MU-NLPC/Calc-aqua_rat huggingface dataset:
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?	Select.
A) 788  B) 144  C) 298  D) 177  E) 191

Solution: Explanation:   The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 6= 
 24 * 6 = 144
144.   Answer: 144
Answer: B
A certain number of workers can do a work in 35 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
Choose the correct choice from the following answers.
A) 25  B) 30  C) 28  D) 24  E) 32

Solution: number of workers = 10* (35-10)/10= 
10* (35-10)/10 = 25
25   25nswer is 25
Answer: A
Rahul went to a shop and bought things worth Rs. 50, out of which 80 Paise went on sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?	Select:
A) 21.4	B) 12.4	C) 41.2	D) 39.2	E) 32.9

Solution: Total cost of the items he purchased = Rs.50   Given that out of this Rs.50, 80 Paise is given as tax   => Total tax incurred = 80 Paise = Rs.80/100   Let the cost of the tax free items = x   Given that tax rate = 8%   ∴ (50−80/100−x)8/100 = 80/100   ⇒ 8(50 −0.8 −x) = 80   ⇒ (50 − 0.8 − x) = 10   ⇒ x = 50 − 0.8−10 = 39.2   39.2)
Answer: D
In how many ways can 4 boys and 3 girls be seated on 8 chairs so that no two girls are together? Select the correct option:	A) 5760	B) 14400	C) 480	D) 56	E) 40320

Solution: Let us take opposite of the constraint.   2 girls sitting together:	:   1 case is GGBGBBBB.   Total number of ways=3!*5!*5 with just shifting the rightmost girl.   Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.   So total number of ways = 3!*5!(5+4+3+2+1)=120*90= 
120*90 = 10_800
10800   Similarly another case is:   GBGGBBBB.   Using the above reasoning, the total number of cases is: 3!*5!*(15)=10800   Let us take 3 girls sitting together   GGGBBBBB   There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways   So total is   2*10800 + 4320= 
  2*10800 + 4320 = 25_920
25920   The total number of possibilities= 8! Ways =40,320   5760nswer is 40320-25920=5760   Hence 5760.
Answer: A
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 5 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?  Choose the most appropriate option.
A) 60 gallons	B) 200 gallons	C) 120 gallons	D) 180 gallons	E) 130 gallons

Solution: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40   Volume of 1/40 part = 5 gallons\   Volume of whole = 5 * 40= 
5 * 40 = 200
200 gallons.   ANSWER:200 gallons
Answer: B
One fourth of one third of two fifth of a number is 15. What will be40% of that number	Choose the correct choice from the following answers.
A) 140
B) 150
C) 180
D) 200
E) 220

Solution: Explanation:   (1/4) * (1/3) * (2/5) * x = 15   then x = 15 * 30= 
15 * 30 = 450
450   40% of 450= 180   Answer: Option 180
Answer: C
There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R? Options: A) 8 B) 10 C) 12 D) 14 E) 15

Solution: Number of ways in which one can travel from P to R   =3×4=12   Answer: Option 12
Answer: C
1000 men have provisions for 17 days. If 500 more men join them, for how many days will the provisions last now?
Choose the correct choice from the following answers:	A) 12.9	B) 12.5	C) 11.3	D) 12.2	E) 12.1

Solution: 1000*17 = 1500*x   x = 11.3   Answer: 11.3
Answer: C
The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
Select the correct option
A) 2:8	B) 2:0	C) 2:2	D) 2:1	E) 2:5

Solution: Let C.P. = Rs. 5x and S.P. = Rs. 7x.   Then, Gain = Rs. 2x   Required ratio = 2x : 5x = 2:5   Answer:2:5
Answer: E
A train moves fast a telegraph post and a bridge 250 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Choices:
A) 70
B) 39
C) 79
D) 75
E) 71

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 250)/20 = y   y = 20.83   Speed = 20.83 m/sec = 20.83 * 18/5 = 75 km/hr.   Answer:75
Answer: D
A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 6 a.m.? Answers:
A) 23 Minutes B) 24 Minutes C) 29 Minutes D) 26 Minutes E) None of these

Solution: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min   then from 4:00p.m-6:00 a.m =14*2= 
14*2 = 28
28 total=29   ANSWER:29 Minutes
Answer: C
The ratio of two quantities is 2 to 5. If each of the quantities is increased by 5, what is the ratio of these two new quantities? Choices
A) 2/5  B) 5/8  C) 7/13  D) 22/25  E) It cannot be determined from the information given.

