MU-NLPC/Calc-aqua_rat huggingface dataset:
It takes Johnson 10 minutes to walk to the car park and 20 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
Select
A) 8:50 a.m	B) 5:50 a.m	C) 7:50 a.m	D) 6:50 a.m	E) 8:30 a.m

Solution: The time it takes Johnson to get to work: time to walk to car park + time to drive     10 + 20= 
  10 + 20 = 30
30 minutes   Johnson needs to get out of the house 30 minutes before 9:00 am at   9:00 - 0:30= 8:30 a.m   correct answer 8:30 a.m
Answer: E
What is the least value of integer N such that N! is divisible by 888 ?
Choose the correct choice from the following options
A) 13 B) 88 C) 31 D) 37 E) D) 888

Solution: 888 = 8*111 = 3*8*37   Hence 888 is a multiple of 37 and we need at least one 37 in N!   Therefore least value of N! is 37!, which will contain all of 3, 8, and 37.   Correct Option: 37
Answer: D
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Pick one.
A) 667 cm2
B) 886 cm2
C) 285 cm2
D) 266 cm2
E) 226 cm2

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (15)   = 285 cm2   Answer: 285 cm2
Answer: C
If -1 < x < 0, which of the following must be true?
I. x^4 < x^3
II. x^6 < 1 – x
III. x^5 < x^2  Options: A) I only B) II only C) III only D) II,III only E) I,II,III only

Solution: Answer : I,II,III only
Answer: E
How many ways are there to arrange the letters in the word freelancer ? Choose the correct choice from the following answers: A) 1 B) 1260 C) 3780 D) 7560 E) 655200

Solution: 10 total words, 3655200, 2R   = 10! / 3! 2! = 655200 Answer 655200
Answer: E
In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 60, what is the least possible difference between n and m.	Choose one.
A) a.1 B) b.3 C) c.5 D) d.7 E) e.9

Solution: 2n+5m=60   try with n=5 and m=10 the equation will be satisfied   2(5)+5(10)=60   so difference between M and N is 5,   ANswer c.5
Answer: C
If the average of ten numbers is 20, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 20  Choose the correct choice from the following answers:
A) all three options  B) I  C) II  D) III  E) I&II

Solution: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.   IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.   all three options
Answer: A
A garrison of 500 men has provisions for 20 days. At the end of 14 days, a reinforcement arrives, and it is now found that the provisions will last only for 3 days more. What is the reinforcement? Pick
A) 500	B) 1000	C) 1500	D) 3000	E) 2000

Solution: 500 ---- 20   500 ---- 6   x ----- 3   x*3 = 500*6   x = 1000   500   -------   500   500nswer: 500
Answer: A
To be considered grade AD, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AD eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AD eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
Choose the most appropriate option.
A) 800	B) 840	C) 864	D) 900	E) 1,080

Solution: We're asked for the smallest possible mass, so what could the lowest mass be per egg AD? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is 840.
Answer: B
There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a black ball has been drawn, find the chance that it came from second group.
Choose the correct choice from the following answers:
A) 2/7
B) 6/35
C) 8/25
D) 28/43
E) 3/5

Solution: Please go through my solution and suggest any mistake.   Chances of selecting a black ball from group 1: 2/7----------------------Chances of selecting a black ball from group 2: 4/5   Thus combined probability of section of black ball from group 1:   3/5 x 2/7 = 6/35   Thus combined probability of section of black ball from group 2:   2/5 x 4/5 = 8/25   Out of these chances, chance of occurrence of first case : (8/25) / (6/35 + 8/25) = 28/43   28/43
Answer: D
A work which could be finished in 10 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Pick one:
A) 15 B) 20 C) 88 D) 71 E) 11

Solution: x ------- 10   (x + 10) ---- 6   x * 10 = (x + 10)6   x = 15   \15nswer: 15
Answer: A
With out any halt a train travels a certain distance with an average speed of 55 km ph , and with halts it covers the same distance at an average speed of 30 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?	Choices
A) 48 min.	B) 12min.	C) 15min.	D) 18min.	E) 19min.

