MU-NLPC/Calc-aqua_rat huggingface dataset:
A swimmer jumps from a bridge over a canal and swims one kilometer stream up. After that first kilometer, he passes a floating cork. He continues swimming for half an hour, then turns around, and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant effort. How fast does the water in the canal flow? Choose the correct choice:
A) 3 km/h	B) 2 km/h	C) 1 km/h	D) 4 km/h	E) 5 km/h

Solution: C   1 km/h   If you have written down a full paper of mathematical formulas, you have been thinking too complicatedly...   It is obvious that the cork does not move relatively to the water (i.e. it has the same speed as the water). Therefore, if the swimmer is swimming away from the cork for half an hour (upstream), it will take him another half hour to swim back to the cork again. Because the swimmer is swimming with constant effort, his speed is constant relatively to the speed of the water. You can look at it as if the water in the river does not move, the cork does not move, and the swimmer swims a certain time away from the cork and then back. Consequently, in that one hour time, the cork has floated from 1 kilometer up stream to the bridge.   1 km/honclusion: The water in the canal flows at a speed of 1 km/h.
Answer: C
Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now?  Choose the correct choice from the following options.
A) 18 years
B) 24 years
C) 27 years
D) 28 years
E) None

Solution: Solution   Present age of (A+B)	= (18x2+3x2) years   = 42 years.   Present age of (A+B+C)	= (22x3) years   = 66 years.   ∴ C's age	= (66 - 42)= 
(66 - 42) = 24
24 years.   Answer 24 years
Answer: B
If x+|x|+y=5 and x+|y|-y=6 what is x+y=?	Choose the correct option:
A) 1
B) -1
C) 3
D) 12
E) 13

Solution: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.   If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).   Answer: C.   Adding both eqn we get 2x +IxI+IyI = 13   Now considering X <0 and y>0   2x-x +y = 13   we get x+y =12   Hence answer should be 12
Answer: D
A man purchases 2 watches for $ 7650. He sells one at 25% profit and the other at a loss of 20%. He neither gains nor loses on the whole. Thus, the cost price of two watches are : Pick one:
A) $ 3400 and $ 7650 B) $7650and $ 4250 C) $3400 and $4250 D) $7650 and $3400 E) $2240 and $ 3500

Solution: x + y = 7650 --- (1)   1.25x + 0.8y = 7650 --- (2)   (2) - (1) --> 0.25x - 0.2y = 0   25x = 20y   x/y = 4/5 = (4*850)/(5*850) = 3400/4250   Answer: $3400 and $4250
Answer: C
n and p are integers greater than 1;
5n is the square of a number;
75 np is the cube of a number.
The smallest value for n + p is Select the correct option
A) 14  B) 18  C) 20  D) 30  E) 50

Solution: n>1   p>1   5∗n=x^2   75 np=y3   n+p=?   Well, a square number is usually the result of himself times himself so in the case of n the least value possible (being 5 a prime) is 5*5   n=5   as for p   75∗5∗p=y3   we know 375 is equal = 53∗31 therefore to obtain a cube we need 32 or 9 -> p=9p=9   p+n=14   14NSWER:14
Answer: A
A truck covers a distance of 376 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?	Select the correct option:  A) 6 hours  B) 5 hours  C) 7 hours  D) 8 hours  E) None

Solution: Explanation :   Speed of the truck = Distance/time = 376/8= 
376/8 = 47
47 kmph   Now, speed of car= (speed of truck + 18) kmph = (47 + 18)= 
(47 + 18) = 65
65 kmph   Distance travelled by car= 376 + 14= 
376 + 14 = 390
390 km   Time taken by car= Distance/Speed = 390/65= 
390/65 = 6
6 hours.   6 hoursnswer – 6 hours
Answer: A
A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit? Choose the correct choice from the following options.
A) 37	B) 299	C) 72	D) .32	E) 01

Solution: Explanation:   Let cost price of lemons be x.   Selling price of lemons becomes CP - loss.   =>SP=x-(20/100)x   =>40=x(80/100)   =>50   So 45 lemons cost Rs 50   Cost of 1 lemon = 50/45 Rs   Cost of 24 lemons = (50/45)*24 =80/3 Rs   Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32   ANSWER:.32
Answer: D
What least number should be added to 1021, so that the sum is completely divisible by 25? Pick:
A) 4
B) 3
C) 2
D) 0
E) 5

