwards again? Choose the correct choice from the following answers.
A) 80 percent.	B) 70 percent.	C) 50 percent.	D) 40 percent.	E) 30 percent.

Solution: C   50 percent.   It is a certainty that atleast two coins will land with the same side face up. It is equally likely that these two coins will land heads up as they will land tails upwards. It is immaterial what occurred in the previous toss.
Answer: C
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?	Options
A) 100  B) 60  C) 30  D) 20  E) 10

Solution: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women   = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5= 
(4 * 3)/(2 * 1) * 5 = 30
30 ways.   ANSWER:30
Answer: C
The radius of a semi circle is 70 cm then its perimeter is?	Select the correct option.
A) 32.8	B) 32.4	C) 360	D) 32.2	E) 32.9

Solution: Diameter = 140 cm   1/2 * 22/7 * 140 +140= 
1/2 * 22/7 * 140 +140 = 360
360   Answer : 360
Answer: C
What is the probability of randomly selecting an arrangement of the letters of the word "MEDITERRANEAN" in which the first letter is E and the last letter is R? Choose one:  A) 1/13  B) 1/20  C) 1/26  D) 1/50  E) 1/100

Solution: There are 13 letters in MEDITERRANEAN, out of which E appears thrice, N appears twice, A appears twice, and R appears twice.   The number of arrangements of MEDITERRANEAN is therefore 13!/3!2!2!2!   The number of arrangements in which the first letter is E and the last letter is R is 11!/2!2!2! (we are left with 11 letters out of which E appears twice, N appears twice and A appears twice).   P=(11!/2!2!2!)/(13!/3!2!2!2!)=11/!2!2!2!∗3!2!2!2!/13!=3!/12∗13=1/26   Answer: 1/26.
Answer: C
A 300 m long train crosses a platform in 38 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Choose the correct choice from the following
A) 288  B) 350  C) 889  D) 276  E) 333

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/38 = 50/3   3x + 900 = 1900 => x = 333 m.   Answer:333
Answer: E
An unbiased die is tossed. Find the probability of getting a multiple of 7
Answers
A) A)1/3 B) B)2/5 C) C)1/4 D) D)2/3 E) E)1/7

Solution: Here S = {1,2,3,4,5,6,7}   1/7 = event of getting a multiple of 3   1/7 = {7}   P(1/7) = 1/7   Answer is 1/7
Answer: E
Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $420 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?	Choices
A) $214 million
B) $1120 million
C) $1144 million
D) $1240 million
E) $1080 million

Solution: Convert units to millions as answer is in millions   1996 Imports = $1.44 bill = $1440 mill   i.e. 1440/12 = $120 mill/month   1997 Imports = $420 mill/2 month   i.e. $210 mill/month   Difference/month = 210-120= 
210-120 = 90
90   Difference/year= $90 mill * 12 = $1080 mill   ANSW$1080 millionR: $1080 million
Answer: E
The end of a blade on an airplane propeller is 15 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet)	Pick:
A) 200π  B) 240π  C) 300π  D) 450π  E) 1,200π

Solution: 450πistance traveled in 1 revolution = 2πr= 2π15/5280   Revolutions in one second= 1320   Revolutions in 60 seconds (one minute)= 1320*60   Total distance traveled= total revolutions *distance traveled in one revolution   1320*60 *2π15/5280= 450π   450π is the answer
Answer: D
What is the unit digit in 7^105 ?	Pick one:
A) 9  B) 7  C) 3  D) 8  E) 5

Solution: Unit digit in 7^105 = Unit digit in [ (7^4)^26 x 7 ]   But, unit digit in (7^4)^26 = 1   Unit digit in 7^105 = (1 x 7) = 7.   Answer 7) 7.
Answer: B
A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 50 extra yellow balls and making ratio of white balls to yellow balls 7/11. How many tennis balls did the retailer order originally.
Choose the correct choice from the following choices.
A) 17.5 B) 130 C) 175 D) 195 E) 220

Solution: White:Yellow = x:(x+50) = 7:11 --> 11x = 7x + 350 --> x = 87.5.   The total # of balls originally x + x = 87.5 + 87.5= 
87.5 + 87.5 = 175
175.   Answer: 175.
Answer: C
The age of Ritu’s mother is 6 times that of Ritu’s age. After 6 years it will be 3 times that of Ritu’s age. what is Ritu’s present age?  Choose the most appropriate option
A) 4 years B) 8 years C) 6 years D) 10 years E) 12 years

Solution: let us consider 'm' be the ritu's mom's age and 'r' be the ritu's present age   Given: m=6r ;   m+6=3(r+6);   6r+6=3r+18;   as we solve for r, we get ritu's age as 4 years.   4 yearsNSWER:4 years
Answer: A
P can do a work in 72 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.  Select the correct option:
A) 7
B) 8
C) 9
D) 10
E) 30

Solution: Work done by P in 1 day = 1/72   Work done by Q in 1 day = 1/9   Work done by R in 1 day = 1/12   Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36   Work done by Q and R in 3 days = 3Ã—7/36 = 7/12   Remaining work = 1 â€“ 7/12 = 5/12   Number of days in which P can finish the remaining work = (5/12) / (1/72)= 
(5/12) / (1/72) = 30
30   Option 30
Answer: E
If the radius of a cylinder is made 3 times and so is the height, what is the new volume of the cylinder divided by the old one? Select the correct option
A) 27. B) 2. C) 6. D) 4. E) 10.

