MU-NLPC/Calc-aqua_rat huggingface dataset:
The speed of a bus increases by 2 kmph after every one hour. If the distance travelled in the first one hour was 35 km, what was the total distance travelled in 12 hours?	Choose one:
A) 550 B) 500 C) 552 D) 560 E) 580

Solution: Dist 1st hr = 35 km   speed of bus by 2 kmph 2nd hr = 37 km   3rd hr = 39 km   tot = 35+37+39+....(12 terms)   12/2(2*35+(12-1)2]   =6*92= 
6*92 = 552
552   ANSWER 552
Answer: C
A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet) Choices: A) 9/(25xy) B) xy/225 C) 225/(xy) D) 225xy E) 25xy/9

Solution: The area of the carpet in feet is xy.   The area in square yards is xy / 9.   The price per square yard is 25 / (xy/9) = 225/(xy).   The answer is 225/(xy).
Answer: C
How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?	Select:  A) 9  B) 15  C) 32  D) 56  E) 72

Solution: Sol. The given word contains 5 different letters.   Taking the vowels EA together, we treat them as one letter.   Then, the letters to be arranged are XTR (EA).   These letters can be arranged in 4! = 24 ways.   The vowels EA may be arranged amongst themselves in 2! = 2 ways.   Number of words, each having vowels together = (24x2) = 48 ways.   Total number of words formed by using all the letters of the given words   = 5! = (5x4x3x2x1) = 120.   Number of words, each having vowels never together = (120-48)= 
(120-48) = 72
72.   Ans: 72
Answer: E
The probability that B can shoot a target two out of two times is 0.5. What is the probability that the target will be missed by B immediately after such two shots? Select
A) 0.25	B) 0.5	C) 0.75	D) 0.4	E) 0.8

Solution: Suppose there are total 'x' shots.   B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.   therefore, 2/x = 0.5 (given)   the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.   thus, the probabilty of missing just after 2 shots is (x-2)/x.   (x-2)/x = 1 - 2/x   = 1 - 0.5= 
1 - 0.5 = 0.5
0.5   Answer : 0.5
Answer: B
In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 12 is
Choose one
A) 8	B) 12	C) 16	D) 1296	E) 24

Solution: I've never seen such kind of question in GMAT before.   OK there can be 4 cases:   |x+y| + |x-y| = 12   A. x+y+x-y = 12 --> x=6   B. x+y-x+y = 12 --> y=6   C. -x-y +x-y= 12 --> y=-6   D. -x-y-x+y=12 --> x=-6   The area bounded by 4 graphs x=6, x=-6, y=6, y=-6 will be square with the side of 4 so the area will be 36*36= 
36*36 = 1_296
1296   Answer:1296
Answer: D
In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?  Choices.
A) 200  B) 120  C) 245  D) 320  E) 147

Solution: (3 men out 6) and (2 ladies out of 5) are to be chosen.   Required number of ways = (6c3x5c2)   = [6x5x4/3x2x1] x [5x4/2x1] = 200.   200ns: 200
Answer: A
Statements: Government has spoiled many top ranking financial institutions by appointing bureaucrats as Directors of these institutions. Assumptions: 1) Government should appoint Directors of the financial institutes taking into consideration the expertise of the person in the area of finance. 2) The Director of the financial institute should have expertise commensurate with the financial work carried out by the institute.	Choose the correct choice from the following choices.
A) Only conclusion I follows  B) Only conclusion II follows  C) Either I or II follows  D) Neither I nor II follows  E) Both I and II follow

Solution: According to the statement, Government has spoiled financial institutions by appointing bureaucrats as Directors. This means that only those persons should be appointed as Directors who are experts in finance and are acquainted with the financial work of the institute. So, both I and II follow.   Both I and II follow
Answer: E
Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet? Select the correct option:
A) 12 sec	B) 3 sec	C) 4 sec	D) 10 sec	E) 5 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (45 + 72)*5/18= 
(45 + 72)*5/18 = 65/2 = around 32.5
32.5 mps.   The time required= d/s = 100/32.5 = 3 sec.   ANSWER:3 sec
Answer: B
At a particular pizza shop, a pizza can be created from any combination of 7 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?  Choose the correct answer:
A) 6  B) 35  C) 120  D) 450  E) 1050

