MU-NLPC/Calc-aqua_rat huggingface dataset:
The salaries of A, B, C are in the ratio 2:3:5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries? Select.
A) 23:33:62
B) 23:33:68
C) 23:33:60
D) 23:32:60
E) 23:23:60

Solution: Let A = 2k, B = 3k and 23:33:60 = 5k   A's new salary = 115/100 of 2k = 23/10 k   B's new salary = 110/100 of 3k = 33/10 k   23:33:60's new salary = 120/100 of 5k = 6k   New ratio = 23k/10 : 33k/10 : 6k = 23:33:60   Answer:23:33:60
Answer: C
600 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ? Choose one:	A) 162	B) 138	C) 60	D) 38	E) 12

Solution: Passed in english = 65%   Passed in maths = 55%   Passed in both = 40% of 55% = 2/5 * (55%) = 22%   Passed in (12nglish + Maths - Both + Neither) 2/5 * (55 )= 
2/5 * (55 ) = 22
22%   Passed in (12nglish + Maths - Both + Neither)= 100%   65 + 55 - 22 + Neither = 100   Neither = 100 - 98= 
100 - 98 = 2
2%= 0.02 * 600= 
0.02 * 600 = 12
12   Answer: 12
Answer: E
If
1 = 5
2 = 10
3 = 15
4 = 20
5 = 25
6 = 30
Then 25 = ?
Hint: Its a logic Riddle not a mathematical riddle  Pick one.
A) 1	B) 2	C) 3	D) 4	E) 5

Solution: 5   5   As stated   5=25 => 25=5   Answer is 5
Answer: E
Robert is traveling from one end of a forest to the other. In order to find his way back, he is leaving morsels of bread in the following pattern: 2 morsels of milk, 3 morsels of white, and 1 morsel of rye. The pattern repeats after he leaves the morsel of rye. If Robert drops 2,000 morsels of bread, what are the last 3 morsels of bread that he drops?	Options
A) rye − milk − milk B) milk − milk − white C) white − rye − milk D) white − white − white E) white − white − rye

Solution: In a single round Robert drops 6 morsels.   Remainder (2000/6) = 2   Final action = 2 drops of milk --> Options B, C, D and E can be eliminated   rye − milk − milknswer: rye − milk − milk
Answer: A
Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 40% in the following week, and increased by 20% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price at the end of the three weeks? Pick one
A) 0.75G  B) 0.8G  C) 0.85G  D) 0.9G  E) 0.95G

Solution: After 3 weeks, the price was 1.2*0.6*1.25*G=0.9G   The answer is 0.9G.
Answer: D
Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 2000 then loss of Pyarelal?	Answers:  A) 1600  B) 1700  C) 1800  D) 1900  E) 1000

Solution: Let the capital of Pyarelal be x, then capital of Ashok=x/9   So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x   Hence out of the total loss of 2000, loss of Pyarelal= 2000*9x/10x=1800   ANSWER:18002000*9 /10= 
2000*9 /10 = 1_800
1800   ANSWER:1800
Answer: C
Every student at Larcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Larcy School?	Choose the correct choice from the following choices:
A) 63	B) 69	C) 74	D) 82	E) 86

Solution: total number of students at Larcy School The answer is 86 or any multiple of 43.86
Answer: E
If x = 3p, where p is a prime number greater than 2, how many different positive even divisors does x have, including x?  Choices:
A) 0 B) 1 C) 2 D) 3 E) It cannot be determined from the information given

Solution: p is prime greater than 2 thus p is odd   3p is odd   Thus no even factors   0ns:0
Answer: A
Three bells commence tolling together and toll at intervals of 2, 4, 6 seconds respectively. In 10 minutes, how many times do they toll together ?	Choose the correct choice from the following options:
A) 51	B) 52	C) 53	D) 54	E) 55

