MU-NLPC/Calc-aqua_rat huggingface dataset:
Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum V in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is Choose the correct choice:  A) 90%  B) 80%  C) 70%  D) 60%  E) 40%

Solution: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:   (a) All 3 investments become worthless.   (b) 2 of the 3 investments become worthless, while 1 doesn’t.   Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.   Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.   The sum of these two probabilities is   0.008 + 0.096= 
  0.008 + 0.096 = 0.104
0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.   The correct answer is A.   This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: A
A cistern is filled by a tap in 3 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how long will it take the leak to empty it? Choose the correct answer
A) 29	B) 28	C) 99	D) 72	E) 61

Solution: 2/7 - 1/x = 1/4   x = 28   Answer: 28
Answer: B
A cyclist covers a distance of 90km in 6 hours. Find the speed of the cyclist.  Choose the correct choice from the following options
A) 30 km/hr.	B) 25 km/hr.	C) 20 km/hr.	D) 15 km/hr.	E) 35 km/hr.

Solution: Speed of the cyclist =D/T =90/6= 
90/6 = 15
15km/hr. Answer : 15 km/hr.
Answer: D
A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
Choices:	A) 17	B) 23	C) 77	D) 26	E) 30

Solution: Explanation :   Let, the number of apples be 100.   On the first day he sells 60% apples i.e.,60 apples. Remaining apples =40.   He throws 15% of the remaining i.e., 15% of 40 = 6.Now he has 40−6=34 apples   The next day he throws 50% of the remaining 34 apples i.e., 17.   Therefore, in total he throws   6+17= 
  6+17 = 23
23 apples.   Answer : 23
Answer: B
Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum? Choices.
A) 30
B) 45
C) 50
D) 25
E) 60

Solution: Let capacity of P be x liters   Then capacity of Q = x/3 liters   capacity of the drum = 60x   Required number of turns = 60x/(x+x/3) = 60x * 3/4x = 45   Answer is 4560  * 3/4= 
60  * 3/4 = 45
45   Answer is 45
Answer: B
In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?	Options:
A) 22  B) 20  C) 25  D) 30  E) 35

Solution: T = (100 * 16500)/(15 * 5000)= 
(100 * 16500)/(15 * 5000) = 22
22 years   22NSWER 22
Answer: A
If x= (y-1)(y+2), then what is the least possible value of x?  Answers:
A) -9/4
B) 9/4
C) 7/4
D) 2
E) 1

Solution: -9/4nswer : -9/4
Answer: A
The area of a triangle is with base 4m and height 5m? Choose the correct choice from the following options.
A) 11	B) 10	C) 99	D) 17	E) 12

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer: 10
Answer: B
A call center has two teams. Each member of Team A was able to process 1/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?
Answers:
A) 3/2
B) 3/4
C) 8/9
D) 1/2
E) 1/5

Solution: Let team B has 8 agents, so team A has 5 agents   Let each agent of team B picked up 5 calls, so total calls by team B = 40   So, each agent in Team A picked up 1 calls, so total calls for team A = 5   Fraction for team B = 40/(40+5) = 8/9 = Answer = 8/9
Answer: C
How many multiples of 5 are there between 1 and 89 ?  Choose the correct choice from the following.
A) 15
B) 20
C) 13
D) 17
E) 22

Solution: 5 multiples are 5,10,15,---------,80,85   It should be mentioned whether 1 and 89 are inclusive.   the answer is   (85-5)/5+1= 
  (85-5)/5+1 = 17
17   Answer is 17
Answer: D
A person takes 20 minutes more to cover a certain distance by decreasing his speed by 20%. What is the time taken to cover the distance at his original speed?
Choose the most appropriate option
A) 2 hour 20 minutes  B) 1 hour 80 minutes  C) 1 hour 20 minutes  D) 8 hour 20 minutes  E) 1 hour 50 minutes

Solution: Let the distance and original speed be d km and k kmph respectively.   d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3   => (5d - 4d)/4k = 1/3 => d = 4/3 k   Time taken to cover the distance at original speed   = d/k = 4/3 hours = 1 hour 20 minutes.   Answer:1 hour 20 minutes
Answer: C
For every positive integer n, the nth term of sequence is given by an= 1/n - 1/(n+1). What is the sum of the first 90 terms?
Choose one:
A) 0 B) 1 C) 25 D) 89/90 E) 90/91