Solution: Number of possible ways to select 1 type of spice = 7c1 = 7   Number of possible ways to select 2 types of cheese = 4c2 = 6   Number of possible ways to select 4 types of meat but without pepperoni and anchovies together   = Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together   = 7c4 - 5c2   =35 - 10= 
35 - 10 = 25
25   Possible ways to garnish the pizza are available to the customer= 7*6 * 25= 
7*6 * 25 = 1_050
1050   Answer 1050
Answer: E
If a and b are positive integers such that a/b = 3.98, which of the following must be a divisor of a?
Choose the correct choice from the following choices:	A) 67	B) 197	C) 91	D) 199	E) 42

Solution: 1) A and B are positive INTEGERS   2) A/B = 3.98   A = 398   B = 100   398/100= 
398/100 = 199/50 = around 3.98
3.98   These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...   A= 199   B = 50   199/50 = 2.86   There is no other way to reduce this fraction, so A must be a multiple of 199 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....   Since A is a multiple of 199, we have to 'factor-down' 199. This gives us only (199), excluding 1 itself. So this number MUST be a factor of A. You'll find the match in the answer choices.   Answer: 199
Answer: D
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?  Pick:  A) 180 m  B) 1870 m  C) 050 m  D) 150 m  E) 110 m

Solution: Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   Answer:150 m
Answer: D
50 is divided into two parts such that the sum of their reciprocals is 1/ 12.Find the two parts.	Choose one.
A) 27 and 23
B) 25 and 25
C) 10 and 40
D) 35 and 15
E) 30 and 20

Solution: Let the two parts be x and (50 - x).   Then, 1 / x + 1 / (50 – x) = 1 / 12 => (50 – x + x) / x ( 50 – x) = 1 / 12   => x2 – 50x + 600 = 0 => (x – 30) ( x – 20) = 0 => x = 30 or x = 20.   So, the parts are 30 and 20.   Answer is 30 and 20.
Answer: E
Calculate the amount that an investor needs to be invest to earn $1023 in interest in 24 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 12% compounded semi-annually?	Choices:
A) 3980	B) 3600	C) 3700	D) 3800	E) 3900

Solution: the approach is substitution,   our interest requirement is $1023 after 24 months, 2 compounding period.   calculate the compound interest on each option and find out the one that yields $1023 in 24 months   3900 yielded $1023   using the formula   A = P(1 + r/n)nt   hence answer is 3900
Answer: E
here's an easy question of averages, but let's try to see innovative ways of solving this.
A class has 12 boys and x girls. Average score of boys and girls is 80 and 92 respectively. the average of the whole class is 86, what is the value of x?
Options
A) a) 6
B) b) 7
C) c) 8
D) d) 10
E) e) 12

Solution: 12(80)+92x/12+x=86   960+92x/12+x=86   960+92x=86(12+x)   960+92x=1032+86x   X's one side, numbers one side we get,   92x - 86x=1032-960   6x=72   hence, x=12   Answer e) 12
Answer: E
Ranjit went to the market with Rs. 100. If he buys 3 pens and 6 pencils he uses up all his money. On the other hand, if he buys 3 pencils and 6 pens he would fall short by 20%. If he wants to buy equal number of pens and pencils, how many pencils can he buy?  Choose one
A) 222
B) 277
C) 267
D) 100
E) 221

Solution: Let price of a pen = x and pencil = y   3x + 6y = 100 ....(i)   and 6x + 3y = 125 ....(ii)   Adding (i) and (ii)   9(x + y) = 225   x + y = 25   multiply by 4   4x + 4y = 100   He can by 4 pens and 4 pencils in Rs. 100.   Answer:100
Answer: D
A movie buff buys movies on DVD and on Blu-ray in a ratio of 13:4. If she returns 2 Blu-ray movies, that ratio would change to 7:2. If she buys movies on no other medium, what was the original number of movies purchased?	Select the correct option
A) 22 B) 28 C) 77 D) 99 E) 119