Solution: Correct Answer: E   Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.   For example, if x = 2 and y = 5, then (x+5)/(y+5) = (2+5)/(5+5) = 7/10. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+5)/(y+5) = (4+5)/(10+5) = 9/15. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (It cannot be determined from the information given.).
Answer: E
In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
Choose the correct choice from the following answers:
A) 5 km/hr  B) 1 km/hr  C) 6 km/hr  D) 3 km/hr  E) 7 km/hr

Solution: A   5 km/hr   Let Abhay's speed be x km//hr.   Then, 30/x - 30/2x = 3   x = 5 km/hr.
Answer: A
If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+4 ?
Choose the correct choice from the following answers:
A) -2 B) 5 C) -3 D) -4 E) -5

Solution: let we put values. a=1, b=3, c=5   5-3-1= 
5-3-1 = 1
1   1+4= 
1+4 = 5
5   Answer :5
Answer: B
A train 240 m long is running at a speed of 60 km/hr. In what time will it pass a bridge 240 m long?  Pick one
A) 28.8 sec B) 20.33 sec C) 60 sec D) 48 sec E) 49 sec

Solution: total length= 240+240= 
240+240 = 480
480   speed=60 km/h=(60*5)/18= 50/3 m/s   time=(480*3)/50= 
(480*3)/50 = 144/5 = around 28.8
28.8 sec.   28.8 secNSWER:28.8 sec
Answer: A
A sum amounts to Rs.4851 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
Choices
A) s.4000  B) s.5000  C) s.4400  D) s.4800  E) s.5800

Solution: s.4400I=4851,R=5,N=2   s.4400I=P[1+R/100]^2   =P[1+5/100]^2   4851=P[21/20]^2   4851[20/21]^2   4400   ANSWER:s.4400
Answer: C
The sub-duplicate ratio of 16:36 is  Choose the correct choice
A) 4:6	B) 1:2	C) 1:3	D) 1:4	E) 2:3

Solution: root(16):root(36)=4:6   4:6NSWER:4:6
Answer: A
Tina and Rebecca had the same number of candies. Tina gave Rebecca 20 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has now how many candies? Choose the correct choice from the following options:
A) 50
B) 48
C) 54
D) 55
E) 60

Solution: T = R   T - 20 ;R + 20   R + 20 = 5 ( T - 20 )   R + 20 =5T - 100   R - 5T = - 120   We knowR = T, so   R - 5T = - 120   Or, R - 5R = -120   Or, - 4R = - 120   Or, R = 30( This is the initital no of Candies Rebecca had)   Candles now she possesses is 30+ 20= 
 30+ 20 = 50
50   So , Rebecca now has 50 candies.   50nswer will be (50) 50
Answer: A
In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?	Choose the correct choice
A) 3 years
B) 2 years
C) 4 years
D) 1 year
E) 5 years

Solution: Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,   [ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3   n = 3 years.   3 yearsNSWER 3 years 3 years
Answer: A
In given series 22, 33, 66, 99, 121, 279, 594 only one number is incorrect. Find out that wrong number Choose the correct answer:	A) 141	B) 131	C) 121	D) 171	E) 279

Solution: Each of the number except 279 is a multiple of 11.   2 x 11=22   3 x 11=33   6 x 11=66   9 x 11=99   11 x 11=121   25 X 11= 275.... so 279 is wrong   54 x 11=594   ANSW279R:279
Answer: E
A committee is reviewing a total of 40x black-and-white films and 4y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?	Choose the correct choice from the following answers.
A) 20/11
B) 16/11
C) 17/11
D) 10/11
E) 19/11

Solution: Say x=y=10. In this case we would have:   40x=200 black-and-white films;   4y=40 color films.   y/x%=10/10= 
10/10 = 1
1% of the black-and-white films, so 4 black-and-white films and all 40 color films, thus total of 44 films were selected.   Color films thus compose 40/44=10/11 of the selected films.   Answer: 10/11
Answer: D
Car A is 16 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?	Options
A) 1.5
B) 2.0
C) 2.5
D) 3.0
E) 3.5