Solution: With halt in 1 hour the train travels 60km   With out halt for traveling same distance it take 55/30 = 11/6 = 110 minutes   :. 50 minutes is the halting time per hour   48 min.NSWER:48 min.
Answer: A
Simplify: 8755 x 95	Options.
A) 831725  B) 787950  C) 875500  D) 43775  E) 87500

Solution: 8755 x 95 = 8755 x (100 - 5)   = 875500- 43775= 
875500- 43775 = 831_725
831725   831725nswer is 831725
Answer: A
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A? Answers
A) C is younger than A  B) 6  C) 12  D) 24  E) None of these

Solution: Sol.   (A + B) - (B + C) = 12 ⇔ A - C = 12.   Answer 12
Answer: C
Ten coins are tossed simultaneously. In how many of the outcomes will the second coin turn up a head?	Choose the correct choice from the following answers.
A) 2^9	B) 2^10	C) 3 * 2^8	D) 3 * 2^9	E) 3 * 2^10

Solution: Fix the second coin as H. The remaining 9 coins have 2^9 outcomes.   2^9ns:2^9
Answer: A
There are 80 people and 3 clubs M, S, and Z in a company. 20 people joined M, 22 people joined S and 15 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?	Choose the correct choice from the following answers:
A) 30	B) 32	C) 34	D) 36	E) 38

Solution: Answer E.   key is 'atmost' here.   so 20 people joined M.   22 people joined S and 15 people joined Z. to get maximum people who did not join any club, 15 people who joined Z are among 22 people who joined S.   so 22+20= 
22+20 = 42
42   80-42= 
80-42 = 38
38
Answer: E
A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?	Choose the correct choice from the following answers
A) 1/2
B) 1/3
C) 3/5
D) 3/7
E) 3/11

Solution: Let b stand for boy and g for girl. The sample space of the experiment is   S = {(g, g), (g, b), (b, g), (b, b)}   Let E and F denote the following events :   E : ‘both the children are girls’   F : ‘at least one of the child is a girl’   Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}   Now E n F = {(g,g)}   Thus P(F) = 3/4   and P (E n F )= 1/4   Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3   1/3)
Answer: B
The value of (34.5*0.473*1.567)/(0.0673*23.25*7.57) is close to	Choices:
A) 2
B) 1.15
C) 2.05
D) 2.16
E) 2.35

Solution: (34.5*0.473*1.567)/(0.0673*23.25*7.57) = 25.5710895/11.845   = 2.16   ANSWER:2.16
Answer: D
Three candidates contested an election and received 3000, 7500 and 6500 votes respectively. What percentage of the total votes did the winning candidate get ? Choose the correct option:	A) 50.2%	B) 45.5%	C) 44.11%	D) 85%	E) 94.2%

Solution: Explanation :   Total number of votes polled = ( 3000 + 7500 + 6500 )= 
( 3000 + 7500 + 6500 ) = 17_000
17000   Required percentage= (7500/ 17000) x 100 %   = 44.11%.   Answer : 44.11%
Answer: C
Albert has a box of crayons. Each box contains 20 different colored crayons. How many crayons does Albert have if he buys 2 additional boxes?	Choices
A) 40	B) 20	C) 80	D) 120	E) 60

Solution: E. 60
Answer: E
The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 9 months. At this time, the construction was behind schedule by how many projects?  Pick one.
A) 34 B) 96 C) 198 D) 204 E) 504

Solution: Project/month :   612/18= 
  612/18 = 34
34   Project in 6 month to be completed= 34*9= 
34*9 = 306
306   Lag :  306-108= 
  306-108 = 198
198   198 is the answer
Answer: C
Its not easy having a mathematics professor as a friend. When she invited you to her house she
says, “All the houses on my side of the street are numbered consecutively in even numbers. There are
Six houses on my Side of my block and sum of their numbers is 9870. You don’t know which block I
live on, and it’s a long street, but I will tell you that I live in the lowest number on my side of the block. What’s the number? Or are you just going to ring the first- numbered doorbell for twenty blocks?  Choose the most appropriate option: A) 22388 B) 2777 C) 199 D) 1640 E) 2912

Solution: Given all the number are even consecutive numbers. This is AP.   Formula for sum of numbers = Sn=n2[2a+(n−1)d]Sn=n2[2a+(n−1)d]   Sum = 9870, n = 6, d = 2   9870=62[2a+(6−1)2]9870=62[2a+(6−1)2]   ⇒ 9870 = 3 (2a + 10)   ⇒ 9840 = 6a   ⇒ a = 1640   Answer:1640
Answer: D
capacity of doing work of A is double than B.if both together finish a work in 12 days,then B alone in how many days will finish the work? Pick
A) 24 days	B) 27 days	C) 36 days	D) 48 days	E) 30 days

