MU-NLPC/Calc-aqua_rat huggingface dataset:
If x = 5/8 and y = -1/2, what is the value of the expression -2x – y^2?  Choose the correct choice from the following choices:
A) -3/2	B) -1	C) 1	D) 3/2	E) 7/4

Solution: -2X- y^2   -2x5/8 - (1/2)^2   -5/4-1/4   -3/2   -3/2 correct
Answer: A
A train left station X at A hour B minutes. It reached station Y at B hour C minutes on the same day, after travelling C hours A minutes (clock shows time from 0 hours to 24 hours). Number of possible value(s) of A is:
Options
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Let's try to get hours and minutes values separately..   Starting time + time taken = Reaching time..   A hours + C hours = B hours -------- (i)   A, C and B cannot have values greater than or equal to 24   B minutes + A minutes = C minutes -------- (ii)   Looking at the two equations, we get that no value of A satisfies both the equations.   Hence, option 0
Answer: A
From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 20 percent. The enrollment on January 1, 1993, was 50 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?  Choose the correct choice from the following choices:
A) 38 B) 39 C) 40 D) 41 E) 42

Solution: 1.20x=50 --> 6/5*x=50 --> x=50*5/6=250/6=~42.   Answer: 42.
Answer: E
A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 17}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?  Choose the correct choice from the following options.
A) 15 B) 16 C) 25 D) 20 E) 36

Solution: By looking at Set A, we can see that it's all primes. Thus, we should immediately break down the elements in Set B to their prime factors. That gives :   Set A = {2,3,5,7,11}   Set B = {2, 2x2, 3x2, 13}   Apart from 2x3x2 (taking 2 from set A) which is the same as 3x2x2(taking 3 from set A); there is nothing which can be repeated. Thus, the total unique product = 20-1 = 25.   25
Answer: C
In the first hour of a two-hour trip, a car traveled 3d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
Choose the correct choice from the following answers
A) d B) 1/3*d C) 1/2*d D) 5/4*d E) 3/2*d

Solution: Solution:   Lets look at the information given in the question...   Total time travelled = 2 hrs   Distance travelled first hour = 3d   Distance travelled second hour = 3d/2   The question is asking for the avg speed at which the car travels for 2 hrs   We know that avg speed = total distance/total time   Lets place the information given in the question to the formula above = (d+3d/2)/2   = 5/4*d   We find that option D is the answer as it gives the same expression as found in our calculation above. Answer option 5/4*d.
Answer: D
Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 53% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Choose the correct choice from the following:
A) 60%  B) 50%  C) 25%  D) 18%  E) 10%

Solution: {Total} = {finance} + {marketing} - {both} + {neither}   100 = 25 + 53 - {both} + 40   {both} = 18%.   Answer: 18%.
Answer: D
Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train? Choose the correct option.
A) 27 7/6
B) 27 7/5
C) 27 7/3
D) 27 7/9
E) 27 7/1

Solution: Relative speed = (40 - 20)= 
(40 - 20) = 20
20 km/hr.= 20 * 5/ 18 = 50/9 m/sec.   Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.   Answer: 27 7/9
Answer: D
What is the least positive integer X for which (X^2) + 164 is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11?  Choose the correct choice
A) 27556
B) 800
C) 796
D) 87
E) 166

Solution: 2 = 2   3 = 3   4 = 2 * 2   5 = 5   6 = 2 * 3   7 = 7   8 = 2 * 2 * 2   9 = 3 * 3   10 = 2 * 5   11 = 11   So (X ^ 2) + 164 = (2 * 2 * 2 * 3 * 3 * 5 * 7 * 11)= 
(2 * 2 * 2 * 3 * 3 * 5 * 7 * 11) = 27_720
27720.   Then (X^2)= 27556.   Then X = 166, which is option 166.
Answer: E
The sum of three consecutive odd natural numbers, each divisible by 3 is 72. What is the largest among them?	Choose the correct choice from the following answers
A) 21
B) 24
C) 27
D) 36
E) 45

Solution: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6   Given, X + X+3 + X+6 = 72   3X = 63   X = 21   The numbers are 21, 24, 27   Therefore the largest number is 27   Answer 27.
Answer: C
Which of the following statements must be true?
1) If x/y is a fraction and y has 17 as one of its prime factors then the resulting decimal will be terminating
2) If x/y is a fraction where 2 and 5 are the only two prime factors of y then the resulting decimal will be terminating.
3) If x/y is a fraction such that y=(10^n -1) for n≥1 then the repeating decimals in the result would just be the digits of the numerator.
4) If the interest is accounted annually then for the first compounded interest would be equal to the simple interest.  Choose the correct choice from the following answers
A) 2,3  B) 2,3,4  C) 1,2,3  D) 2,4  E) 1,3

