MU-NLPC/Calc-aqua_rat huggingface dataset:
If 15 men, working 9 hours a day, can reap a field in 16 days, in how many
days will 18 men reap the field, working 8 hours a day? Choose the correct choice from the following options:	A) 12	B) 16	C) 8	D) 15	E) 10

Solution: Let the required number of days be x.   More men, Less days (indirect proportion)   Less hours per day, More days (indirect proportion)   Men 18 : 15   Hours per day 8: 9 } : :16 : x   (18 x 8 x x)=(15 x 9 x 16)<=> x=(44 x 15)144 = 15   Hence, required number of days = 15.   Answer is 15.
Answer: D
The measures of the 2 acute angles of a triangle are in the ratio of 2:7. What are the measures of the 2 angles?
Choose the correct choice from the following options:
A) 60°
B) 70°
C) 80°
D) 90°
E) 100°

Solution: If the ratio of the two angles is 2:7, then the measures of two angles can be written as 2x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence   2x + 7x = 90   9x = 90   x = 10   Measures of the two acute angles are   2x = 2 × 10 = 20°   7x = 7 × 10 = 70°   70°
Answer: B
Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet? Options:
A) 7.18
B) 7.12
C) 7.43
D) 7.59
E) 7.71

Solution: T = (141 + 165)/ (80 + 65) * 18/5   T = 7.59   Answer:7.59
Answer: D
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is?	Pick.
A) Rs. 9600	B) Rs. 8500	C) Rs. 8450	D) Rs. 8400	E) Rs. 9400

Solution: Ratio of their shares = 22500 : 35000 = 9 : 14   Deepak's share = Rs. (13800 * 14/23) = Rs. 8400 ANSWER "Rs. 8400
Answer: D
If there is exactly one root of the equation x^2 + ax + 2b, where a and b are positive constants, what is b in terms of a?  Choose the correct choice from the following
A) a/2
B) a
C) 3a/2
D) a^2/2
E) a^2/8

Solution: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1   Here b = a   c= 2b   a = 1   substituting these values in 1, we have   a^2 = 8b => b =a^2/8   Answer is a^2/8.
Answer: E
If x > 0.5, which of the following could be the value of x? Choose the correct choice from the following
A) √0.007  B) √0.006  C) √0.008  D) √0.5  E) √0.009

Solution: Answer : √0.5
Answer: D
A man sells a horse for Rs.860 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?  Choices:
A) 287 B) 879 C) 967 D) 900 E) 998

Solution: CP = SP + 1CP = SP - g   860 + x = 980 - 2x   3x = 120 => x   = 40   CP = 860 + 40= 
860 + 40 = 900
900   Answer:900
Answer: D
(23341379 x 72) = ?
Select.
A) 1680579288  B) 1223441288  C) 2142579288  D) 2142339288  E) None of these

Solution: Explanation :   23341379 x 72 = 23341379(70 + 2) = (23341379 x 70) + (23341379 x 2)   = 1633896530 + 46682758= 
1633896530 + 46682758 = 1_680_579_288
1680579288. 1680579288nswer : Option 1680579288
Answer: A
Average marks of a,b,c is 48. When d joins average becomes 47. E has 3 more marks than d. Average marks of b,c,d,e is 48. What is the marks of a?  Choose the correct choice from the following
A) 43
B) 44
C) 45
D) 46
E) 47

Solution: a+b+c=144   a+b+c+d=188   d=44   e=47   b+c+d+e=192   b+c=101   a=43   43NSWER:43
Answer: A
In a 2000 census, 51.27% of the population are male, and 48.73% are female. What is the ratio of men to every 100 women?	Choose the correct choice from the following:	A) 110:100	B) 105:100	C) 95:100	D) 85:100	E) 120:100

