MU-NLPC/Calc-aqua_rat huggingface dataset:
A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 73 marks. The maximum marks are?  Choose the correct choice from the following answers:
A) 450
B) 300
C) 500
D) 600
E) 175

Solution: Let the maximum marks be x   Then, 33% of x = 125+73   33x/100 = 198   x = 600   Answer is 600
Answer: D
Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. five years from today, the difference between the age of the boy and the combined ages of the girls will be Choose the correct choice from the following answers: A) 1 B) 2 C) -4 D) –2 E) –1

Solution: Approach I (Plugin's)   Girl I ............... Girl II ................ Boy   1 ....................... 1 ........................ 3 (Assume the current ages)   1 + 1 < 3 .......... (Satisfies the given condition)   1 Year later there ages are   2 ....................... 2 ......................... 4   2 + 2= 
2 + 2 = 4
4 ............ (Satisfies the given condition)   After 5 years there ages are   6 ....................... 6 ............................ 8   Difference= 8 - (6+6) = 8 - 12 = -4   Answer = -4
Answer: C
Two trains are traveling towards the same direction. First train is moving at speed of 100 km/hour and second train 200 km/hour.When will the head of first train start overtaking the second train.  Choose the correct choice from the following answers:	A) 2 hour	B) 1 hour	C) 2.5 hour	D) 3.5 hour	E) 4 hour

Solution: Difference between the speed of two trains 750 – 500 = 250 km. In 60 minutes, the second train reduces the gap from the first train by 100 km. So, to reduce the gap of 250 km, the train will take 180 minutes or 2.5 hours.   Answer: 2.5 hour.
Answer: C
If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is? Choose the correct choice from the following answers
A) 100	B) 272	C) 287	D) 189	E) 289

Solution: 4/3 π * 10 * 10 * 10 = 8 * 4/3 πr3   r = 5   4π * 5 * 5 = 100π   100nswer:1004  * 5 * 5= 
4  * 5 * 5 = 100
100π   100nswer:100
Answer: A
Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was five times as old as Sam. How old is Jim now?
Pick:
A) 42 B) 46 C) 50 D) 54 E) 58

Solution: J = 2F = 2(S+9) = 2S+18   J-6 = 5*(S-6)   (2S+18)-6 = 5S-30   S = 14 and so J = 46   The answer is 46.
Answer: B
A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?	Choose the correct choice:
A) 11
B) 24
C) 55
D) 66
E) 71

Solution: Distance from A and B be 'd'   Average Speed = total distance/total time   Average Speed = (2d)/[(d/20) + (d/30)]   = (2d)/[5d/60) => 24 kmph.   Answer: 24
Answer: B
12 : 8 seconds :: ? : 4 minutes Pick:
A) 10
B) 15
C) 6
D) 8
E) 7

Solution: 12*4=8*x   x=6   ANSWER:6
Answer: C
) A cube is painted blue on all of its surfaces. It is then cut in to 27 smaller cubes of equal size. Find how many smaller cubes have no color?
Choose the correct choice from the following: A) 1 B) 3 C) 8 D) 5 E) 7

Solution: If the cube is cut in to 27 smaller cubes, then number of separations made = n = 3 (since 3×3×3=27). Number of smaller cubes with no color = (n–2)3 = (3–2)3 = 13 = 1   1nswer:1
Answer: A
A train 700 m long can cross an electric pole in 40 sec and then find the speed of the train?  Choose the most appropriate option:	A) 987	B) 271	C) 72	D) 27	E) 63

Solution: Length = Speed * time   Speed = L/T   S = 700/40= 
700/40 = 35/2 = around 17.5
17.5 M/Sec   Speed= 17.5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 63 Kmph   Answer:63
Answer: E
Find the least number must be subtracted from 964807 so that remaining no.is divisible by 8?
Select:	A) 7	B) 6	C) 5	D) 4	E) 3

Solution: On dividing 964807 by 15 we get the remainder 7, so 7 should be subtracted   7
Answer: A
In 1995 a certain store had 1,800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $60 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?  Choose the correct answer:
A) $0	B) $4,000	C) $8,000	D) $32,000	E) $40,000