Solution: 1021 Ã· 25 = 40 with remainder = 21   21 + 4= 
21 + 4 = 25
25.   Hence 4 should be added to 1021 so that the sum will be divisible by 25   4nswer: Option 4
Answer: A
A and B put in Rs.300 and Rs.500 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.200 where as B does not. In what ratio should they divide the second year's profit? Choose the correct choice
A) 39:40 B) 39:49 C) 15:16 D) 14:18 E) 39:41

Solution: Explanation:   3: 5   A = 3/8*200= 
3/8*200 = 75
75   375: 400   39:40   Answer:15:16
Answer: C
Calculate the average mark scored by Nancy if she obtained the following scores in an examination: 65, 78, 89, 51 and 69 marks (out of 100) in English Language, Physics, Mathematics, Chemistry and Biology? Choose the correct answer.
A) 40.4  B) 60.4  C) 50.4  D) 70.4  E) 79.4

Solution: Explanation:   Average mark = 65+78+89+51+69/5=70.4   Answer: Option 70.4
Answer: D
If 183 is divisible by 11, find the value of the smallest natural no. N?  Pick one.
A) 5 B) 7 C) 9 D) 10 E) 11

Solution: In aptitude tests , we get questions on divisibility by 11.   A number is divisible by 11, when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11   The given number is N183.   (Sum of digits at EVEN places) – (sum of digits at ODD places)=0   (8 + N)- (3+1)= 0   (8 + N) - 4 = 0   Here the value of N must be 7   7
Answer: B
The salary of a person was reduced by 35%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?  Select the correct option.
A) 50% B) 32% C) 25% D) 54% E) 29%

Solution: Let the original salary be $100   New salary = $65   Increase on 65 = 35   increase on 100 = 35/65 *100 = 54%(APPROXIMATELY)   Answer is 54%
Answer: D
A hostel had provisions for 250 men for 36 days. If 50 men left the hostel, how long will the food last at the same rate?
Choose the correct option.
A) 30	B) 45	C) 50	D) 60	E) 65

Solution: A hostel had provisions for 250 men for 36 days   If 50 men leaves the hostel, remaining men = 250 - 50= 
250 - 50 = 200
200   We need to find out how long the food will last for these 200 men.   Let the required number of days= x days   More men, Less days (Indirect Proportion)   (men) 250 : 200 :: x : 36   250×36=200x   5×36=4x   x=5×9=45   ANSWER 45
Answer: B
The average (arithmetic mean) of 27, 32, and 64 is 6 less than the average of 29, 42, and x. What is x?
Answers:
A) 62
B) 64
C) 66
D) 68
E) 70

Solution: The average of 27, 32, and 64 is 41.   The average of 29, 42 and x is 47.   Then 29 + 42 + x = 141.   x = 70.   The answer is 70.
Answer: E
Ramesh can finish a piece of work in 14 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
Choose the correct choice from the following answers.
A) 8/3 days
B) 9/3 days
C) 10/3 days
D) 14/3 days
E) 7/3 days

Solution: Ramesh can finish a piece of work in 14 days. Rohan is twice as efficient as Ramesh.   So Rohan can finish a piece of work in 7 days.   days needed to finish the same amount of work = 1/(1/7+1/14)=14/3 days   ANSWER:14/3 days
Answer: D
If a town of 15,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to? Choose the correct choice from the following answers
A) a.16000 B) b.17000 C) c.18000 D) d.19000 E) e.20000

Solution: 1% is quite small and hence the answer is a.16000)
Answer: A
In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.  Choose one
A) 129,500	B) 129,600	C) 129,700	D) 129,800	E) 129,900

Solution: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.   For this particular question : Increase in the population every 2 seconds = 6-3= 
6-3 = 3
3 people.   Total 2 second interval in a day= 24*60*60/2 = 43,200   Population increase = 43,200 * 3 = 129,600. Hence 129,600.
Answer: B
How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Choose the correct choice from the following:	A) 11	B) 36	C) 99	D) 88	E) 61

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 600 * 3/50= 
600 * 3/50 = 36
36 sec.   Answer: 36
Answer: B
The value of (7x10^7)(7x10^8) is closest to which of the following?  Choices:
A) 10^11	B) 10^12	C) 10^17	D) 10^14	E) 10^18

