MU-NLPC/Calc-aqua_rat huggingface dataset:
Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.4 km respectively. The time taken by the slower train to cross the faster train in seconds is?  Choose the correct choice from the following choices.
A) 12	B) 77	C) 48	D) 99	E) 36

Solution: Relative speed = 60 + 90= 
60 + 90 = 150
150 km/hr.= 150 * 5/18 = 125/3 m/sec.   Distance covered = 1.10 + 0.4= 
1.10 + 0.4 = 1.5
1.5 km= 1500 m.   Required time = 1500 * 3/125= 
1500 * 3/125 = 36
36 sec.   Answer: 36
Answer: E
A boat covers a certain distance downstream in I hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph. what is the speed of the boat in still Water?  Pick one:
A) 12kmph  B) 13kmph  C) 15kmph  D) 16kmph  E) None

Solution: Solution   Let the speed of the boat in still water be x kmph. Then,   Speed downsteram	= (x + 3) kmph.   Speed upsteram	= (x - 3) kmph.   = (x+3)x1   = (x - 3)x3/2 kmph.   = 2x+6 = 3x-9   x= 15 kmph.   Answer 15kmph
Answer: C
How many integers k greater than 100 and less than 600 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
Select the correct option.
A) 40	B) 60	C) 70	D) 80	E) 90

Solution: Not sure if this is the shortest.. But this is how I did this   There are 8 sets of integers with hundreds and units digits exchanged that satisfies k + 99.   1. 102 | 201 (satisfies k+99, where k = 102)   2. 203 | 302 (satisfies k+99, where k = 203)   3. ...   4. 405 | 504   Each set has 10 such numbers.   1. 102 | 201 (still k+99 holds good)   2. 112 | 211   3. 122 | 221   4. 132 | 231   5. ...   6. ...   7. ...   8. ...   9. 182 | 281   10. 192 | 291   Therefore, 4 sets with 10 such number in each set will give 4 x 10 = 40 integers.   40
Answer: A
In a container there are two solutions; solution A and solution B in the ratio of 3 : 4. If 8 litres of solution A is added, the ratio becomes 11:12. What is the total quantity in the container after adding the extra 8 litres ?  Choose the correct option
A) 96 liters B) 104 liters C) 94 liters D) 92 liters E) 112 liters

Solution: Let Solution A : Solution B be = 3x : 4x.   (Solution A / Solution B) = (3x + 8) / 4x = 11 / 12 =11 / 12   36x + 96 = 44x => 8x = 96 => x = 12.   Solution A + Solution B = 3x + 8 + 4x = 32 + 8 + 48 = 92 liters   Option 92 liters
Answer: D
The simple interest on a sum of money will be Rs.600 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Choose the correct answer:
A) 1277	B) 2977	C) 1200	D) 2769	E) 1971

Solution: P --- 10 ---- 600   P --- 5 ----- 300   3P --- 5 ----- 900   ------   => 1200   Answer: 1200
Answer: C
How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?	Choose the correct option:	A) 50 sec	B) 16 sec	C) 31 sec	D) 26 sec	E) 25 sec

Solution: The distance to be covered = Sum of their lengths = 200 + 300= 
200 + 300 = 500
500 m.   Relative speed= 72 -36= 
72 -36 = 36
36 kmph= 36 * 5/18= 
36 * 5/18 = 10
10 mps.   Time required= d/s = 500/10= 
500/10 = 50
50 sec.   50 secnswer:50 sec
Answer: A
Jill has 35 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?	Choose one:	A) 3	B) 60	C) 9	D) 12	E) 14

Solution: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 35 1 3/4w = 35w=20The total number of jars = 3w =60Answer: 60
Answer: B
The digital sum of a number is the sum of its digits. For how many of the positive integers 24-90 inclusive is the digital sum a multiple of 7?	Choose the correct choice from the following answers.
A) 10	B) 8	C) 14	D) 16	E) 20

Solution: is there other way than just listing?   25   34   43   52   59   61   68   70   77   86   10 ways..   10
Answer: A
In a camp, there is a meal for 80 men or 200 children. If 135 children have taken the meal, how many men will be catered to with remaining meal? Choose the correct choice from the following answers
A) 41 B) 35 C) 26 D) 48 E) 49

Solution: C   26   There is a meal for 200 children.   135 children have taken the meal.   Remaining meal is to be catered to 65 children.   Now, 200 children 80 men.   65 children = (80 /200)x 65= 26 men.
Answer: C
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 18 seconds. Find the length of the faster train?  Answers.
A) 270	B) 277	C) 187	D) 180	E) 271

