MU-NLPC/Calc-aqua_rat huggingface dataset:
The concentration of spirit in three different vessels A, B and C are 30%, 50% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
Pick one.
A) 32.54%	B) 33%	C) 34.67%	D) 35%	E) 36.62%

Solution: Quantity of spirit in new solution=(4*30/100)+(5*50/100)+(6*25/100)=1.2+2.5+1.5= 
1.2+2.5+1.5 = 5.2
5.2 liters   So % concentration of spirit=100*5.2/(4+5+6)=34.67%   ANSWER:34.67%
Answer: C
The side of a rhombus is 24 m and length of one of its diagonals is 18 m. The area of the rhombus is?  Choose the correct answer:
A) 410.47
B) 403.47
C) 420.47
D) 400.47
E) 300.47

Solution: area of the rhombus = 1/2 * p * √4(a)2 - (p)2   a= 24 ; p = 18   A=1/2 * 18 *√4(24)2 - (18)2   =1/2 * 18 *√2304 - 324   =1/2 * 18 *√1980   A =400.47   Answer : 400.47
Answer: D
If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
Select
A) 298 B) 278 C) 299 D) 480 E) 276

Solution: Let the sum be Rs. P. Then,   [P(1 + 25/(2 * 100))2 - P] = 510   P[(9/8)2 - 1] = 510.   Sum = Rs. 1920   So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480   Answer: 480
Answer: D
If the number a60,858,61b is evenly divisible by 88, what are the values of a and b? Select: A) b = 6, a = 6 B) b = 2, a = 3 C) b = 2, a = 1 D) b = 4, a = 6 E) b = 4, a = 3

Solution: a60,858,61b, divisible by 88.   Factors of 88 = (8)(11)   Divisible by 8: if the last 3 digits of the number are divisible by 8.   61b/8 => 616/8= 
616/8 = 77
77=> b = 6   Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.   a6085861-6 => a608585-5 => a60858-0 => a6085-8 => a607-7 => a60-0 => a6-0= 
6-0 = 6
> a6=> 66/11= 
66/11 = 6
6.   So a= 6.   b = 6, a = 6nswer: b = 6, a = 6
Answer: A
From a pack of cards, two cards are drawn one after the other, with replacement. What is the probability that the first card is a club and the second card is a king or queen?	Choices:
A) 2/13 B) 3/13 C) 1/26 D) 1/52 E) 3/52

Solution: P(club) = 1/4   P(king or queen) = 2/13   P(club then a king/queen) = 1/4 * 2/13 = 1/26   The answer is 1/26.
Answer: C
Select the non termination decimal among the following.
Choose the correct choice:
A) 22/3
B) 3/4
C) 4/5
D) 7/8
E) 9/10

Solution: A. Non terminating decimal means that 22/3 = 7.33333 and so on.
Answer: A
Two pipes A and B can fill a cistern in 9 and 18 minutes respectively, and a third pipe C can empty it in 24 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Select the correct option:
A) 6 min
B) 7 min
C) 8 min
D) 10 min
E) 17 min

Solution: 1/9 + 1/18 - 1/24   = 1/8   8/1= 
8/1 = 8
8   Answer:8 min
Answer: C
How many liters of water must be evaporated from 50 liters of a 8-percent sugar solution to get a 10-percent solution? Select:
A) 8  B) 10  C) 12  D) 14  E) 16

Solution: 8% of a 50 liter solution is 4L which is 10% of the solution at the end.   The solution at the end must be 40 L.   We need to evaporate 10 liters.   The answer is 10.
Answer: B
The salary of a worker is first increased by 20% and afterwards reduced by 20%. What is the net change in the worker's salary? Choose the correct option.
A) 4% decrease
B) 8% decrease
C) 4% increase
D) 8% increase
E) no change

Solution: Let x be the original salary.   The final salary is 0.8(1.2x) = 0.96x   The answer is 4% decrease.
Answer: A
A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 36 years and that of the grandchildren is 6 years. What is the average age of the family?
Select:
A) 28 4â„7 years	B) 31 5â„7 years	C) 32 years	D) 27 1â„2 years	E) None of these

Solution: Required average = (67Ã—2+36Ã—2+6Ã—3/2+2+3)   =224/7= 
224/7 = 32
32 years   Answer 32 years
Answer: C
How many digits to the right of the decimal point are there in the product of .32655 * 65.01?
Options.
A) 8	B) 5	C) 4	D) 6	E) 7