Solution: Now coming to the process m(D) = 13x and b(D) = 4x   now from the next line the new eqn becomes 13x/ (4x -2) = 7/2   Solving it 26x = 28x -14   x =7   which means m (d) = 91 and b(d) = 28   SO total initially is m(d) + b(d) = 119   119
Answer: E
On a test, 15% of the students received an A, 60% of the remaining students received a below a B. What percentage of the students received a B?  Choose the correct choice:	A) 15% of the students received a B.	B) 60% of the students received a B.	C) 51% of the students received a B.	D) 66% of the students received a B.	E) None of these.

Solution: None of these.xplanation:Let total number of students be 100,Then, number of students who received an A = 15.Number of students receiving below a B = 60% of 85 = 51.Total number of students arriving alone = 100 – (15 + 51) = 34.Thus, 34% of the students received a B.Answer: Option None of these..
Answer: E
John tossed a fair coin 4 times. What is the probability that the coin landed heads up exactly twice?	Choose the correct choice from the following choices
A) 0.15	B) 0.25	C) 0.3	D) 0.35	E) 0.4

Solution: The probability is exactly same as the cion landed tail up once. That is 4*(1/2)^4 = 4/16 =0.25.   The answer is, therefore, (0.25).
Answer: B
A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement? Choices
A) 2777	B) 2565	C) 9877	D) 1900	E) 1557

Solution: 2000 ---- 54   2000 ---- 39   x ----- 20   x*20 = 2000*39   x = 3900   2000   -------   1900   Answer:1900
Answer: D
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections E of the 4 items can Amanda make? Pick one:
A) 9	B) 12	C) 14	D) 15	E) 60

Solution: Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?   3! / 1!2! * 6! / 3!3!   E=3*20= 
3*20 = 60
60   E. 60
Answer: E
Which of the following equations is NOT equivalent to 4a^2 = b^2 - 9 ?  Choose the correct choice from the following:  A) 4a^2 + 9 = b^2  B) 4a^2 - b^2 = -9  C) 4a^2= (b + 3)(b - 3)  D) 2a = b - 3  E) a^2 = (b^2-9)/4

Solution: 4a^2 = b^2 - 9   The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.   Looking at Answer D, we have....   2a = b - 3   While you COULD take the square root of both sides of the original equation, it's important to note that the square root of b^2 - 9 is NOT (b-3).   b^2 - 9 can be factored into (b-3)(b+3), but neither of these parentheses is the square root of b^2 - 9.   You can see the proof when you square either of the two parentheses:   (b-3)^2 = b^2 - 6a + 9   (b+3)^2 = Y^2 + 6a + 9   Thus, 2a = b - 3 is NOT equivalent to the prompt.
Answer: D
A basketball player succeeds with 70% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
Choose one
A) 0.952 B) 0.964 C) 0.973 D) 0.985 E) 0.992

Solution: P(missing all 3 free throws) = 0.3^3 = 0.027   P(succeeding at least once) = 1 - 0.027= 
1 - 0.027 = 0.973
0.973   The answer is 0.973.
Answer: C
A car takes 8 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Pick one:	A) 10Kmph	B) 45Kmph	C) 60Kmph	D) 55Kmph	E) 30Kmph

Solution: Time = 8   Distence = 540   3/2 of 8 hours = 8 * 3/2= 
8 * 3/2 = 12
12 Hours   Required speed= 540/12= 
540/12 = 45
45 Kmph   45Kmph)
Answer: B
Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 45 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
Choose the correct choice from the following:  A) 590 liters  B) 540 liters  C) 740 liters  D) 560 liters  E) 580 liters

