MU-NLPC/Calc-aqua_rat huggingface dataset:
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?  Choose the correct choice from the following options
A) 20 years	B) 21 years	C) 23 years	D) 25 years	E) 26 years

Solution: Explanation:   Let the average age of the whole team be x years.   11x - (26 + 29) = 9 (x - 1)   => 11x - 9x = 46   => 2x = 46   => x = 23.   So, average age of the team is 23 years. Answer: 23 years
Answer: C
A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?  Choices:
A) 767 kmph
B) 55 kmph
C) 54 kmph
D) 33 kmph
E) 37 kmph

Solution: D = 100 + 125= 
100 + 125 = 225
225   T= 15   S = 225/15 * 18/5= 
225/15 * 18/5 = 54
54 kmph   Answer: 54 kmph
Answer: C
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 80 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad? Choose the correct choice.
A) 16 B) 18 C) 40 D) 24 E) 30

Solution: Time taken = Total Distance / Relative Speed   Total Distance = 80 kms   Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4= 
6+ 4 = 10
10 kms/hr   Time taken= 80 / 10= 
80 / 10 = 8
8 hrs   Distance traveled by Brad= Brad's speed * time taken = 6 * 8 = 40 kms... Answer - 40
Answer: C
The average salary of all the workers in a workshop is Rs. 9500. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
Select the correct option
A) A)23 B) B)21 C) C)52 D) D)56 E) E)12

Solution: Let the total number of workers be x. Then,   9500x   = (12000 * 7) + 6000(x - 7)   => 3500x = 42000   = x =12.   Answer:12
Answer: E
Car A runs at the speed of 42km/hr & reaches its destination in 6hr. Car B runs at the speed of 52 km/h & reaches its destination in 9h. What is the respective ratio of distances covered by Car A & Car B? Choose the correct answer.
A) 11 : 6
B) 7 : 13
C) 13 : 7
D) 15 : 6
E) 13 : 6

Solution: Sol. Distance travelled by Car A = 42 × 6 = 252 km   Distance travelled by Car 7 : 13 = 52 × 9 = 468 km   Ratio = 252/468= 7 : 13   7 : 13
Answer: B
From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
Answers:
A) 2/1223
B) 1/122
C) 1/221
D) 3/1253
E) 2/153

Solution: Let s is the sample space. then   n(s ) = 521/2212 = 1326   E = event of getting 2kings out of 4   n(E) = 41/2212 = 6   P(E) = 6/1326 = 1/221   Answer is 1/221
Answer: C
IF
1= O
2= T
3= T
4=F
5= F
THEN 6=?
Select.
A) S B) J C) K D) L E) M

Solution: IF   1= O... First letter of ONE.   2= T.... First letter of TWO.   3= T   4=F   5= F   THEN 6=S ... First letter of SIX.   SNSWER:S
Answer: A
The sum of the mean, the median, and the range of the set {1, 2, 4,6,8,10,12} equals which one of the following values? Choose the correct choice from the following options.
A) 2.6 B) 14.23 C) 22.14 D) 8.6 E) 10

Solution: set {1, 2, 4,6,8,10,12}   Mean = (1+2+4+6+8+10+12)/7 = 6.14   Meadian = Middle term = 6   Range = Highest - Lowest = 12-1 = 10   Mean+Median+Range = 6.14+6+10= 
6.14+6+10 = 22.14
22.14   Answer: Option 22.14
Answer: C
A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained? Choose the correct choice from the following options
A) 9:1 B) 9:2 C) 9:8 D) 9:5 E) 9:0

Solution: Explanation:   Milk = 3/5 * 20= 
3/5 * 20 = 12
12 liters, water= 8 liters   If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.   Remaining milk = 12 - 6= 
12 - 6 = 6
6 liters   Remaining water= 8 - 4= 
8 - 4 = 4
4 liters   10 liters of pure milk are added, therefore total milk= (6 + 10)= 
(6 + 10) = 16
16 liters.   The ratio of milk and water in the new mixture= 16:4 = 4:1   If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10= 
4/5 * 10 = 8
8 liters.   Amount of water removed= 2 liters.   Remaining milk = (16 - 8)= 
(16 - 8) = 8
8 liters.   Remaining water= (4 -2)= 
(4 -2) = 2
2 liters.   The required ratio of milk and water in the final mixture obtained= (8 + 10):2 = 18:2 = 9:1.   9:1nswer: Option 9:1
Answer: A
If x is an odd negative integer and y is an even integer, which of the following statements must be true?
I. (x - 2y) is odd
II. xy^2 is an even negative integer
III. (y^2 - x) is an odd negative integer	Choose the correct choice from the following answers
A) I only B) II only C) I and II D) I E) II and III