Solution: Product of is .32655 * 65.01 is 21.2290155.   Therefore number of digits to right of decimal point is 7   Answer is 7.
Answer: E
Laura has a deck of standard playing cards with 18 of the 54 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
Pick one:
A) 1/4  B) 1/3  C) 5/26  D) 12/42  E) 13/42

Solution: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.   If there is no replacement then how is the (P) that the 10th card is 18/54 ??   there are many cases here to be considered here if there is no replacement such as:   H- Denotes heart X-may be any diamond, spade or club.   1. HXXXXXXXXH   2. HHXXXXXXXH   3. HHHXXXXXXH   .   .   .   .   .   9. HHHHHHHHHH   10. XXXXXXXXXH   All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.   For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 18/54 = 1/3 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....   1/3
Answer: B
A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?	Choose the correct choice from the following options:
A) 24/91
B) 24/90
C) 24/97
D) 24/95
E) 24/93

Solution: This is a case of without replacement. We have to multiply two probabilities. 1. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black.   6C114C1×8C113C1=24/91   24/91nswer:a
Answer: A
If y exceeds x by 20%, then x is less than y by? Select the correct option
A) 16 2/8%	B) 16 8/3%	C) 16 2/3%	D) 76 2/3%	E) 17 2/3%

Solution: X=100	y=120   120------20   100-------? => 16 2/3%   Answer:16 2/3%
Answer: C
1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?  Choose the correct choice from the following choices
A) 82 days  B) 26 days  C) 32 days  D) 34 days  E) 25 days

Solution: 1600 ---- 28 days   1600 ---- 24   1200 ---- ?   1600*24 = 1200*x   x = 32 days   Answer:32 days
Answer: C
A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 4k2,k21, where k represents a digit that occurs twice, how many values could n have?	Choose the correct choice from the following answers: A) 2 B) 3 C) 6 D) 5 E) 4

Solution: 4k2k21   Taking sum of the numericals = 4 + 2 + 2 + 1= 
4 + 2 + 2 + 1 = 9
9   We require the values of K such that they are also divisible by 3   402021   432321   462621   492921   Answer= 4 = 4
Answer: E
One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a? Choose the correct choice from the following answers
A) 29 B) -27 C) 28 D) 7 E) None of these

Solution: Let the roots of the quadratic equation be x and 3x.   Sum of roots = -(-12)= 
-(-12) = 12
12   a + 3a= 4a = 12 => a = 3   Product of the roots = 3a2 = 3(3)2 = 27.   ANSWNone of theseR:None of these
Answer: E
Find the angle between the hour hand and the minute hand of a clock when 3.25.  Options:
A) 47 1/2° B) 45 1/2° C) 48 1/2° D) 46 1/2° E) 42 1/2°

Solution: angle traced by the hour hand in 12 hours = 360°   Angle traced by it in three hours 25 min (ie) 41/12 hrs=(360*41/12*12)° =102 1/2°   angle traced by minute hand in 60 min. = 360°.   Angle traced by it in 25 min. = (360 X 25 )/60= 150°   Required angle = 1500 – 102 1/2°= 47 1/2°   47 1/2°nswer is 47 1/2°.
Answer: A
A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square floor that has an area of 65 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?	Choose the correct option:
A) A.3/16  B) 1/4  C) C.1/2  D) 53/65  E) 7/8

Solution: Area of the rectangular rug = 2*6= 
2*6 = 12
12   Fraction not covered by the rug= (Total Area - Rug area) / Total Area   = (65 - 12)/65   = 53/65=53/65
Answer: D
2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 16 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?	Choose the correct choice from the following options.
A) 12 km/hr  B) 16.5 km/hr  C) 17 km/hr  D) 18 km/hr  E) None of these

Solution: Explanation :   Total distance covered by B=16*6= 
16*6 = 96
96kmTotal time taken by 12 km/hr to cover same distance=2+6= 
2+6 = 8
8 hrsaverage speed of 12 km/hr=96/8= 
96/8 = 12
12 km/hr   12 km/hrnswer : 12 km/hr
Answer: A
A trader sells 85 meters of cloth for Rs. 8500 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Choose the correct choice from the following answers
A) Rs. 80
B) Rs. 85
C) Rs. 90
D) Rs. 95
E) None of these

