MU-NLPC/Calc-aqua_rat huggingface dataset:
Three pieces of timber 30 m, 35 m and 45 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?	Choose the correct choice from the following choices
A) 7 m
B) 4 m
C) 5 m
D) 6 m
E) None of these

Solution: Answer   Greatest possible length of each plank = H.5 m.F of 30, 35, 45 = 5 m   5 morrect Option: 5 m
Answer: C
A software programmer does 30% of the work in 80% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?	Choose the most appropriate option.
A) 13x /15 B) 15x/15 C) 7x/15 D) 2x/30 E) 13x/30

Solution: Take X=30 lines   80% of 30 = 24 lines   20% of 30 = 6 lines   W - R - T   6 lines - r1 - 24 (first 80% of the 30 days)   24 lines - r2 - 6 ( last 20% of the 20 days)   r1 = 1/4r2 = 4   Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1   => 6 * 4 + 8 * 1/4 = 24 + 2= 
24 + 2 = 26
26   Insert, X=30 in all options => 7x/15 is the answer.
Answer: C
On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets rain cloud, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?	Pick one.
A) 1/8
B) 1/6
C) 1/7
D) 1/5
E) 1/4

Solution: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is 2/14 = 1/7. Answer: 1/7
Answer: C
The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 38 students?  Choose the correct choice from the following:  A) 14 years  B) 7 years  C) 19 years  D) 21 years  E) None

Solution: Solution   Sum of the ages of 14 students	= (16 x 35) - (14 x 21)   = 560 - 294.= 
560 - 294. = 266
266.   ∴ Required average= 266 / 38= 
266 / 38 = 7
7 years.   Answer 7 years
Answer: B
Find the average marks of all the students in 2 separate classes, if the average marks of students in the first class of 58 students is 67 and that of another class of 52 students is 82.
Choices:  A) 74.1  B) 56.3  C) 67.8  D) 79.7  E) 19.4

Solution: Sum of the marks for the class of 58 students = 58 * 67= 
58 * 67 = 3_886
3886   Sum of the marks for the class of 52 students= 52 * 82= 
52 * 82 = 4_264
4264   Sum of the marks for the class of 110 students=   3886 + 4262 = 8150   74.1verage marks of all the students = 4200/80   = 74.1   74.1nswer:74.1
Answer: A
The average of first six prime numbers:	Answers:
A) 5.6	B) 11.2	C) 12.9	D) 6.83	E) 7.4

Solution: Explanation:   The first six prime numbers is 2, 3, 5, 7, 11, 13   Average =41 /6 = 6.83   Answer: Option 6.83
Answer: D
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is  Select the correct option
A) 36  B) 40  C) 99  D) 13  E) 12

Solution: Let there be x pupils in the class.   Total increase in marks = (x * 1/2) = x/2.   x/2 = (83 - 63) => x/2 = 20 => x = 40.   Answer: 40
Answer: B
In an electric circuit, two resistors with resistances G and H are connected in parallel. In this case, if I is the combined resistance of these two resistors, then the reciprocal of I is equal to the sum of the reciprocals of G and H. What is I in terms of G and H?	Choose the correct answer.
A) (GH)  B) (G+H)  C) GH/(G + H)  D) (G-H)  E) NONE OF THESE

Solution: The wording is a bit confusing, though basically we are told that 1/I= 1/G + 1/H, from which it follows that I=GH/(G + H).   Answer: GH/(G + H)
Answer: C
There are 38 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Pick
A) 435 B) 367 C) 703 D) 997 E) 261

Solution: Explanation:   Total number of persons = n = 38   Shake hands involve only 2 persons = r = 2   Number of shake hands = n703r = 387032   387032 = (38 * 37) /(2 * 1)= 
(38 * 37) /(2 * 1) = 703
703   ANSWER:703
Answer: C
If x=−a^4, which of the following must be true?
I. x is negative.
II.If a is negative then x is negative.
III. a is non-negative.
Choose the correct answer:
A) I and II only	B) I only	C) II only	D) III only	E) II and III only

Solution: I. x is negative --> not necessarily true   II. x is non-negative. m can take ANY value: positive, negative, zero. We don't have any restrictions on its value;   III. If a is negative then x is negative.   Answer: II only (II only).
Answer: C
Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern?
Choose the correct choice from the following answers:
A) 197 min
B) 100 min
C) 177 min
D) 176 min
E) 186 min