Solution: The ratio of A to B, where   A = the percent of males, and   B = the percent of females.   A = 51.27   B = 48.73   A:B = 51.27:48.73   So, 100(5,127/4,873):100   Giving a male to female ratio of 105.20 men for every 100 women.   Answer is 105:100
Answer: B
During the first two weeks of January, the total rainfall in Springdale was 35 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?  Choose the correct answer:	A) 5 inches	B) 6 inches	C) 9 inches	D) 10 inches	E) 21 inches

Solution: Total rainfall in 2 weeks = 35 inches.   Assume the rainfall in second week = 1.x   Rainfall in first week = x   Total rainfall = 2.5x = 35 inches   x = 14 and 1.5x = 21   Rainfall during second week = 21 inches   Option 21 inches
Answer: E
In Country X a returning tourist may import goods with a total value of $500 or less tax free, but must pay an 8 percent tax on the portion of the total value in excess of $500. What tax must be paid by a returning tourist who imports goods with a total value of $730 ?  Choose the most appropriate option:
A) $58.40  B) $40 .00  C) $24.60  D) $18.40  E) $16.00

Solution: The tourist must pay tax on $730 - $500 = $230. Thus the amount to be paid is 0.08*$230 730 -  500= 
730 -  500 = 230
$230. Thus the amount to be paid is 0.08*$230= $18.40.   Answer: $18.40.
Answer: D
The length of the bridge, which a train 145 metres long and travelling at 45 km/hr can cross in 30 seconds, is?  Choose the correct choice from the following
A) 76 m  B) 178 m  C) 230 m  D) 187 m  E) 176 m

Solution: Speed = [45 X 5/18] m/sec   = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (145 + x)/30 = 25/2   => 2(145 + x)= 750 => x = 230 m.   Answer: 230 m
Answer: C
The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 90 black cars in the lot, how many red cars are there in the lot?  Select the correct option.
A) 11	B) 33	C) 24	D) 27	E) 32

Solution: 33 is correct   R/33 = 3/8 and 33 =90   R = 90*3/8 = 33
Answer: B
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Choose the correct choice:	A) 250	B) 276	C) 280	D) 285	E) None of these

Solution: Explanation:   Since the month begins with a Sunday, to there will be five Sundays in the month.   Required average   = {510 x 5 + 240 x 25 }/30   =	8550/30= 
8550/30 = 285
285   ANSWER:285
Answer: D
P, Q and R have Rs.8000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R? Choose the correct option:
A) Rs.3200	B) Rs.3600	C) Rs.2400	D) Rs.4000	E) None of these

Solution: Let the amount with R be Rs.r   r = 2/3 (total amount with P and Q)   r = 2/3(8000 - r) => 3r = 16000 - 2r   => 5r = 16000 => r = 3200.   Rs.3200NSWER:Rs.3200
Answer: A
In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?	Choose the correct choice from the following answers:
A) 360
B) 720
C) 480
D) 5040
E) None of these

Solution: Treat B and T as a single letter. Then the remaining letters (5 + 1 = 6) can be arranged in 6! ways. Since, O is repeated twice, we have to divide by 2 and the B and T letters can be arranged in 2! ways.   Total no. of ways = 6!×2!/2=720   Answer 720
Answer: B
In an examination, 34% of total students failed in Hindi, 44% failed in English and 22% in both. The percentage of these who passed in both the subjects is :
Options:
A) 23
B) 37
C) 28
D) 44
E) 81

Solution: Explanation:   Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)   Fail in Hindi or English = 34 + 44 â€“ 22 = 56   Therefore students who passed = 100 â€“ 56 = 44.   Answer: 44
Answer: D
The radius of a cylinder is 10 m, height 12 m. The volume of the cylinder is:  Choose the most appropriate option:
A) 2200 B) 5500 C) 3300 D) 3771.4 E) 4400

Solution: Cylinder volume = Ï€r(power2)h   = 22/7 Ã— 10 Ã— 10 Ã— 12   = 3771.4 m(power3)   Answer is 3771.4.
Answer: D
A boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours)  Choose one.
A) 700	B) 378	C) 2696	D) 1207	E) 1712