Solution: SP of 1m of cloth = 8500/85 = Rs. 105   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 100 - Rs. 15 = Rs. 85.   ANSWER:Rs. 85
Answer: B
How much more would Rs.15000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly? Choose the correct choice from the following answers
A) A)Rs.3,961.50 B) B)Rs.3,962.50 C) C)Rs.3,963.50 D) D)Rs.3,964.50 E) E)Rs.3,965.50

Solution: 15000(11/10)4 - 15000(6/5)2 = 3,961.50   Rs.3,961.50NSWER:Rs.3,961.50
Answer: A
Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 9-week period?
Choices
A) $570	B) $790	C) $630	D) $830	E) $715

Solution: OFFICIAL SOLUTION:   (D) First, we need to add up the wages over the past 7 weeks: $406 + $413 + $420 + $436 + $395 + $410 + $360 = $2840.   To average $500 over 9 weeks, the salesman would need to earn: $500 × 9 406 +  413 +  420 +  436 +  395 +  410 +  360= 
406 +  413 +  420 +  436 +  395 +  410 +  360 = 2_840
$2840.   To average $500 over 9 weeks, the salesman would need to earn: $500 × 9= $4500.   Subtract $2840 from $4500 to determine how much he would need to earn, in total, over the next 2 weeks to average $500 for the 9 weeks: $4500 – $2840 = $1660.   Dividing $1660 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $1660/2= 
1660/2 = 830
$830.   The correct answer is choice ($830).
Answer: D
A student was asked to find the arithmetic mean of the numbers 13,31,78,92,115,103,68,10,57,21,34 and a. He found the mean to be 60. What should be the remainder in the place of a?	Select.
A) 98	B) 105	C) 120	D) 165	E) 132

Solution: We have (13+31+78+92+115+103+68+10+57+21+34+a) / 12 = 60   622+a= 720   a = 98   98nswer is 98
Answer: A
How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a vowel, and each letter can be used only once? Choose the correct choice from the following:
A) 21
B) 42
C) 120
D) 600
E) 720

Solution: Vowel: E O   120onsonants: V R M N T   First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)   Fifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)   Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter   Second letter can be filled in 5 Ways   Third letter can be filled in 4 Ways   Fourth letter can be filled in 3 Ways   So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 1 ways = 120   Answer 120
Answer: C
Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.	Choose the correct choice from the following answers
A) 82	B) 89	C) 93	D) 98	E) 69

Solution: Solution: Total of 80 numbers = 80*42= 
80*42 = 3_360
3360;   Now, total of 85 numbers= 85*45= 
85*45 = 3_825
3825;   Hence, sum of 5 numbers= 3825-3360= 
3825-3360 = 465
465;   Average of five numbers= 465/5= 
465/5 = 93
93.   Solve while reading Method:   Average of 80 number was 42, when 5 more numbers are added average become 45, that means 3 is given to each number to make their average 45 and 5 numbers also keep 45 as to maintain the entire average.   So, the sum of five numbers= 240+225= 
240+225 = 465
465,   Hence, average of five numbers= 93.   Answer: Option 93
Answer: C
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost of the article.  Choose the correct choice from the following options
A) 30  B) 40  C) 50  D) 60  E) 70

Solution: Let 50.P=100   Gain=25%   S.P=125   Supposed 50.P=80   Gain=30%   S.P=(130*80)/100= 
(130*80)/100 = 104
104   Diff=(125-104)= 
(125-104) = 21
21   Diff 21 when 50.P=100   then Diff 10.50 when 50.P=(100*10.50)/21= 
(100*10.50)/21 = 50
50   ANSWER:50
Answer: C
if abcd is four digit highest number that is divisible by 10.9.22 give remainder 4,9,10. find bc
Select the correct option.
A) 75  B) 89  C) 95  D) 98  E) 97

Solution: 9954.............>95   ANSWER:95
Answer: C
Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71, 84, ___? Choose the most appropriate option:  A) 35  B) 36  C) 37  D) 98  E) 109

Solution: The numbers increase at a somewhat steady rate, so you have to figure out how much   you have to add to each number to produce the next in the sequence:  3 + 5= 
 3 + 5 = 8
8; 8 + 6= 14;    14 + 7= 
 14 + 7 = 21
21; 21 + 8= 29, and so on. The rule for the sequence is to add successively larger   numbers to each number; therefore, the next number is   84 + 14= 
  84 + 14 = 98
98.   correct answer 98)98
Answer: D
Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points? Choose the correct answer
A) 25 Fruits  B) 20 Fruits  C) 23 Fruits  D) 21 Fruits  E) 27 Fr5uits