Solution: The keyword here isGross Profit:   Gross Profit = (Selling Price - Original Price)*(# of Items Sold)   So lets figure out what the Gross Profit for 1995:   GP1995 = (50-30)*(1000)= 
(50-30)*(1000) = 20_000
20000   And the Gross Profit for 1996:   GP1996= (60-30)*(800)= 
(60-30)*(800) = 24_000
24000   So the difference would be:   24000-20000= 
24000-20000 = 4_000
4000   ANSWER: B. 4000
Answer: B
What is the exact probability that, when rolling six fair dice, at least one of the dice shows a 6?  Choose the most appropriate option:
A) 1 B) 31031/46656 C) 5/6 D) 35625/46656 E) 1/6

Solution: For each dice, the probability of not rolling a 6 is 5/6. The total probability of not rolling a 6 is (5/6)^6. The correct answer is thus 1 - (5/6)^6 = 31031/46656, so the answer is 31031/46656.
Answer: B
A family pays $900 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?  Choose the correct choice from the following choices:
A) $1,000
B) $1,200
C) $1,400
D) $1,500
E) $1,700

Solution: Assuming the medical expenses are $1000 or more, the family pays $900 + $400 = $1300.   The total amount paid by insurance plan for the first $1000 of expenses is $600.   The insurance will pay another $700 when the medical expenses are $1700.   The answer is $1,700.900 +  400= 
900 +  400 = 1_300
$1300.   The total amount paid by insurance plan for the first $1000 of expenses is $600.   The insurance will pay another $700 when the medical expenses are $1700.   The answer is $1,700.
Answer: E
The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child? Choices:
A) 10
B) 12
C) 16
D) 19
E) 20

Solution: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20   x = 4.   x+12= 4+12= 
4+12 = 16
16   16
Answer: C
65% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
Select:
A) (a) 15%
B) (b) 5%
C) (c) 10%
D) (d) 20%
E) (e) 25%

Solution: so 35% employees don't have VCD devices.   25% employees don't have MO   20% employees don't have ACs   15% employees don't have WM   Summ of employees that don't have some device = 35%+25%+20%+15% = 95% < 100%   So definitely at least 5% employees have 4 devices.   ans: (b) 5%35 +25 +20 +15= 
35 +25 +20 +15 = 95
95% < 100%   So definitely at least 5% employees have 4 devices.   ans: (b) 5%
Answer: B
Insert the missing number.
2, 6, 12, 20, 30, 42, (....)	Pick one.
A) 56  B) 38  C) 72  D) 66  E) 19

Solution: Explanation:   The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7   So, the next number is 7 x 8 = 56.   56nswer: 56) 56
Answer: A
A person traveled 3 equal distances 20km/hr, 30km/hr, 60km/hr then find its avg speed?	Choose the correct choice from the following.
A) 20km/hr B) 30km/hr C) 22km/hr D) 19km/hr E) 31km/hr

Solution: avg speed = 3xyz/(xy+yz+zx)   required answer is = 3*20*30*60/ (600+1800+1200)= 
3*20*30*60/ (600+1800+1200) = 30
30km/hr   Answer is 30km/hr
Answer: B
How many minutes will be used to cover distance of 520m, if a man running at the speed of 15km/hr? Options:
A) 125 sec B) 124 sec C) 114 sec D) 115 sec E) 117 sec

Solution: Explanation:   Distance = time × speed   = 125 sec.   125 secnswer: 125 sec
Answer: A
A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 6 hours, then the distance covered at 40 kmph is	Choose the correct choice.
A) 220 km	B) 120km	C) 100km	D) 140km	E) none of these

Solution: Let the partial distance covered at 40 kmph be X   Let the another partial distance covered at 60 kmph be (250 - x)   Thus, x/40 - (250 - x)/60 = 6   or, x/40 + (250 - x)/60 = 6   or, (3x + 500 - 2x)//120 = 6   or 500 + x = 720   x=220   220 kmNSWER:220 km
Answer: A
A and B can do a piece of work in 30 days and 30 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? Choose the most appropriate option:  A) 30days  B) 35days  C) 40days  D) 45days  E) 50days

Solution: Explanation:   (30days+B)’s 10 days work = 10[1/30+1/30]=10[1+1/30]= 2/3   30days complete remaining work in   2/3*30= 
  2/3*30 = 20
20   Total work= 10+20= 
10+20 = 30
30days   30daysnswer: Option 30days
Answer: A
A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.	Answers.
A) 83.5% B) 87.5% C) 88.5% D) 89.5% E) Rs 484

