MU-NLPC/Calc-aqua_rat huggingface dataset:
If after 600 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used? Pick:
A) 180 grams
B) 220 grams
C) 250 grams
D) 350 grams
E) 1200 grams

Solution: I too think 1200 grams should be the answer.   My reasoning is   The h20 content in 200 gms of water is 1   h20 content in 24% solution is 0.76   Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84   Let amount of solution be X   Then the equation can be set up   600*1 + 0.76X = 0.84 (X+600)   0.08X = 96   8X = 9600   X = 1200 (ANS 1200 grams)
Answer: E
It is currently 8:34 PM. At what time in the morning was it exactly 39,668 minutes ago?	Choose the correct choice from the following answers
A) 7:22	B) 7:24	C) 7:26	D) 7:28	E) 7:30

Solution: Divide 39,668 by 60 to convert to minutes: 39,668/60 = 661 R8. That is 661 hours, 8 minutes. All of the answer choices are during the same hour before :34, so we can assume the 661 hours takes the time back into the 7AM hour to 7:34AM. Going back 8 more minutes yields the time 7:26AM. 7:26
Answer: C
Toby is four years younger than Debby. Thrice the sum of the ages of Toby and Debby equals their mother’s age. If the age of the mother is 36, find the ages of Toby and Debby?  Choose the correct choice from the following choices
A) 10 and 14  B) 5 and 9  C) 4 and 8  D) 6 and 10  E) 12 and 16

Solution: Let the age of Debby be x and Toby be x-4   3 ( x + x-4 ) = 36   x = 8   The ages of Toby and Debby are 4 and 8.   Answer : 4 and 8
Answer: C
There are 27 different three-digit integers that can be formed using only the digits 2, 3 and 4. If all 27 of the integers were listed, what would their sum be?	Choose the correct choice from the following options:	A) 8991	B) 9001	C) 9011	D) 9021	E) 9031

Solution: There must be nine 2's in the hundreds place, nine 2's in the tens place, and nine 2's in the units place. This is also true for the 3's and 4's. Then the sum is:   9(222+333+444)=9*(999)= 
9*(999) = 8_991
8991.   The answer is 8991.
Answer: A
The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?	Pick one:
A) 2/27
B) 1/42
C) 1/18
D) 1/38
E) None

Solution: Answer: Option 1/42   2/3 : 6/7 : 1/3 : 1/8 = 1/42
Answer: B
What is the value of n if the sum of the consecutive odd intergers R from 1 to n equals 169?  Choices.
A) 47 B) 25 C) 37 D) 33 E) 29

Solution: Before you tackle this question you must first understand that the question is comprised of two key parts, 1st is finding out how manytermsis in that sequence and 2nd whatactual number valuethat term is. In an arithmetic progression, in this case consecutive odd integers 1, 3, 5, ...., there are two set of rules.   Rule #1 (Arithmetic Sequence): xn = a + d(n-1) Identifies what the actual # in the sequence would be. Each number in the sequence has a term such as 1(is the first term), 3(is the second term) and so on. So if I were to ask you to find out what the 10th term is of that sequence you would use that formula to find that value.   a=1 (first term)   d=2 (the common difference) remember in the sequence 1, 3, 5, 7 the common difference is always 2   *On a side note we use n-1 because we don't have d in the first term, therefore if we were solving for the first term we would get 0 as n-1 and 0 times d would give us 0, leaving only the first term. This works regardless what your first term is in any sequence.   But remember the question asksWhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169?which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is, in this case it would be the last number in that sequence. In order to find that we first need to knowhow many terms(how many of the n there is) in order to be able to plug n in this formula given we know what the sum is. For that to happen we need to use Rule #2.   Rule #2 (Summing an arithmetic series): 169 = n/2(2a+(n-1)d). Given the question gives us what the sum is (169 in this case) we would simply use this formula to solve for n. Once we solve for n (13 in this case) we can simply plug n into the first formula (rule 1) and find the value.   It feels very confusing and difficult at first, but once you identify the steps all you need to do is plug and play. We have the sum (169) of a sequence, the number of terms in that sequence is (unknown). Rule #2 tells us how many numbers there are in that sequence and Rule #1 gives us what that last term is.
Answer: B
Of the a students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?  Answers
A) a + w- x- y	B) a - w- x- y	C) a- w - x + y	D) w + x + y- z	E) w - x - y - z