Solution: Explanation:   A boat travels at the speed of 14 km/hr in still water.   => Speed of stream = 1.2 kmph   => Speed of boat downstream becomes 14 + 1.2= 
14 + 1.2 = 15.2
15.2 kmph=> Speed of boat upstream becomes 14 - 1.2= 
14 - 1.2 = 12.8
12.8 kmph   Total time taken in the journey= Journey downstream + Journey upstream   Therefore, 4864(1/12.8 + 1/15.2) = 700 hours   700NSWER: 700
Answer: A
If n is a prime number greater than 7, what is the remainder when n^2 is divided by 12 ?
Choose the correct choice: A) 0 B) 1 C) 2 D) 3 E) 5

Solution: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 7, square it and see what would be the remainder upon division of it by 12.   n=11 --> n^2=121 --> remainder upon division 121 by 12 is 1.   Answer: 1.
Answer: B
700 + 6 × 4 = ? Select the correct option:  A) 820  B) 202  C) 420  D) 724  E) None of these

Solution: 700 + 6 × 4 = ?   or, ? = 700 + 24= 
700 + 24 = 724
724   Answer 724
Answer: D
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?	Choose the correct choice from the following answers
A) 32 years B) 36 years C) 40 years D) 48 years E) 58 years

Solution: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.   (2/5 x + 8) = 1/2 (x + 8)   2(2x + 40) = 5(x + 8) => x = 40   ANSWER:40 years
Answer: C
5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope.The letter is said to be put in correct position if for example letter 1 goes into envelope 1.Now what is the probability that all letters be put into wrong envelopes?	Choose one:  A) 1/3  B) 2/3  C) 11/120  D) 11/30  E) 76/120

Solution: This Q is based on derangement, a permutation in which all elements are in the wrong position.   Number of derangements = n!(12!−13!+14!+...+((−1)n)n!)n!(12!−13!+14!+...+((−1)n)n!).. Of Course it can be derived but thats not required..   Since there are 5 letters and 5 envelopes:-   Derangements=5!(12!−13!+14!−15!)Derangements=5!(12!−13!+14!−15!)   => 120(1/2−1/6+1/24−1/120)=60−20+5−1=44.120(1/2−1/6+1/24−1/120)=60−20+5−1=44.   Total possible ways = 5! = 120.   therefore required prob, P=44/120=11/30.   ans 11/30
Answer: D
A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11:00 a.m.?  Choose the most appropriate option
A) 8
B) 7
C) 6
D) 15
E) 3

Solution: Sol.   Relative speed = (2 + 3)= 
(2 + 3) = 5
5 rounds per hour.   So, they cross each other 5 times in an hour.   Hence, they cross each other 15 times before 11:00 a.m.   Answer 15
Answer: D
In track last week, the boys ran 20 laps. The girls ran 10 more
laps. Each lap is a 1/10th of a mile. How many miles did the girls run?  Pick
A) 1 mile
B) 3 miles
C) 5 miles
D) 7 miles
E) 9 miles

Solution: The girls ran 20 + 10= 
20 + 10 = 30
30 laps. 30 x 1/10= 30/10, which reduces to 3.   The girls ran 3 miles   correct answer 3 miles
Answer: B
In covering a distance of 30 km, Amla takes 2 hours more than Peter. If Amla doubles his speed, then he would take 1 hour less than Peter. Amla’s speed is :  Choose the correct choice from the following answers:	A) 7 kmph	B) 6.5 kmph	C) 5.5 kmph	D) 5 kmph	E) None

Solution: Sol.   Let Peter’s speed be x km/hr.   Then, 30/x - 30/2x = 3   ⇔ 6x = 30   ⇔ x = 5 km/hr   Answer 5 kmph
Answer: D
If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, including n? Choose the correct choice from the following answers.
A) two	B) three	C) four	D) six	E) eight