Solution: a1 = 1 - 1/2   a2 = 1/2 - 1/3   a3 = 1/3 - 1/4   etc...   a90 = 1/90 - 1/91   The sum of these terms is 1-1/91 = 90/91   The answer is 90/91.
Answer: E
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Select the correct option
A) 70/7 sec
B) 80/7 sec
C) 40/7 sec
D) 60/7 sec
E) 90/7 sec

Solution: B   Relative speed = (54 + 72)* 5/18 = 7 * 5= 
7 * 5 = 35
35 mps.   The time required= d/s = (100 + 100 + 200)/35   = 400/35 = 80/7 sec.
Answer: B
What is the difference between the place value of 1 in the numeral 7119? Select:
A) 150
B) 160
C) 180
D) 90
E) 210

Solution: 100 - 10= 
100 - 10 = 90
90   90
Answer: D
A person incurs 5% loss by selling a watch for $1140. At what price should the watch be sold to earn 5% profit?  Select:
A) $1260	B) $1150	C) $1542	D) $1000	E) $1292

Solution: Let the new selling price be $x   (100-loss%): (1st S.P.) = (100+gain%):(2nd S.P.)   (100-5)/1140 = (100+5)/x   x = 105*1140/95= 
105*1140/95 = 1_260
1260   $1260nswer is $1260
Answer: A
An unbiased cubic die is thrown.What is the probability of getting a multiple of 2 and 3?  Choose the correct choice from the following answers:
A) 1/6 B) 2/6 C) 3/6 D) 1 E) 1/12

Solution: Here S={1,2,3,4,5,6}   Let E be the event of getting the multiple of 3   then ,E={3,6}   Let F be the event of getting the multiple of 2   then ,E={2,4,6}   Let G be the event of getting the multiple of 2 and 3   then ,G={6}   P(G)=n(G)/n(S)=1/6   answer option 1/6) 1/6.
Answer: A
In a mixture of a, b and c, if a and b are mixed in 3:5 ratio and b and c are mixed in 8:5 ratio and if the final mixture is 35 liters, find the amount of b?
Pick:
A) 15.73	B) 15.79	C) 15.77	D) 15.72	E) 15.71

Solution: Ans: As b is common in both ratios, we should equate b in both ratios by multiplying suitable numbers.   a:b = 3 : 5 = 24 : 40   b:c = 8 : 5 = 40 : 25   Now a : b : c = 24 : 40 : 25.   15.73mount of b in the mixture = 4089×354089×35 = 15.73   15.73nswer:
Answer: A
A garden has 50,000 trees. 12% of the trees are guava trees, 15% are orange trees, 10% are coconut trees and the rest are mango trees. Find the number of mango trees. Pick:
A) 30000
B) 30200
C) 30800
D) 31200
E) 31500

Solution: Mango Trees = (100 - 12 - 15 - 10)= 
(100 - 12 - 15 - 10) = 63
63%.   Number of Mango trees= 63% of 50000 = 31,500.   ANSW31500R : OPTION 31500
Answer: E
How many numbers with distinct digits are possible product of whose digits is 28?	Choose the correct choice from the following choices: A) 6 B) 4 C) 8 D) 12 E) 14

Solution: DETAILED SOLUTION   Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74.   Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.   We cannot have three digits as (2, 2, 7) as the digits have to be distinct.   We cannot have numbers with 4 digits or more without repeating the digits.   So, there are totally 8 numbers.   8orrect Answer: 8
Answer: C
A man’s wages were decreased by 50%. Again, the reduced wages were increased by 50%. He has a loss of?
Choose the correct option.
A) 35%
B) 25%
C) 20%
D) 30%
E) none of these

Solution: Here, x = - 50 and y = 50   Therefore, the net % change in value   = ( x + y + xy/100) %   = [- 50 + 50 + ( -50 x 50)/100]% or - 25%   Since the sign is negative, there is loss of 25%   ANSWER:25%
Answer: B
Convert the 13/36 m/s into kilometers per hour?	Select the correct option.
A) 1.8 kmph
B) 1.6 kmph
C) 1.3 kmph
D) 3.3 kmph
E) 1.9 kmph

Solution: 13/36 m/s   = 13/36 * 18/5   = 13/10= 
13/10 = 13/10 = around 1.3
1.3 kmph.   Answer:1.3 kmph
Answer: C
A can do a piece of work 60 days. B can do work in 20 days. In how many days they will complete the work together?
Choose the correct choice from the following choices
A) 12 days B) 16 days C) 15 days D) 17 days E) 18 days