Solution: let B do work in 1 day=x,then A do work in 1 day=2x   (x+2x)=1/12=3x=1/12,x=1/36   work of B in 1 day=1/36   B alone finish the work in 36 days   answer 36 days
Answer: C
Find the value of 72519 x 9999 = m? Choose one:  A) 346568796  B) 235467889  C) 766444332  D) 725117481  E) 235656788

Solution: 72519 x 9999 = 72519 x (10000 - 1)   = 72519 x 10000 - 72519 x 1   = 725190000 - 72519= 
725190000 - 72519 = 725_117_481
725117481   725117481
Answer: D
Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?
Pick:
A) II
B) IV
C) IX
D) 14
E) 12

Solution: There will be two series.   1st : VI, V , ?? , III (decreasing by 1 in roman letters of numbers)i.e,6,5,4   2nd : 10, 11, 12 , 13 (Increasing by 1 number)   Final sequence : VI, 10, V, 11, 1V, 12, III   ANSWER:IV
Answer: B
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:  Select the correct option:
A) 10º  B) 75º  C) 90º  D) 130º  E) 180º

Solution: Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º.   Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º.   Required angle = (130 - 120)= 
(130 - 120) = 10
10º.   10ºnswer 10º
Answer: A
Which of the following is equal to the value of 2^2 + 2^2 + 3^2 + 3^2 + 3^2 ?	Choose the correct choice:	A) 2^8 + 3^3	B) 2^4+ 3^5	C) 2^3 + 3^3	D) 2^4 + 3^3	E) 2^3 + 3^5

Solution: 2^2 + 2^2 + 3^2 + 3^2 + 3^2   = 2 (2^2) + 3 (3^2)   = 2^1 (2^2) + 3^1 (3^2)   = 2^(1+2) + 3^(1+2)   = 2^3 + 3^3   Ans: 2^3 + 3^3
Answer: C
The number N is 5,H48, where H represents the hundred's digit. If N is divisible by 11, what is the value of H	Choose the correct choice from the following choices:
A) 1
B) 7
C) 6
D) 5
E) 2

Solution: If the number is divisible by 11, then the alternate digits' sum must be divisible by 11 or difference is 0. Only 1 yields such a number.   1nswer: 1
Answer: A
The digital sum of a number is the sum of its digits. For how many of the positive integers 24-100 inclusive is the digital sum a multiple of 7? Choose the correct choice from the following options:
A) 7
B) 11
C) 14
D) 16
E) 20

Solution: is there other way than just listing?   25   34   43   52   59   61   68   70   77   86   95   11 ways..   11
Answer: B
In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least two “heartless” draws on the first two draws, not picking the first heart until at least the third draw? Pick:  A) 1/2  B) 9/16  C) 11/16  D) 13/16  E) 15/16

Solution: A full deck of 52 cards contains 13 cards from each of the four suits. The probability of drawing a heart from a full deck is 1/4. Therefore, the probability of “not heart” is 3/4.   P(at least three draws to win) = 1 – P(win in two or fewer draws)   Furthermore,   P(win in two or fewer draws) = P(win in one draw OR win in two draws)   = P(win in one draw) + P(win in two draws)   Winning in one draw means: I select one card from a full deck, and it turns out to be a heart. Above, we already said: the probability of this is 1/4.   P(win in one draw) = 1/4   Winning in two draws means: my first draw is “not heart”, P = 3/4, AND the second draw is a heart, P = 1/4. Because we replace and re-shuffle, the draws are independent, so the AND means multiply.   P(win in two draws) =(3/4)*(1/4) = 3/16   P(win in two or fewer draws) =P(win in one draw) + P(win in two draws)   = 1/4 + 3/16 = 7/16   P(at least three draws to win) = 1 – P(win in two or fewer draws)   = 1 – 7/16 = 9/16   Answer = 9/16
Answer: B
Jim wishes to buy 3 gifts that cost 31 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
Choose the correct option
A) $39	B) $47	C) $7	D) $17	E) $27

Solution: $31 + $9 + $12 = $52 needed   1/4 x $52 31 +  9 +  12= 
31 +  9 +  12 = 52
$52 needed   1/4 x $52= $13 on hand   $52 - $13 = $39 to earn   correct answer $3952 -  13= 
52 -  13 = 39
$39 to earn   correct answer $39
Answer: A
Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?	Choose the most appropriate option
A) 20
B) 21
C) 24
D) 26
E) 27