Solution: Relative speed of car A is 58-50= 
58-50 = 8
8 miles per hour, to catch up 16 miles and drive 8 miles ahead so to drive 24 miles it'll need 24/8= 
24/8 = 3
3 hours.   Answer: 3.0
Answer: D
A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?	Answers
A) 2 B) 4 C) 5 D) 6 E) 24

Solution: C   C.P. of 6 toffees = Re. 1   S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5   For Rs. 6/5, toffees sold = 6. For re. 1.   Toffees sold = 6 * 5/6= 
6 * 5/6 = 5
5
Answer: C
A certain list of 300 test scores has an average (arithmetic mean) of 85 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d ? Choose the correct choice from the following answers
A) 80 and 80  B) 85 and 85  C) 80 and 90  D) 85 and 80  E) 85 and 90

Solution: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.   So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.   According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.   Closest to the mean are 85 and 85 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.   Answer: 85 and 85
Answer: B
If the price of a computer were reduced by 13 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)	Choose one:  A) $844.10  B) $891.10  C) $1,051.90  D) $1,132.30  E) $1,259.60

Solution: Let X be the initial price of computer without discount   then price (final) after discount should be=X(1-16/100)------->X(67/77)=A(say)   means X=A*(77/67).....   so initial price to be integer(As per stem) final price must be multiple of 67   if we check options all were divisible by 67 except option (A)..which is Ans.   $844.10ns $844.10
Answer: A
19 people went to a hotel for combine dinner party 13 of them spent Rs. 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19. What was the total money spent by them.	Choose the correct choice from the following choices
A) 1628.4  B) 1534  C) 1492  D) 1496  E) None of these

Solution: Solution: Let average expenditure of 19 people be x.   then,   19x = 13*79+6*(x+4);   Or, 19x = 13*79+6x+24;   Or, x = 80.84;   So, total money spent = 80.84*19 = Rs. 1536.07.   Answer: Option None of these
Answer: E
Boy sells a book for Rs. 450 he gets a loss of 10%, To gain 10%, at price he should sell? Choices
A) Rs.400  B) Rs.450  C) Rs.550  D) Rs.600  E) Rs.650

Solution: Find Selling Price to gain 10 %.   Now, we are asked to find selling price to gain 10% profit.   Hint:   Selling Price = (100 + Gain%) × C.P.   100   Selling Price = (100 + 10) × 500   100   Selling Price = (110) × 500   100   Therefore, selling Price = Rs.550   Rs.550
Answer: C
A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?
Choose the correct answer: A) at 10:30 am B) at 11:30 am C) at 12:30 pm D) at 1:30 pm E) at 2:30 pm

Solution: The filling rate is 1/4 and the draining rate is 1/5.   The combined rate of filling and draining is 1/4 - 1/5 = 1/20.   Let x be the number of hours before the drain was opened.   x/4 + (14-x)/20 = 1   5x + 14 - x = 20   4x = 6   x = 1.5   The answer is 10:30 am.   The answer is at 10:30 am.
Answer: A
In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally? Choose one.
A) 20% B) 25% C) 30% D) 35% E) 40%

Solution: Let x be the number of cars and let y be the number of cars parked illegally.   4%*x = 20%*y   y/x = 1/5 = 20%   The answer is 20%.
Answer: A
P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?	Options:	A) 17:9	B) 17:76	C) 17:9	D) 17:2	E) 17:3

Solution: P:Q = 85000 : 15000 = 17:3.   Answer: 17:3
Answer: E
Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?  Select the correct option.
A) 20000 B) 10000 C) 25000 D) 34000 E) 30000

Solution: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000   30000
Answer: E
A watch which gains uniformly is 2 minutes low at noon on monday and is 4 min.48 sec fast at 2 p.m on the following monday. when was it correct ? Choices
A) 2.10 p.m on wednesday.
B) 2.20 p.m on wednesday.
C) 2.30 p.m on wednesday.
D) 2.40 p.m on wednesday.
E) 2.00 p.m on wednesday.

