MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the sum of the multiples of 4 from 40 to 80, inclusive?
Choose the correct choice from the following choices
A) 560
B) 660
C) 800
D) 760
E) 480

Solution: The formula we want to use in this type of problem is this:   Average*Total Numbers=Sum   First, find the average by taking the sum of the F + L number and divide it by 2:   A = (F + L)/2   Second, find the total numbers in our range by dividing our F and L numbers by 4 and add 1.   (80/4) - (40/4) + 1   Multiply these together so what we show Average*Total Numbers=Sum   (80 + 40)/2 * (80/4) - (40/4) + 1 = Sum   60 *11= 
60 *11 = 660
660   660
Answer: B
Mrs. Rodger got a weekly raise of $115. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.  Pick one:  A) $ 145.  B) $ 146  C) $ 115  D) $ 148  E) None

Solution: Solution:   Let the 1st paycheck be x (integer).   Mrs. Rodger got a weekly raise of $ 115.   So after completing the 1st week she will get $ (x+115).   Similarly after completing the 2nd week she will get $ (x + 115) + $ 115.   = $ (x + 115 + 115)   = $ (x + 230)   So in this way end of every week her salary will increase by $ 115.   Answer $ 115
Answer: C
Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 6 days?
Choose one
A) 2/5
B) 1/6
C) 1/3
D) 1/9
E) 2/6

Solution: A's one day's work = 1/30   B's one day's work = 1/45   (A + B)'s one day's work = 1/30 + 1/45 = 1/18   The part of the work completed in 6 days = 6 (1/18) = 1/3.   ANSWER 1/3
Answer: C
In 130 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:	Select the correct option:  A) 20 m  B) 25 m  C) 22.5 m  D) 26 m  E) 12 m

Solution: Distance covered by B in 9 sec. =	130/45 x 9	m = 26 m.   A beats B by 26 metres.   Answer: Option 26 m
Answer: D
The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $700 per sq. metre.  Choose the correct choice.
A) $12537.50 B) $13537.50 C) $14437.50 D) $16437.50 E) $18537.50

Solution: C   Area =5.5×3.75 sq. metre.   Cost for 1 sq. metre. = $700   Hence, total cost   =5.5×3.75×700= $14437.50
Answer: C
If it is true that x > -3 and x < 7, which of the following must be true?	Choose the correct choice from the following choices:  A) x > 3  B) x < -7  C) x < 3  D) -7 < x < 3  E) none of the above.

Solution: the range is -3 < x < 7   A. x > 3 - no because x can be between -3 < x < 3   B. x < -7 - no because the values of x are always >-7   C. x < 3 - no because x can be between 3 < x < 7   D. -7 < x < 3 - no because x can be between 3 < x < 7   E. none of the above.   Answer: none of the above.
Answer: E
A bucket contains 2 mixtures A and B in the ratio 3:2. If 5 liters of the mixture is replaced by 5 liters of liquid B, then the ratio of the two liquids becomes 3:5. How much of the liquid A was there in the bucket?
Pick:
A) 8liters B) 10liters C) 12liters D) 15liters E) 18liters

Solution: 1st ratio = 3:2   2nd ratio = 3:5   Difference of cross products ratio = 3*5-3*2= 
3*5-3*2 = 9
9   common factor of the 1st ratio= (quantity replaced/sum of terms in 1st ratio) + (Quantity replaced*term 8liters in 2nd ratio/Difference)   = (5/5) + (5*3/9) = 1+5/3 = 2.67   Quantity of 8liters = 3*2.67 = 8liters approximately   8litersnswer is 8liters
Answer: A
A dishonest dealer professes to sell goods at the cost price but uses a weight of 900 grams per kg, what is his percent? Choose the correct choice from the following answers.
A) 11	B) 25	C) 77	D) 88	E) 15

Solution: 900 --- 100   100 --- ? => 11%   11nswer:11
Answer: A
3, 4.5, 6.75, 10.13, 15.18, (...)  Choose the most appropriate option
A) 60
B) 60.75
C) 22.78
D) 32.52
E) 88

Solution: 3   (3Ã—3)Ã· 2 = 4.5   (4.5Ã—3)Ã· 2 = 6.75   (6.75Ã—3)Ã· 2 = 10.13   (10.18Ã—3)Ã· 2 = 15.18   (15.18Ã—3)Ã· 2 = 60.75   Answer is 22.78
Answer: C
The Income of an woman increase consistently by 25% per year. If his present salary is Rs. 30000 then what will his salary be after 3 years ?  Choose the most appropriate option.
A) 50840	B) 52840	C) 51740	D) 51830	E) 51840