Solution: A   25 Fruits   Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.   For the first sack:   He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,   (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M   M = 10   Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.   Now he must get rid of the second sack.   For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.   (Space in First Sack) N = (Remaining fruits in second sack) 30 – N   N = 15   Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer: A
If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,876,397 minutes earlier? (Assume standard time in one location.)
Choose the correct choice from the following:
A) 6:30	B) 6:25	C) 6:17	D) 6:12	E) 6:08

Solution: 6:27 minus 2,876,397 in any way must end with 0.   The only answer choice which ends with 0 is A.   The answer is 6:30.
Answer: A
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?	Pick:
A) 50 km B) 16 km C) 18 km D) 29 km E) 19 km

Solution: Let the actual distance traveled be x km. Then,   x/10 = (x + 20)/14   4x - 200 =>x = 50 km.   50 kmnswer:a
Answer: A
Which of the following is not a leap year?  Choose one.
A) 700
B) 800
C) 900
D) 1000
E) 1200

Solution: The century divisible by 400 is a leap year.   The year 700 is not a leap year.   700nswer: Option 700
Answer: A
Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 144 seconds. The length of each train is:	Choose the correct option
A) 82m	B) 150m	C) 172m	D) 200m	E) None of these

Solution: Explanation:   The relative speed of train is 46-36= 
46-36 = 10
10 Km/hr= (10 X 5) / 18 = 25/9 m/s10×518=259m/s   In 144 secs the total distance traveled is 144x25/9 = 400 m.   Therefore the length of each train is = 400/2= 
400/2 = 200
200 m.   Answer 200m
Answer: D
21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
Answers: A) 8/41 B) 9/31 C) 9/42 D) 7/31 E) 9/41

Solution: The probability that first toy shows the even number,   =1021=1021   Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.   Hence, probability that second toy shows the even number,   =920=920   Required probability,   =(1021)×(920)=(1021)×(920)   =9/42   9/42
Answer: C
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?	Choose one.
A) 33 1/8%  B) 33 1/2%  C) 33 1/3%  D) 33 6/3%  E) 32 1/3%

Solution: 675 ---- 225   100 ---- ? => 33 1/3%   Answer:33 1/3%
Answer: C
Simplify: 5793405 x 9999	Choose the most appropriate option:
A) 57925286595
B) 57928256595
C) 57989252865
D) 57568226348
E) None of them

Solution: 5793405 x 9999=5793405(10000-1)   =57934050000-5793405= 
57934050000-5793405 = 57_928_256_595
57928256595.   Answer is 57928256595
Answer: B
A man buys a cycle for Rs. 1600 and sells it at a loss of 12%. What is the selling price of the cycle? Choose one:
A) 1410  B) 1420  C) 1430  D) 1408  E) 1540

Solution: S.P. = 88% of Rs. 1600 = 88/100 x1600= Rs. 1408   answer : 1408
Answer: D
Angela, Bernie, and Colleen can complete a job, all working together, in 3 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 4 hours. How long would it take Colleen, working alone, to complete the entire job?
Choices:
A) 8 hours  B) 10 hours  C) 12 hours  D) 16 hours  E) 20 hours

Solution: A+B+C complete the job in 3 hours.   A+B complete the job in 4 hours.   A+B and C complete the job in 3 hours -->1/(A+B) + 1/C = 1/3-->1/4+1/C=1/3 ----> C=12 hours. ANS 12 hours
Answer: C
A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered? Choices.
A) 24.5
B) 28.5
C) 30
D) Data inadequate
E) None of these

Solution: Explanation:   Let C.P. be Rs. 100.   Then, S.P. = Rs. 123.50   Let marked price be Rs. x. Then, 95/100 x = 123.50   x = 12350/95 = Rs. 130   Now, S.P. = Rs. 130, C.P. = Rs. 100   Profit % = 30%.   ANSWER IS 30
Answer: C
The average number of shirts with Salman, Ambani and Dalmiya is 40, if all of them reached a shopping mall in Delhi and purchased 8 shirts each of them then average number of shirt each of them now has Select.
A) 66
B) 63
C) 48
D) can't be determined
E) None of these