Solution: Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours   \therefore The watch gains \inline \left ( 2+4\frac{4}{5} \right ) min. or \inline \frac{34}{5} min. in 170 hrs.   Now, \inline \frac{34}{5} min. are gained in 170 hrs.   \inline \therefore 2 min are gained in \inline \left ( 170\times \frac{5}{34}\times 2 \right ) hrs = 50 hrs   \inline \therefore Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at 2 p.m on wednesday.   Answer 2.00 p.m on wednesday.
Answer: E
A portion of the 85% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced? Answers:
A) 5/13 B) 6/13 C) 9/13 D) 13/9 E) 13/6

Solution: Let the original amount of 85 percent solution = x and amount replaced be y   0.85(x - y)+ 0.2y = 0.4 x   0.85x -0.85y+0.2y = 0.4x   0.45x = 0.65y   9x = 13y   y = 9x/13   So, amount replaced = 9/13 of original amount   ANSWER:9/13
Answer: C
Sujit incurred a loss of 45% on selling an article for Rs.3740/-. What was the cost price of the article?	Choose the correct choice from the following
A) Rs.5725/- B) Rs.5080/- C) Rs.6250/- D) Rs.6750/- E) None of these

Solution: Explanation:   45% loss means SP of Rs.3740/- is 55% of CP   :. CP = 3740x100/55 = Rs.6800/-   Answer: Option None of these
Answer: E
By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Choose the correct choice from the following
A) 8
B) 9
C) 12
D) 16
E) 18

Solution: Explanation:   80% --- 12   120% --- ?     80/120 * 12= 
  80/120 * 12 = 8
8   8NSWER IS 8
Answer: A
A can do a job in 18 days and B can do it in 24 days. A and B working together will finish twice the amount of work in days?  Choose the correct choice from the following options
A) 22 1/6
B) 22 1/2
C) 20 4/7
D) 22 1/9
E) 22 1/1

Solution: 1/18 + 1/24 = 7/72   72/7 = 72/7 *2 = 20 4/7 days   Answer: 20 4/7
Answer: C
If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs 1920 less than the principal. What was the principal? Choose the correct choice from the following options:  A) 1500  B) 2500  C) 2507  D) 3200  E) 2400

Solution: P - 1920 = (P*5*4)/100   P = 2400   Answer: 2400
Answer: E
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is:  Choices:	A) 22	B) 50	C) 99	D) 35	E) 12

Solution: Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr.Answer: 35
Answer: D
3/4th of a number exceeds its 2/3rd by 8. What is the number?  Choose the correct choice from the following answers:
A) 22 B) 77 C) 28 D) 96 E) 26

Solution: Explanation:   Let the number be x.   3/4x = 2/3x + 8   Multiply by 12   9x = 8x + 96   x = 96   ANSWER:96
Answer: D
A and B start a business jointly. A invests Rs 16000 for 8 month and B remains in the business for 4 months. Out of total profit, B claims 2/7 of the profit . How much money was contributed by B? Choose the correct choice:
A) 12800
B) 13000
C) 11500
D) 12500
E) 12000

Solution: B claims 2/7 of the profit   12800 claims remaining 5/7 of the profit   => 12800 : B =5/7:2/7=5:2   Let the money contributed by B =b   Then 12800:B =16000×8:b×4   Therefore,   16000×8:b×4=5:2   16000×8×2=b×4×5   16000×2×2=b×5   3200×2×2=b   b=12800   12800nswer is 12800.
Answer: A
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 502 to 600 inclusive?	Options.
A) 23,550	B) 27,550	C) 31,550	D) 35,550	E) 39,550

Solution: 2 + 4 + 6 + 8 +...+ 100 = 2550   502 + 504 + ... + 600 = 50(500) + (2+4+...+100) = 25,000 + 2550 = 27,550   The answer is 27,550.
Answer: B
0.999999+0.111111=?
Options
A) 1  B) 1.0001  C) 1.0021  D) 1.111  E) 1.11111

Solution: 0.999999 + 0.111111   = 0.999999 + 0.11111 + 0.000001   = (0.999999 + 0.000001) + 0.11111   = 1 + 0.11111= 
1 + 0.11111 = 1.11111
1.11111   1.11111
Answer: E
If a cyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent, what percent of the original speed is the total increase in speed?  Choose the correct choice from the following choices.
A) 10% B) 40% C) 43% D) 64% E) 140%