Solution: We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12   The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?   12:   1,12   2,6   3,4   How many of these divisors are EVEN? 2, 4, 6, 12 …..4 even divisors.   ANSWER:four
Answer: C
S, T and U are inner angles in a triangle. If S= T+ U, what can't be the size of T? Choose one:
A) 960 DEGREES
B) 9770 DEGREES
C) 9570 DEGREES
D) 940 DEGREES
E) 90 DEGREES

Solution: Given S= T+ U, and S, T and U are inner angles in a triangle. Thus S+ T+ U= 180   T+ U+ T + U= 180 => 2(T+ U) = 180 => T+ U= 90. Thus beta will be less than 90.   Hence the answer is 90 DEGREES.
Answer: E
When n is divided by 11, the remainder is 6. When n is divided by 19, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?	Choose one:
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: N = 11 q + 6   N = 19 z + 6   Equating   11 Q + 6 = 19z+6   19z=11q   19z/11 = q   since q is an integer Z must be divisible by 19.   Hence 11
Answer: A
A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays,the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?  Choose one:
A) 4  B) 14  C) 34  D) 27  E) 46

Solution: If the begger can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.   correct answer is 14)14
Answer: B
If pqr = 0 , rst = 1 , and spr = 0, which of the following must be zero?
Choose the correct choice from the following answers
A) P	B) Q	C) R	D) S	E) T

Solution: rst = 1 which means neither r / s/ t is 0   r x pq = 0 , we know r is not 0 from above hence either p or q must be 0.   s x p x r = 0, we know from first expression that r an p are not 0 hence p =0.   option P
Answer: A
In the rectangular coordinate system, if the line x = 8y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?  Choose the correct option:
A) 1/2
B) 1/3
C) 1/4
D) 1/5
E) 1/6

Solution: x = 8y+5, and thus y = x/8 - 5/8   The slope is 1/8.   The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2   p/2 = 1/8 and thus p = 1/4   The answer is 1/4.
Answer: C
A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 540 kilos of plankton, how many kilos did he consume on the sixth hour?
Answers.
A) 38	B) 47	C) 50	D) 53	E) 63

Solution: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is  540/9= 
 540/9 = 60
60, so the median is also 60, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 63.   option 63.
Answer: E
A dealer marks his goods 20% above cost price. He then allows some discount on it and makes a profit of 8%. The rate of discount is :  Choose the correct choice from the following.
A) 8%	B) 11%	C) 21%	D) 10%	E) none of the above

Solution: Let C.P.=Rs.100   Marked price = Rs.120, S.P. = Rs.108   10%iscount = [12120×100][12120×100]% = 10%   Ans is : 10%
Answer: D
In a bag there are 10 black balls and 25 blue balls and 15 white balls. A ball is drawn at random. What is the probability of getting a white ball?	Choices: A) 2/5 B) 3/10 C) 4/10 D) 5/10 E) 3/5

Solution: total balls = 10+25+15= 
10+25+15 = 50
50   probability of getting a white ball= 15/50 = 3/10 . correct option is 3/10
Answer: B
Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 6 : 3?	Choose the correct answer:
A) 16 B) 45 C) 277 D) 92 E) 11

Solution: Let the distances between city A to B and B to C be 6x km and 3x km respectively.   Total time taken to cover from A to C   = (6x)/40 + (3x)/60 = (18x + 6x)/120 = 24x/120 = x/5 Average speed = (6x + 3x)/(x/5) = 45 kmph.   Answer:45
Answer: B
An article is bought for Rs.675 and sold for Rs.900, find the gain percent?  Choose the correct option.
A) 30 1/3%
B) 33 1/3%
C) 23 1/3%
D) 35 1/3%
E) 29 1/3%

Solution: 33 1/3%   33 1/3%   675 ---- 225   100 ---- ? => 33 1/3%
Answer: B
A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train?
Answers.
A) 150 meter  B) 170 meter  C) 156 meter  D) 300 meter  E) 154 meter