Solution: Work done by the third pipe in 1 min   = 1/50 - (1/60 + 1/75)   = - 1/100.   [-ve sign means emptying]   The third pipe alone can empty the cistern in 100 min.   Answer: 100 min
Answer: B
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 25 percent on clothing, 25 percent on food, and 50 percent on other items. If Jill paid a 10 percent tax on the clothing, no tax on the food, and an 2 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Select:
A) 3
B) 4.5
C) 4
D) 3.5
E) 5

Solution: Assume she has $200 to spend.   TAX   Clothing = 25% = $50= $5   Food = 25% = $ 50 = $0.00   Items = 50% = $ 100 = $ 2.00   Total tax = $20.00   % of total amount = 7/200 * 100= 
7/200 * 100 = 7/2 = around 3.5
3.5%   Answer 3.5
Answer: D
A train 100 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is:  Options:
A) 16 km/hr.
B) 33 km/hr.
C) 21 km/hr.
D) 49 km/hr.
E) 76 km/hr.

Solution: Speed of the train relative to man =100/20m/sec=5 m/sec.   =5 x	18/5	km/hr   = 18 km/hr.   Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr.   x - 15 = 18   x = 33 km/hr.   ANSWER:33 km/hr.
Answer: B
Mohan purchased 13 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?	Choose the most appropriate option.
A) A)Rs.598	B) B)Rs.594	C) C)Rs.596	D) D)Rs.546	E) of these

Solution: Explanation:   Price of 13 kgs of rice at Rs.26/kg = 13x26 = Rs.338   Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208   Therefore, Total amount = Rs.338+Rs.208 = Rs.546.   Answer: Option Rs.546
Answer: D
A 90 cm long wire is to be cut into two pieces so that one piece will be 2/7th of the other, how many centimeters will the shorter piece be?  Options: A) A)73 B) B)20 C) C)83 D) D)21 E) E)52

Solution: Explanation:   1: 2/7 = 7: 2   2/9 * 90= 
2/9 * 90 = 20
20   Answer: Option 20
Answer: B
A student completes a 3 part exam as follows. The student completes sections A in 24 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?	Choose the correct choice from the following answers:
A) 7:8 B) 6:7 C) 5:6 D) 4:5 E) 3:4

Solution: The time spent on section B and section C is 18 minutes each.   The ratio of C to A is 18:24 = 3:4   The answer is 3:4.
Answer: E
Indu gave Bindu Rs.3750 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest? Answers
A) 1 B) 2 C) 6 D) 4 E) 9

Solution: 3750 = D(100/4)2   D = 6   Answer:6
Answer: C
If in a $300 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
Pick:
A) 100mln B) 200mln C) 300mln D) 400mln E) 500mln

Solution: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $300 mln portfolio, x+2x=3x=300 mln from where x=100 mln.   100mlnnswer: 100mln
Answer: A
Michael has some coins in his pocket consisting of dimes, nickels, and pennies. He has two
more nickels than dimes, and three times as many pennies as nickels. How many of each kind
of coin does he have if the total value is $0.52?	Choose the correct option.
A) 1 dimes, 2 nickels, and 4 pennies.	B) 2 dimes, 4 nickels, and 12 pennies.	C) 5 dimes, 5 nickels, and 6 pennies.	D) 7 dimes, 8 nickels, and 12 pennies.	E) 5 dimes, 4 nickels, and 3 pennies.

Solution: This problem involves money.   The question asks, “How many of each kind of coin”.   There is more than one unknown. So when doing the let statement, start with the   smallest quantity, in this case, the number of dimes.   Let x the number of dimes   x+2 the number of nickels   3x+2= the number of pennies   The value of all the dimes$0.10x plus the value of all the nickels$0.5(x+2) plus the   value of all the pennies$0.01(3)(x+2) equals the total value, $0.52.   Write the equation.   0.10x+0.05(x+2)+0.03(x+2)=0.52   10x+5(x+2)+3(x+2)=52   10x+5x+10+3x+6=52   18x=36   x=2   x+2=4   3(x+2)=12   The answer: Michael has 2 dimes, 4 nickels, and 12 pennies.   correct answer 2 dimes, 4 nickels, and 12 pennies.
Answer: B
A school’s annual budget for the purchase of student computers increased by 50% this year over last year. If the price of student computers increased by 50% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?  Select the correct option:
A) 1%
B) 2%
C) 3%
D) 0%
E) 5%