Solution: Explanation:   In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.   4/15A=2/5B   A=(2/5∗14/4)B   A=3/2B   A/B=3/2   A:B=3:2   B's Share = 2/5∗1210=484   Option Rs 484
Answer: E
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Choose the most appropriate option:
A) 40  B) 99  C) 77  D) 66  E) 32

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 360 + 140= 
360 + 140 = 500
500 m   Required time= 500 * 2/25= 
500 * 2/25 = 40
40 sec   40nswer: 40
Answer: A
What are the last two digits of 36*28*61*83*73*62? Choose the correct choice from the following options
A) 11
B) 09
C) 07
D) 05
E) 04

Solution: 36*28*61*83*73*62=   We have to focus on the last two digits only, so 36*28=08*61=88*83=04   04*73=92 therefore 92*62=04   Hence Answer is 04
Answer: E
The overall age of X and Y is 11 year greater than the overall age of Y and Z. Z is how many decades younger that X?
Choose the correct choice from the following answers
A) 11  B) 15  C) 12  D) 17  E) 19

Solution: 11   11   (X + Y) â€“ (Y + Z) = 11   X â€“ Z = 11
Answer: A
If x = 2^8 and x^x = 2^k, what is k?  Choose the correct choice from the following choices.
A) 2^15	B) 2^14	C) 2^13	D) 2^12	E) 2^11

Solution: Solution:   We know that x=2^8   which implies x^x = (2^8)^(2^8) = 2^(8 * 2^8) [because (x^y)^z = x^(y*z))]   so 2^(2^3 * 2^8) = 2^(2^(3+8)) [because x^a * x^b = x^(a+b)]   therefore x^x = 2^(2^11)   Given that x^x=2^k   so 2^(2^11) = 2^k   Since the base is same the exponent will also be same   therefore k = 2^11   Answer: 2^11
Answer: E
A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?	Choose the correct answer.
A) 90
B) 52
C) 63
D) 87
E) 10

Solution: Explanation:   Let number of notes of each denomination be x.   Then x + 5x + 10x = 480   16x = 480   x = 30.   Hence, total number of notes = 3x = 90.   90nswer:90
Answer: A
The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches?	Select:  A) 66  B) 83.5  C) 84  D) 95  E) 76

Solution: sum of last 4 matches = (10 × 66) – (6 × 54)= 336   Average =   336/4= 
336/4 = 84
84   ANSWER:84
Answer: C
Two persons starting from the same place walk at a rate of 8kmph and 15kmph respectively. What time will they take to be 14 km apart, if they walk in the same direction?
Choose one.
A) 7 hrs  B) 2 hrs  C) 5 hrs  D) 12 hrs  E) 6 hrs

Solution: The relative speed of the boys = 15kmph – 8kmph   = 7 kmph   Distance between them is 8.5 km   Time= 14km / 7 kmph =2 hrs   Answer : 2 hrs
Answer: B
17 times a positive integer is more than its square by 70, then the positive integer is	Choose the correct choice from the following options:  A) 13  B) 10  C) 11  D) 12  E) 14

Solution: Explanation:   Let the number be x. Then,   17x = x2 + 70   => x2 - 17x + 70 = 0   =>(x - 7)(x - 10) = 0   => x = 7 or 10   Answer: 10
Answer: B
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?  Choose the most appropriate option.
A) 288
B) 350
C) 889
D) 276
E) 234

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer:350
Answer: B
If log 2 = 0.3010 and log 3 = 0.4771, the values of log5 512 is Choose the correct choice from the following
A) 3.879	B) 3.875	C) 3.872	D) 3.828	E) 3.192

Solution: ANS: log5512 = {\color{3.875lack} \frac{\log 512}{\log 5}} = {\color{3.875lack} \frac{\log 2^{9}}{\log (\frac{10}{2})}} ={\color{3.875lack} \frac{9\log 2}{\log10-\log 2 }} ={\color{3.875lack} \frac{(9\times 0.3010)}{1-0.3010 }} ={\color{3.875lack} \frac{2.709}{0.699 }} ={\color{3.875lack} \frac{2709}{699 }} =3.876   Answer: 3.875) 3.875
Answer: B
A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? Answers
A) 12 min	B) 16 min	C) 18 min	D) 15 min	E) 19 min

Solution: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.   Relative speed of A and B = 6 - 1= 
6 - 1 = 5
5 rounds per hour.   Time taken to complete one round at this speed= 1/5 hr   = 12 min.   12 minnswer:12 min
Answer: A
If .005^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?	Choose the correct choice from the following.
A) 0	B) 8	C) 9	D) 10	E) 11