Solution: Statement 3: Let's try some examples:   1/9 = 0.11111.....   23/99 = 0.2323232323.....   61/999 = 0.061061061061061.....   Statement 3 is always true.   Statement 4: I think first year is implied by the word "first".   Let's take principal = 100 and interest rate = 20%   Compound interest after 1 year = 100*(1+1/5) - 100= 
100*(1+1/5) - 100 = 20
20   Simple interest after 1 year= (100*20*1)/100= 
(100*20*1)/100 = 20
20   Let's take principal= 300 and interest rate = 50%   Compound interest after 1 year = 300*(1+1/2) - 300= 
300*(1+1/2) - 300 = 150
150   Simple interest after 1 year= (300*50*1)/100= 
(300*50*1)/100 = 150
150   Statement 4 is always true.   Answer (2,3,4).
Answer: B
There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 16 other amateurs, what is the total number of chess games possible to be played in the tournament? Choose the correct option:	A) 10	B) 20	C) 40	D) 60	E) 120

Solution: Each person is one participant of 4 games. So there are in all 16*5= 
16*5 = 80
80 instances of one participant games. But each game has 2 participants so total number of games= 80/2= 
80/2 = 40
40   40
Answer: C
The unit digit in the product (293 * 567 * 917 * 343) is: Select the correct option:
A) 2  B) 1  C) 6  D) 8  E) 10

Solution: Explanation:   Unit digit in the given product = Unit Digit in (3*7*7*4) = 1   ANSWER: 1
Answer: B
Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?  Choose the correct choice from the following choices:	A) 2/11	B) 2/9	C) 4/13	D) 3/14	E) 3/17

Solution: Here, n(S) = 52   There are 13 cards of diamond (including one king) and there are 3 more kings.   Let E = event of getting a diamond or a king.   Then, n(E) = (13 + 3)= 
(13 + 3) = 16
16   P (E)= 16 / 52 = 4/13   4/13
Answer: C
What is the sum of the prime factors of1549 and the prime factors of 5049? Choices
A) 73	B) 63	C) 65	D) 74	E) 75

Solution: The prime factors of 5049 are 3*3*3*11*17   The prime factors of 1549 are 3*3*7*23   3+3+3+3+3+11+17+7+23= 
3+3+3+3+3+11+17+7+23 = 73
73. 73 is the correct answer
Answer: A
Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next?	Pick one:
A) 52
B) 56
C) 96
D) 128
E) None

Solution: Explanation: This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.   Answer: Option 56
Answer: B
which number need to add to 859622 to get a number exactly divisible by 456?
Choose the correct choice from the following options:
A) 678342 B) 546546 C) 576765 D) 645235 E) 859622

Solution: Dividend = Quotient * Divisor + Reminder   859622 / 456 gives quotient = 1885 and reminder = 62.   So, the next number divisible by 456 is 456 places infront of 456 * 1885   Which means 456 – 62 = 394 should be added to 859622.   859622
Answer: E
96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Choose the correct choice from the following options
A) 76  B) 76  C) 42  D) 58  E) 45

Solution: x/7 = y/9   => x:y   = 7:9   7/16 * 96= 
7/16 * 96 = 42
42   Answer: 42
Answer: C
How many 1/6s are there in 37 1/2?
Choose one
A) 225	B) 425	C) 520	D) 600	E) 700

Solution: Required number = (75/2)/(1/6)   = (75/2 x 6/1)   = 225.   225NSWER:225
Answer: A
P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 135 days, in how many days can R alone complete the remaining work?  Choose the correct choice from the following answers:
A) 50 days  B) 92.4 days  C) 100 days  D) 150 days  E) 80 days

Solution: P works 25% more efficiently than Q: Something that takes Q 5 days, takes P 4 days   Q works 50% more efficiently than R: Something that takes R 7.5 days, takes Q 5 days   P alone takes 50 days less than Q: For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 385 days   P works for 60 days--> 60/200 work done => 30%   Q works for 135 days--> 135/250 work done => 54%   24% work left ... R alone will take 24% * 385 = 92.4 days   Answer is (92.4 days)
Answer: B
Carina has 115 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have? Choose the correct choice from the following options:
A) 5	B) 7	C) 6	D) 4	E) 3