Solution: Relative speed = (72 - 36) * 5/18 = 2 * 5= 
2 * 5 = 10
10 mps.   Distance covered in 18 sec= 18 * 10= 
18 * 10 = 180
180 m.   The length of the faster train= 180 m.   Answer: 180
Answer: D
During a sale, a store sells 20 percent of its remaining stock each day, without replenishment. After four days, what fraction of its original stock has it sold?	Choose the correct choice from the following answers:
A) 1/625	B) 256/625	C) 61/125	D) 64/125	E) 369/625

Solution: Let's pick a smart number for the initial amount. The store sold 20 percent each day, hmm, after looking at the answer choices 625 is used pretty often, so let's pick it.   1st day: 125 items sold, 500 left   2nd day: 100 items sold, 400 left   3rd day: 80 sold, 320 left   4th day: 64 sold, 256 left   Sum The Sold Items=125+100+80+64= 
125+100+80+64 = 369
369−−>369/625   Answer 369/625
Answer: E
A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective. Choose the correct option.
A) 1/127 B) 1/191 C) 1/138 D) 1/132 E) 1/126

Solution: Out of nine, five are good and four are defective. Required probability   = ⁴C₄/⁹C₄ = 1/126   Answer: 1/126
Answer: E
From a group of 3 balls and 3 bats, 4 are to be randomly selected. What is the probability that equal numbers of balls and bats will be selected? Select
A) 1/5 B) 2/5 C) 4/5 D) 1 E) 3/5

Solution: Using the first example, here is the probability of THAT EXACT sequence occurring:   BBbb = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10   Each of the other 5 options will yield the exact SAME probability....   eg   BbBb = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10   So we have 6 different options that each produce a 1/10 chance of occurring.   6(1/10) = 6/10 = 3/5   Final Answer:   3/5
Answer: E
In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?  Pick:  A) 243  B) 255  C) 256  D) 287  E) 300

Solution: Andrew can select one or more than one of his 8 gang.   => Required number of ways = 28 – 1= 255.   255
Answer: B
A car travels at a speed of 60 miles per hour. How far will it travel in 5 hours?  Choices.
A) 425 miles  B) 625 miles  C) 300 miles  D) 225 miles  E) 625 miles

Solution: During each hour, the car travels 65 miles. For 5 hours it will travel   60 + 60 + 60 + 60 + 60 = 5 *65 = 300 miles correct answer 300 miles
Answer: C
The calendar for the year 2007 will be the same for the year	Answers:
A) 2017
B) 2018
C) 2014
D) 2016
E) None of these

Solution: Explanation :   For a year to have the same calendar with 2007 ,the total odd days from 2007 should be 0.   Year	2007	2008	2009	2010	2011	2012   Odd Days	1	2	1	1	1	2   Year	2013	2014	2015	2016	2017   Odd Year	1	1	1	2	1   Take the year 2014 given in the choice.   Total odd days in the period 2007-2013 = 5 normal years + 2 leap year   = 5 x 1 + 2 x 2 = 9 odd days   = 2 odd day (As we can reduce multiples of 7 from odd days which will not change anything)   Take the year 2016 given in the choice.   Number of odd days in the period 2007-2015 = 7 normal years + 2 leap year   = 7 x 1 + 2 x 2 = 11 odd days   = 4 odd days   (Even if the odd days were 0, calendar of 2007 will not be same as the calendar of 2016 because 2007 is not a leap year whereas 2016 is a leap year. In fact, you can straight away ignore this choice due to this fact without even bothering to check the odd days)   Take the year 2017 given in the choice.   Number of odd days in the period 2007-2016 = 7 normal years + 3 leap year   = 7 x 1 + 3 x 2 = 13 odd days   = 6 odd days   Take the year 2018 given in the choice.   Number of odd days in the period 2007-2017 = 8 normal years + 3 leap year   = 8 x 1 + 3 x 2 = 14 odd days   = 0 odd day (As we can reduce multiples of 7 from odd days which will not change anything)   Also, both 2007 and 2018 are not leap years.   Since total odd days in the period 2007-2017 = 0 and both 2007 and 2018 are of same type, 2018 will have the same calendar as that of 2007. Answer : Option 2018
Answer: B
The rate of increase of the price of sugar is observed to be two percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 18 per kg. The inflation rate for the years 1994 and 1995 are expected to be 6% each. The expected price of sugar on January 1, 1996 would be
Choose the correct choice from the following answers.
A) 20.99 B) 21.9 C) 25.4 D) 20.19 E) None of these