Solution: LCM of 2, 4, 6 is 12.   So, after each 12 seconds, they would toll together.   Hence, in 10 minutes, they would toll 10*60 seconds / 12 seconds = 50 times   But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).   So, total tolls together = 50+1= 
50+1 = 51
51   51nswer: 51
Answer: A
One-third of Ramani’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has 150000 as total savings, how much he saved in Public Provident Fund?	Choose the correct choice from the following choices:  A) 60000  B) 50000  C) 90000  D) 30000  E) None of these

Solution: Ratio of Ramani’s savings in NSC and PPF = 3: 2   His savings in PPF = 2⁄5 × 150000 = 60000   60000nswer 60000
Answer: A
Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 27 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
Choose the correct answer
A) 4 B) 6 C) 9 D) 18 E) 20

Solution: Based on the original number of shares, the range would be: 112 - 45= 
112 - 45 = 67
67   However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:   V 68   W 112   X 36   Y 121   Z 45   Now the range is   121 - 36= 
  121 - 36 = 85
85   The INCREASE in the range requires us to compare thenewrange to theoldrange:   85 - 67= 
  85 - 67 = 18
18   18
Answer: D
Swetha takes a trip and drives 8 hours from Town A to Town C at a rate of 40 miles per hour. On her way back, Swetha drives 30 miles per hour and stops in Town Y which is midway between Town A and Town C. How many hours does it take Swetha to drive from Town C to Town B?	Choose the correct choice from the following answers: A) 1.01 B) 1.25 C) 1.53 D) 5.33 E) 2.0

Solution: distance from A to C =8 hr* 40 mph= 320 miles   hence distance from B to C= 1/2*320= 
1/2*320 = 160
160   time=160/30=5.33 hrs   IMO: 5.33
Answer: D
The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 22,000 is made?  Select.
A) 328897
B) 120000
C) 118000
D) 277768
E) 188871

Solution: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000   SP such that a profit of Rs. 22,000 is made = 96,000 + 24,000 = Rs. 1,18,000   Answer: 118000
Answer: C
In each term of a sequence, 12 is added to get the next term. If the first term is 5, what is the forty-fifth term?
Choose the correct answer.
A) 533
B) 595
C) 513
D) 562
E) 531

Solution: 1rst term + 44 terms = 5 + 12+12+12+12+12+12+12+...+12 (44 times)   5 + (12 x 44) = 5 + 528= 
5 + 528 = 533
533   533nswer 533
Answer: A
A two digit number is 18 less than the sum of the squares of its digits. How many such numbers are there? Choose the correct choice from the following answers:
A) 1  B) 2  C) 3  D) 4  E) 5

Solution: suppose the digit 10x+y.   so, 10x+y=x^2+y^2-18   =>(x-6)(x-4)=(y-7)(-y-6)   so conddition satisfied for x=6,4 and y=7 so no of digit 2. 67,47.   ANSWER:2
Answer: B
The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher	Choose one:
A) 30 Years
B) 31 Years
C) 32 Years
D) 34 Years
E) 49 Years

Solution: Total age of students is 32X16 = 512 Years   Total age inclusive of teacher = 33X (16+1) = 561   So, Teacher's age is 561-512= 
561-512 = 49
49 Yrs   There is a shortcut for these type of problems   Teacher's age is 16+(33X1)= 49 Years   49 Years
Answer: E
City A and City B are 140 miles apart. Train C departs City A, heading towards City B, at 4:00 and travels at 40 miles per hour. Train D departs City B, heading towards City A, at 5:30 and travels at 20 miles per hour. The trains travel on parallel tracks. At what time do the two trains meet?
Choose the most appropriate option.
A) 5:00
B) 7:30
C) 6:00
D) 6:30
E) 7:00

