MU-NLPC/Calc-aqua_rat huggingface dataset:
If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/8
Pick one: A) None B) I only C) III only D) II and III only E) I, II, and III

Solution: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.   On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.   We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us I only as the only possible answer.
Answer: B
A sum of Rs. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is ?  Choose the correct choice from the following choices:  A) 23  B) 87  C) 84  D) 26  E) 19

Solution: Given total sum = Rs. 427   And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.   => 3A = 4B = 784   But given   => A + B + 84 = 427   Now express A and B in terms of 84 i.e   => (784/3) + (784/4) + 84 = 427   => 84 = 84   Answer: 84
Answer: C
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Choose the correct choice from the following options
A) 45 km/hr	B) 50 km/hr	C) 54 km/hr	D) 55 km/hr	E) 56 km/hr

Solution: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.   ANSWER:50 km/hr
Answer: B
What percent of 10 is 10 percent of 1?
Select
A) 0.1%	B) 1%	C) 10%	D) 90%	E) 100%

Solution: 10 percent of 1 is equal to 0.1   So we have to compute what percent of 10 is 0.1. so this means we have to compute what percent of 100 is 1....so 1%   Answer 1%.
Answer: B
Running at the same constant rate, 6 identical machines can produce a total of 330 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes? Choose the correct choice from the following options
A) 648  B) 1800  C) 2200  D) 10800  E) 10900

Solution: Let the required number of bottles be x.   More machines, More bottles (Direct Proportion)   More minutes, More bottles (Direct Proportion)   Machines	6	:	10	:: 330 : x   Time (in minutes)	1	:	4   6 x 1 x x = 10 x 4 x 330   x =	(10 x 4 x 330)/(6)   x = 2200.   ANSWER:2200
Answer: C
If p and r are integers, and p^2 = 18r, then r must be divisible by which of the following?  Choose the correct answer.
A) 2  B) 4  C) 5  D) 7  E) 9

Solution: Ans: D   Solution: for p to be an int 18 r must be whole square of a number.   18r= 9*2*r   to make it whole square we need 9   so r can must be divisible by 9y where y is itself a whole square.   so 9 is the ans
Answer: E
Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 2 hours and machine B produces k bottles in 4 hours. How many hours does it take machines A and B, working simultaneously, to produce 15k bottles? Choose the correct choice
A) 10  B) 15  C) 12  D) 20  E) 18

Solution: A's rate = k/2   B's rate = k/4   k/2 + k/4 = 3k/4   15k / (3k/4) = 20 hours   The answer is 20.15  / (3 /4)= 
15  / (3 /4) = 20
20 hours   The answer is 20.
Answer: D
There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?  Select the correct option:
A) 1/13  B) 2/13  C) 3/17  D) 4/17  E) 8/21

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(8/21) = 8/21.
Answer: E
The relationship between quantities m and n is expressed by the equation 11m = 5(n - 52). If the difference between the two chosen values of n is 40, what is the difference in the corresponding values of m?	Select:
A) 200/11	B) 42/11	C) 60/11	D) 150/11	E) 14

Solution: 200/11nother Simple way   11m=5(n-52)   200/11ssume n = 52 to make one side equal to 0   then 11m=0   and m = 0   Repeat it by assuming n as 52+40 i.e 92   11m= 5(92-52)   11m=200   m=200/11   diff = 200/11 - 0 = 200/11   200/11nswer : 200/11
Answer: A
A paint store mixes 3/4 pint of red paint and 2/3 pint of white paint to make a new paint color called Perfect Pink. How many pints of red paint would be needed to make 33 pints of Perfect Pink paint?	Choices
A) 9	B) 16	C) 17	D) 25 1/3	E) 28 1/2

Solution: 3/4 pint is required to make 3/4 + 2/3 = 17/12 pint of perfect pink   so 17/12 pint requires 3/4 pint of red..   1 pint will require 3/4 * 12/17=9/17..   33 pints will require 9/17 * 33= 17 pints..   17
Answer: C
ramu sells gud for 27 per kg. but he has two plates for wighting one plate is 10% shorter then other.. he put 1 kg weight on shorter plat and apple on other plat.. at the end their is no profit no loss..what is cost price of apple	Choose the most appropriate option.
A) 30	B) 40	C) 50	D) 60	E) 70

Solution: ramu is making profit of 10% on weight because he puts 1 kg on shorter site.   to balance this profit if there is decrease of 1/10 in weight then there should be increse of 1/9 in price so 1/9 of 27=3   cost price=27+3= 
27+3 = 30
30   ans=30   30NSWER:30
Answer: A
Working alone, machine X can manufacture 1,000 nails in 16 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?	Choose the most appropriate option
A) 3 9/17
B) 5 1/3
C) 7
D) 7 3/11
E) 8 4/7