Solution: Speed = 60*(5/18) m/sec   = 50/3 m/sec   Length of Train (300 meteristance)   = Speed * Time     (50/3) * 18= 
  (50/3) * 18 = 300
300 meter   Answer:300 meter
Answer: D
Walking at 40% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?	Choose the correct choice.
A) 16
B) 36
C) 42
D) 48
E) 54

Solution: speed is inversly proprtional to time   walking at 40% of speed meand 2/5s takes 5/2t.   It takes 24 minutes extra to cover the distance. then   5/2t=t+24   5t=2t+48   3t=48   t=16.   Option 16 is correct
Answer: A
If x^4 + y^4 = 85, then the greatest possible value of x is between:
Choose the correct choice from the following choices:
A) 0 to 2	B) 2 to 4	C) 4 to 6	D) 6 to 8	E) 8 to 10

Solution: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.   We're told that X^4 + Y^4 = 100. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....   X^4 = 100   Looking at the answers, it makes sense to see what 3^4 equals....   3^4 = 81   Since that is BELOW 85, and 6^4 will clearly be MORE than 85, we have the correct answer.   Final Answer:   2 to 4
Answer: B
If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?  Choose the correct option.
A) 33 1/7%	B) 33 6/3%	C) 33 1/3%	D) 39 1/3%	E) 33 1/4%

Solution: 1/4 33 1/3%P = 210 SP = 21*(80/100) = 168   SP = 840*(120/100)= 
840*(120/100) = 1_008
1008   1008 - 168= 
1008 - 168 = 840
840   3/4 SP= 630   Gain = 210   630 --- 210   100 --- ? => 33 1/3%   Answer:33 1/3%
Answer: C
Two water pumps, working simultaneously at their respective constant rates, took exactly 9 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?	Select the correct option: A) 12 B) 14 C) 15 D) 16 E) 18

Solution: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.   (x+1.5x) = 2.5x = 1/9 of the capacity of the whole pool per hour.   The rate of the fast pump is (1.5/2.5)*1/9 = 1/15 of the whole pool per hour.   The time it takes the faster pump to fill the pool would be 15 hours.   The answer is 15.
Answer: C
A sum of Rs. 125000 amounts to Rs. 14500 in 4 years at the rate of simple interest. What is the rate of interest?	Choose the correct option.
A) 3% B) 4% C) 5% D) 6% E) 7%

Solution: S.I. = (14500 - 12500) = Rs. 2000\   Rate = (100 * 2000) / (12500 * 4)= 
(100 * 2000) / (12500 * 4) = 4
4%   ANSWER:4%
Answer: B
The largest 4 digit number exactly divisible by 77 is?	Pick one.
A) 9935
B) 9933
C) 9944
D) 9954
E) 9960

Solution: Largest 4-digit number = 9999   77) 9999 (129   9933   Answer : 9933
Answer: B
A library has an average of 140 visitors on Sundays and 80 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
Choose the correct answer: A) 90 B) 100 C) 105 D) 110 E) 125

Solution: Explanation:   Since the month begins with a Sunday, so there will be five Sundays in the month,   Required average = (140 * 5 + 80 * 25) / 30 = 2700/30= 
2700/30 = 90
90   90nswer: 90) 90
Answer: A
If 4a = 16b and 5b = 13c, Find a:b:c?
Answers.
A) 52:13:5
B) 13:7:52
C) 7:13:52
D) 7:13:54
E) None of these

Solution: Explanation:   (4a = 16b ==> a/b = 16/4)   and (5b = 13c ==> b/c = 13/5)   ==> a:b = 16:4 and b:c = 13:5   a:b:c =52:13:5   52:13:5nswer: Option 52:13:5
Answer: A
50 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple? Select the correct option:	A) 47	B) 46	C) 54	D) 57	E) 62