Solution: 51840xplanation :   Income = 30000 x 1.2 x 1.2 x 1.2 = 51840   Answer : Option 51840
Answer: E
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace? Choose the correct choice
A) 1/2324	B) 2/13235	C) 2/5525	D) 5525/2	E) None

Solution: Let Q denote the event that the card drawn is queen and A be the event that   the card drawn is an ace. Clearly, we have to find P (QQA)   Now P(Q) = 4/52   Also, P (Q|Q) is the probability of second queen with the condition that one queen has   already been drawn. Now there are three queen in (52 - 1)= 
(52 - 1) = 51
51 cards.   Therefore P(Q|Q)= 3/51   P(A|QQ) is the probability of third drawn card to be an ace, with the condition   that two queens have already been drawn. Now there are four aces in left 50 cards.   Therefore P(A|QQ) = 4/50   By multiplication law of probability, we have   P(QQA) = P(Q) P(Q|Q) P(A|QQ)   = 4/52 × 3/51 × 4/50   = 2/5525.   2/5525
Answer: C
To be considered grade AE, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AE eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AE eggs are used, the shells are all discarded, and no mass is lost in the cooking process?	Choose the correct answer.
A) 800 B) 840 C) 864 D) 900 E) 1,080

Solution: We're asked for the smallest possible mass, so what could the lowest mass be per egg AE? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is 840.
Answer: B
A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? Choose one:
A) 5	B) 4	C) 7	D) 3	E) 5.1

Solution: M = 5.5   S = 1.5   DS = 7   US = 4   AS = (2 * 7 * 4) /11 = 5.1   Answer: 5.1
Answer: E
A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
Select.
A) 150 metre B) 380 metre C) 350 metre D) 200 metre E) 250 metre

Solution: Speed of the train =300/18 m/s=50/3 m/s   Distance covered in 39 seconds=39 Ã— 50/3 =650 metre   Length of the train =650-300= 
650-300 = 350
350 metre   ANSWER: 350 metre
Answer: C
The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $1.30 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
Choose the correct choice from the following options
A) a) $ 1.80 B) b) $ 1.95 C) c) $ 2.40 D) d) $ 2.70 E) e) $ 3.00

Solution: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).   Therefore the price in 1980 = $1.3*1.5 = $1.95.   Answer: b) $ 1.95.
Answer: B
Find the area, diameter = 10m. Choose the correct answer:
A) 78.24 square meter
B) 78.57 square meter
C) 78.26 square meter
D) 24.24 square meter
E) 24.43 square meter

Solution: Diameter = 10 meter.   Radius = diameter/2.   = 10/2.= 
10/2. = 5
5 meter.   Area of a circle= Ï€r2.   Here, pi (Ï€) = 3.14 meter, radius (r) = 5.   Area of a circle = 3.14 Ã— 5 Ã— 5..   = 3.14 Ã— 25.   = 78.57 square meter ANSWER : 78.57 square meter
Answer: B
The sides of a rectangular region measured to the nearest centimeter are 10 cm and 6 cm. Out of the following which is the largest possible value of actual area of rectangle ? Choose the most appropriate option.
A) 48	B) 65.25	C) 52.29	D) 44	E) 41.25

Solution: acan be anywhere between 9.5 and 10.4 andbcan be anywhere between 5.5 and 6.4.   Hence max area can be 10.4*6.4 eq 66.56.   largest value which is near to 66.56 is 65.25.   Hence 65.25.
Answer: B
How many different three-digit multiples of 5 can be composed of digits 2, 3, 6, and 5 if none of the digits is repeated?  Choices:
A) 3
B) 6
C) 10
D) 12
E) 18

Solution: = 3c2 x 2 = 6   can you explain your method. i solved it differently   XYZ, where Z must be 5. therefore 1 variation of digit in Z.   Y can be any of the 3 possible choices.   X can be any of the 2 possible choices.   2+3+1= 
2+3+1 = 6
6   6
Answer: B
A block of wood has dimensions 10cm x 10cm x 40cm. The block is painted red and then cut evenly at the 20 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red? Select
A) 5%	B) 10%	C) 15%	D) 20%	E) 25%

Solution: The area of each half is 100+4(200)+100 = 1000   The area that is not painted is 100.   The fraction that is not painted is 100/1000 = 1/10 = 10%   The answer is 10%.
Answer: B
From a circular sheet of paper with a radius of 20cm,four circles of radius 5cm each are cut out.what is the ratio of the uncut to the cut portion?	Pick one:
A) 1:3
B) 4:1
C) 3:1
D) 4:3
E) 2:3