Solution: rate of machine x = 1000/16   (1000/16 + y)5=1000   y=200-125/2=275/2   275/2 * t = 1000   t=7 3/11   D. 7 3/11
Answer: D
A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Choices: A) 104 kmph B) 176 kmph C) 298 kmph D) 186 kmph E) 268 kmph

Solution: 624/6= 
624/6 = 104
104 kmph   104 kmphnswer:104 kmph
Answer: A
At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long A will the conference last if there are a total of 6 seminars that day?  Choices.
A) 5 hours and 15 minutes	B) 5 hours and 20 minutes	C) 5 hours and 25 minutes	D) 5 hours and 30 minutes	E) 5 hours and 35 minutes

Solution: Shouldnt the answer be 5 hours 20 mins?   5 hours and 20 minutesreak = b   Seminar= 10b   9am to 11:40am= 160mins   3s+b=160   30b+b=160   b=160/31   6 seminar will take   6s+2b   =60b+2b   =62b   60 +2= 
60 +2 = 62
62b=62*160/31= 
62*160/31 = 320
320   A=5 hours 20 mins.5 hours and 20 minutes
Answer: B
A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss? Pick one
A) 9	B) 8	C) 7	D) 5	E) 3

Solution: (30*30)/100= 
(30*30)/100 = 9
9%loss   9nswer: 9
Answer: A
Of the goose eggs laid at a certain pond, 1/3 hatched and 4/5 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
Choose the correct choice from the following answers
A) 1025 B) 1075 C) 1125 D) 1175 E) 1225

Solution: Let x be the number of eggs that were laid.   (2/5)(4/5)(1/3)x = 120   (8/75)x = 120   x = 1125   The answer is 1125.
Answer: C
The average expenditure of a man for the first five months is Rs.300 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
Select the correct option.
A) Rs.140	B) Rs.150	C) Rs.190	D) Rs.225	E) none

Solution: Explanation:   Total income = Rs.(300Ã—5+130Ã—7+290)=Rs.2700   Average monthly income   = Rs. (2700/12)=Rs.225   Correct Option: Rs.225
Answer: D
225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees  Choose the correct choice from the following answers
A) 10  B) 12  C) 14  D) 16  E) 18

Solution: 26 trees have 25 gaps between them,   Required distance (225/25) = 10   10
Answer: A
The length of box 12 Cm long, 8 Cm breadth and 9Cm height. Find the length of pencil in that box? Choose the correct choice from the following
A) 19	B) 14	C) 17	D) 16	E) 13

Solution: Diagonal (d) = √l(power2)+b(power2)+h(power2)   = √12(power2)+8(power2)+9(power2)   = √144+64+81= 
144+64+81 = 289
√289=> 17 17m   Answer is 17.
Answer: C
The average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results? Choose the most appropriate option.
A) 30
B) 25
C) 48
D) 50
E) None

Solution: Answer   Sum of 85 result = sum of 20 result + sum of 65 result.   = 20 x 65 + 65 x 20   = 2600   Correct Option: 30
Answer: A
The average of 10 numbers was calculated as 20. It is discovered later on that while calculating the average, one number, namely 86, was incorrectly read as 26. What is the correct average?  Choose the correct choice from the following answers.
A) 22	B) 23	C) 24	D) 25	E) 26

Solution: 10*20 - 26 + 86= 
10*20 - 26 + 86 = 260
260   260 / 10= 
260 / 10 = 26
26   The answer is 26.
Answer: E
In one hour, a boat goes 11km along the stream and 5 km against it. Find the speed of the boat in still water	Choose one:	A) 6	B) 7	C) 8	D) 9	E) 10

Solution: Explanation:   We know we can calculate it by 1/2(a+b)   => 1/2(11+5) = 1/2(16) = 8 km/hr   ANSWER IS 8
Answer: C
If the function Q is defined by the formula Q = 5w/(4vf(z^2)), by what factor will Q be multiplied if w is quadrupled, f is doubled, and z is tripled?
Pick one.
A) 1/9
B) 2/9
C) 4/9
D) 3/9
E) 2/27