Solution: orange+mango-apple=7   mango+apple-orange=10   apple=50   orange+mango+apple=4   50+10+4-7= 
50+10+4-7 = 57
57 like apple   ANSWER:57
Answer: D
There are some pigeons and hares in a zoo. If heads are counted, there are 130. If legs are counted, there are 580. The number of hares in the zoo is?  Choose one:
A) 120  B) 182  C) 190  D) 137  E) 160

Solution: 130*2= 
130*2 = 260
260   580   -----   320   1----2   ?----320= 160   Answer:160
Answer: E
If the sales tax be reduced from 4 (1/2) % to 3 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 10500? Choices:	A) Rs. 105	B) Rs. 150	C) Rs. 146	D) Rs. 135	E) None of these

Solution: Explanation:   Required difference = (4 (1/2) of Rs. 10500) - (3 (1/2) of Rs. 10500)   = (9/2– 7/2) % of Rs. 10500   = (1) x (1/100) x 10500   = Rs. 105   Rs. 105NSWER Rs. 105
Answer: A
The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Choose the correct choice.
A) 26	B) 56	C) 22	D) 29	E) 21

Solution: 1 to 11 = 11 * 50= 
11 * 50 = 550
550   1 to 6= 6 * 49= 
6 * 49 = 294
294   6 to 11= 6 * 52= 
6 * 52 = 312
312   6th= 294 + 312 – 550   = 56   Answer:56
Answer: B
A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 5/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
Select the correct option:
A) 9/80
B) 3/10
C) 303/800
D) 69/160
E) 497/800

Solution: The first circuit doesn't matter.   Prob(relay fails) = 1 - Prob(relay succeeds)   Prob(2+3 work) = 1 - 3/16 = 13/16   Prob(4+5 work) = 1 - 3/10 = 7/10   Prob(relay fails) = 1 - Prob(2+3 work AN69/160 4+5 work) = 1 - (13/16)(7/10) = 1 -91/160 = 69/160   69/160
Answer: D
30 pens and 75 pencils were purchased for 630. If the average price of a pencil was 2.00, find the average price of a pen.	Choose the correct choice from the following answers:
A) 10	B) 11	C) 12	D) 13	E) 16

Solution: Since average price of a pencil = 2   ∴ Price of 75 pencils = 150   ∴ Price of 30 pens = (630 – 150) = 480   ∴ Average price of a pen = 480⁄60 = 16   Answer 16
Answer: E
Which one of the following numbers is divisible by 11?	Answers
A) 4823718	B) 8423718	C) 8432718	D) 4832718	E) 4852718

Solution: Explanation:   4832718 = (4+3+7+8) – (8+2+1)= 
(8+2+1) = 11
11   So, the given number is divisible by 11   Answer:4832718
Answer: D
In an electric circuit, three resistors with resistances r1, r2 and r3 are connected in parallel. In this case, if R is the combined resistance of these three resistors, then the reciprocal of R is equal to the sum of the reciprocals of r1, r2 and r3. What is R in terms of r1, r2 and r3?  Choose the correct choice from the following choices
A) (r1 + r2 + r3)  B) r1r2r3  C) 1/(x + y)  D) r1r2r3/(r1 + r2 + r3)  E) (r1 + r2 + r3)/r1r2r3

Solution: The wording is a bit confusing, though basically we are told that 1/R = 1/r1 + 1/r2 + 1/r3, from which it follows that r=r1r2r3/(r1 + r2 + r3).   Answer: r1r2r3/(r1 + r2 + r3).
Answer: D
The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot at the rate of 26.50 per metre is 5,300, what is the length of the plot (in metres)? Options
A) 40 B) 120 C) 50 D) Data inadequate E) None of these

Solution: Perimeter of the rectangular plot = [(b + 20) + b] × 2   = 5300/26.5= 
5300/26.5 = 200
200=200   ∴ (2b + 20)2 = 200   ⇒ b = 40   ⇒ l = 40 + 20= 
40 + 20 = 60
60 m   Answer None of these
Answer: E