Solution: {Total} = {French} + {German} - {Both} + {Neither}   a = x + y - w + {Neither}   {Neither} = a + w - x - y.   a + w- x- ynswer: a + w- x- y.
Answer: A
The speed of a boat in still water is 14 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 8 minutes is	Choose the correct choice from the following
A) 1.6 km  B) 2.5 km  C) 3.6 km  D) 4 km  E) None of these

Solution: Explanation:   Speed downstreams	=(14+ 5)= 
(14+ 5) = 19
19 kmph.   Distance travelled= (19 x 8/60)km   = 2.5 km   Option 2.5 km
Answer: B
The sum w of prime numbers that are greater than 60 but less than 70 is  Choose the correct answer:	A) 67	B) 128	C) 191	D) 197	E) 260

Solution: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.   Let's list the numbers from 61 to 69.   61, 62, 63, 64, 65, 66, 67, 68, 69   Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.   We are now left with: 61, 63, 65, 67, 69   We can next eliminate 65 because 65 is a multiple of 5.   We are now left with 61, 63, 67, 69.   To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.   We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.   Thus, we can eliminate 63 and 69 from the list because they are not prime.   Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum w of 61 and 67 is 128.   Answer 128.
Answer: B
A plant manager must assign 12 new workers to one of five shifts. She needs a first, second, and third shift, and two alternate shifts. Each of the shifts will receive 4 new workers. How many different ways can she assign the new workers?  Choose the most appropriate option: A) 1485 B) 2700 C) 3300 D) 4860 E) 5400

Solution: whatever : my take selecting team of 4 out of 12 to assign to the shifts = 12C4 = 495 ways.   now 4 out of 12 means total of 3 group possible.   so putting them in shifts = counting methode: first, second, third,   = 3*2*1= 
3*2*1 = 6
6   here alt and alt are the same: so  6/2= 
 6/2 = 3
3 ways.   total ways of selecting= (selecting 4 out of 12)*arranging those teams in shifts   = 495*3= 
495*3 = 1_485
1485   1485ns: 1485
Answer: A
If a - b =2 and
a2+b2=36
, find the value of ab. Options.
A) 16	B) 32	C) 48	D) 12	E) 62

Solution: Explanation:   We know   2ab=(a2+b2)âˆ’(aâˆ’b)2   2ab=36âˆ’4=32   =>ab=16   Option 16
Answer: A
Tom bought 2 shares and sold them for $88 each. If he had a profit of 10% on the sale of one of the shares but a loss of 12% on the sale of the other share, then on the sale of both shares Tom had	Choose the correct choice:
A) a loss of $4
B) a profit of $4
C) a profit of $8
D) a loss of $8
E) neither a profit nor a loss

Solution: total CP = 8800/110 + 8800/88 = 80 + 100= 
80 + 100 = 180
180   SP=88*2= 
88*2 = 176
176   loss= Rs 4/-   a loss of $4nswer: a loss of $4
Answer: A
Machine A produces 100 parts thrice as fast as Machine B does. Machine B produces 100 parts in 30 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes?	Pick one: A) 20 B) 80 C) 40 D) 60 E) 50

Solution: Machine B produces 100 part in 30 minutes. Machine A produces 100 parts thrice as fast as B, so Machine A produces 100 parts in  30/3= 
 30/3 = 10
10 minutes.   Now, Machine A produces 100 parts in 10 minutes which is 100/10= 
100/10 = 10
10 parts/minute.   10 parts X a total of 6 minutes= 60   60
Answer: D
By investing in 1623% stock at 64, one earns Rs. 1500. The investment made is
Pick:	A) Rs. 9600	B) Rs. 7500	C) Rs. 5640	D) Rs. 5760	E) Rs. 6760

Solution: Explanation :   Market Value = Rs.64   Face Value is not given and hence take it as Rs.100   16 2/3% of the face value = 50/3   ie, to earn 50/3, investment = Rs.64   Hence, to earn Rs.1500, investment needed = 64×3×1500/50=5760   Answer : Option Rs. 5760
Answer: D
In a game of 80 points; A can give B 5points and C 15 points. Then how many points Bcan give C in a game of 60 ?
Choose the correct choice from the following:
A) 8	B) 9	C) 10	D) 11	E) 12