Solution: We just need to find the factor thats all,   w -> quadrupled -> 4w   f-> doubled -> 2f   z-> tripled -> 3Z   Hence, Z^2 = 9Z^2   W is in numerator, and f*z in denominator.   Hence,   Additional factor being introduced = 4/2*9   =4/18 = 2/9 = 2/9
Answer: B
A Train requires 12 seconds to pass a pole while it requires 27 seconds to cross a stationary train which is 300 mtrs long. Find the speed of the train.  Choose the correct choice from the following options.
A) 60 kmph  B) 75 kmph  C) 80 kmph  D) 85 kmph  E) 72 kmph

Solution: In 12s the train crosses the pole and in 27 sec the train crosses one more stationary train   In 15 sec the train travels a distance of 300 mtrs   Speed = 300/15= 
300/15 = 20
20 m/s= 20 (3600/1000) = 20 * 18/5= 
20 * 18/5 = 72
72 kmph   Answer: 72 kmph
Answer: E
Machine A and machine B are each used to manufacture 220 sprockets. It takes machine A 10 hours longer to produce 220 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?  Choose the correct choice from the following options:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: Machine B: Takes x hours to produce 220 sprockets   Machine 2: Takes (x+10) hours to produce 220 sprockets   Machine B: In 1 hour, B makes 220/x sprockets   Machine 2: In 1 hour, 2 makes 220/(x+10) sprockets   Equating:   1.1(220/(x+10)) = 220/x   242/(x+10) = 220/x   242x = 220x+2200   22x = 2200   x = 100   2 makes  220/(110)= 
 220/(110) = 2
2 sprockets per hour   2nswer : 2
Answer: A
There was a cycle race going on. 1/5th of the those in front of a person and 5/6th of those behind him
gives the total number of participants. How many people took part in the race?	Select the correct option
A) 31 B) 39 C) 30 D) 33 E) 34

Solution: Explanation :   Let total participants be (x+1)   Then   => (1 / 5) * x + (5/6) * x = x+1   => 31x/30=x+1   => x=30   So total participants (x+1)=31   Hence (A) is the correct answer.   31nswer : 31
Answer: A
The rate of a certain chemical reaction is directly proportional to the concentration of chemical B present and inversely proportional to the concentration of chemical A present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical B required to keep the reaction rate unchanged.
Options
A) 10 % decrease B) 50% decrease C) 40% decrease D) 30% increase E) 100% increase

Solution: Let's say here is the formula of how B and A affects the reaction speed:   rate = B/A   After the concentration A is increased by 100%, the percentage of A   become 2A, to keep 'rate' the same, need to have 2B being doubled.   Which means A increased by 100%.   Answer : 100% increase
Answer: E
Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
Select the correct option
A) 334  B) 500  C) 265  D) 197  E) 121

Solution: Let the investment in 9% stock be Rs. x.   Then, investment in 10% stock = Rs. (9800 - x).   9	x x =	10	x (9800 - x)   75	80   3x	=	9800 - x   25	8   24x = 9800 x 25 - 25x   49x = 9800 x 25   x = 500   Answer:500
Answer: B
Mr. Mike sold two books at $2.20 each. Based on the cost, his profit one was 20% and his loss on the other was 30%. On the sale of the books. Find the amount of his profit or loss?	Choose the correct choice from the following choices
A) lost 10 cents	B) lost 4 cents	C) broke even	D) lost amount 0.22 cents.	E) gained 10 cents

Solution: 20 % profit on $ 2.20   = $ 20/100 × 2.20   = $ 0.20 × 2.20   = $ 0.44   Similarly, 30 % loss on $ 2.20   = $ 30/100 × 2.20   = $ 0.30 ×2.20   = $ 0.66   Therefore, in one book his profit is $ 0.44 and in the other book his loss is $ 0.66.   loss amount 0.22 cents.   Answer is lost amount 0.22 cents..
Answer: D
The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers	Choose the correct choice from the following
A) 28,22
B) 28,17
C) 27,17
D) 26,17
E) 28,19

Solution: If two numbers are x, y   x-y=11 --(i) & (x+y)/5=9 --(ii)   Solving (i) & (ii), x=28, y=17   ANSWER:28,17
Answer: B
The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
Pick:	A) 10 and 30	B) 12 and 18	C) 24 and 64	D) 21 and 63	E) 22 and 44

Solution: 64 has only the prime 2 (64=2^6) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.   The answer is 24 and 64.
Answer: C
What is the sum of all 3 digit positive integers that can be formed using the digits 1, 3, and 5, if the digits are allowed to repeat within a number?  Answers.
A) 4551	B) 5661	C) 6771	D) 7881	E) 8991