Solution: Explanation :   Increase in the price of sugar = (6+2)= 
(6+2) = 8
8%   Hence, price of the sugar on Jan 1, 1996=> (18 * 108 * 108)/( 100 * 100 ) = Rs 20.99.   20.99nswer : 20.99
Answer: A
If [P] denotes the least integer greater than or equal to P and [P] = 0, which of the following statements must be true?	Select the correct option: A) P = 0 B) -1 < P <= 0 C) 0 < P <= 1 D) -1 <= P < 0 E) 0 <= P < 1

Solution: The answer for this is 0 < = P < = 1   However it is not available in the options. The match to the above is-1 < P <= 0   Answer = -1 < P <= 0
Answer: B
A man can row 24 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of the stream? Options.
A) 6  B) 12  C) 18  D) 15  E) 20

Solution: Let man's rate upsteam be X kmph   Then his rate of downstream = 3X kmph   Rate still water = 1/2 (3X + X) = 2X   2X = 24   X = 12   Rate of upstream = 12   Rate of downstream = 36   Rate of stream 1/2 ( 36 - 12) = 12 kmph   Answer is 12.
Answer: B
Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a girl sitting at window seat in the slower train in 32 seconds. Find the length of the faster train ? Choose the correct choice from the following answers.
A) 170 m	B) 100 m	C) 270 m	D) 320 m	E) None of these

Solution: Explanation:   Relative speed = (72 - 36) x 5/18 = 2 x 5 = 10 mps.   Distance covered in 32 sec = 32 x 10 = 320 m.   The length of the faster train = 320 m.   ANSWER IS 320 m
Answer: D
If a man can cover 10 metres in one second, how many kilometres can he cover in 3 hours 45 minutes? Choose the correct choice from the following choices.
A) 288 B) 162 C) 145 D) 135 E) 130

Solution: 10 m/s = 10 * 18/5 kmph   3 hours 45 minutes = 3 3/4 hours = 15/4 hours   Distance = speed * time = 10 * 18/5 * 15/4= 
10 * 18/5 * 15/4 = 135
135 km.   Answer: 135
Answer: D
A certain fraction is equivalent to 2/5. If the numerator of the fraction is increased by 4 and the denominator is doubled, the new fraction is equivalent to 1/3. What is the difference of the numerator and denominator of the original fraction?
Pick one:
A) 49
B) 9
C) 28
D) 26
E) 21

Solution: x/y = 2/5 -> 1   (x+4)/2y = 1/3 -> 2   Divide 1 by 2 :   => 2x/(x+4) = 6/5   => 5x = 3x + 12   => x = 6   => y = 5/2 * 6= 
5/2 * 6 = 15
15   so x - y= 9   The answer is 9
Answer: B
A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number R of ways this can be done is: Answers
A) 122  B) 210  C) 216  D) 217  E) 225

Solution: We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.   We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.   For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.   Second step:   We have two set of numbers:   1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:   1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.   0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96   120+96= 
120+96 = 216
216=R   Answer: 216.
Answer: C
Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 120 percent of the sum paid to B, how much is B paid per week? Choose the most appropriate option.
A) Rs.130	B) Rs.140	C) Rs.150	D) Rs.250	E) Rs.280

Solution: Let the amount paid to A per week = x   and the amount paid to B per week = y   Then x + y = 550   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250)
Answer: D
wo passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Choose the most appropriate option.
A) 227
B) 444
C) 277
D) 298
E) 212

Solution: 1h ----- 5   ? ------ 60   12 h   RS = 16 + 21= 
16 + 21 = 37
37   T= 12   D = 37 * 12= 
37 * 12 = 444
444   Answer: 444
Answer: B
Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 49 years. The age of E is?
Choose the correct choice from the following answers:
A) 45  B) 47  C) 48  D) 49  E) 46

Solution: Solution   5 years ago average age of A,B,C,D = 45 years   => 5 years ago total age of A, B, C, D = 45 x 4 = 180 years   => Total present age of A, B, C, D = 180 + 5x4 = 200 years   If E's present age is x years = 200+x/5= 49   x=45 years. 45nswer 45
Answer: A
A luxury liner, Queen Marry II, is transporting several cats as well as the crew (sailors, a cook, and one-legged captain) to a nearby port. Altogether, these passengers have 16 heads and 45 legs. How many cats does the ship host?
Choose one
A) 3
B) 6
C) 9
D) 8
E) 7