Solution: If x is an odd negative integer and y is an even integer, which of the following statements must be true?   I. (x - 2y) is odd   x - is always negative and odd   2y - can be 0, when y=0, or always even integer (positivie or negative)   odd integer +/- even integer = always odd   I statement is always true   II. xy^2 is an even negative integer   y can be 0 => xy^2 = 0 (non-negative even) => II statement is not true   III. (y^2 - x) is an odd negative integer   y can be 0 => -x will be positive => III statement is not true   basing on above, only I statement will always be true   answer is I
Answer: D
What is the remainder if 7^8 is divided by 100?
Choose the correct answer:  A) 7  B) 1  C) 9  D) 10  E) 11

Solution: 7^8 can be written as (7^4)^2   If we divide 7^4 by 100 the reminder is 1   So, (7^4)^2 by 100, the reminder is 1^2 = 1   Answer : 1
Answer: B
If it takes a machine 2⁄3 minute to produce one item, how many items will it produce in 1 hours?  Choose one:  A) 1⁄3  B) 4⁄3  C) 90  D) 120  E) 180

Solution: 1 item takes 2/3 min so it takes 60 min to produce x   2x/3=60 the x=90   Answer:90
Answer: C
Two identical trains AA and BB running in opposite direction at same speed tale 2 min to cross each other completely. The number of bogies of AA are increased from 12 to 16. How much more time would they now require to cross each other?  Pick one
A) 40 Sec B) 50 sec C) 60 sec D) 20 sec E) 25 sec

Solution: Total initial bogies is 12+12=2412+12=24   Additional bogies =16âˆ’12=4   24 bogies is   12+12= 
  12+12 = 24
24   additional bogies= 16 - 12= 
16 - 12 = 4
4   24 bogies take 2 min    2*60/24 *4= 
 2*60/24 *4 = 20
20 sec   ANSWER 20 sec
Answer: D
In how many Q ways can a four-letter password be chosen, using the letters A, B, C, D, E, and/or F, such that at least one letter is repeated within the password?  Choices:
A) 720
B) 864
C) 900
D) 936
E) 1,296

Solution: Total number of four letter passwords = 6*6*6*6= 
6*6*6*6 = 1_296
1296 ------(1)   Total number of passwords in which no letter repeats= 6C4*4!= 15*24= 
15*24 = 360
360------(2)   therefore required value Q= (1)-(2)= 1296-360=936.936
Answer: D
When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of W?
Choose the most appropriate option
A) 7	B) 8	C) 9	D) 10	E) 11

Solution: A simple and elegant solution.   As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1   39-15= 
39-15 = 24
24   24 divide by 3 is 8.   Meaning mean of the n terms is 15+8= 39-16= 
39-16 = 23
23   Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.   W*23 +39= 25*(W+1)   W = 7   Ans. (7)
Answer: A
An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 12%. Also, if a customer will “buy at least 10” items they will deduct an additional 8% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
Pick
A) $92.00	B) $88.00	C) $87.04	D) $80.96	E) $80.00

Solution: Without any discount Sam should pay 10*10= 
10*10 = 100
$100. Now, the overall discount would be slightly less than 20%, thus he must pay slightly more than $80. Only answer choice D fits.   Answer: $80.96.
Answer: D
The labeled price of a table is Rs. 6,000. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table? Pick:
A) Rs. 4956
B) Rs. 6195
C) Rs. 6425
D) Rs. 7200
E) None of these

Solution: Explanation:   Labeled price = Rs. 6,000   By giving 5% discount on labeled price, the selling price is   = 95 / 100 * 6,000 = Rs. 5700   By earning 15% profit on the selling of price Rs. 5700 the cost price is   = 100 / 115 * 5700 = Rs. 4956   Therefore, approximate cost is 4956   Rs. 4956NSWER Rs. 4956
Answer: A
A certain amount earns simple interest of 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned? Choose the correct choice
A) 35	B) 350	C) 245	D) Cannot be determined	E) None of these

Solution: Let p and r be the principal amount and rate of interest respectively.   Then, p×r×7/100=1750   or, pr = 25000   Now, SI = p×(r+2)×7/100=1750   We have to find the value of   p×(r+2)×7/100−p×r×7/100= M - 1750   M = SI when the rate of interest is 2% more. When we solve this equation, we find that we have two variables and one equation. Therefore, can’t be determined the correct answer.   Answer Cannot be determined
Answer: D
A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 10 a.m.? Pick one:
A) 5
B) 6
C) 7
D) 8
E) 10