Solution: L15 daysM = 60, Ratio= 60:20=3:1   No of days= 60/(3 + 1) = 90/4 = 15 days   ANSWER:15 days
Answer: C
A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is
Choose the correct choice:  A) 36  B) 40  C) 15  D) 20  E) 10

Solution: Explanation :   Let the person has x Rs , then price of 50 oranges or 40 mangoes is x Rs.   Therefore, from given information x = (x / 10) + (x / 2) + Amount left.   Hence, the amount left to buy oranges is (2x / 5) , since price of 50 oranges or 40 mangoes is x Rs , hence price of 1 orange, 1 mango is (x / 50), (x / 40) respectively.   Hence, he can buy (2 /5) x 50 = 20 oranges.   Answer : 20
Answer: D
Before a salary increase, the weekly salary of a worker for 42 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour? Choose the correct choice from the following options
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Let x be the original salary per hour.   Let y be the salary per hour after the increase.   40y=42x   y=(42/40)= 
(42/40) = 21/20 = around 1.05
1.05x   The salary increased 5%.   The answer is 5.
Answer: C
How can a cake(circular) be cut into 8 pieces by making just 3 cuts?  Choose the correct choice from the following answers:
A) 21
B) 787
C) 37
D) 26
E) 01

Solution: Explanation:   Cut the cake using three mutually perpendicular planes. It leaves 8 pieces, one each in each octant.   21nswer21
Answer: A
Kathleen can paint a room in 2 hours, and Anthony can paint an identical room in 7 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
Choose the correct choice:
A) 28/9
B) 4/3
C) 15/8
D) 9/4
E) 15/4

Solution: (1/2 + 1/7)t=2   t=28/9   28/9nswer: 28/9
Answer: A
If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 34	Choose the correct choice from the following answers:
A) 2	B) 3	C) 5	D) 7	E) 9

Solution: P Ã· 44 = 432   => P = 432 * 44= 
432 * 44 = 19_008
19008   P / 34= 19008 / 34 = 559, remainder = 2   2
Answer: A
How should be added in order to make 2345672 this number is divisible by 9?
Choose the correct choice from the following options.
A) 5	B) 6	C) 7	D) 8	E) 9

Solution: Sum of the numbers 2345672 is 29 which is not multiple of 9   Add 7 which makes the sum 36 which is multiple of 9   So digit becomes 2345679 (as we know that if sum multiple of 9 then it is divisible of 9)   Answer:7
Answer: C
If 8 spiders make 8 webs in 8 days, then 1 spider will make 1 web in how many days? Choose the correct choice from the following options:
A) 7	B) 6	C) 5	D) 8	E) 3

Solution: Let the required number days be x.   Less spiders, More days (Indirect Proportion)   Less webs, Less days (8irect Proportion)   spiders 1:8   Webs 8:1   1 x 8 x x = 8 x 1 x 8   => x= 8   Answer is 8
Answer: D
How many multiples of 5 are there between 1 and 36, exclusive?  Choose the correct choice from the following answers.
A) 2
B) 5
C) 6
D) 7
E) 9

Solution: 7   multiples of 5 between 1 and 36 exclusive.   from 5 * 1 upto 5*7, (1,2,3,4,...,7). Hence, 7 multiples !   correct option is 7
Answer: D
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Regine
II. Stephanie
III. Brian Choose the correct option:	A) I only	B) II only	C) III only	D) I or II only	E) II, or III

Solution: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.   Min time one could complete the race is  20/8= 
 20/8 = 5/2 = around 2.5
2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5= 
2*2.5 = 5
5. So Brian could not have won the race.   There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.   Answer: II, or III.
Answer: E
Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg. How much amount did he pay to the shopkeeper?	Select.
A) A)1055 B) B)1075 C) C)1145 D) D)1070 E) E)1080

Solution: Cost of 8 kg grapes = 70 × 8 = 560.   Cost of 9 kg of mangoes = 65 × 9 = 585.   Total cost he has to pay = 560 + 585= 
560 + 585 = 1_145
1145.   1145)
Answer: C
Determine the value of (25/32+50/64)*2
Choose the most appropriate option:	A) 25/8	B) 25/4	C) 25/6	D) 3	E) none

Solution: Solution:   Both fractions should be reduced before performing arithmetic operations. We get (25/32+2.25/2.32)*2=(25/32+25/32)*2=2*(25/32)*2=4(25/32)=25/8   25/8nswer 25/8
Answer: A
Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 330 grams of compound X?	Pick.
A) 54
B) 162
C) 250
D) 275
E) 322