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
A truck carrying cans of soup contains P stacks. Each stack contains Q cases, and each case contains 3Q cans. How many cans of soup are contained in 6 trucks?
Select:
A) 18PQ^2 B) 6P C) 18P/Q^2 D) 6Q^2/P E) 3PQ^2

Solution: There are 3Q cans in each case.   There are 3Q^2 cans in each stack.   There are 3PQ^2 cans in each truck.   There are 18PQ^2 cans in 6 trucks.   The answer is 18PQ^2.
Answer: A
A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:	Choose the correct choice from the following.
A) 16	B) 32	C) 54	D) 68	E) 86

Solution: R G W B Y is the bead pattern and it repeats.   Bead want to end with White.   So, the 3rd, 8th, 13th, 18th... beads will be W.   So, number of beads - 3 has to be divisible by 5 for it to be a White bead.   For those conditions, option D(68) only satisfy.   i.e., 68 - 3 = 65 and that also divisible by 5.   S0, 68   ANSWER:68
Answer: D
The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 3/7. The probability that none of them will be alive for 10 more yrs, is Choose one:  A) 1/2  B) 1  C) 1/7  D) 3/4  E) 2

Solution: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/7   Ans.(1/7)
Answer: C
How many hours in one year?  Choose the correct choice from the following answers.
A) 365	B) 52	C) 1024	D) 8760	E) No one knows

Solution: The day has 24 hours, and the year contains 365 days.   So the hours exist in one year is the multiplication of 24 by 365.   So the answer = 365*24= 
365*24 = 8_760
8760 hours   So the correct answer is 8760
Answer: D
If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))? Pick one.
A) 81
B) 16
C) 300
D) 256
E) 625

Solution: f(c)=c^2   f(f(c)) = (c^2)^2 = c^4   Therefore f(f(c)) will be numbers that are 4th power of other numbers.   Checking the options:   81 = 3^4   16 = 2^4   300. This cannot be written as the 4th power of any number   256 = 4^4   625 = 5^4   Answer: 300
Answer: C
Half of 6 percent written as decimal is  Choose the most appropriate option.
A) 5  B) 0.5  C) 0.05  D) 0.005  E) 0.03

Solution: 0.03xplanation:   It will be 1/2(6%) = 1/2(6/100) = 1/200 = 0.03   Option 0.03
Answer: E
Indu gave Bindu Rs.2500 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?	Select the correct option
A) 5 B) 2 C) 9 D) 4 E) 1

Solution: 2500   = 4(100/4)2   4 = 4   Answer: 4
Answer: D
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes? Choose the correct choice
A) 3  B) 9  C) 3^5  D) 25  E) 215

Solution: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.   Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.   Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.   Therefore, the total number of ways the 5 letters can be posted in 3 boxes is   3 * 3 * 3 * 3 * 3 = 3^5   ANSWER 3^5 3^15
Answer: C
A goods train runs at the speed of 72 km/hr and crosses a 210 m long platform in 26 sec. What is the length of the goods train?
Answers:
A) 382  B) 782  C) 278  D) 310  E) 881

Solution: Speed = 72 * 5/18= 
72 * 5/18 = 20
20 m/sec.   Time= 26 sec.   Let the length of the train be x meters.   Then, (x + 210)/26 = 20   x = 310 m.   Answer: 310
Answer: D
In a race with 9 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?  Choose the correct choice from the following choices:
A) 35  B) 120  C) 504  D) 840  E) 604,800

Solution: Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 9 choices ,for silver 8 remain (one who got gold cannot be given silver) and for bronze 7 choices remain.   So total possibilities=9*8*7   504orrect answer 504=504
Answer: C
Out of four numbers ,the average of first three is 20 and that of the last three is 15. If the last number is 18,the first number is : Choose one:
A) 22
B) 33
C) 77
D) 99
E) 27

Solution: Explanation:   Let the numbers be a,b,c,d   Given, a + b + c = 60, b + c + d = 45   Now, d = 18   thus, b + c + 18 = 45 ⇒ b + c = 27   Putting the value of b + c in a + b + c = 60   a + 27 = 60 ⇒ a = 33   Answer: 33
Answer: B
If (a) '1 2 3' stands for 'These are girls', (b) '135' stands for 'girls are clever' and (c) '156' stands for 'clever girls sing', which numerical stands for 'clever'?	Options
A) 1 B) 4 C) 2 D) 3 E) 5