Solution: A: B = 80 : 75, A : C = 80 : 65.   B/C = ( B/ 8 * 8/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5   Therfore ,In a game of 60, B can give C 8 points   Option 8
Answer: A
The area of a square is equal to three times the area of a rectangle of dimensions 49 cm * 27 cm. What is the perimeter of the square?	Choose the correct choice from the following answers:
A) 380 cm  B) 264 cm  C) 252 cm  D) 324 cm  E) 296 cm

Solution: Area of the square = s * s = 3(49 * 27)   => s = 7 * 3 * 3= 
7 * 3 * 3 = 63
63 cm   Perimeter of the square= 4 * 63= 
4 * 63 = 252
252 cm.   Answer: 252 cm
Answer: C
There are 6 more women than there are men on a local co-ed softball team. If there are a total of 16 players on the team, what is the ratio of men to women?  Select the correct option.
A) 10/16  B) 6/16  C) 4/16  D) 5/11  E) 4/10

Solution: w = m+6   w+m = 16   m+6+m = 16   2m = 10   m = 5   w = 11   ratio:5:11   Ans: 5/11
Answer: D
When 5 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?  Answers:
A) 32  B) 150  C) 60  D) 27  E) 11

Solution: Explanation:   Let the number be   5 + 1/2[1/3(a/5)] = a/15   => 5 = a/30 => a = 150   Answer:150
Answer: B
A dozen eggs and 10 pounds of grapes are currently at the same price. If the price of a dozen eggs rises by 7 percent and the price of oranges rises by 3 %. How much more will it cost to buy a dozen eggs and 10 pounds of oranges .  Choose the correct choice from the following answers:
A) 2% B) 4% C) 5% D) 15% E) 10%

Solution: Say currently both a dozen eggs and 10 pounds of grapes cost $100 (they are at the same price). So, to buy a dozen eggs and 10 pounds of grapes we need $100.   After the increase, the price of a dozen eggs will be $107 and the price of 10 pounds of grapes will be $103. So after the increase, to buy a dozen eggs and 10 pounds of grapes we'll need $210.   Increase = 10%.   Answer: 10%.
Answer: E
Kathleen can paint a room in 4 hours, and Anthony can paint an identical room in 5 hours. How many hours would it take Kathleen and Anthony to paint both rooms if they work together at their respective rates?
Choose the correct choice from the following choices
A) 8/15  B) 40/9  C) 15/8  D) 9/4  E) 15/4

Solution: (1/4 + 1/5)t=2   t= 40/9   Answer: 40/9
Answer: B
12 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? Choose the correct choice from the following choices:
A) 190	B) 132	C) 210	D) 220	E) 225

Solution: Though 2*(12C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.   The first guy has to play 2 matches with the rest of 11, so he'll play 22 matches.   Similarly, second guy has to play with the rest of 10 as his 2 games with the first guy are already played. So he plays 20 matches.   This continues like this and the total matches are 22+20+18...+2   22+20+...+2 = 2(11+10+...+1) = 2((11*12)/2) = 11*12= 
11*12 = 132
132.   ANSWER:132
Answer: B
What is 15 percent of 34  Choose one
A) 5.1	B) 4.1	C) 3.1	D) 2.1	E) None of these

Solution: Explanation:   It will be 15% of 34   = (15/100) * 34= 
(15/100) * 34 = 51/10 = around 5.1
5.10   5.1nswer: Option 5.1
Answer: A
If two positive numbers are in the ratio 1/9 : 1/5, then by what percent is the second number more than the first? Choose the correct choice from the following answers
A) 67%. B) 70%. C) 60%. D) 68%. E) 80%.

Solution: Given ratio = 1/9 : 1/5 = 5 : 9   Let first number be 5x and the second number be 9x.   The second number is more than first number by 4x.   Required percentage = 4x/5x * 100 = 80%.   Answer: 80%.4 /5  * 100= 
4 /5  * 100 = 80
80%.   Answer: 80%.
Answer: E
The average (arithmetic mean) of 4 positive integers is 40. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?
Choose the correct choice from the following answers: A) 55 B) 69 C) 100 D) 109 E) 115

Solution: a + b + c + d =160   a + b = 90   c + d =70   Greatest possible = 69 (Just less than 1)   Answer = 69
Answer: B
A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
Choose the most appropriate option.
A) 3/5 B) 3/7 C) 2/5 D) 3/11 E) 3/13