Solution: Train C has traveled 20 mi in the half hour before Train D has started its journey.   140-20= 
140-20 = 120
120   40+20= 
40+20 = 60
60 mph   120 mi/ 60 mph= 2 hrs   5:30pm + 2 hrs = 7:30pm   Answer:   B. 7:30
Answer: B
A and B can do a piece of work in 6 days, B and C in 8 days, C and A in 12 days. How long will C take to do it?  Choose the correct choice.
A) 48 days B) 55 days C) 24 days D) 33 days E) 40 days

Solution: 2c = 1/8 + 1/12 – 1/6= 1/24   c = 1/48 => 48 days   48 daysnswer: 48 days
Answer: A
A man sells a horse for Rs.2000 and loss something, if he had sold it for Rs.3100, his gain would have been double the former gain. Find the cost price of the horse? Choices:  A) 1025  B) 1225  C) 1000  D) 1100  E) 1200

Solution: CP = SP + 1CP = SP - g   2000 + x = 3200- 2x   3x = 1200 => x = 400   CP = 800 + 400= 
800 + 400 = 1_200
1200   Answer: 1200
Answer: E
When asked what the time is,a person answered that the amount of time left is 3/5 of the time already completed.what is the time. Choose the correct answer:	A) 2 PM	B) 9 PM	C) 3 PM	D) 8 PM	E) 6 PM

Solution: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)   24−x=3/5x⇒x=15   Time is 3 PM   Answer:3 PM
Answer: C
Dana borrows 6000 pounds annually for her college education. If Dana gives her parents 2% of that amount back each month, how much will she still owe her parents after three years of college? Choose one
A) 13680	B) 13885	C) 14005	D) 14280	E) 14680

Solution: dana borrows 6000 and returns 2% per month.   so returns 120 per month. and 1440 per year.   so dana owes  6000-1440= 
 6000-1440 = 4_560
4560 per year.   after 3 years she will owe 13680.   13680ns (13680)
Answer: A
A water tank is one-fifth full.Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes.If both the pipes are open,how long will it take to empty or fill the tank completely? Choose the correct choice from the following answers:  A) 6 min.to empty  B) 9 min.to empty  C) 5 min.to empty  D) 4 min.to empty  E) 3 min.to empty

Solution: Explanation:   Clearly,pipe B is faster than pipe A and so,the tank will be emptied.   part to be emptied = 1/5   part emptied by (A+B) in 1 minute=(1/6-1/10)=1/15   so, the tank will be emptied in 3 min   Answer: 3 min.to empty
Answer: E
The 4 sticks in a complete bag of Pick-Up Sticks are all straight-line segments of negligible width, but each has a different length: 1 inch, 2 inches, 3 inches, and 4 inches, respectively. If Tommy picks a stick at random from each of 3 different complete bags of Pick-Up Sticks, what is the probability A that Tommy CANNOT form a triangle from the 3 sticks?
Choose the correct option:
A) 11/32	B) 13/32	C) 15/32	D) 17/32	E) 19/32

Solution: In order to form a triangle, the sum of two sides must be greater than the third side.   So we can choose the combination of numbers which will NOT result in a triangle.   Favorable outcomes:   1,1,4 (4>1+1): 3 ways of arriving at this (1,1,4), (1,4,1), (4,1,1) or   1,2,4 (4>1+2): 6 ways of arriving at this (1,2,4), (1,4,2), (2,1,4), (2,4,1), (4,1,2), (4,2,1) which is same as 3!   1,3,4 (4=1+3): 6 ways of arriving at this   2,2,4 (4=2+2): 3 ways of arriving at this   1,1,3 (3>1+1): 3 ways of arriving at this   1,2,3 (3=1+2): 6 ways of arriving at this   1,1,2 (2+1+1): 3 ways of arriving at this   Overall favourable outcomes: 30   Total outcomes:  4*4*4= 
 4*4*4 = 64
64 (4 ways of choosing a stick from each of the 3 bags)   Probability A that a triangle is not formed= 30/64 = 15/32   15/32 is the correct option here.
Answer: C
The average of marks obtained by 120 boys was 40. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
Choose the correct choice from the following choices:
A) 100	B) 110	C) 125	D) 130	E) 145