Solution: a's +co +ca +cats = 16. sa's + 1 +1 +cats =16 or sa's +cats =14.   sa's(2) +2 +1 +cats*4 =45 sa's*2 +cats*4 = 42 or sa's +cats*2 =21 or 14-cats +cat*2 =21   then cats =7   7
Answer: E
When the positive integer k is divided by the positive integer n , the remainder is 11. If k/n = 61.2 , what is the value of n?
Choose the correct choice from the following choices.
A) 9  B) 20  C) 65  D) 70  E) 81

Solution: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:   We're told that K and N are both INTEGERS.   Since K/N = 61.2, we can say that K = 61.2(N)   N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.   With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)   Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH   Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.   Final Answer:   65
Answer: C
The surface area of a sphere is 4πR^2, where R is the radius of the sphere. If the surface area of sphere A is eight times as large as the surface area of sphere B, then the radius of sphere A is how many times the radius of sphere B? Pick:
A) 2  B) 2√2  C) 4  D) 2π  E) π·√8

Solution: R1 : Radius of sphere A   R2 : Radius of sphere B   As per question,4πR1^2=8∗4πR2^2   or R12=8∗R2^2   or R1 = 2√2R2. Hence, 2√2
Answer: B
A sum of Rs. 2717 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?  Choose the correct choice from the following answers.
A) 1642
B) 1672
C) 1632
D) 2789
E) 6386

Solution: (x*8*3)/100 = ((2717 - x)*3*5)/100   24x/100 = 40755/100 - 15x/100   39x = 40755 => x = 1045   Second sum = 2717 – 1045   =1672   Answer:1672
Answer: B
A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many Q ways can the test be completed if every question is unanswered? Options:
A) 24  B) 120  C) 625  D) 720  E) 1024

Solution: 5 choices for each of the 4 questions, thus total Q of 5*5*5*5 = 5^4 = 625 ways to answer all of them.   Answer: 625.
Answer: C
Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 20% vinegar, dressing P comprises what percentage of the new dressing?  Select the correct option
A) 60% B) 50% C) 40% D) 30% E) 20%

Solution: Let x be the percentage of dressing P in the new dressing.   0.3x + 0.1(1-x) = 0.20   0.2x = 0.10   x = 0.5 = 50%   The answer is 50%.
Answer: B
A small company reduced its faculty by approximately 13 percent to 195 employees. What was the original number of employees?  Choose the correct choice from the following
A) 182
B) 208
C) 220
D) 224
E) 302

Solution: If x is the original number of employees, then after 13% reduction in employees number is .87x   but we are given .87x = 195   x = 224   So the original number of employees is 224   Correct Answer - 224
Answer: D
A factory has a fixed cost of $43,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5, what is the number of items must be sold monthly for the factory to cover its cost exactly?
Answers.
A) 9,000
B) 14,000
C) 17,200
D) 22,500
E) 27,000

Solution: selling price - 17,200ost price = 2.5 so per unit profit =2.5   cost to recover =43000   no of items required = 43000/2.5= 
43000/2.5 = 17_200
17200   Answer: 17,200
Answer: C
85% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?	Answers:  A) (a) 15%  B) (b) 5%  C) (c) 10%  D) (d) 20%  E) (e) 25%

Solution: so 15% employees don't have VCD devices.   25% employees don't have MO   20% employees don't have ACs   15% employees don't have WM   Summ of employees that don't have some device = 15%+25%+20%+15% = 75% < 100%   So definitely at least 25% employees have 4 devices.   ans: (e) 25%15 +25 +20 +15= 
15 +25 +20 +15 = 75
75% < 100%   So definitely at least 25% employees have 4 devices.   ans: (e) 25%
Answer: E
There are 17 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station? Choose one:
A) 156  B) 167  C) 157  D) 342  E) 380

Solution: The total number of stations = 19   From 19 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 19P₂ ways.   ²⁰P₂ = 19 * 18= 
19 * 18 = 342
342.   Answer: 342
Answer: D
In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?  Choices
A) 5/21
B) 3/7
C) 4/7
D) 5/7
E) 16/21