Solution: Relative speed = Speed of A + Speed of B (? they walk in opposite directions)   = 2 + 3= 
2 + 3 = 5
5 rounds per hour=> They cross each other 5 times in 1 hour   Time duration from 8 am to 10 am = 2 hour   Hence they cross each other 10 times before 10 am   Answer is 10
Answer: E
When the scores of the top four students are deleted, the average score of the remaining 66 students falls by 6 marks. Assume that it is possible for two or more students to have the same net score. What is the minimum score possible for the fourth ranking student if no student got a net score of more than 352? Options
A) 280  B) 320  C) 300  D) 340  E) 350

Solution: Explanation :   Sum of score of top four students = 1356   Maximum possible score possible for top three students = 352*3= 
352*3 = 1_056
1056   Hence the minimum possible score for the 4th student= 300   Answer : 300
Answer: C
A and B can do a work in 60 days; B and C can do it in 120 days; A and C can do it in 80 days. In what time A alone can do the work?
Choose the correct choice from the following choices:
A) 100	B) 90	C) 80	D) 70	E) 60

Solution: (A+B)’s one day’s work = 1/60   (B+C)’s one day’s work = 1/120   (A+C)’s one day’s work = 1/80   Adding we get, 2(A+B+C)’ s one day’s work= 1/60 + 1/120 + 1/80   = 28/720   = 14/365   (A+B+C)’ s one day’s work = 14*1/365*2 = 14/720   So, A’s one day’s work = 14/720 - 1/120 = 1/90   A alone can do the work in 90 days.   ANSWER:90
Answer: B
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 200 m. Then, A wins by: Choose the correct choice from the following answers
A) 60 m	B) 100 m	C) 43m	D) 20m	E) 23m

Solution: To reach the winning post A will have to cover a distance of (500 - 200)m, i.e., 300 m.   While A covers 3 m, B covers 4 m.   While A covers 300 m, B covers 4 x 300/3	m	= 400 m.   Thus, when A reaches the winning post, B covers 400 m and therefore remains 100 m behind.   A wins by 100 m.   Answer:	100 m
Answer: B
IN Common Wealth Games an athlete runs 280 meters in 24 seconds. Hisspeed is ? Choose the correct choice from the following choices:  A) 25 km/hr  B) 42.42 km/hr  C) 30 km/hr  D) 32 km/hr  E) None of these

Solution: Explanation :   (280/1000)/(24/3600)=42.42 km/hr   Answer : 42.42 km/hr
Answer: B
In a throw of dice what is the probability of geÆ«ng number greater than 1 Choose the correct choice from the following answers:	A) 1/2	B) 1/3	C) 1/5	D) 5/6	E) None of these

Solution: None of thesexplanation:   Number greater than 1 is 2, 3, 4, 5 & 6, so only 5 number   Total cases of dice = [1,2,3,4,5,6]   So probability = 5/6   Answer: None of these
Answer: E
4^5^6^7^8^9^10 find unit digit  Select the correct option: A) 2 B) 3 C) 4 D) 5 E) 6

Solution: guys first find out unit digit of4^5ie is 4 then   4^6 unit digit its 6   then 6^7^8^9^10=6 bcz 6 unit digit alway 6   ANSW6R:6
Answer: E
Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes? Pick
A) 11 B) 21 C) 33 D) 51 E) 61

Solution: Explanation:   Let the pipe B be closed after x minutes.   30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16   => x = 14/16 * 24= 
14/16 * 24 = 21
21.   Answer:21
Answer: B
Simple interest on a sum at 9% per annum for 2 years is Rs.200. The C.I. on the same sum for the same period is?
Choose the correct choice from the following
A) 201.1 B) 201.5 C) 200.4 D) 109.1 E) 81.1

Solution: SI = 100 + 100   CI = 100 + 100 + 1.1= 
100 + 100 + 1.1 = 201.1
201.1   201.1nswer: 201.1
Answer: A
A walks at 30 kmph and 30 hours after his start, B cycles after him at 55 kmph. How far from the start does B catch up with A? Choices.
A) 1200km  B) 1980km  C) 2000km  D) 2500km  E) 3600km

Solution: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 30 hours.   x/30 - x/55 = 30   x = 1980 km   Answer is 1980km
Answer: B
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:  Choose the correct answer.
A) 8.5 km/hr B) 10 km/hr C) 12.5 km/hr D) 9 km/hr E) 8 km/hr