Solution: Answer   Required average   = Old average + New average   = 40 + 8= 
40 + 8 = 48
48   48orrect Option: 48
Answer: C
Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 50 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Choose the correct choice from the following answers
A) 17 1/4 min  B) 28 1/7 min  C) 17 1/7 min  D) 17 1/8 min  E) 15 15/19 min

Solution: 1/20 + 1/30 - 1/50 = 19/300   300/19 = 15 15/19   Answer:15 15/19 min
Answer: E
If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? Choose the correct choice from the following answers.
A) 1/7 km	B) 3/5 km	C) 5/5 km	D) 4/4 km	E) 4/5 km

Solution: 4/5 km   4/5 km   x/3 – x/4 = 4/60   x = 4/5 km
Answer: E
A positive whole number has factors of 2 and 4. The number MUST be divisible by: I. 16 II. 8 III. 4  Choices: A) I & II B) II & III C) III D) I E) II

Solution: 4 , 8 is not divisible by 16.But 16 is divisible by 2,4,8   So answer is I   Answer : I
Answer: D
What is the probability of a/b will be an integer when a=2x3y and b=2l3m and all of x, y, I, m are positive integers?	Choose the correct answer
A) 1/6	B) 2/3	C) 1/2	D) 1/4	E) 3/4

Solution: There r 4 numbers to be filled i.e, x,y,l,m   out of which only one condition satisfies to get a/b as integer   ANSWER:1/4
Answer: D
A Fruit Seller buys lemons at 2 for a rupee and sells them at 5 for three rupee. His profit percentage is Choose the correct choice from the following answers
A) 30%  B) 50%  C) 60%  D) 20%  E) None

Solution: C.P of 2 Lemons= Re 1   So, C.P of 5 Lemons= 5*1/2=5/2   S.P of 5 Lemons= Rs 3   Therefore, Profit Percentage={(3-5/2)5/2}100 =20%   Answer: Option 20%
Answer: D
8 3/4 + 7 2/17 - 9 1/15=?
Choose the correct choice:
A) 7 719/1020
B) 9 817/1020
C) 9 719/1020
D) 6 817/1020
E) None of them

Solution: Given sum=8+3/4+7+2/17-(9+1/15)   =(8+7-9)+(3/4+2/17-1/15)   =6+(765+120-68/1020   =6 817/1020   Answer is 6 817/1020
Answer: D
A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 32 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up	Choose the correct choice from the following answers.
A) 6 2/3
B) 15
C) 20
D) 25
E) 35

Solution: Here is how I did it:   The cyclist travels 32 miles in 60 mins, so in 5 mins he will travel [(32*5)/60] miles, which equals 8/3 miles in 5 mins.   Now the hiker travels 4 miles in 60 mins. To travel 8/3 miles, he will take [(60*8/3)/4= 
(60*8/3)/4 = 40
40 mins.   Hence 40-5= 
40-5 = 35
35 mins   35
Answer: E
What decimal fraction is 30 ml of a litre ?  Choose the correct choice from the following:
A) .3
B) .0003
C) .003
D) 0.03
E) None of these

Solution: Answer   Required fraction = 30/1000   = 3/100= 
3/100 = 3/100 = around 0.03
.03   Correct Option: 0.03
Answer: D
Simplify: 896 x 896 - 204 x 204 Pick one:
A) 761200
B) 761400
C) 761800
D) 761500
E) None of them

Solution: (896)^2 - (204)^2 = (896 + 204) (896 - 204) = 1100 x 692 = 761200.   761200nswer is 761200.
Answer: A
The sum of digits of a two digit number is 10,The difference between the digits is 6. Find the number	Choose one
A) 85  B) 94  C) 82  D) 72  E) None

Solution: Description :   => x+y=10, x-y=6   Adding these 2x =16   => x=8, y=2.   Thus the number is 82   Answer 82
Answer: C
In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row?
Answers.
A) 10 B) 11 C) 13 D) 14 E) 16

Solution: Let x be the number of cans in row 1.   The total number of cans is x + (x+3) + ... + (x+27) =   10x + 3(1+2+...+9) =   10x + 3(9)(10)/2 =   10x + 135   Since the total is less than 150, x must equal 1.   The number of cans in the 5th row is 1 + 3(4) = 13   The answer is 13.
Answer: C