Solution: Let the number of boys who passed = X.   Then, 39 x X + 15 x (120 - X) = 120 x 40   24X = 4800 - 1800   => X = 3000/24= 
3000/24 = 125
125   Hence, the number of boys passed= 125.   ANSWER:125
Answer: C
(A% of 2B + B% of A) is equal to ?
Choose the correct choice from the following answers.
A) A% of B  B) B% of A  C) 3% of AB  D) AB% of 3  E) None

Solution: Answer   A% of 2B + B% of A =2AB/100 + AB/100   = 23AB/100 = 3% of AB   3% of ABorrect Option: 3% of AB
Answer: C
If 18 is 15 percent of 30 percent of a certain number, what is the number?	Choose the correct choice from the following options:
A) 9 B) 36 C) 40 D) 81 E) 400

Solution: The math involved in this question can be 'set up' (and dealt with) in a variety of ways.   Here, if you're going to take a calculation-based approach, converting the percents to fractions would likely help you speed up (and avoid the last bit of math).   We're told that 18 is 15 percent of 30 percent of a certain number. We're asked for that number.   18 = (.15)(.3)(X)   18 = (3/20)(3/10)(X)   18 = (9/200)(X)   Since 9/200 is a relatively small fraction (it's far less than 10%), we know that 18 is LESS than 10% of X. Based on the given answer choices, there's only one number that is LARGE enough to fit that description....   Final Answer:   400
Answer: E
if x+y+z =1. then xy+yz+zx is	Choose one:  A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6

Solution: 1/2+1/2+0= 
1/2+1/2+0 = 1
1   xy=1/2*1/2=1/4   ANSWER:1/4
Answer: C
If HARD is coded as 1357
and SOFT is coded as 2468
what will 21448 stand for?	Choose the correct answer:	A) SHOOR	B) SHOOA	C) SHOOT	D) SHEOT	E) SWOOT

Solution: HARD = 1357 => 1=H, 3=A , 5=R , 7=D   SOFT = 2468 => 2=S, 4=O , 6=F , 8=T   so, 21448 = SHOOT   ANSWER:SHOOT
Answer: C
A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?  Choose the correct choice from the following choices.
A) 48pi/x
B) 75x
C) 48x
D) 24x
E) x/75

Solution: The larger rim must circulate for the same number of inches the smaller rim does.   C = (pi)d   C(small): (pi)*14   C(large): (pi)*35   Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*14*60 = (pi)*(840) inches   (pi)*(840) = (pi)*(35)(x)   pi*(24) = pi*(x)   24=x   Answer: 24x
Answer: D
A veterinarian surveys 26 of his patrons.He discovers that 14 have dogs, 10 have cats, and 5 have fish.Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish.If no one has all three kinds of pets, how many patrons have none of these pets?
Choose the correct choice from the following answers
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: no. of patron have dogs = 14   no. of patron have cats = 10   no. of patron have fish = 5   no. of patron have dogs and cats = 4   no. of patron have dogs and fish = 3   no. of patron have cats and fish = 1   no. of patron have all three pets = 0   no. of patron have only dogs = 7   no. of patron have only cats = 5   no. of patron have only dogs = 1   So total no. of patron have pets =7+5+1+4+3+1= 
7+5+1+4+3+1 = 21
21   So no. of patron don't have any pets=26-21= 
26-21 = 5
5   5 patrons don't have any these pets   ANSWER:5
Answer: C
At a meeting of the 9 Joint Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the 9 Chiefs of Staff be seated around a circular table?	Select the correct option: A) 120 B) 480 C) 960 D) 2520 E) 6050

Solution: Bunuel, I'm also a little confused with the number of arrangements of n distinct objects in a circle. Why is it given by (n-1)!. In theveritasanswer they say:answer E (6050), should be the number of ways to arrange all 7 without the seating restriction given. Is this incorrect?6050
Answer: E
Find the odd man out. 1, 9, 16, 51, 121, 169, 225	Choose the correct choice from the following choices: A) 169 B) 51 C) 16 D) 1 E) 121