Solution: area of uncut=(400-100)3.14   area of cut=4*25*3.14=(100)3.14   ratio=3:1   ANSWER:3:1
Answer: C
Fonzie, Aunt Bee and Lapis paid $7,000, $8,000 and $9,000 respectively to buy a map to Capt. Plaidstache's treasure. When they found it, the treasure turned out to be worth a cool $900,000. How much of it should Lapis get?	Choose the correct choice from the following answers.
A) $300,000
B) $320,000
C) $335,000
D) $336,500
E) $337,500

Solution: A = 7000   B = 8000   C = 9000   A share 7 parts, B share 8 parts & C share 9 parts   Total 24 parts -----> 900000   ----> 1 part -------> 37500   C share = 9 parts -----> 337500   $337,500
Answer: E
If there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if the total number of wheels is 46?	Choose the correct choice from the following choices:	A) 11	B) 12	C) 13	D) 14	E) 15

Solution: four wheeler=11*4= 
11*4 = 44
44(max)   2 wheel=1   so no of 4 wheeler=11   11NSWER:11
Answer: A
If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first 4 flips but not on the last flip?  Choose the correct option.
A) 1/2 B) 1/4 C) 1/8 D) 1/16 E) 1/32

Solution: P(HHHHT) = 1/2*1/2*1/2*1/2*1/2 = 1/32   The answer is 1/32.
Answer: E
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is  Choose the correct option:
A) 2.3 m
B) 4.6 m
C) 7.8 m
D) 9.2 m
E) None

Solution: Solution   Let AB be the wall and BC be the ladder.   Then, < ABC	= 60°   AC	= 4.6 m.;   AC/BC	= cos 60°   = 1 /2   ‹=›BC=2×AC   =(2× 4.6) m   = 9.2 m   Answer 9.2 m
Answer: D
A two digit number is 18 less than the square of the sum of its digits. How many such numbers are there? Choose the correct option:  A) 22,33  B) 22,22  C) 221,1  D) 63,82  E) 23,17

Solution: Option 2   Take N = 10a+b.   Given that, (10a+b)+18 = K2 = (a+b)2   Given number = K2 - 18 = (10a+b)   That means, when we add 18 to the given number it should be a perfect square. So K2 takes the following values. 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ....   1 to 16 are ruled out as if we subtract 18 from them, the resulting number is a single digit number.   Now  25 - 18= 
 25 - 18 = 7
7   36 - 18= 
36 - 18 = 18
18   49 - 18= 
49 - 18 = 31
31   64 - 18= 
64 - 18 = 46
46   81 - 18= 
81 - 18 = 63
63   100 - 18= 
100 - 18 = 82
82   121 - 18= 
121 - 18 = 103
103   Now 63, 82 satisfies.   Answer:63,82
Answer: D
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 63 kmph, find the speed of the stream?
Options
A) 15  B) 19  C) 14  D) 21  E) 16

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 63/3= 
63/3 = 21
21 kmph.   Answer:21
Answer: D
How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits A equal to 28?	Choose the most appropriate option.
A) 14  B) 24  C) 28  D) 48  E) 96

Solution: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.   Start from the largest number possible 9874.   Then the next largest number possible is 9865.   After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.   So you have two solutions. Each can be rearranged in 4!=24 ways. So A=24+24=48.48
Answer: D
The average marks obtained by 120 candidates in a certain examinationis 35.if the average marks of passed candidate is 39 and that of the failed candidates is 15,what is the no. of candidates who passed the examination?	Choose the correct choice from the following
A) 80
B) 100
C) 120
D) 140
E) 150

Solution: Let No. of passed candidates are x   So, x * 39 + (120 – x) 15= 120 * 35   x = 100   100
Answer: B
A speaks truth in 75% and B in 80% cases. In what percentage of cases are they likely to contradict each other when narrating the same incident?
Choose the correct option:
A) 35
B) 30
C) 25
D) 20
E) None of these

Solution: Let the truth spoken by A and B be pl and p2   respectively, i.e., pl = 3⁄4 and p2 = 4⁄5   They will contradict each other only when one speaks truth and the other is lying.   i.e., 3⁄4 × 1⁄5 + 4⁄5 × 1⁄4 = 3⁄20 + 4⁄20 = 7⁄20 = 35⁄100 i.e, 35%   35nswer 35
Answer: A
The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is Select the correct option.
A) 1008  B) 1015  C) 1022  D) 1032  E) 1043

Solution: Required Number = (L.C.M of 12, 16, 18,21,28)+7   = 1008 + 7= 
1008 + 7 = 1_015
1015   Answer: 1015
Answer: B
The distance between West-Town to East-Town is 14 kilometers. Two birds start flying simultaneously towards one another, the first leaving from West-Town at a speed of 5 kilometers per minute and the second bird, leaving from East-Town, at a speed of 2 kilometers per minute. What will be the distance, in kilometers, between the meeting point and West-Town? Choose the correct choice from the following answers:
A) 3.	B) 7.	C) 10.	D) 12.	E) 15.