Solution: Man's speed with the current = 15 km/hr   => speed of the man + speed of the current = 15 km/hr   speed of the current is 2.5 km/hr   Hence, speed of the man = 15 - 2.5= 
15 - 2.5 = 12.5
12.5 km/hr   man's speed against the current= speed of the man - speed of the current   = 12.5 - 2.5= 
12.5 - 2.5 = 10
10 km/hr   ANSWER:10 km/hr
Answer: B
Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 6 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)  Choose the most appropriate option.
A) 7/10	B) 15/14	C) 4/5	D) 5/4	E) Cannot be determined

Solution: 7/10verage Speed of Jack =Distance/ Time   = 42 /6= 
42 /6 = 7
7   7/10verage Speed of Jill= 42/(4.2)= 
42/(4.2) = 10
10   Ratio of 7/10verage speed of Jack to Jill= 7/10   7/10nswer 7/10
Answer: A
A man can row downstream at 22 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?	Choose one
A) 13, 3 B) 12, 6 C) 15, 3 D) 14, 4 E) 16, 6

Solution: Explanation:   Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 22 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 32 => x = 16, y = 6.   Answer: Option 16, 6
Answer: E
If x=y=2z and xyz=256 then what is the value of x?
Select the correct option
A) 12	B) 8	C) 16	D) 6	E) 2

Solution: Given that x=y=z.   so,x=y,   x=2z,   y=2z.   given xyz=256   =>(2z)*(2z)*z=256   =>4z^3=256   =>z=4   then x=2z   =2(4)   =8   ANSWER:8
Answer: B
Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 50 per kg. How much amount did he pay to the shopkeeper?  Pick:
A) A)1000
B) B)1010
C) C)1065
D) D)1075
E) E)1080

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 9 kg of mangoes = 50 × 9 = 450.   Total cost he has to pay = 560 + 450= 
560 + 450 = 1_010
1010.   1010)
Answer: B
There are 1000 students in a school and among them 20% of them attends chess class. 10% of the students who are in the chess class are also enrolled for swimming. No other students are interested in swimming so how many will attend the swimming class if all enrolled attends?
Pick one
A) 1  B) 10  C) 100  D) 50  E) 20

Solution: 20% of 1000 gives 200. so 200 attends chess and 10% of 200 gives 20.   so 20 enrolled for swimming   Answer: 20
Answer: E
Find the odd man out. 1,4,9,16,20  Options:  A) 8  B) 10  C) 25  D) 6  E) 14

Solution: Explanation :   1^2=1   2^2=4   3^2=9   4^2=16   5^2=25   Hence, it is clear that 25 should have come instead of 20   Answer : Option 25
Answer: C
Havid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?  Choose the correct choice from the following:
A) 5/6*d
B) 7/3*d
C) 10/3*d
D) 7/2*d
E) 9/2*d

Solution: Havid has d books;   Jeff has d/3 books;   Paula has 2d books;   Total = d+d/3+2d=10d/3.   Answer: 10/3*d.
Answer: C
Mike needs 30% to pass. If he scored 212 marks and falls short by 25 marks, what was the maximum marks he could have got?	Select the correct option.
A) 343	B) 677	C) 790	D) 867	E) 932

Solution: If Mike had scored 25 marks more, he could have scored 30%   Therefore, Mike required 212 + 25= 
212 + 25 = 237
237 marks   Let the maximum marks be m.   Then 30 % of m= 237   (30/100) × m = 237   m = (237 × 100)/30   m = 23700/30= 
23700/30 = 790
790   Answer:790
Answer: C
Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 24 white marbles. How many red marbles could be in bag A?	Choose the most appropriate option:  A) 1  B) 3  C) 4  D) 6  E) 8

Solution: 6 is the answer.   Bag A-   R:W:B = 2:6:9   Let W in bag A be 6K   Bab B -   R:W = 1:4   Let W in bag B be 4P   W = 24 = 6K+4P   => K =2, P=3   Total Red's in bag A will be 2K = 4   4
Answer: C
The timing of a college is from 12 p.m to 4.20 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
Options.
A) 52 minutes B) 45 minutes C) 30 minutes D) 48 minutes E) 58 minutes

Solution: Explanation:   Total time a student spends in college = 4 hours 20 minutes = 260 minutes   As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes   Hence, the duration of each lecture is = (260 – 20)/5   = 48 minutes   ANSWER 48 minutes
Answer: D
On dividing 12401 by a certain number, we get 76 as quotient and 13 as remainder. What is the divisor?	Choose the correct choice from the following choices:
A) 163  B) 785  C) 852  D) 456  E) 852

Solution: Divisor *quotient+remainder=dividend   divisor=(dividend)-(remainder)/quotient     (12401-13)/76= 
  (12401-13)/76 = 163
163   163nswer(163)
Answer: A
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 15, 25 and 30, what is the minimum possible range in scores of the three test-takers?
Choose the correct choice from the following answers:
A) 25	B) 30	C) 35	D) 15	E) 10