Solution: Explanation:   (a) '1 2 3' ===>'these are girls'   (b)'1 3 5' ===>'girls are clever'   (c)'1 5 6' ===>' clever girls sing'   From statements (a) and (b) above we can notice that the set of numbers “1” and ”3” would stand for the set of words “girls ” and “are” (through not respectively). Thus the code number for clever would be “5” ( and the code number for “these” would be “2”). The statement (c) becomes redundent. (superfluous)   ANSW5R: 5
Answer: E
The length of minute hand of a clock is 5.4 cm. What is the area covered by this in 20 minutes
Options:  A) 15.27  B) 16.27  C) 17.27  D) 30.54  E) 30.27

Solution: area of circle is pi*r^2   but in 20 minutes area covered is  (20/60)*360= 
 (20/60)*360 = 120
120 degree   so formula is pi*r^2*(angle/360)=3.14*(5.4^2)*(120/360)=30.54 cm^2   ANSWER:30.54
Answer: D
Evaluate: 55 - 12*3*2 = ?	Select: A) 47 B) 52 C) 32 D) 12 E) 22

Solution: 47ccording to order of operations, 12?3?2 (division and multiplication) is done first from left to right   12**2 = 4* 2= 
4* 2 = 8
8   Hence   55 - 12*3*2= 55 - 8= 
55 - 8 = 47
47   correct answer 47
Answer: A
A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?  Choose the correct choice from the following:
A) 352  B) 350  C) 3529  D) 3520  E) 3501

Solution: Speed = 300/18 = 50/3 m/sec.   Let the length of the platform be x meters.   Then, (x + 300)/39 = 50/3   3x + 900 = 1950 => x = 350 m.   Answer: 350
Answer: B
In an increasing sequence of 12 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?  Choose the correct choice: A) 552 B) 668 C) 774 D) 888 E) 990

Solution: let the first term of the sequence be x   since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 12 terms)   now,   sum of first 4 terms =268   or,   4x+16=268   x=252/4= 
252/4 = 63
63   Thus the answer can now be calculated by either summing up 63+65+67+... 12th term   or   s=n/2(2a+(n-1)d   =12/2(2*63+(11*2))   =6(126+22)=888   888
Answer: D
How many consonants are present between the first and sixth vowel in the sequence of English alphabet ? Select:
A) 12	B) 13	C) 11	D) 10	E) None of these

Solution: Explanation:   Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z   There are only five vowels, hence there are no consonants between first and sixth vowel.   ANSWNone of theseR None of these
Answer: E
What is the total surface area in square meters of a rectangular solid whose length is 5 meters, width is 4 meters, and depth is 1 meters? Choose the correct choice from the following
A) 48 m2
B) 40 m2
C) 50 m2
D) 58 m2
E) 62 m2

Solution: Surface Area of a cuboid = 2(lb+bh+lh) = 2(5*4+4*1+5*1)=2(20+4+5)=2*29= 
2*29 = 58
58 m2   Answer : 58 m2
Answer: D
Find the odd man out
864, 420, 200, 90, 40, 16, 6
Choose the most appropriate option.
A) 90 B) 200 C) 16 D) 40 E) 6

Solution: 6x2+4=16   16x2+8=40   40x2+12=92   92x2+16=200.. and so on.90   90NSWER:90
Answer: A
Running at their respective constant rates, machine X takes 6 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?	Pick one:	A) 8	B) 6	C) 4	D) 10	E) 12

Solution: Together they make 5/4 w widgets in 3 days. So they make w widgets in 3*4/5 = 12/5 days.   1/(t+2) + 1/t = 5/12   Now, calculating this is really cumbersome so try to plug in options to get to the answer.   If machine X takes 12 days to produce 2w widgets, it would take 6 days to make w widgets, t would be 4.   1/6 + 1/4 = 5/12   It works so t = 4.   8nswer : 8
Answer: A
In a certain quiz that consists of 8 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?	Choose the correct choice: A) 39 B) 40 C) 44 D) 48 E) 52

Solution: x   x+4   x+8   x+12   x+16   x+20   x+24   x+28   8x+112=360   8x=248   x=31   3rd question =31+8 = 31+8= 
31+8 = 39
39   39nswer 39
Answer: A