Solution: Time taken by the birds to meet = 14/(5+ 2)= 
14/(5+ 2) = 2
2 mins   Distance traveled by the bird traveling from West-Town= 5 * 2= 
5 * 2 = 10
10   Answer: 10.
Answer: C
If a boat is rowed downstream for 96 km in 3 hours and upstream for 88 km in 11 hours, what is the speed of the boat and the river?
Choose the correct choice from the following options
A) 12 , 20
B) 20 , 20
C) 20 , 11
D) 20 , 12
E) 12 , 12

Solution: Explanation:   If x: speed of boats man in still water   y: speed of the river   20 , 12ownstream speed (20 , 12s) = x + y   Upstream speed (Us) = x â€“ y   x = (20 , 12s + Us) / 2   y = (20 , 12s â€“ Us) / 2   In the above problem 20 , 12s = 32 ; Us = 8   x = (32 + 8) / 2 = 40/2= 
40/2 = 20
20 km/hr   y= (32 - 8)/2 = 24/2= 
24/2 = 12
12 km/hr   ANSWER: 20 , 12
Answer: D
A bag marked at $250 is sold for $120. The rate of discount is? Choose the correct choice from the following choices.
A) 10% B) 25% C) 20% D) 52% E) 45%

Solution: Rate of discount = 130/250 * 100= 
130/250 * 100 = 52
52%   Answer is 52%
Answer: D
Rs 3500 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part.	Answers.
A) s 4000  B) s 2800  C) s 1800  D) s 1500  E) s 1550

Solution: Explanation :   Average rate = (144/3500)*100 = 4.11   Ratio = 8.85:11.14   So, first part = (8.85/20)*3500 = Rs 1550.   Answer : s 1550
Answer: E
A rectangular farm has to be fenced one long side, one short side and the diagonal. If the cost of fencing is Rs.10 per meter. The area of farm is 1200 m2 and the short side is 30 m long. How much would the job cost?
Choose the correct option:	A) 1276	B) 1200	C) 2832	D) 1299	E) 1236

Solution: Explanation:   l * 30 = 1200 è l = 40   40 + 30 + 50= 
40 + 30 + 50 = 120
120   120 * 10= 
120 * 10 = 1_200
1200   Answer: Option 1200
Answer: B
The radius of a semi circle is 2.1 cm then its perimeter is? Answers.
A) 32.5	B) 11.12	C) 32.1	D) 10.8	E) 32.3

Solution: 36/7 r = 2.1 = 10.80   Answer:10.8
Answer: D
Boy purchased two flats for Rs.5,00,000. On one he gains 15 % while on the other he losses 15%. How much does he gain or lose?	Choices:
A) 2%	B) 2.15%	C) 2.25%	D) 2.50%	E) 3.34%

Solution: Generally in such cases, there is always loss.   So always remember, when two materials are sold and if one material gets profit and the other gets a loss, then use the trick shown below to calculate the loss.   Loss% = 2.25%ommon loss and gain% 2 = x 2   10 10   Therefore, here common loss and gain % = 15%   Hence,   Loss% = 15 2 = 2.25%   2.25%
Answer: C
For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is? Choose the correct choice from the following answers.
A) 1:2 B) 3:4 C) 4:5 D) 5:7 E) 5:9

Solution: Let the speed of the train be x km/hr and that of the car be y km/hr.   Then, 120 + 480 = 8 1 + 4 = 1 ....(i)   x y x y 15   And, 200 + 400 = 25 1 + 2 = 1 ....(ii)   x y 3 x y 24   Solving (i) and (ii), we get: x = 60 and y = 80.   Ratio of speeds = 60 : 80 = 3 : 4   3:4
Answer: B
To furnish a room in a model home an interior decorator is to select 2 chairs and 3 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 6 chairs in the warehouse and if 150 different combinations are possible, how many tables are there in the warehouse?	Choose the correct choice from the following.
A) A)5  B) B)8  C) C)10  D) D)15  E) E)30