Solution: Lets say 5 and 10 ounce packages be x and y respectively.   Given that, 5x+10y=115 and x=y+2. What is the value of y.   Substituting the x in first equation, 5y+10+10y=85 ->y=105/15.= 
105/15. = 7
7   7
Answer: B
If n + 16 is a positive odd integer, which of the following must be true about the sum of the next four integers?	Choose the correct choice from the following answers.
A) It is a multiple of 3
B) It is a multiple of 4
C) It is a prime number
D) It is a multiple of 5
E) It is a multiple of 2

Solution: n+16 is a positive odd integer. This means n will be an odd integer   The next 4 integers would be: n + 16, n + 17, n + 18, n + 19   Sum = 4n + 70   This sum will always be even.   Option It is a multiple of 2
Answer: E
A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in --- days.  Select.
A) 5 5⁄11	B) 4 5⁄11	C) 6 4⁄11	D) 6 5⁄11	E) 7 5⁄11

Solution: Explanation :   5 5⁄11 can complete the work in 12 days working 8 hours a day   => Number of hours 5 5⁄11 can complete the work = 12×8 = 96 hours   => Work done by 5 5⁄11 in 1 hour = 1/96   B can complete the work in 8 days working 10 hours a day   => Number of hours B can complete the work = 8×10 = 80 hours   => Work done by B in 1 hour = 1/80   Work done by 5 5⁄11 and B in 1 hour = 1/96 + 1/80 = 11/480   => 5 5⁄11 and B can complete the work in 480/11 hours   5 5⁄11 and B works 8 hours a day   Hence total days to complete the work with 5 5⁄11 and B working together   = (480/11)/ (8) = 60/11 days = 5 5⁄11 days   5 5⁄11nswer : Option 5 5⁄11
Answer: A
If a certain sample of data has a mean of 20.0 and a standard deviation of 4.0, which of the following values is more than 2.5 standard deviations from the mean?	Choose the correct choice from the following:  A) 12.0  B) 13.5  C) 17.0  D) 23.5  E) 26.5

Solution: The standard deviation is 4. 2.5 standard deviations, which is just 2.5 x 4.0 is 10.0. The only answer more than 10.0 away from the mean is 12.0.
Answer: A
A group of 7 teenagers recently visited the Japanese Restaurant. The total bill for the meal, including 20% gratuity, came to $840. On average, how much did the meal of each individual cost before gratuity?  Choose the correct choice from the following options.
A) $160	B) $96	C) $90	D) $10	E) $55

Solution: 7 teenagers - so total 7 people   The bill $840 includes 20% gratuity... so the actual cost of dinner was $700   Now, the cost per person will be $700/7 which is $10   Option $10
Answer: D
If 48 machine can finish a job in 80 days, then how many more machines would be needed to finish the job in one -fifth less time?  Choices:
A) a. 4  B) b. 8  C) c. 10  D) d. 12  E) e. 16

Solution: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5= 
6*5 = 30
30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign   30/3= 
  30/3 = 10
10 employees to do the job, because you want to get a total of 30 hours of work from the employees.   We can solve this problem identically. If 48 machines (identical ones, I assume) work simultaneously for 80 days, they will do a total of 48*80 machine-days of work. So the job requires 48*80 days of machine work in total. We instead want the job done in 1/5 less time, so in 64 days. So we'll need 48*80/64= 
48*80/64 = 60
60 machines, or 12 additional machines.   d. 12
Answer: D
The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?	Pick one:  A) 10 kmph  B) 20 kmph  C) 16 kmph  D) 18 kmph  E) 19 kmph

Solution: Speed of the boat in still water = (60+100)/2= 
(60+100)/2 = 80
80 kmph. Speed of the stream= (100-60)/2= 
(100-60)/2 = 20
20 kmph.Answer: 20 kmph
Answer: B
By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?  Options:
A) 20 B) 99 C) 88 D) 77 E) 61

Solution: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3= 
40 * 3 = 120
120x km   He covered 2/3 * 120= 
2/3 * 120 = 80
80x km in 1/3 * 3x= x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph.   20nswer: 2040 /2= 
40 /2 = 20
20 kmph.   20nswer: 20
Answer: A
How many numbers between 100 and 600 are divisible by 2, 3, and 7 together?	Options
A) 112 B) 77 C) 267 D) 12 E) 99