Solution: 0.005^4= (5*10^-3)^4 = 625*10^-12 = 0.625*10^-9 which would have 9 zeros to the right of the decimal point. The answer is 9.
Answer: C
A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:	Choose the correct answer:
A) 4.6%	B) 3.6%	C) 6.4%	D) 7.8%	E) 8.9%

Solution: C   6.4%   Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.   = $ 4000 × 5/100.   = $ 4000 × 0.05.   = $ 200.   Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.   = $ 3500 × 4/100.   = $ 3500 × 0.04.   = $ 140.   Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.   Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.   = $ 160.   Total invested amount = $ 4000 + $ 3500 = $7500.   Remaining invest amount = $ 10000 - $ 7500 = $ 2500.   We know that, Interest = Principal × Rate × Time   Interest = $ 160,   Principal = $ 2500,   Rate = r [we need to find the value of r],   Time = 1 year.   160 = 2500 × r × 1.   160 = 2500r   160/2500 = 2500r/2500 [divide both sides by 2500]   0.064 = r   r = 0.064   6.4%hange it to a percent by moving the decimal to the right two places r = 6.4 %   Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: C
If three distinct positive divisors of 64 are randomly selected, what is the probability that their sum will be less than 32?  Choose the correct choice from the following options: A) 1/3 B) 1/2 C) 2/7 D) 10/21 E) 15/28

Solution: The positive divisors are 1, 2, 4, 8, 16, 32, 64.   If any of the first five are chosen, the sum will be less than 32.   P(sum is less than 32) = 5/7 * 4/6 * 3/5 = 12/42 = 2/7   The answer is 2/7.
Answer: C
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m?	Choose the correct answer.
A) 29798
B) 27908
C) 78902
D) 25000
E) 27000

Solution: 27 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   27 = 1/100 * x => x   = 27000   Answer: 27000
Answer: E
A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is? Choose the correct choice from the following options: A) 238 B) 150 C) 988 D) 210 E) 171

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 140)/25 = x/15 => x = 210 m.   Answer: 210
Answer: D
A certain number of machines can do a work in 100days. If there were 10 machines more it could be finished in 10days less. How many machines are there? Choose the correct answer:
A) 50	B) 40	C) 90	D) 100	E) 60

Solution: Original number of machines = 10 * (100-10)/10= 
10 * (100-10)/10 = 90
90 machines   Answer is 90
Answer: C
For which of the following functions f is f(y) = f(1-y) for all y?
Choose the correct choice from the following choices.
A) f (x) = 1 - x B) f (x) = 1 - x^2 C) f (y) = y^2 - (1 - y)^2 D) f (y) = y^2*(1 - y)^2 E) f (y) = y/(1 - y)

Solution: I remember seeing this problem in a GMATprep test. I think choice D should be F(y)=(y^2) (1-y)^2. If that is true then substituting (1-y) for will give us the same function back and the answer choice is f (y) = y^2*(1 - y)^2, where the function is multiplicative
Answer: D
The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#27?  Options:
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: First, let's translate the expression 21#27, using the definition given:   21#27 = 21×24×27   We need the prime factorization of this product.   Let's factor out 3 from each multiple.   21#27 = 3^3(7×8×9)   Now let's replace each consecutive integer with its prime factorization:   21#27 = 3^3(7×2^3×3^2)   Let's group the prime bases:   21#27 = 2^3×3^5×7   The sum of the exponents is  3 + 5 + 1= 
 3 + 5 + 1 = 9
9   The answer is 9.
Answer: D
A rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge. If the floor is 12 meters by 10 meters, what is the area of the rug in square meters?
Answers.
A) 30  B) 28  C) 36  D) 42  E) 24

Solution: A strip of 3 meters is covering the inner rectangular rug for all 4 sides.   Length of inner rug = 12-(2*3)   breadth of inner rug= 10-(2*3)   Area of Rug= 6 * 4= 
6 * 4 = 24
24 sq. mt   Ânswer: 24
Answer: E
Of the diplomats attending a summit conference, 14 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?  Choices
A) 72
B) 96
C) 108
D) 120
E) 180