Solution: let the sped be 100   an increase of 30%   the speed now is 130   a further increase of 10% on 130 =13   total increase =43 on 100 =43% 43%
Answer: C
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *5 + 3 and *5 + 5, inclusive?	Select the correct option:
A) None
B) One
C) Two
D) Three
E) Four

Solution: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *5 would be divisible by all numbers from 1 to 5.   => *5+3 would give me a number which is a multiple of 3 and therefore divisible (since *5 is divisible by 3)   In fact adding anyprimenumber between 1 to 5 to *5 will definitely be divisible.   So the answer is none (A)!   Supposing if the question had asked for prime numbers between *5 + 3 and *5 + 11 then the answer would be 1. For *5 +3 and *5 + 13, it is 2 and so on...   None
Answer: A
If P and Q are positive integers, P - 2 is divisible by 4 and Q - 1 is divisible by 6, all of the following could be the value of P - Q Except?	Choose the correct option:
A) 3	B) 1	C) 15	D) 4	E) 29

Solution: P-2 = 4Q   => P = 4Q + 2 = 2,6,10,14,18,22,26,30,34,38,42,46,50   Q-1 = 6P   => Q = 6P + 1 = 1,7,13,19,25,31,37,43,49,55,61,67,73   3=10-7   1=14-13   15=34-19   29=42-13   So , we can see that all the answer choices are possible here except 4
Answer: D
The length of a bridge in meters, which a train 120-meters long and traveling at 45 km/hr can cross in 30 seconds is?  Choose the correct choice from the following choices
A) 255
B) 285
C) 315
D) 345
E) 375

Solution: 45 km/h = 45000 m/3600 s = 12.5 m/s   In 30 seconds, the train can go 30(12.5) 45000  /3600= 
45000  /3600 = 25/2 = around 12.5
12.5 m/s   In 30 seconds, the train can go 30(12.5)= 375 meters   Let x be the length of the bridge.   x+120 = 375 meters   x = 255 meters   The answer is 255.
Answer: A
Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be? Choose the correct answer.
A) 2  B) 3  C) 4  D) 5  E) 7

Solution: 2 + 3 + 5 + 7 + 11= 
2 + 3 + 5 + 7 + 11 = 28
28 ( sum is even)   Least number= 2   2
Answer: A
A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey? Answers
A) 20	B) 30	C) 35	D) 45	E) 50

Solution: Ans.(A)   Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: A
In a group of ducks and cows, the total number of legs are 36 more than twice the no. of heads. Find the total no.of buffaloes.
Pick one.
A) 10  B) 12  C) 13  D) 15  E) 18

Solution: Let the number of buffaloes be x and the number of ducks be y   => 4x + 2y = 2 (x + y) + 36   => 2x = 36 => x = 18   18
Answer: E
Three coworkers P , T , R meet for Dinner. P had 5 sandwiches, T had 3 and R had none. Both PT share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PT, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.  Choose the correct choice from the following answers.
A) a) 5$  B) b) 3 $  C) c) 7 $  D) d) 4 $  E) e) 5.5 $

Solution: we got total 8 sandwiches ....we are dividing equally in 3 people.   per person: 8/3   initially   p:8   T:3   r:0   now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.   now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r   ok we have 8 dollars for 8/3 sandwich   therefore for 7/3 sandwich we will get 7 dollars.   hence p should get 7 dollars.   hence c) 7 $
Answer: C
Which of the following could be the sum of the reciprocals of two prime numbers?  Choose the correct choice from the following options.
A) 7/15  B) 11/12  C) 11/30  D) 8/15  E) 19/77

Solution: 10/12 it is   8/15=(1/3) + (1/5)   Answer - 8/15
Answer: D
The average age of 6 persons living in a house is 23.5 years. Three of them are majors and their average age is 42 years. The difference in ages of the three minor children is same  Pick:
A) 6 years
B) 5 years
C) 3 years
D) 8 years
E) 9 years

Solution: B   5 years   Total age of six persons = 23.5 × 6 = 141 years Total age of three major persons = 42 × 3 = 126 years   ∴ Total age of three minor children = 141 – 126 = 15 years The difference in ages of the three minor children is same. Therefore, we take ages may be: 5, 5, 5; 3, 5, 7; 2, 5, 8 and 1, 5, 9 In all the cases, median will be 5 years   Mean age of minor children = 15/3= 
15/3 = 5
5 years
Answer: B