Solution: Explanation:   As the division is by 2, 3, 7 together, the numbers are to be divisible by:  2*3*7= 
 2*3*7 = 42
42   The limits are 100 and 600   The first number divisible is 42*3= 
42*3 = 126
126   To find out the last number divisible by 42 within 600:   600/42= 14.28   Hence, 42*14 = 588 is the last number divisible by 42 within 600   Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12   ANSWER: 12
Answer: D
Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 2/3 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used? Choose the correct choice from the following:	A) 18	B) 144	C) 175	D) 216	E) 264

Solution: Total paint initially = 360 gallons   Paint used in the first week = (2/3)*360= 
(2/3)*360 = 240
240 gallons.   Remaning paint= 120 gallons   Paint used in the second week = (1/5)*120= 
(1/5)*120 = 24
24 gallons   Total paint used= 264 gallons.   Option 264
Answer: E
the average distance between the sun and a certain planet is approximatly 2.7 10^10 inches. which of the following is the closest to the average distence between sun and the planet in kelometers? (1 km is approx 3.9 x 10^4 inches) Choose the correct choice: A) 6.9 x(10)^6 B) 6.9 x(10)^4 C) 6.9 x(10)^3 D) 6.9 x(10)^5 E) 6.9 x(10)^2

Solution: No need to solve entire problem.   6.9 x(10)^5istance in KM = 27*(10)^10/39*(10)^4 which is -270*(10)^9/39*(10)^4 = 6.9 x(10)^5   Answer : 6.9 x(10)^5
Answer: D
A company D has 10 percent of the employees are secretaries and 20 percent are salespeople. If there are 70 other employees of Company D, how many employees does Company D have?  Options.
A) 100  B) 162  C) 180  D) 152  E) 250

Solution: Let the total number of employees in the company be x   % of secretaries = 10%   % of salespeople = 20%   % of of employees other than secretaries and salespeople = 100 -30= 
100 -30 = 70
70%   But this number is given as 70   so 70% of x= 70   x = 100   Therefore there a total of 100 employees in the company D   Correct answer - 100
Answer: A
A train 160m long is running at 30kmph. In how much time will it pass a platform 120m long?
Choose one
A) 15.89 seconds
B) 24.36 seconds
C) 15.96 seconds
D) 14.93 seconds
E) 22.23 seconds

Solution: 14.93 secondsistance travelled = 160 + 120= 
160 + 120 = 280
280mSpeed= 30 * 5/8 = 75/4mTime = 280 * 4/75 = 14.93 SecondsAnswer : 14.93 seconds.
Answer: D
A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is  Choose the correct choice from the following answers.
A) 3220 B) 4830 C) 5120 D) 6420 E) None

Solution: Solution   Clearly,l = (48 - 16)= 
(48 - 16) = 32
32 m   ‹=›b = (36 -16)= 
(36 -16) = 20
20 m,   ‹=›h = 8 m..   Volume of the box =(32x20x8) m3	= 5120 m3.   Answer 5120
Answer: C
What is the difference between the place value of 7 in the numeral 894577?  Choose the most appropriate option:
A) 83 B) 77 C) 53 D) 63 E) 87

Solution: 63ifference between the place values of 7 =70-7= 
70-7 = 63
63   Answer is 63
Answer: D
Pipe A can fill a tank in 8 hours, pipe B in 4 hours and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled?	Choose the correct answer:  A) 3.4 hr  B) 2.4 hr  C) 2 hr  D) 2.8 hr  E) 3 hr

Solution: Part filled by pipe A in 1 hour = 1/8   Part filled by pipe 2.4 hr in 1 hour = 1/4   Part filled by pipe C in 1 hour = 1/24   Part filled by pipe A, pipe 2.4 hr and pipe C in 1 hour = (1/8)+(1/4)+(1/24)=1024   i.e, pipe A, pipe 2.4 hr and pipe C together can fill the tank in 24/10= 
24/10 = 12/5 = around 2.4
2.4 hour   Answer is 2.4 hr
Answer: B
W=√[2√63 + 2/(8+3√7)] = Pick:
A) 8 + 3√7 B) 4 + 3√7 C) 8 D) 4 E) √7

Solution: In these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7)   sqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}]   W=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4   Answer is 4.4
Answer: D
If the units digit of n^31 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47	Select:
A) Only I
B) Only II
C) Only III
D) I and II
E) II and III

Solution: I tried in this way.   Given n^31 units digit is 7.   If at all we have to get 7 as units digits only 3 and 7 series has 7   3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81   7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)   We have n^31 - then divide 31 by 4 = reminder 3.   Then we have for only 7^3 - we have units digit as 3.   Hence 47^31 = 7 (units).   Option Only II is correct answer , and with 41^31 we always get 1 as units digit and 43^31 - we get units as 3.
Answer: B
.
On dividing a number by 357, we get 37 as remainder. On dividing the same number 17, what will be the remainder ?
Choose the correct option:
A) 0	B) 3	C) 5	D) 3	E) 11