Solution: total number of fractions =2+10= 
2+10 = 12
12   element B constitutes=10 out of 12 parts of X   So in 330 gms of X have 330*10/12= 
330*10/12 = 275
275 gms of B   and  330-275= 
 330-275 = 55
55 gms of A.   cross check:- A/B= 55/275 =2/10 (as given)   Ans 275
Answer: D
A 16% stock yielding 10% is quoted at :  Select
A) 83.33
B) 110
C) 112
D) 120
E) 160

Solution: Solution   To earn Rs. 10, money invested = Rs. 100.   To earn Rs. 16, money invested = Rs.(100/10X16) = Rs. 160.   âˆ´ Market value of Rs. 100 stock =Rs. 160   Answer 160
Answer: E
You collect flowers. Suppose you have 89 flowers. You plucked 77 flowers from tree. How many flowers do you have now.? Pick one
A) 89  B) 166  C) 77  D) 12  E) 37

Solution: Solution   You have 89 flowers..   you plucked 77 flowers :   89 + 77= 
  89 + 77 = 166
166 flowers   So you have 166 flowers   Correct answer: 166
Answer: B
Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours, the tank shall be full?  Choose the most appropriate option: A) 2hrs B) 4hrs C) 5hrs D) 6hrs E) 7hrs

Solution: A's work in 1 hour = 1/6   B's work in 1 hour = 1/4   A+B 2 hour's work when opened alternately = 1/6 + 1/4 = 5/12   A+B 4 hour's work when opened alternately = 10/12 = 5/6   Remaining part = 1-5/6 = 1/6   it is A's turn and 1/6 part is filled by A in 1 hour.   Total time taken to fill the tank = 4+1= 
4+1 = 5
5hrs   Answer is 5hrs
Answer: C
A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?	Choose the correct choice from the following choices:
A) 5.2 hrs B) 2.9 hrs C) 12 hrs D) 7.2 hrs E) 1.4 hrs

Solution: Net part filled in 1 hour = (1/6 - 1/12) = 1/12   The cistern will be filled in 12/1 hrs i.e., 12 hrs.   Answer:12 hrs
Answer: C
A train covers a distance of 36km in 12 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?	Choose the most appropriate option
A) 300 m
B) 1000 m
C) 120 m
D) 200 m
E) 500 m

Solution: Speed = (36/12 * 60) km/hr   = (180 * 5/18) m/sec   = 50 m/sec.   Length of the train   = 50 * 10= 
50 * 10 = 500
500 m.   Answer: 500 m
Answer: E
If air is called green , green is called blue, blue is called water, sky is called yellow, yellow is called water and water is called water, then what is the color of clear sky ?  Choose the correct choice from the following options:
A) Blue	B) Sky	C) Water	D) Yellow	E) Black

Solution: Explanation:The colour of clear sky is 'blue' and as given, 'blue' is called 'water'.So, the colour of clear sky is 'water'.Answer: Water
Answer: C
A jar full of whiskey contains 40% alcohol. A part of
this whiskey is replaced by another containing 19% alcohol
and now the percentage of alcohol was found to be 26%.
The quantity of whiskey replaced is?	Choose the correct choice from the following answers:	A) 2/3	B) 1/3	C) 1/5	D) 1/4	E) 1/8

Solution: Strength of first jar 40% Strength of 2nd jar 19%   Mean Strength 26%   7 14   So,ratio of 1st and 2nd quantities =7:14 =1:2   Therefore required quantity replaced =2/3.   2/3NSWER 2/3
Answer: A
A corporation paid $7 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $100 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $100 million in profits?	Choose one:
A) 6% B) 14% C) 114% D) 23% E) 43%

Solution: Difference in Ratios = (30/100) - (7/50) = (8/50)   % 114%hange = (114%hange (8/50) / Original ratio (7/50)) *100 = 114%   Answer - 114%
Answer: C
7 people average age is 30. youngest person age is 7. find average of the people when youngest was born.	Choose the correct choice from the following answers:
A) 23
B) 24
C) 25
D) 26
E) 27

Solution: average age of people =30   so have total age =210   before 7 years we have to deduct each person age by seven years   210-49= 
  210-49 = 161
161   so average age would be 161/7= 
161/7 = 23
23   23NSWER:23
Answer: A
George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare and buys 10 mangoes. How many oranges can he buy?  Choose the correct choice from the following answers
A) 25  B) 30  C) 20  D) 16  E) 12