Solution: let v and v' be the original and the changed volume   now   v=pir^2h   v'=pi(3r)^2(3h)   v'=27v   27.) 27
Answer: A
Find the compound interest on $1200 for 3 years at 20% p.a. if CI is component yearly?
Options:
A) $120	B) $150	C) $874	D) $250	E) $300

Solution: A = P(1 + R/100)^T   = 1200(1 + 20/100)^3   =$2074   $874I = $874   Answer is $874
Answer: C
Find 40 % of 320 Pick one
A) 96	B) 94	C) 128	D) 74	E) 110

Solution: We know that R % of m is equal to R/100 × m.   So, we have 40 % of 320   40/100 × 320   = 128   Answer:128
Answer: C
Two trains are moving in opposite directions with speed of 70 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. the slower train cross the faster train in --- seconds Choose the correct choice from the following answers:
A) 56 B) 45 C) 47 D) 26 E) 25

Solution: Explanation:   Relative speed = 70+90= 
70+90 = 160
160 km/hr (Since both trains are moving in opposite directions)   Total distance= 1.1+.9= 
1.1+.9 = 2
2km   Time= 2/160 hr = 1/80 hr = 3600/80 seconds = = 45 seconds   Answer: Option 45
Answer: B
Statement : A large majority of the work force in India is unorganised. Most of them earn either the minimum or uncertain wages while others are engaged in sundry jobs.
Conclusions :
I. The workers in the organised sector get better facilities and stay longer in their jobs.
II. Some workers in the unorganised sector of the work force have a regular and fixed income.	Choose the correct choice from the following choices
A) Only conclusion I follows  B) Only conclusion II follows  C) Either I or II follows  D) Neither I nor II follows  E) Both I and II follow

Solution: Explanation:   Conclusion I is not stated in the statement.   Only Conclusion II follows.   Option Only conclusion II follows
Answer: B
When 1 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number? Choices.
A) 30
B) 81
C) 60
D) 27
E) 11

Solution: Explanation:   Let the number be   1 + 1/2[1/3(a/5)] = a/15   => 1 = a/30 => a = 30   30nswer:30
Answer: A
The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 18 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?	Choose the correct choice from the following answers:	A) 51.25	B) 52.5	C) 53.75	D) 55.0	E) 55.5

Solution: Rate of flow of water in second hour = 18 gallons per hour   Rate of flow of water in first hour = 18/(3/2)= 
18/(3/2) = 12
12 gallons per hour   Rate of flow of water in third hour= (125/100)* 18 = (5/4) * 18= 
(5/4) * 18 = 45/2 = around 22.5
22.5 gallons per hour   Number of gallons of water that flowed through the pipe during the entire 3 hours= 12+18+22.5= 
12+18+22.5 = 52.5
52.5 gallons   Answer 52.5
Answer: B
A school has 4 section of Chemistry in Class X having 60, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student. Choose the correct option
A) 50
B) 52
C) 51
D) 53
E) None of the above

Solution: Required average marks   = 60Ã—50+35Ã—60+45Ã—55+42Ã—45/60+35+45+42   = 3000+2100+2475+1890/182   = 9465â„182 = 52   Answer 52
Answer: B
A man has Rs.700 in the denominations of five-rupee notes,ten-rupee notes and 20-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 choices:
A) 20
B) 70
C) 60
D) 90
E) 80

Solution: Let number of notes of each denomination be x.   Then 5x +10x + 20x = 700   35x = 700   x = 20.   Hence, total number of notes = 3x = 60.   Answer is 60
Answer: C
A man engaged a servant on the condition that he would pay him Rs.500 and a uniform after one year service. He served only for 9 months and received uniform and Rs.300, find the price of the uniform?
Pick one.
A) s.80 B) s.85 C) s.90 D) s.300 E) s.120

Solution: 9/12 = 3/4 * 500= 
3/4 * 500 = 375
375   300   -------------   75   1/4 -------- 75   1 --------- ?=> Rs.300   ANSWER:s.300
Answer: D
P and Q invested in a business. They earned some profit which they divided in the ratio of 2:3. If P invested Rs.60, 000, the amount invested by Q is:  Choose the correct choice from the following.
A) Rs. 65,000 B) Rs. 70,000 C) Rs. 80,000 D) Rs. 90,000 E) Rs. 60,000

Solution: Suppose Q invested Rs.y. Then, y = 60,000/y = 2/3   or y = 60000/2 * 3   = 90,000.   ANSWER:Rs. 90,000
Answer: D
The arithmetic mean of the scores of a group of students in an exam was 61. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of the remaining 55% is:  Choose the correct choice from the following:
A) 45	B) 50	C) 67.72 approximately	D) 74.6 approximately	E) None of these

Solution: Let the required mean score be x. Then, 20 x 80 + 25 x 31 + 55 x x = 61 x 100   1600 + 775 + 55x = 6100   55x = 3725   x = 3725/55 = 67.72   Answer : 67.72 approximately
Answer: C
A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that Not all the mangoes are spoiled. Choices
A) 1/495  B) 394/395  C) 494/495  D) 1/395  E) 4/395

Solution: Required probability = 1 – 1/495   = 494/495.   ANSWER:494/495
Answer: C
How many integers between 100 and 160, inclusive, cannot be evenly divided by 3 nor 5?  Select the correct option.
A) 32  B) 27  C) 25  D) 35  E) 29

Solution: The total numbers between 100 and 160, inclusive, is 61.   3*34= 
3*34 = 102
102 and   3*53= 
  3*53 = 159
159 so the number of multiples of 3 is 20.   5*20= 
5*20 = 100
100 and   5*32= 
  5*32 = 160
160 so the number of multiples of 5 is 13.   However, the multiples of 15 have been counted twice.   15*7= 
15*7 = 105
105 and   15*10= 
  15*10 = 150
150 so the number of multiples of 15 is 4.   Thus the total number is  61-20-13+4= 
 61-20-13+4 = 32
32.   The answer is 32.
Answer: A