Solution: Explanation :   Each of the given numbers except 51 is a perfect square   Answer : Option 51
Answer: B
A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,586.25. How many boxes of plain cookies did she sell? Select the correct option:
A) 0
B) 233
C) 500
D) 695
E) 790

Solution: Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)   790quating for X   (0.75)*X +(1.25)*(1585-X)=1586.25   =>x=790   790
Answer: E
How long does a train 100 m long traveling at 60 kmph takes to cross another train of 170 m in length has a speed of 40 kmph?  Choose the correct option:  A) 1.42 sec  B) 16.8 sec  C) 5 sec  D) 1.68 sec  E) 3.6 sec

Solution: D = 100 m   S = (60+40) * 5/18 = 250/3   T = 100 * 9/250= 
100 * 9/250 = 18/5 = around 3.6
3.6 sec   ANSW3.6 secR:3.6 sec
Answer: E
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Select.
A) 23 years	B) 24 years	C) 25 years	D) 26 years	E) None of these

Solution: Explanation:   Let the average age of the whole team by x years.   11x - (26 + 29) = 9(x -1)   11x - 9x = 46   2x = 46   x = 23.   So, average age of the team is 23 years.   23 yearsNSWER IS 23 years
Answer: A
The area of a triangle is with base 4m and height 5m? Choose the correct choice:
A) 11
B) 10
C) 88
D) 26
E) 32

Solution: 1/2 * 4 * 5= 
1/2 * 4 * 5 = 10
10 m2   Answer: 10
Answer: B
The ratio of number of boys and girls in a school is 2:5. If there are 420 students in the school, find the number of girls in the school?	Answers
A) 150 B) 250 C) 300 D) 370 E) 280

Solution: Let the number of boys and girls be 2x and 5x   Total students = 420   Number of girls in the school = 5*420/7= 
5*420/7 = 300
300   Answer is 300
Answer: C
If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {6, 7}, what is the probability that xy will be even?  Choose the correct choice from the following answers:
A) 1/6
B) 1/3
C) 1/2
D) 2/3
E) 5/6

Solution: Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 1/6   1/6nswer: 1/6
Answer: A
What is the probability that when a hand of 6 cards is drawn from a well shuffled deck of 52 cards, It contains 2 Queen?	Choose the correct choice from the following:
A) 1/23445	B) 113/22434	C) 29187by1017926	D) 1017926/29187	E) None of these

Solution: nCr = n!/(n-r)!r!   Total number of possible hands = 52C6   52C6 = (52!)/((52-6)! × 6!)   52C6 = 61075560.   Number of hands with 2 Queen and 4 non-Queen cards = 4C2 × 48C4   4C2 = (4!)/(2! × 2!) = 6.   4829187by10179264 = (48!)/(44! × 4!) = 3 × 47 × 46 × 45 = 291870   (other 2 cards must be chosen from the rest 48 cards)   P (2 Queen) = (429187by10179262 × 4829187by10179264)/5229187by10179266 = 29187/1017926   29187by1017926
Answer: C
Jake wants to invite 9 friends to his 8th birthday party. Each invitation requires 2 stamps to mail, costing 12 cents each. How much will Jake have to spend on stamps to send invitations to his 9 friends? Select:
A) $1.08
B) $1.41
C) $1.74
D) $1.98
E) $2.16

Solution: 2 stamps multiplied by 12 cents = 24 cents per invitation. 24 cents multiplied by 9 invitations = 216 cents = $2.16, hence answer : $2.16.
Answer: E
A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? Choose the correct option
A) 28%
B) 20%
C) 22%
D) 16%
E) 27%