Solution: {Total} = {French} + {Russian} - {Both} + {Neither}   {Total} = 14 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total}   Solving gives {Total} = 180.   Answer: 180.
Answer: E
Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 9 on the two dice?	Choose the most appropriate option:
A) 4/9  B) 5/9  C) 7/18  D) 11/18  E) 7/36

Solution: There are 36 possible outcomes for two dice.   The number of outcomes with an even number on the first die is 3*6= 
3*6 = 18
18.   The number of outcomes with a sum of 9 is 4.   We need to subtract the outcomes that have both an even number on the first die and a sum of 9 because we have counted those outcomes twice. This number of outcomes is 2.   The number of outcomes with either an even number on the first die or a sum of 9 is  18+4-2= 
 18+4-2 = 20
20.   The probability is 20/36=5/9.   The answer is 5/9.
Answer: B
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 42 kmph, find the speed of the stream?	Choose the correct choice
A) 16 kmph	B) 18 kmph	C) 14 kmph	D) 79 kmph	E) 27 kmph

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= 42/3= 
42/3 = 14
14 kmph.   Answer: 14 kmph
Answer: C
A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?	Choose the correct choice:	A) 10	B) 20	C) 30	D) 40	E) 50

Solution: 10'S sal = 40% of B =40% Of (25% of C) = 40/100(25/100*100) % Of C = 10%   10NSWER 10
Answer: A
An article is bought for Rs.560 and sold for Rs.340, find the loss percent?
Select:
A) 36%
B) 38%
C) 16%
D) 39%
E) 12%

Solution: 560 ---- 220   100 ---- ? => 39%   Answer:39%
Answer: D
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a odd number written on it?	Choose the correct option:
A) 1/12	B) 1/10	C) 1/8	D) 1/42	E) 5/9

Solution: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)   P(+ on 1st pick) = 5/10   P(+ on 2nd pick) = 4/9   P(+ on 3rd pick) = 3/8   P(+ on 4rd pick) = 2/7   5/10*4/9*3/8*2/7=1/42   1/42
Answer: D
A chemical tank of capacity 2000m3 which is 65% full is found to be leaking. The chemical in the tank needs to be transported to a new destination using tanker trucks. If the capacity of a truck is 16m3 which can be filled upto 93% full. How many truck loads would be needed to transport the chemical?
Select
A) 64 B) 71 C) 85 D) 92 E) 97

Solution: Volume of chemical in the tank=2000x0.65=1300   Volume of the truck=16x.93=15.36   Number of truck loads needed= 1300/15.36=84.63â‰ˆ85   Answer: 85
Answer: C
The average of 65 numbers is 40. If two numbers, 79 and 60 are discarded, then the average of the remaining numbers is nearly
Answers:
A) 28.32 B) 39 C) 38.78 D) 39.06 E) 30

Solution: Explanation :   Total sum of 63 numbers = (65*40) - (79 +60) = 2600 - 139= 
2600 - 139 = 2_461
2461   Average= 2457/63 = 39.06   Answer : 39.06
Answer: D
If x+y=10z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z? Choose the correct choice from the following answers:
A) 4z-1
B) 3z
C) 5z
D) z/3
E) 3z/2

Solution: Pick any number like X=12, Y=18 and Z= 3 so that X+Y=10Z, now then the arithmetic mean will be   (12+18+3)/3= 
  (12+18+3)/3 = 11
11. Now, just look at the answers and put the value of Z there.   (4z-1) 4.3-1=11,it can be the answer, lets check us the other options   (B) 3.3=6, no   (C) 5.3=15, no   (D) 3/3, no   (E) (3.3)/2=3, no   so the answer will be 4z-1..
Answer: A
In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is theprobability that the extracted ball would turn onto be white, if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ? Choose the correct choice from the following
A) 3/5	B) 5/8	C) 6/7	D) 7/8	E) 6/7

Solution: Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.   ∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]   = 1/4 [(4 + 3 + 2 + 1)/4] = 5/8   5/8
Answer: B
A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?  Choose the most appropriate option:
A) 65 km/hr
B) 17 km/hr
C) 55 km/hr
D) 50 km/hr
E) 15 km/hr

Solution: Speed of the train relative to man = 125/10 = 25/2 m/sec.   = 25/2 * 18/5= 
25/2 * 18/5 = 45
45 km/hr   Let the speed of the train be x km/hr. Then, relative speed= (x - 10) km/hr.   x - 10 = 45 => x = 55 km/hr.   Answer: 55 km/hr
Answer: C