Solution: multiplying these we get,   49 x 10^7 x 10^8   = 4.9 x 10^16   which is closer to 10^17   Answer: 10^17
Answer: C
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (3,-1), (3, 8), (12, 2), (12,-7)?
Choose the correct choice from the following choices.
A) 69
B) 75
C) 81
D) 87
E) 93

Solution: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:   Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.   We can now determine the area of the quadrilateral:   Area = 1/2 × (9 + 9) × 9 = 81.   The answer is 81.
Answer: C
An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 80% is a passing grade, what is the probability that Brian passes?  Choose the most appropriate option: A) 1/16 B) 37/256 C) 1/2 D) 219/256 E) 125/256

Solution: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.   If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.   So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.   Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.   The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 125/256.   125/256
Answer: E
If the product of two numbers is 51216 and their H.C.F. is 33, find their L.C.M. Pick:
A) 600
B) 680
C) 582
D) 560
E) None of these

Solution: Explanation:   H582F * L582M = 51216, because we know   Product of two numbers = Product of H582F and L582M   L582M = 51216/88= 
51216/88 = 582
582   Option 582
Answer: C
A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 2k1,k24, where k represents a digit that occurs twice, how many values could n have?  Choose the correct answer:	A) 1	B) 2	C) 3	D) 4	E) 10

Solution: 2k1k24   Taking sum of the numericals = 2 + 1 + 2 + 4= 
2 + 1 + 2 + 4 = 9
9   We require the values of K such that they are also divisible by 3   201024   231324   261624   291924   Answer= 4 =4
Answer: D
The story of Rapunzel is legendary, but do you know how long it took her to grow her hair so long? First of all, her tower was 22 feet high. On average, her hair would grow 2 feet per year. However, she also had to trim her hair occasionally so that it would continue to grow strong enough to hold a man's body weight. These would amount to cutting off 1/2 foot of her hair every 8 months. Assuming she was bald from the beginning and the prince could jump 3 feet up from the ground to grab the hair, how many months of hair growth would Rapunzel need to be united with her prince charming?  Choices:  A) 211.2  B) 132  C) 130.29  D) 150.86  E) 182.4

Solution: Needed length of hair = 22 feet minus 3 feet (Prince's jump) = 19 feet of hair   Annual growth rate: 2 feet hair growth per year   Annual loss rate calculation: 1/2 foot divided by 8 months = 1/16 monthly, times 12 = 3/4 foot hair loss per year   N182.4T annual growth rate: 2 minus 3/4 = 1.25 feet hair growth per year   Y182.4ARS needed to grow: 19 (feet needed) divided by 1.25 (yearly growth) = 15.2 years   MONTHS needed to grow: 15.2 years x 12 months in a year = 182.4 months   The correct option is 182.4) 182.4 months.
Answer: E
12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done. Pick.
A) 360  B) 384  C) 432  D) 470  E) None

Solution: Solution:   Given there are 12 numbered chairs, such that chairs numbered 1 to 8 should be occupied.   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.   The various combinations of chairs that ensure that no two men are sitting together are listed.   (1, 3, 5,__), The fourth chair can be 5,6,10,11 or 12, hence 5 ways.   (1, 4, 8, __), The fourth chair can be 6,10,11 or 12 hence 4 ways.   (1, 5, 8, __), the fourth chair can be 10,11 or 12 hence 3 ways.   (1, 6, 8,__), the fourth chair can be 10,11 or 12 hence 3 ways.   (1,8,10,12) is also one of the combinations.   Hence, 16 such combinations exist.   In case of each these combinations we can make the four men inter arrange in 4! ways.   Hence, the required result =16*4!= 384.   Answer: Option 384
Answer: B
If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area? Answers:	A) 25% increase	B) 25% decrease	C) 50% decrease	D) 50% increase	E) 75% increase

Solution: Let original length =10   original breadth =10   Then, original area =10×10=100   Length is halved   ⇒ New length =10/2= 
10/2 = 5
5   breadth is tripled.   ⇒ New breadth=10×3=30   New area =5×30=150   Increase in area= new area - original area   =150−100=50   Percentage increase in area=increase area/original area×100   =50/100×100   =50%   ANSWER:50% increase
Answer: D
Ann's mother is 20 years older than her. In 2 years, however, Ann's mother will be three times older than Ann. How old is Ann now? Choose the correct choice.
A) 7 years
B) 8 years
C) 9 years
D) 10 years
E) 11 years