Solution: I simply looked at the 3 different possible scores for each individual test: 15,30,25   We have to find the minimum range:    30-15= 
 30-15 = 15
15   30-25= 
30-25 = 5
5   25-15= 
25-15 = 10
10   The find the minimum range, you have to make the set of the 5 scores as small as possible.   Which means that 4 of the 5 scores of each individual person is zero.   5*5= 
5*5 = 25
25.   25nswer:25
Answer: A
There are 30 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?  Choose the correct answer: A) 435 B) 367 C) 361 D) 297 E) 261

Solution: Explanation:   Total number of persons = n = 30   Shakehands involve only 2 persons = r = 2   Number of shakehands = nCr = 30C2   30C2 = (30 * 29) /(2 * 1)= 
(30 * 29) /(2 * 1) = 435
435   nCr= (n!) / r! (n – r)!   = 30! / 2! 28!   = 435   435NSWER:435
Answer: A
A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2 and 4/5 hours to fill the tank. The leak can drain all the water of the full tank in how many hours? Choose the correct choice from the following answers: A) 4 B) 5 C) 6 D) 7 E) 8

Solution: The rate of the pump + leak = 5/14   1/2 - leak's rate = 5/14   leak's rate = 1/2 - 5/14 = 1/7   The leak will empty the tank in 7 hours.   The answer is 7.
Answer: D
P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together? Choices
A) 491/2)
B) 4(1/2)
C) 4(1/8)
D) 7(1/2)
E) 4(5/2)

Solution: Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.   Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9 of the total   They would take 9/2 days = 4 (1/2) days to complete the work working together.   Answer:7(1/2)
Answer: D
At present George is 10 years older than Jason. After 5 years George will be twice the age of Jason. Find their present age.	Choose the correct choice:	A) 2 and 12	B) 6 and 16	C) 4 and 14	D) 10 and 20	E) 5 and 15

Solution: Let the present age be x and x+10   After 5 years ages will be x+5 and x+15   2 (x + 5) = x + 15   x = 5   Hence the present ages are 5 and 15   Answer : 5 and 15
Answer: E
A cyclist traveled for two days. On the second day the cyclist traveled 6 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
Choices:
A) 5 mph
B) 10 mph
C) 20 mph
D) 30 mph
E) 40 mph

Solution: SOLUTION:   D = 280 Mi   T = 12 hrs   Đây 1 time = T1   Dây 2 time = T2   T2 - T1 = 4 hrs ----- (I)   T1 + T2 = 12 hrs ----- (II)   Adding I and II, T2 = 8 hrs and T1 = 4 hrs   Dày 1 Rate = R1   Dây 2 Rate = R2   R1 - R2 = 10 mph   í.ẹ. R1 = 10 + R2   280 = 8R2 + 4R1   í.ẹ. 280 = 8R2 + 4 (10 + R2)   í.ẹ. R2 = 20 mph   5 mphNSWER: 5 mph
Answer: A
If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?  Choose the correct choice from the following choices:
A) 77
B) 78
C) 79
D) 80
E) 81

Solution: A two-digit number "cd" can be expressed algebraically as 10c+d.   The sum of A + B = (10c+d)+(10d+c)=11(c+d).   The only answer that is a multiple of 11 is 77.   The answer is 77.
Answer: A
The value of B+5B(BB)(2B)when B = 3 is:	Select the correct option
A) 900  B) 810  C) 809  D) 803  E) 813

Solution: Solution:   B+5B(BB)(2B)   Put the value of B= 3 in the above expression we get,   3+ 15(33)(2 x 3)   = 3+ 15(3 Ã— 3)(2 Ã— 3)   = 3 + 810= 
3 + 810 = 813
813   Answer : 813
Answer: E
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5250. The monthly income of P is?  Choose the correct option
A) A)Rs.4078 B) B)Rs.4000 C) C)Rs.4050 D) D)Rs.4027 E) E)Rs.4020

Solution: Let P, Q and R represent their respective monthly incomes. Then, we have:   P + Q = (5050 * 2)= 
(5050 * 2) = 10_100
10100 --- (i)   Q + R= (6250 * 2)= 
(6250 * 2) = 12_500
12500 --- (ii)   P + R= (5200 * 2) = 10500 --- (iii)   Adding (i), (ii) and (iii), we get:   2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv)   Subtracting (ii) from (iv), we get, P = 4050.   P's monthly income = Rs.4050.   Answer: Rs.4050
Answer: C