Solution: Let x be the number and y be the quotient. Then,   x = 357 x y + 37   = (17 x 21 x y) + (17 x 2) + 3   = 17 x (21y + 2) + 3)   Required remainder = 3.   Answer: Option 3
Answer: D
The value of 1/(1-x) + 1/ (1+x) + 2/(1+x^2) + 4/(1+x^4)  Choose the correct answer:  A) 8/(1-x^8)  B) 4x/(1+x^2)  C) 4/(1-x^6)  D) 4/(1+x^4)  E) 4x/(1-x^4)

Solution: Highlighted part has mistake as the exponent of x must be 4 in last term   CORRECT QUESTION ISThe value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) = ?   Solution is as mentioned below...   one more way that could get the answer in the type of eqn and choices given is to substitute some value for x...   0 would be better as the eq has constant term free of term 'x'..   the Eq gives us 8 as the ans , as also only choice 8/(1-x^8)..
Answer: A
What is the tens digit of 36^5?	Answers
A) 1	B) 7	C) 5	D) 3	E) 9

Solution: 36^5 = 6^7   (6^2)=6*6= 
6*6 = 36
36   (6^3)= 36*6 = .16   (6^4)= .16*6 = ..96   (6^5) = ..96*6 = ..76   (6^6) = ..76*6 = ...56   (6^7) = ....56*6 = ....36   If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...   Continue the pattern up to 6^7 ( dont actually calculate full values) and answer is 3: 3
Answer: D
For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 945 what is the least possible value of k?	Choose the most appropriate option:
A) 5  B) 7  C) 9  D) 11  E) 13

Solution: 945 = 3*3*3*5*7   Thus k must include numbers at least up to the number 9 so that there are at least three appearances of 3 (that is: 3, 6, and 9).   The answer is 9.
Answer: C
Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer?
Choose the correct choice:  A) 2828  B) 2338  C) 377  D) 4266  E) 288

Solution: CI = 14800{ [ 1 + 13.5/100]2 - 1 }   = 14800 { [1 + 27/200]2 - 1   = 14800 { 2 + 27/200}{27/200}   = (74)[2 + 27/200](27) =   1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266.Answer: 4266
Answer: D
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 25%. Their gross income from sales for one month increases by what percent? Pick one:	A) 5%	B) 7.5%	C) 10%	D) 12.5%	E) 15%

Solution: Let P be the original price and let x be the number of items sold originally.   The original income is P*x.   After the changes, the income is 0.9P*1.25x = 1.125*(P*x), an increase of 12.5%.   The answer is 12.5%.0.9 *1.25= 
0.9 *1.25 = 1.125
1.125*(P*x), an increase of 12.5%.   The answer is 12.5%.
Answer: D
If $ 5,000 is invested in an account that earns 12% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest? Choose one
A) $ 4	B) $ 8	C) $ 12	D) $ 16	E) $ 432

Solution: Solution   Amount ($ 12I) = P+(1+r/n)^nt = 5000+(1+0.12/2)^2= 5412   Amount (SI) = P+PTR/100 = 5000+(5000*1*12/100)=5400   Difference = 5412-5400= 
5412-5400 = 12
12 $   $ 12
Answer: C
If x < 12, then it must be true that...
Choose the correct choice from the following options:
A) -x < -12 B) -x - 2 < 14 C) -x + 2 < -10 D) x + 2 < 10 E) x - 3 < 14

Solution: A. -x < -12 --> x>12. Not true.   B. -x - 2 < 14 --> x>-16. Not true, consider x=-20.   C. -x + 2 < -10 --> x>12. Not true.   D. x + 2 < 10 --> x<8. Not true, consider x=10.   E. x - 3 < 14 --> x<17. Since given that x<12, then x is for sure less than 13. Thus this statement must be true.   Answer: x - 3 < 14.
Answer: E
If you roll a fair-sided die twice, what is the probability of getting a (4.4) double? Choose the correct choice from the following choices:
A) 1/2  B) 1/4  C) 1/12  D) 1/3!  E) 1/24

Solution: total no. in two dice (1,1) ,(2,2) .....(6,)   Total number of events= 6*6   Total events of getting same pair(4, 4) = 6   Probability= 6/6*6= 1/6=1/3!   1/3!
Answer: D