Solution: 900 ---- 180   100 ---- ? => 20%   Answer: 20%
Answer: B
Find the angle between the hour and the minute hand of a clock when the time is 3.25.	Pick one.
A) 47.5	B) 47.9	C) 47.1	D) 47.3	E) 47.6

Solution: Formula : θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|   47.5ngle = 11/2 × 25 – 30×3 = 95/2= 
95/2 = 95/2 = around 47.5
47.5   47.5nswer:47.5
Answer: A
The cost price of 21 articles is equal to selling price of 18 articles.find gain or loss percentage.
Options.
A) 45/3%  B) 10/3%  C) 40/3%  D) 20/3%  E) 50/3%

Solution: Cost Price of each article be Rs 1   Cost Price of 18 articles =Rs18 ,selling price of 18 articles =Rs 21.   Gain%=[(3/18)*100]%=50/3%   Answer is 50/3%.
Answer: E
X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work? Select.
A) 3	B) 5	C) 6	D) 7	E) 9

Solution: Work done by X in 1 day = 1/18   Work done by Y in 1 day = 1/15   Work done by Y in 10 days = 10/15 = 2/3   Remaining work = 1 – 2/3 = 1/3   Number of days in which X can finish the remaining work = (1/3) / (1/18)= 
(1/3) / (1/18) = 6
6   6
Answer: C
The number of arrangements that can be made with the letters of the word PETER so that the vowels occupy the even places?
Choose one.
A) 18  B) 20  C) 40  D) 12  E) 14

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 3! i.e., 24 ways.   Hence the total ways are  2 * 6= 
 2 * 6 = 12
12.   Answer:12
Answer: D
Jerry went to a shop and bought things worth Rs. 45, out of which 30 % went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Choose the correct option
A) 19	B) 19.7	C) 21.3	D) 29.5	E) 39.7

Solution: Total cost of the items he purchased = Rs.45   Given that out of this Rs.45, 30 % is given as tax   => Total tax incurred = 30 % = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (45−30/100−x)6/100 = 30/100   ⇒ 6(45 −0.3 −x) = 30   ⇒ (45 − 0.3 − x) = 5   ⇒ x = 45 − 0.3 − 5 = 39.7   39.7)
Answer: E
A box contains 10 tablets of medicine A and 16 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.
Choices:	A) 12	B) 15	C) 17	D) 18	E) 21

Solution: The worst case scenario will be if we remove all 16 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of   16+2= 
  16+2 = 18
18 tablets.   Answer:18.
Answer: D
The number 189 is equal to the sum of the cubes of two integers. What is the product of those integers?
Choose the correct choice from the following answers.
A) 8  B) 15  C) 20  D) 27  E) 39

Solution: 4^3+ 5^3= 189 the number is 4*5= 
4*5 = 20
20   20
Answer: C
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 25 miles behind the slower one. How far apart are the two trains at 5 o'clock?	Select the correct option:
A) 60 miles  B) 80 miles  C) 90 miles  D) 65 miles  E) 400 miles

Solution: Answer = D. 65 miles   Relational speed = 130 - 100= 
130 - 100 = 30
30 miles per hour   In 3 hours, difference= 30 * 3= 
30 * 3 = 90
90 miles   Fast train trailing 25 miles, so effective difference= 90 - 25= 
90 - 25 = 65
65 miles
Answer: D
A shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set? Pick:	A) 1/7	B) 1/4	C) 5/14	D) 11/28	E) 27/28

Solution: 2/8 * 1/7 = 2/56   1-(2/56) = 54/56 = 27/28   Answer 27/28
Answer: E
For positive integers x and z, which of the following can be written as z^2? Choose the correct choice
A) x^2+1  B) x^2-1  C) x^2-24  D) x^2+11  E) x^2-11

Solution: Plug values: if x=6, then 6^2-11=25   The question asks which of the following CAN be written as z^2. If x=6, then x^2-11 CAN be written as 5^2.   Answer: x^2+11
Answer: D