Solution: Let the amount of money be 200   Let cost of 1 Orange be 4   Let cost of 1 mango be 5   He decides to retain 10% of 200 = 20 for taxi fare, so he is left with 180   He buys 20 mangoes ( @ 5) so he spends 100   Money left is 80 (180 - 100)   No of oranges he can buy = 80/4= 
80/4 = 20
>20   So, George can buy 10 Oranges.   20
Answer: C
If selling price is doubled, the profit triples. Find the profit percent?
Choose the correct answer:
A) 187 B) 100 C) 177 D) 165 E) 122

Solution: Let C.P. be Rs. x and S.P. be Rx. y.   Then, 3(y - x) = (2y - x) => y = 2x   Profit = (y - x) = Rs. (2x - x) = Rs. x   Profit % = x/x * 100 = 100%.   Answer: 100
Answer: B
A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?	Select:  A) 2 days  B) 4 days  C) 5 days  D) 6 days  E) 9 days

Solution: sax Work done by Afar 3 days : i   J   .. Remzming war — 1   .Work done by (A + B) for 1 day :   . Work done by a for 1 day   6 days   6 days
Answer: D
A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Choose the correct option:
A) 8 sec	B) 6 sec	C) 4 sec	D) 3 sec	E) 1 sec

Solution: Speed of train relative to man = 60 + 6= 
60 + 6 = 66
66 km/hr.= 66 * 5/18 = 55/3 m/sec.   Time taken to pass the men = 110 * 3/55= 
110 * 3/55 = 6
6 sec   Answer:6 sec
Answer: B
The greatest possible length which can be used to measure exactly the length 6m ,2m 85cm, 4m 95 cm is? Pick.
A) 25cm
B) 101cm
C) 56cm
D) 42cm
E) 15cm

Solution: Required length = H.C.F of 600cm, 285cm, 495cm = 15cm   Answer is 15cm
Answer: E
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?	Choose the most appropriate option
A) 1/129  B) 1/199  C) 1/122  D) 1/121  E) 1/126

Solution: Out of nine, five are good and four are defective. Required probability   = 4C4/9C4 = 1/126   Answer:1/126
Answer: E
A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:  Choose the correct choice from the following answers
A) 10  B) 12  C) 13  D) 14  E) 15

Solution: dividend rs 20 = 9/200*20 = 9/5   Rs 12 is an income Rs 100   9/5 is an income   (100/12*9/5)= 
  (100/12*9/5) = 15
Rs 15   ANSW15R 15
Answer: E
Aaron will jog from home at 4 miles per hour and then walk back home by the same route at 8 miles per hour. How many miles from home can Aaron jog so that he spends a total of 3 hours jogging and walking?  Choose the correct choice from the following options
A) 2 B) 10 C) 12 D) 8 E) 15

Solution: xyt/(x+y)   x= 4, y=8 t= 3   4*8*3/4+8 = 96/12= 
96/12 = 8
8   Answer : 8
Answer: D
When the integer x is divided by 12, the remainder is 3. Which of the following, when divided by 12, will have a remainder of 6 ?
I. 2x
II. 6x
III. 4x + 6	Choose the correct choice:
A) I only  B) II only  C) III only  D) I and II only  E) I, II, and III

Solution: is it E.   x= 12*a + 3   2x = 12*2*a + 6   6x = 12*6*a + 18 ( 18 = 12+6)   4x + 6 = 12*4*a + 18 (18 = 12 + 6)
Answer: E
The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 55 sq. cm. Find the length of the rectangle.
Answers.
A) 16cm	B) 18cm	C) 15cm	D) 20cm	E) 23cm

Solution: Explanation:   Let breadth = x. Then, length = 2x. Then,   (2x - 5) (x + 5) - 2x * x = 55 => 5x - 25 = 55 => x = 16.   Length of the rectangle = 16 cm.   16cmnswer: Option 16cm
Answer: A
A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water? Choose the correct choice from the following answers
A) 7 kmph	B) 8 kmph	C) 4 kmph	D) 9 kmph	E) 3 kmph

Solution: 30 --- 3 DS = 10   ? ---- 1   18 ---- 3 US = 6   ? ---- 1 M = ?   M = (10 + 6)/2= 
(10 + 6)/2 = 8
8   Answer: 8 kmph
Answer: B
A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 50 meters, what is the height of the building (in meters)?  Choose the correct choice:
A) 16
B) 20
C) 24
D) 28
E) 32

Solution: The height:length ratio will be equal in both cases.   18 / 45 = x / 50   x = 20   The answer is 20.
Answer: B