Solution: # of selections of 2 out of 7 - C27=21C72=21;   # of selections of 2 people which are not siblings - C12∗C12C21∗C21 (one from first pair of siblings*one from second pair of siblings)+C12∗C13C21∗C31 (one from first pair of siblings*one from triple)+ C1^_2*C^1_3(one from second pair of siblings*one from triple) =4+6+6= 
4+6+6 = 16
16=4+6+6= 
4+6+6 = 16
16.   P=16/21   ANSW16/21R:16/21
Answer: E
Village X has a population of 78000, which is decreasing at the rate of 1200 per year. Village Y has a population of 42000, which is increasing at the rate of 800 per year .in how many years will the population of the two villages be equal? Choose the correct choice from the following choices.
A) 15
B) 19
C) 11
D) 18
E) 13

Solution: Let the population of two villages be equal after p years   Then, 78000-1200p=42000+800p   2000p=36000   p=18   Answer is 18.
Answer: D
Find the average of the series : 312, 162, 132, 147 and 122?  Choose the correct option.
A) 170
B) 175
C) 180
D) 185
E) 195

Solution: Average = (312 + 162 + 132 + 147+ 122)/5 = 875/5= 
875/5 = 175
175   ANSWER:175
Answer: B
In 1979 approximately 1/3 of the 38.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these passengers used Logan Airport that year?
Choose the correct choice from the following answers:
A) 18.6 B) 9.3 C) 6.2 D) 3.1 E) 1.6

Solution: number of   passengers using Kennedy airport = 38/3 =~12.67   Passengers using Miami airport = 12.67/2=~6.3   passengers using logan airport = 6.3/4 =~1.58   so 1.6
Answer: E
583 is related to 293 in the same way as 488 is related to
Choose the correct choice from the following choices:
A) 2338  B) 378  C) 277  D) 299  E) 271

Solution: Explanation:   Sum of digits of the first number is 2 more than the sum of digits of the second number.   Answer: 378) 378
Answer: B
When the positive integer k is divided by the positive integer n , the remainder is 13. If k/n = 81.2 , what is the value of n?
Choose the correct answer:	A) 9	B) 20	C) 55	D) 70	E) 81

Solution: Here's an approach that's based on Number Properties and a bit ofbrute forcemath:   We're told that K and N are both INTEGERS.   Since K/N = 81.2, we can say that K = 81.2(N)   N has tomultiply outthe .2 so that K becomes an INTEGER. With the answers that we have to work with, N has to be a multiple of 5. Eliminate A and E.   With the remaining answers, we can TEST THE ANSWERS and find the one that fits the rest of the info (K/N = 81.2 and K/N has a remainder of 11)   Answer B: If N = 20, then K = 1624; 1624/20 has a remainder of 4 NOT A MATCH   Answer C: If N = 55, then K = 4466; 4466/55 has a remainder of 11 MATCH.   Final Answer:   20
Answer: B
How many odd three-digit integers greater than 800 are there such that all their digits are different? Choose the correct answer:
A) 40 B) 56 C) 72 D) 81 E) 104

Solution: In the range 800 - 900:   1 choice for the first digit: 8;   5 choices for the third digit: 1, 3, 5, 7, 9 (as the number is odd);   8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.   1*5*8= 
1*5*8 = 40
40.   In the range 900 - 999:   1 choice for the first digit: 9;   4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's the first digit);   8 choices for the second digit: 10 digits - first digit - third digit= 8 digits.   1*4*8= 
1*4*8 = 32
32.   Total:  40+32= 
 40+32 = 72
72.   Answer: 72
Answer: C
Square M is inscribed in circle N. If the perimeter of M is 20, what is the circumference of N?	Pick one.
A) 33√ 2π
B) 2√ 2π
C) 6√ 2π
D) 7√ 2π
E) 5√ 2π

Solution: square forms two right angled triangles.   Any time we have a right angle triangle inside a circle, the hypotenuse is the diameter.   hypotenuse here = diagonal of the square = 5 sqrt(2) = diameter   => radius = 2.5 sqrt(2)   Circumference of the circle = 2pi r = 5 pi sqrt(2)   Answer is 5√ 2π.
Answer: E
Which of the following is non negative?	Answers:
A) (c-0.9)(c-1)	B) (c+1)(c-1)	C) (c-0.9)(c-0.9)	D) (c-0.9)(c+0.9)	E) c(c+1)

Solution: 5-sec approach:   C. (c-0.9)(c-0.9) = (c-0.9)^2. The square of a number is always non-negative.   Answer: (c-0.9)(c-0.9).
Answer: C