Solution: Pick numbers.   Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1= 
100/1 = 100
100;   This year: budget= $150, price = $1.5 --> the number of computers purchased = 150/1.5= 
150/1.5 = 100
~100.00   Increase in the number of computers purchased= 0%   Answer: 0%.
Answer: D
If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 1
II. 0
III. 2  Options.
A) II only
B) III only
C) I and II only
D) II and III only
E) I and III only

Solution: Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.   n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.   It can be 1 for n=2 and 2 for n=5.   Answer: I and III only.
Answer: E
Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity E for the round trip?  Choose the correct choice from the following answers
A) 24 miles per hour
B) 48 miles per hour
C) 50 miles per hour
D) 53 1/3 miles per hour
E) 68 miles per hour

Solution: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.   Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.   D = (R)(T)   120 = (40)(T)   120/40= 
120/40 = 3
3= T   3 hours to drive to SD   On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.   D = (R)(T)   120 = (60)(T)   120/60= 
120/60 = 2
2= T   2 hours to drive to SD   Total Distance = 240 miles   Total Time = 3+2= 
3+2 = 5
5 hours   Average Speed= 240/5= 
240/5 = 48
48 miles/hour   Final Answer:   48 miles per hour
Answer: B
10 women will complete a job in 7 days and 10 children take 14 days to complete the job. How many days will 5 women and 10 children take to complete the work? Choose the correct answer:
A) 5  B) 6  C) 7  D) 10  E) 12

Solution: woman 1 day work = 1/70   1 child 1 day work = 1/140   (5 + 10) = 5/70+10/140   day work = 1/14+1/14=1/7   ===>7 days   ANSWER 7
Answer: C
Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim or Renee will win?  Options
A) 5/6 B) 2/3 C) 1/2 D) 5/12 E) 1/3

Solution: There are 3*3= 
3*3 = 9
9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Jim or Renee winning the game is (favorable outcomes) / (total # of outcomes)= 6/9 = 2/3.   Answer: 2/3
Answer: B
Pipe A can fill a tank in 10 hours, pipe B in 15 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?  Choose the correct choice from the following:
A) 2
B) 2.5
C) 3
D) 5
E) None

Solution: Sol.   Part filled by (A + B + C) in 1 hour = (1/10 + 1/15 + 1/30) = 1/5.   âˆ´ All the three pipes together will fill the tank in 5 hours.   Answer 5
Answer: D
A student got twice as many sums wrong as he got right. If he attempted 27 sums in all, how many did he solve correctly ?	Choose one:
A) 12	B) 16	C) 18	D) 9	E) 12

Solution: Explanation:   Suppose the boy got x sums right and 2x sums wrong.   Then, x + 2x = 27 3x = 27 x = 9.   Answer:9
Answer: D
Find the cost of fencing around a circular field of diameter 32 m at the rate of Rs.1.50 a meter?
Options
A) 287  B) 132  C) 150.9  D) 158  E) 267

Solution: 2 * 22/7 * 16 = 100.6   100.6 * 1 1/2 = Rs.150.9   Answer: 150.9
Answer: C
A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.2 km long? Choose the correct choice from the following answers
A) 2 mins 14 sec B) 2 mins 34 sec C) 162 sec D) 244 sec E) 2 mins 44 sec

Solution: D = 25 * 60 + 1200= 
25 * 60 + 1200 = 2_700
2700 m   T= 2700/60 * 18/5= 
2700/60 * 18/5 = 162
162 sec   ANSWER:162 sec
Answer: C
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds i
Choose the correct answer:
A) 1:3
B) 3:2
C) 3:4
D) 4:2
E) None of these

Solution: Explanation:   Let the speeds of the two trains be x m/sec and y m/sec respectively.   Then, length of the first train = 27x metres,   and length of the second train = 17y metres.   27x +17y / x + y =23   27x + 17y = 23x + 23y   4x = 6y   x/y=3/2   ANSWER IS 3:2
Answer: B
A carpenter worked alone for 2 day on a job that would take him 6 more days to finish. He and another carpenter completed the job in 4 more days. How many days would it have taken the second carpenter to do the complete job working alone?	Choices:
A) 4 2/3
B) 7
C) 8
D) 14
E) 24