Solution: Total number of ways to choose 6 chairs from 5= 6C2=15   Total number of combination=150   That means we need get 10 combinations from the selection of tables....   Screening through the answers.... 5C3=10..... 10*15=150   Answer is 5... 5
Answer: A
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is Choose the correct choice from the following
A) 20 years  B) 21 years  C) 22 years  D) 24 years  E) 23 years

Solution: Explanation:   Let the son's present age be x years. Then, man's present age = (x + 24) years   => (x + 24) + 2 = 2(x + 2)   => x + 26 = 2x + 4   So, x = 22   Answer: Option 22 years
Answer: C
The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle Pick one
A) 45o	B) 45o	C) 66o	D) 72 degree	E) None of these

Solution: Solution:   Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24o.   => a – b = 24.   Since the average of the two angles is 54o, we have (a+b)/2 =54.   Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields,   [{a+(a−24)}/2] =54   2a−24 = 54*2   2a−24 = 108   2a = 108 +24   2a =132   a =66   Also,   b=a−24=66−24=42.   Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is   180o, a+b+c =180.   Putting the previous results into the equation yields 66+42+c =180.   Solving for c yields c =72   Hence, the greatest of the three angles a, b and c is c, which equ   Answer: Option 72 degree
Answer: D
Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B,
each at a constant rate of speed. Their first meeting is 90 miles from city A. After reaching their
respective destinations and immediately turning around, their second meeting is 30 miles from city B.
What is the distance in miles between city A and city B?	Choose the correct choice from the following answers.
A) 90 B) 120 C) 125 D) 150 E) 240

Solution: let d=distance between cities A and B   bus 1 distance to first meeting=90 miles   bus 1 distance from first to second meeting=(d-90)+30=d-60 miles   bus 2 distance to first meeting=d-90 miles   bus 2 distance from first to second meeting=90+(d-30)=d+60 miles   because both buses take the same time for the pre-meeting leg, and   the same time for the inter-meeting leg, and their speeds remain   constant, their ratios between pre-meeting distance and inter-meeting   distance should be the same   therefore, 90/(d-60)=(d-90)/(d+60)   d^2=240d   d=240 miles   240
Answer: E
Three friends-whose walking rates are 1 ft./sec., 3ft./sec.,and 6ft./sec. start together walking in the same direction around a circular track that is 420 feet in circumference.After how many minutes are the three of them together again?  Choose the correct answer.
A) 5 mins  B) 10 mins  C) 15 mins  D) 3 mins  E) 7 mins

Solution: The time they take will be what the 1st friend takes to complete one circumference as he is the slowest and that is the point all 3 of them will be together at the end of 7 mins.   7 mins
Answer: E
(0.66)(power 3) - (0.1)(power 3)/ (0.66)(power 2) + 0.066 + (0.1)(power 2) is:
Choose the most appropriate option:
A) 0.86
B) 0.56
C) 0.96
D) 0.69
E) 0.76

Solution: Given expression   = (0.66) (power 3) - (0.1)(power 3) / (0.66)(power 2) + (0.66 x 0.1) + (0.1)(power 2)   = a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)   = (a - b)   = (0.66 - 0.1)= 
(0.66 - 0.1) = 0.56
0.56   Answer is 0.56
Answer: B
144 choclates are distributed to children with the same number. What can’t be the range including the number of children?	Pick one:  A) 1~10  B) 50~60  C) 20~30  D) 10~20  E) 70~80

Solution: -> In 144=1*144=2*72=4*36=6*24=8*18=9*16, you can come up with 4 cases.   Amongst these cases, what is not included is B. 50~60. Therefore, the answer is 50~60.
Answer: B
Two friends A, B decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share 4 time, no apples were left.How many apples were there?	Choose one:
A) 250	B) 255	C) 254	D) 253	E) 251

Solution: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 8 times. So answer is (2^8)-1=255   ANSW251R:251
Answer: E
On his drive to work, Leo listens to one of three radio stations A, B or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.25 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Choices:
A) 0.027  B) 0.09  C) 0.417  D) 0.578  E) 0.9

Solution: Probability he hears a song is like:   Tune to A and likes what he is hearing = 0.25   Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.75 * 0.25= 
0.75 * 0.25 = 0.1875
0.1875   Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to C and finally falls in love with the program= 0.75^2 * 0.25 = 0.1406   Total = 0.578   Ans 0.578
Answer: D
The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :	Choose the correct choice from the following answers.
A) 15
B) 16
C) 18
D) 20
E) None of these

Solution: Let the larger number be x.   Then, x -12 = 20% of x<>x-(x/5)=12   4x/5=12<=> x=(12∗5)/5=15.   15nswer :15
Answer: A