Solution: At the present:   Ann's mother is 20 years older than Ann, thus   Ann's age is x   Ann's mother's age is y=x+20   In 2 years from now:   Ann's mother is three times older than Ann, thus   Ann's age is x+2   Ann's mother's age is y+2=3 (x+2)   To calculate Ann's age, we'll take both equations:   y=x+20   y+2=x+20+2=3 (x+2)   x+22=3x+6   2x=16   x=8   Ann is currently 8 years old.   ANSWER: 8 years
Answer: B
The radius of a semicircular plot is 25. What is the approximate perimeter of the plot?
Select:	A) 114	B) 150	C) 129	D) 25	E) 57

Solution: perimeter of a circle =2pi*r   perimeter of a semicircle = pi*r + 2r   aprox perimiter = 3.14*25 + 2*25= 
3.14*25 + 2*25 = 128.5
128.50 approximately 129   answer 129
Answer: C
The LCM and HCF of two numbers are 10000 and 1000 respectively. Find the larger of the two numbers if their sum is 11000.  Choose the most appropriate option
A) 10000  B) 562  C) 352  D) 576  E) 594

Solution: There are 2 approaches in solving this.   Methode 1.   HCF * LCM = The Actual Number.   10000* 1000= 
10000* 1000 = 10_000_000
10000000   So the answer which we are looking for has to be a factor of 10000000.   So among the options shortlist the answers by eliminating those numbers which is not divisible by 10000000. and then take the highest number as the answer as the question asks abt the highest number.   answer is 10000
Answer: A
A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
Choose the correct choice from the following choices:
A) 1/190
B) 1/20
C) 1/9
D) 1/10
E) 1/92

Solution: The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9   Answer: 1/9.
Answer: C
The average weight of 19 students is 15kg. by the admission of a new student the average weight is reduced to 14.6 kg. the weight of the new student is ?
Choose the correct choice from the following answers: A) 10.6 kg B) 10.8 kg C) 7 kg D) 14.9 kg E) None

Solution: Answer   Weight of new student = Total weight of all 20 students - Total weight of initial 19 students   = (20 x 14.6 - 19 x 15) kg   = 7 kg.   7 kgorrect Option: 7 kg
Answer: C
A man engaged a servant on the condition that he would pay him Rs.900 and auniform after 1year service. He served only for 9months and received uniform and Rs.650, find the price of the uniform?	Choose the most appropriate option
A) Rs.80
B) Rs.100
C) Rs.120
D) Rs.145
E) Rs.156

Solution: 9/12 = 3/4 * 900= 
3/4 * 900 = 675
675   650   -------------   25   1/4 -------- 25   1 --------- ?=> Rs.100   Rs.100
Answer: B
A lent Rs. 5000 to B for 2 years and Rs 3000 to C for 4 years on simple interest at the same rate of interest and received Rs 2200 in all from both of them as interest. The rate of interest per annum is
Options
A) 9%  B) 10%  C) 11%  D) 12%  E) None of these

Solution: Explanation:   Let R% be the rate of simple interest then,   from question we can conclude that   (5000∗R∗2/100)+(3000∗R∗4/100)=2200   <=>100R+120R=2200   <=>R=10%   Option 10%
Answer: B
A child was looking for his father. He went 90 m in the east before turning to his right. he went 20 m before turning to his right afain to lok for his father at his uncles place 30 m from this point. His father was not there. From there he went 100m north before meeting hiss father in a street. How far did the son meet his father from the starting point.  Pick.
A) 137	B) 100	C) 2977	D) 126	E) 191

Solution: From the diagram, A100 = 90 - 30= 
90 - 30 = 60
60 and 100D= 100 - 20= 
100 - 20 = 80
80   AD=A1002+100D2−−−−−−−−−−√=602+802−−−−−−−−√=100AD=A1002+100D2=602+802=100   Answer:100
Answer: B
Enrollment in City College in 1980 was 85/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?  Options:
A) 100%  B) 16 2/3 %  C) 200%  D) 253%  E) 183 1/3%