Solution: A carpenter worked only 2 day on something that takes him 6 MORE days.   Means;   Carpenter finishes his work in 8 days.   Let his buddy finish the same task in x days.   Respective rates per day:   2/8 AND 1/x   To complete 1 work:   First guy worked for 6 days @ rate=1/8 per day.   Second one worked for 4 days @ rate=1/x per day   Expression:   Days*Rate=Work   6*2/8+4*1/x=1=3/2+4/x=1   3x+8=2x   x=8   x=8 days.   Ans:8
Answer: C
If the numbers 1 to 99 are written on 99 pieces of paper, (one on each) and one piece is picked at random, then What is the probability that the number drawn is neither prime nor composite? Pick one:
A) 1/50	B) 1/25	C) 1/99	D) 1	E) 2

Solution: There are 25 primes, 73 composite numbers from 1 to 100. The number   which is neither prime nor composite is 1.   Therefore, required probability = 1/99.   ANSWER:1/99
Answer: C
Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 3. If n is greater than 30, what is the remainder that n leaves after division by 30? Choose the correct option:
A) 3
B) 12
C) 18
D) 22
E) 28

Solution: The theory says:   if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder.   e.g:   9 when devided by 5 leves the remainder 4 : 9=5*1+4   it can also leave the remainder 4-5 = -1 : 9=5*2 -1   back to the original qtn:   n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5   ==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5   ==> n when devided by 5 and 6 leaves the same remainder -2.   what is n?   LCM (5,6)-2 = 30-2= 
30-2 = 28
28   CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3   However, the qtn says n > 30   so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5   nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders.   hence n could be anything that is in the form 28 + (some multiple of 6 and 5)   observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6)= 30.   hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 22.   22
Answer: D
For any number y, y* is defined as the greatest positive even integer less than or equal to y. What is the value of 5.0– 5.0*?
Select the correct option:
A) 0.2
B) 1.2
C) 1.8
D) 2.2
E) 1.0

Solution: Since y* is defined as the greatest positive even integer less than or equal to y, then 5.0* = 4 (the greatest positive even integer less than or equal to 5.0 is 4).   Hence, 5.0 – 5.0* = 5.0 - 4= 
5.0 - 4 = 1
1.0   Answer: 1.0.
Answer: E
Consider a sequence of numbers given by the expression 7 + (a - 1) * 5, where n runs from 1 to 80.What is the sum of this series ?
Choose the correct choice from the following options:
A) 409 B) 1636 C) 16360 D) 16000 E) 15360

Solution: terms in this sequence are 7,12,17----402   now since this is an a.p. with a common difference of 5. therefore its sum can be given as   a(f+l)/2----------------1)   a= total no. of terms =80   f= first term=7   l= last term=402   subsituting values in the expression 1 we have   80(7+402)/2   = 40(409)   =16360=16360
Answer: C
If ABC is a quarter circle and a smaller circle is inscribed in it; if radius of quarter circle is 1.414units. Find the radius of smaller circle	Choose the correct choice from the following answers:
A) 0.586  B) 0.687  C) 0.784  D) 0.874  E) 0.974

Solution: if r be radius of smaller circle then   distance b/n centres = √2 * r   so, r + r√2 = R here,R = 1.414 =√2   => r=(√2 -1)R   r = 0 .586 unit   0.586NSWER:0.586
Answer: A
If e and b are positive numbers, and e^3 + b^3 = 75, then the greatest possible value of e is between:	Choose the correct choice from the following
A) 0 and 3	B) 3 and 5	C) 4 and 5	D) 5 and 7	E) 6 and 9

Solution: Yes the question is ambiguous, and the answer is certainly not C between 4 and 5 .   The question stated: e and b are positive numbers but not positive integers.   so fractions are allowed to be a part of calculation.   So if the answer is C then the value 4.5 = 9/2 must comply the equation.   (9/2)^3 + b^3 = 75   so, b^3 = -129/8 , which is not possible according to the question.   Moreover the question didn't mentioninclusive or not, so we can't assume that b is 4 .   hi asif,   question is correct IMO.   Sincemaximumvalues areuniqueso you cant take any value and make it satisfy with equation   question is asking that maximum value ofa(means that unique value ofa) is between...   its not saying all value of that range will satisfy.
Answer: C
A row of seats in a movie hall contains 10 seats. 3 Girls and 7 boys need to occupy those seats. What is the probability that no two girls will sit together?
Answers:
A) 7/15
B) 2/15
C) 4/15
D) 6/15
E) 9/15