Solution: Let E be the event that ‘number 4 appears at least once’ and F be   the event   that ‘the sum of the numbers appearing is 6’.   Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),   (5,4), (6,4)}   and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}   We have P(E) = 11/36   and P (F) = 5/36   Also EnF = {(2,4), (4,2)}   Therefore P(EnF) = 2/36   the required probability   P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.   2/5)
Answer: C
The measurements obtained for the interior dimensions of a rectangular box are 60 cm by 60 cm by 90 cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
Choose the most appropriate option.
A) 14,500 B) 14,600 C) 14,400 D) 14,700 E) 14,800

Solution: The options are well spread so we can approximate.   Changing the length by 1 cm results in change of the volume by 1*60*90= 
1*60*90 = 5_400
5400 cubic centimeters;   Changing the width by 1 cm results in change of the volume by 60*1*90= 
60*1*90 = 5_400
5400 cubic centimeters;   Changing the height by 1 cm results in change of the volume by 60*60*1= 
60*60*1 = 3_600
3600 cubic centimeters.   So, approximate maximum possible difference is 5400 + 5400 + 3600= 14,400 cubic centimeters.   Answer: 14,400
Answer: C
On 14th Aug, 2001 Tuesday falls. What day of the week was it on 14th Aug, 2000?  Answers:
A) Monday	B) Tuesday	C) Wednesday	D) Thursday	E) Friday

Solution: Explanation:   14th Aug 2001 – 14th Aug 2000 = 52 weeks 1 day. So Mondayug 14th 2000 is behind one day = Monday   Mondaynswer: Monday
Answer: A
John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam two years ago?
Choose the correct choice from the following choices
A) 2 B) 4 C) 6 D) 8 E) 16

Solution: j= 3s   after 6 years   j +6 = 2(s+6)   j= 2s+6   2s +6 = 3s   s= 6   two years ago   s= 6-2= 
6-2 = 4
4   4 is the answer
Answer: B
The average of first five prime numbers greater than 20 is? Choose the correct choice from the following:  A) 32.5  B) 32.9  C) 32.3  D) 32.2  E) 32.1

Solution: 23 + 29 + 31 + 37 + 41= 
23 + 29 + 31 + 37 + 41 = 161
161/5= 
161/5 = 161/5 = around 32.2
32.2   Answer:32.2
Answer: D
A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hour? Choose the correct choice
A) 7 km/hr	B) 7.2 km/hr	C) 8.9 km/hr	D) 9 km/hr	E) 9.2 km/hr

Solution: Speed = 600 m/sec.   5 x 60   = 2 m/sec.   Converting m/sec to km/hr   = 2 x 18 km/hr   5   = 7.2 km/hr   7.2 km/hr
Answer: B
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is? Options:
A) 19 : 7
B) 17 : 5
C) 19 : 8
D) 19 : 5
E) 29 : 5

Solution: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres   Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4= 
19/4 = 19/4 = around 4.75
4.75 litres   As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 4.75 : 1.25 = 19 : 5.   Answer:19 : 5
Answer: D
Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 36/49, what is the probability that the next one she draws will be pink?
Answers
A) 1/7	B) 4/7	C) 3/7	D) 16/49	E) 40/49

Solution: The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 36/49 = (6/7) * (6/7)   Therefore probability that the next one she draws is pink = 1/7   Option (1/7)
Answer: A
If 15 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days? Choose the correct choice from the following choices.
A) 78 days.
B) 165 days.
C) 49 days.
D) 48 days.
E) 67 days.

Solution: B   165 days.   From the above formula i.e (m1*t1/w1) = (m2*t2/w2)   so (15*6*88/1) = (6*8*d/1)   on solving, d = 165 days.
Answer: B
0,9,1,2,8,7,3,4,6,5,?	Choose the most appropriate option
A) 0	B) 6	C) 5	D) 7	E) 8

Solution: 0=10   10,9 8,7 6,5   1,2 3,4 5,6   Ans is 5   ANSWER:5
Answer: C
In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many T eggs does the plant process per day? Choose one
A) 100
B) 300
C) 400
D) 3,000
E) 4,000

Solution: Straight pluggin in for me. As usual, I started with C and got the answer.   Lets' back calculate and see what we get   Let us consider eggs processed each day to be 400   So Initial ratio of eggs processed and rejected is 96:4 or 24:1   So out of 400 eggs, there will be 384 eggs processed and 16 rejected.   Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there T=384+12= 
384+12 = 396
396 eggs accepted and 4 rejected...and the ratio will be 99:1   Bingo...this is what the questions says....   Its always a good idea to start with 400.
Answer: C
36 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
Choose one.
A) 33	B) 66	C) 88	D) 44	E) 281