Solution: The number of these 3-digit numbers is   3*3*3= 
  3*3*3 = 27
27   Each digit 1, 3, and 5 will appear in the ones, tens, and hundreds place 9 times each.   The sum equals 9(111) + 9(333) + 9(555)= 9(999) = 8991   The answer is 8991.
Answer: E
A straight fence is to be constructed from posts 8 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)  Choose the correct choice from the following choices
A) 17 B) 28 C) 35 D) 39 E) 50

Solution: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}   The minimum length is with 2 posts = 0.5 + 5 + 0.5= 
0.5 + 5 + 0.5 = 6
6 feet. To increase the fence, each time we should add{post= 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:   6 feet;   8 + 5.5= 
8 + 5.5 = 13.5
13.5 feet;   11.5 + 5.5= 19 feet;   17 + 5.5 = 24.5 feet;   22.5 + 5.5 = 30 feet;   28 + 5.5 = 35.5 feet;   33.5 + 5.5 = 41 feet.   ...   We skipped 39 feet.   Answer: 39.
Answer: D
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of q square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)  Choose the correct choice from the following answers:
A) (5,280 mt) / 12 q
B) (5,280 pt) / 12m
C) (5,280 pmt) /12
D) (5,280)(12m) / pt
E) (5,280)(12p) / mt

Solution: Given that: 1 gallon of paint covers an area ofqsquare feet. Question:how many gallonsof paint will be needed ...   In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/q, so q must be in the denominator: eliminate all but A and D.   Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.   (5,280 mt) / 12 qnswer: (5,280 mt) / 12 q.
Answer: A
Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite direction for 4 miles and then turn to left and run for another 3 miles.
what is the distance between the the two twins when they stop ?  Choices:
A) 11 miles	B) 10 miles	C) 9 miles	D) 12 miles	E) 13 miles

Solution: 10 miles   10 miles
Answer: B
In the biology lab of "Jefferson" High School there are 0.037*10^5 germs, equally divided among 148000*10^(-3) Petri dishes. How many germs live happily in a single dish?	Options.
A) 10 B) 25 C) 35 D) 40 E) 55

Solution: 0.037*10^5 can be written as 3700   148000*10^(-3) can be written as 148   Required= 3700/148= 
3700/148 = 25
25   ANSWER:25
Answer: B
The bankerâ€™s gain on a sum due 3 years hence at 12% per annum is Rs. 180. The bankerâ€™s discount is Answers.
A) Rs.960 B) Rs.840 C) Rs.1020 D) Rs.680 E) None

Solution: Solution   T.D	=(B.G x 100 / R x T)   = Rs.(180x100/12 x 3)   = Rs.500.   B.D   =Rs(500+ 180)   = Rs.680.   Answer Rs.680
Answer: D
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?  Choose the correct choice from the following answers: A) 39 B) 27 C) 30 D) 288 E) 291

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer: 30
Answer: C
An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 9 businessmen, how many possible team submissions are possible?
Select:  A) 76  B) 100  C) 162  D) 198  E) 202

Solution: P(at least one Tech)= p(total) - P( no tech)   =13c3 - 9c3   =198 (Ans :198 )
Answer: D
If the cost price of 65 chocolates is equal to the selling price of 50 chocolates, the gain percent is :	Choices:  A) 35%  B) 10%  C) 20%  D) 30%  E) 33%

Solution: Explanation :   Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 50 chocolates = Rs. 50;   S.P. of 50 chocolates =Rs. 65.   .'. Gain% = 15*100/50= 
15*100/50 = 30
30%   Answer : 30%
Answer: D
A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?  Choose the correct choice from the following choices:
A) 2:6
B) 2:9
C) 2:3
D) 2:2
E) 2:1

Solution: Let the principal be P and rate of interest be R%.   Required ratio = [(P * R * 6)/100] / [(P * R * 9)/100] = 6PR/9PR = 6/9 = 2:3   Answer: 2:3
Answer: C
If 0 < Z < Y, Z is an odd number and Y is a prime number, which of the following can be the value of Z + Y ?	Choose the correct option:  A) 11.  B) 13.  C) 17.  D) 10.  E) 15.