Solution: Total # of ways for the 7 boys to stand = 7!   After these boys have stood in their positions, there are 8 positions for the 3 girls to occupy.   # of ways for the girls to choose 3 positions = 8C3   # of ways of arranging themselves = 3!   Hence, total # of ways for the girls = 8C3 times 3!   Overall, # of ways when no two girls are together = 7! times 8C3 times 3!   n(S) = n(Sample space for these 10 students) = 10!   Hence, probability for no two girls to sit together = 7! * 8C3 * 3! / 10!   = 8C3 * 3! / (10 * 9 * 8)   = (8 * 7 * 6 ) / (10 * 9 * 8)   = (7*6) / (10*9)   =7/15   7/15NSWER:7/15
Answer: A
Tom drives from town R to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between R and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour? Choose the correct choice from the following choices.
A) 12 B) 20 C) 24 D) 30 E) 36

Solution: Let's assume that it takes 4 hours to go from point R to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to   120/6= 
  120/6 = 20
20   Hence the answer is 20.
Answer: B
What is the true discount on a bill of Rs.2916 due in 3 years hence at 8% C.I.?	Choose the most appropriate option.
A) rs.600
B) rs.601
C) rs.602
D) rs.603
E) NONE OF THESE

Solution: Explanation:   PW=Amount/(1+R/100)t   ANSWER IS rs.602
Answer: C
A person can swim in still water at 12 km/h. If the speed of water 10 km/h, how many hours will the man take to swim back against the current for 8km?  Choose the correct answer:  A) 4  B) 7  C) 5  D) 9  E) 6

Solution: M = 12   S = 10   US = 12 - 10= 
12 - 10 = 2
2   D= 8   T = 8/2= 
8/2 = 4
4   4nswer: 4
Answer: A
Which of the following CANNOT be the median of the 3 positive integers a, b, and c? Choose one.
A) a B) c C) a+c D) (a+c)/2 E) (a+c)/3

Solution: The median of a set with odd number of terms is justa middle term, so it's a, b or c. Eliminate A and B right away. Now, the median can also be (a+c)/2 and (a+c)/3 (for example: {1, 2, 3} and {1, 2, 5}).   But since a, b, and c are positive integers then it no way can be a+c . Why? Because a middle term (the median) cannot possibly be greater than two terms (a and c) in a set with 3 terms.   Answer: a+c.
Answer: C
if the length of rectangle is three times of its breadth.if the area of rectangle is 6075 sq.m,then calculate the length? Select the correct option.
A) 145	B) 135	C) 75	D) 140	E) none of these

Solution: let breadth=x,length = 3x.   area of rectangle=length*breadth=3x^2=6075   x^2=2025,x=√2025=45 m   length=135 m   answer 135
Answer: B
30^10 / 210^5=?	Choose the most appropriate option.
A) 6^5 B) 5^6 C) (30/7)^5 D) 6^3 E) 15^3

Solution: 30^10 / 210^5=?   A. 6^5   B. 5^6   C. (30/7)^5   D. 6^3   E. 15^3   -> 30^10 / 210^5=(30^10)/(7^5)(30^5)=(30^5)/(7^5)=(30/7)^5.   Thus, (30/7)^5 is the answer.
Answer: C
By weight, liquid X makes up 1.5 percent of solution P and 6.5 percent of solution Q. If 200 grams of solution P are mixed with 800 grams of solution Q, then liquid X accounts for what percent of the weight of the resulting solution?
Choose the most appropriate option:	A) 4.5%	B) 5.0%	C) 5.5%	D) 5.8%	E) 6.0%

Solution: The number of grams of liquid X is 1.5(200)/100 + 6.5(800)/100 = 3 + 52= 
3 + 52 = 55
55 grams.   55 / 1000= 5.5%   The answer is 5.5%.
Answer: C