Solution: (36 * 8)/30 = (x * 6)/50 => x =80   80 – 36 = 44   Answer: 44
Answer: D
A certain box has 12 cards and each card has one of the integers from 1 to 12 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 12 cards? Choose the most appropriate option:
A) 1/11 B) 2/23 C) 3/34 D) 4/45 E) 5/56

Solution: The average of the numbers is 6.5   The total number of ways to choose 2 cards from 12 cards is 12C2 = 66.   The ways to choose 2 cards with a sum less than the average are:   {1,2},{1,3},{1,4},{1,5},{2,3},{2,4}   The probability is 6/66 = 1/11   The answer is 1/11.
Answer: A
In a can, there is a mixture of milk and water in the ratio 4:3. If the can is filled with an additional 8 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can?	Choose the correct choice from the following options:  A) 40  B) 36  C) 32  D) 28  E) 24

Solution: Let C be the capacity of the can.   (4/7)*(C-8)+8=(2/3)*C   12C-96+168=14C   2C=72   C=36   The answer is 36.
Answer: B
A van takes 6 hours to cover a distance of 378 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?	Pick
A) 50 Kmph
B) 60 Kmph
C) 70 Kmph
D) 42 Kmph
E) 90 Kmph

Solution: Time = 6   42 Kmphistence = 378   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 378/9= 
378/9 = 42
42 Kmph   42 Kmph
Answer: D
A day-trader plans to invest a total of $23,200 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment? Pick:
A) $2,800	B) $3,000	C) $3,600	D) $3,800	E) $3,900

Solution: We can also just keep track of theHUNDREDS DIGITS(since the hundreds digit is different for each answer choice).   Total of 14 minimized investments = (14)(1400) = $???600   The 15th investment + $???600 = $23,200   So, theHUNDREDS DIGITSof the 15th investment must be 6   Answer: $3,600
Answer: C
A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship? Choose the correct choice from the following:
A) 11
B) 12
C) 13
D) 14
E) 15

Solution: Answer: 11 cartons total; 7 large boxes (7 * 8 = 56 boxes), 4 small boxes (4*10 = 40 boxes),11 total cartons and 96 boxes.   11nswer 11
Answer: A
If a square mirror has a 20-inch diagonal, what is the approximate perimeter E of the mirror, in inches?	Options:	A) 40	B) 60	C) 80	D) 100	E) 120

Solution: if you draw the square and diagonal inside the square. u can see square becomes part of two triangles opposite to each other.   And We know the property of the triangle, addition of two sides of triangle must be greater than its diagonal in order to complete the triangle. And each side must be less than 20 and perimeter E must be less than 80, so we can eliminate answer choice C, D and E.   so Side 1 + side 2 > 20, that means Side 1 or Side 2 must be > 10. so we can eliminate the answer choice A.   Now we are left with is 60
Answer: B
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.25 km and 1.00 km respectively. The time taken by the slower train to cross the faster train in seconds is?  Answers
A) 48	B) 9	C) 7	D) 67	E) 54

Solution: :   Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.25 + 1.0= 
1.25 + 1.0 = 2.25
2.25 km= 2250 m.   Required time = 2250 * 3/125= 
2250 * 3/125 = 54
54 sec.   Answer: 54
Answer: E
A family pays $800 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
Choose the correct choice
A) $1,000 B) $1,200 C) $1,400 D) $1,600 E) $2,000

Solution: Assuming the medical expenses are $1000 or more, the family pays $800 + $400 = $1200.   The total amount paid by insurance plan for the first $1000 of expenses is $600.   The insurance will pay another $600 when the medical expenses are $1600.   The answer is $1,600.800 +  400= 
800 +  400 = 1_200
$1200.   The total amount paid by insurance plan for the first $1000 of expenses is $600.   The insurance will pay another $600 when the medical expenses are $1600.   The answer is $1,600.
Answer: D
The sum of ages of 4 children born 2 years different each is 36 years. What is the age of the Elder child?  Choose the correct choice from the following answers.
A) 8  B) 9  C) 10  D) 12  E) 17

Solution: Let the ages of children be x, (x + 2), (x + 4), (x + 6) years.   Then, x + (x + 2) + (x + 4) + (x + 6) = 36   4x = 24   x = 6.   x +6= 
 +6 = 6
6+6= 
6+6 = 12
12   Answer : 12
Answer: D