Solution: If Z is odd ,implies Z(odd)+y(odd/even prime)=(Even/Odd)   If Y is even, the 2 is the even prime , therefore y=2z=1 since 0<Z<Y therefore Z+Y =3. But 3 is not an option   which implies y is odd,   Now Z(odd)+Y(odd)=Even   10 is the only option that is even=10.
Answer: D
on dividing a N by 9,remainder is 8. the quotient obtained when divided by 11,leaves remainder 9. now the quotient when divided by 13,leaves remainder 8. find the remainder when when the N is divided by 1287
Choose the correct answer:
A) 871
B) 881
C) 891
D) 904
E) 987

Solution: take from the last step division   suppose no. is n which is divided by 13 and remainder 8 = 13n+8   now 13n+8 will be the no. which is divided by 11 and remainder is 9   = [11*(13n+8)]+9   now this no. is used for the very first step which is divider is 9 and remainder is 8   ={9*[11*(13n+8)]+9}+8 solve and ans is 881   ANSWER:881
Answer: B
If the current in a circuit equals 0 A, it is likely that the	Choose the correct answer
A) 22	B) 37	C) 36	D) 28	E) 22

Solution: Answer: Option 28
Answer: D
I have a basket of 500 apples.
I want to divide them equally into 20 places.
How long will it take to divide if for each 25 apples counted i spent 5 minutes ?	Pick one:
A) 199
B) 100
C) 60
D) 5
E) 20

Solution: 500 apples divided by 20 is 25. If it takes 5 minutes to sort out 25 apples then it would take 100 minutes to perform the same task 20 times   Answer is 100
Answer: B
The number of permutations of the letters of the word 'MESMERISE' ?  Choose the correct choice from the following answers: A) 9!/(2!)2 3! B) 9!/(2!)2 8! C) 9!/(2!)2 6! D) 9!/(9!)2 3! E) 9!/(2!)3 3!

Solution: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.   The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.   Number of arrangements = 9!/(2!)2 3!   9!/(2!)2 3!nswer: 9!/(2!)2 3!
Answer: A
A carton contains 25 bulbs, 8 of which are defective. What is the probability that if a sample of 4 bulbs is chosen, exactly 2 of them will be defective ?
Pick one
A) (8/25) x (7/24) x (17/23) x (16/22)  B) (4C2) x (8/25) x (7/24) x (17/23) x (16/22)  C) (8/26) x (8/24) x (17/33) x (16/22)  D) None of these  E) Cannot be determined

Solution: Explanation :   The probability that exactly two bulbs are defective and exactly two are not defective will be given by   (4C2) x (8/25) x (7/24) x (17/23) x (16/22)   Answer : (4C2) x (8/25) x (7/24) x (17/23) x (16/22)
Answer: B
How many times in a day, the hands of a clock are shows opposite directions ? Choose one
A) 12 B) 20 C) 21 D) 23 E) 22

Solution: Sol.   In 12 hours, the hands coincide or are in opposite direction 11 times.   âˆ´ In 24 hours, the hands coincide or are in opposite direction 22 times a day.   ( between 5 and 7 they point in opposite directions at 6 o'clock only)   Answer 22
Answer: E
If 2994 Ã· 14.5 = 171, then 29.94 Ã· 1.45 = ?
Options:
A) 17.1
B) 17.3
C) 17.5
D) 17.7
E) 17.2

Solution: 29.94/ 1.45 = 299.4/14.5   = (2994/14.5) x 1/10) [ Here, Substitute 171 in the place of 2994/14.5 ]   = 171/10= 
171/10 = 171/10 = around 17.1
17.1   17.1nswer is 17.1.
Answer: A
Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04) Options.
A) 0.56  B) 0.71  C) 0.45  D) 0.67  E) 0.71

Solution: Option '0.56'
Answer: A
The perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters. What is the length of the yard if the area of the yard is 40 meters squared? Pick one.
A) 12	B) 10	C) 8	D) 14	E) 16

Solution: Perimeter of rectangular yard = 2(l + b) = 36 --> l + b = 18   Area = l * b = 40   b = 18 - l   l(18 - l) = 40   18l - l^2 = 40   l^2 - 18l + 40 = 0   Upon simplifying we get l = 5 or 8. Only 8 is there in the answer choice.   Answer: 8
Answer: C
A train 110 m long is running with a speed of 56 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 choice from the following:
A) 5 B) 6.4 C) 7 D) 8 E) 9

Solution: Speed of train relative to man = 56 + 6= 
56 + 6 = 62
62 km/hr.= 62 * 5/18 = 155/9 m/sec.   Time taken to pass the men = 110 * 9/155 = 6.4 sec.   Answer: Option 6.4
Answer: B
If A : B= 1 : 4 and B : C = 2 : 3, then A : B : C is:  Choices.
A) 4:14:24
B) 8:6:9
C) 2:5:7
D) 6:4:7
E) 2:8:12

Solution: A:B=1:4, B:C=2:3, A:B:C=1Ã—2:2Ã—4:4Ã—3   â‡’ 2:8:12   Answer: 2:8:12.
Answer: E