Solution: Assume 100 enrollments present in 1990   85/3 % of 1990 = enrollments on 1980   enrollments on 1980 = 28.33   % change = (enrollment in 1990 - enrollment in 1980)*100/(enrollment in 1980)   =(100 - 28.33) *100 / 28.333   = 7166.67 / 28.333   = 253 %   Ans - 253%
Answer: D
The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 12 homes?
Choose the correct choice.
A) $200,000	B) $210,000	C) $215,000	D) $220,000	E) $230,000

Solution: IMO the answer has to be D.   5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 12 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 12x=120,000.   x=10,000.   The 12 houses are sold at $10,000 profit or at $210,000. (ANSWER $210,000)
Answer: B
Abbey's income is 30 percent more than Abigail's income, and Abigail's income is 35 percent less than Jenny's income. What percent of Jenny's income is Abbey's income?
Choose the correct choice from the following options:	A) 84.5%	B) 81.5%	C) 82.5%	D) 83.5%	E) 86.5%

Solution: Jenny's income = 100 (assume);   Abigail's income = 65 (40 percent less than Jenny's income);   Abbey's income = 84.5 (30 percent more than Abigail's income).   Thus, Abbey's income (84.5) is 84.5% of Juan's income (100).   84.5%nswer: 84.5%
Answer: A
Thirty percent of a number is 21 less than four fifth of that number. What is the number ? Choices
A) 42  B) 40  C) 230  D) 130  E) 125

Solution: Let the number be x.   Then, 4*x/5 â€“30% of x) = 21   4x/5 â€“30x/100 = 21   x = 42.   42nswer 42.
Answer: A
In a company there are 5 partners A,B,C,D,E. They invested money in the ratio of 1:2:3:4:5. If after one year if there is a profit of Rs.15,000. Then share of E will be ? Choose the correct choice from the following.
A) 3000	B) 4000	C) 5000	D) 6000	E) 7000

Solution: 5 partners A,B,5000,D,E are invested money in the ratio of 1:2:3:4:5   Total profit = 15000   share of E = Profit*ratio(E)/(ratio(A)+ratio(B)+ratio(5000)+ratio(D)+ratio(E))   = 15000*5/(1+2+3+4+5)= 
15000*5/(1+2+3+4+5) = 5_000
5000   ANSWER:5000
Answer: C
What is 15% of 2/3 of 0.4?  Options.
A) 0.09 B) 0.9 C) 9 D) 90 E) None of the above

Solution: The best way to solve these questions is to convert every term into fraction   (15/100)*(2/3)*(4/10) = 120/3000= 
120/3000 = 1/25 = around 0.04
0.04   Option 0.09
Answer: A
what is the remainder when 30^72^87 is divided by 11. Choose the correct answer.
A) 5  B) 7  C) 1  D) 3  E) 4

Solution: let us take N=72^87   eq is..30^N/11=8^N/11   here cyclicity of 8 is 10   then N/10=72^87/10=2^87/10   here cyclicity of 2 is   then 87%4=3(3rd cycle of 2)....i.e2^3%10=8(8th cycle of8)   therefore final ans is 8^8%11=5   5NSWER:5
Answer: A
A certain bakery baked a batch of 530 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch? Choose one:
A) 166	B) 275	C) 413	D) 438	E) 533

Solution: Cookies which have both nuts and chocolate chips = 105   Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that   batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x   (105+x)/(530+x) = 6/10   =>1050 + 10x = 3180 + 6x   => 4x = 2130   => x = 532.5   Therefore x = 533   Answer 533
Answer: E
Two friends want to buy a snack. They combine their money and find they have $3.45, consisting of quarters, dimes, and nickels. If they have 31 coins and the number of quarters is half the number of nickels, how many quarters do they have? Choose the correct choice from the following answers
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Let x be the number of quarters. Then 2x is the number of nickels.   (1) 25x + 10x + 10D = 345. Then 7x + 2D = 69   (2) 3x + D = 31. Then 6x + 2D = 62   Let's subtract equation (2) from equation (1).   x = 7   The answer is 7.
Answer: C
The average age of a husband and a wife is 28 years when they were married eight years ago but now the average age of the husband, wife and child is 26 years(the child was born during the interval). What is the present age of the child? Choices:	A) 2 years	B) 6 years	C) 9 years	D) 4 years	E) 1 years

Solution: 36 * 2= 
36 * 2 = 72
72   26 * 3= 
26 * 3 = 78
78   -----------   6 years   Answer:6 years
Answer: B