Solution: 1/12 + 1/15 - 1/x   = 1/15   x = 12   12 * 45= 
12 * 45 = 540
540   Answer:540 liters
Answer: B
A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 850 in 4 years. The rate of interest per annum is?	Options
A) 2 1/2 %	B) 4%	C) 5%	D) 6 2/3 %	E) 6 1/4%

Solution: S.I. on Rs. 800 for 1 year = (850 - 800) = Rs. 50 Rate = (100 * 50)/(800 * 1) = 6 1/4%   ANSW6 1/4%R:6 1/4%
Answer: E
There are 133 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
Answers:
A) 10
B) 11
C) 12
D) 13
E) 14

Solution: IMO 12   Take each answer choice and substract it from 133 and the divided this with 11.   11
Answer: B
What is the place value of 7 in the numeral 7259  Choose the correct choice from the following choices:
A) A)2700
B) B)2800
C) C)2900
D) D)7000
E) E)3000

Solution: 7 * 1000= 
7 * 1000 = 7_000
7000   7000
Answer: D
Which is the least number that must be subtracted from 1856 so that the remainder when divided by 7, 12, 10 is 4?	Select
A) 168 B) 172 C) 182 D) 140 E) 160

Solution: First we need to figure out what numbers are exactly divisible by 7,12,10. This will be the set {LCM,LCMx2,LCMx3,...}   LCM(7,12,10) = 42*10= 
42*10 = 420
420   The numbers which will leave remainder 4 will be {420+4, 420x2 +4, ,...}   The largest such number less than or equal to 1856 is 420*4+4 or 1684   To obtain this you need to subtract 172.   172
Answer: B
A train 150 m long running at 72 kmph crosses a platform in 20 sec. What is the length of the platform?
Choose the correct answer.
A) 443 m	B) 354 m	C) 450 m	D) 350 m	E) 250 m

Solution: 250 m   250   250 m = 72 * 5/18= 
72 * 5/18 = 20
20= 400 â€“ 150 = 250
Answer: E
In a village of 2,700 people, 900 people are over 70 years old and 1200 people are female. It is known that 60 percent of the females are younger than 70 years old. If no one in the village is 70 years old, what is the probability that a person chosen at random is either a male or younger than 70 years old?	Choose the correct choice from the following answers.
A) 4/5 B) 5/7 C) 13/15 D) 37/45 E) 79/90

Solution: The number of people younger than 70 years old is   2700-900= 
  2700-900 = 1_800
1800   The number of females older than 70 years old is   0.4*1200= 
  0.4*1200 = 480
480   The number of males older than 70 years old is   900-480= 
  900-480 = 420
420   The number of people who are either male or younger than 70 is  1800+420= 
 1800+420 = 2_220
2220.   P(a person is younger than 70 or male)= 2220/2700 = 37/45   The answer is 37/45.
Answer: D
There are 2 sections A and B in a class, consisting of 60 and 70 students respectively. If the average weight of section A is 60kg and that of section B is 80kg, Find the average of the whole class?
Choose one:
A) 50.78kg
B) 49.32kg
C) 70.76kg
D) 69.15kg
E) 70.89kg

Solution: Total weight of 60+70 students = 60*60 + 70*80 = 3600+5600= 
3600+5600 = 9_200
9200/130= 70.76 kg   Answer is 70.76kg
Answer: C
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Choose the correct choice from the following options.
A) 65 Kmph  B) 70 Kmph  C) 72 Kmph  D) 75 Kmph  E) 78 Kmph

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   ANSWER:72 Kmph
Answer: C
Henry answered 3/5 of the questions he was given for homework in the first hour, 5/17 of the remaining questions in the second hour and the remaining x questions in the third hour where x is an integer. How many questions was Henry given for homework?	Choose the correct choice
A) x	B) (85/12)*x	C) (85/24)*x	D) (85/36)*x	E) (85/48)*x

Solution: Let Q be the number of homework questions.   Q = 3Q/5 + (5/17)(2Q/5) + x   Q = 51Q/85 + 10Q/85 + x   24Q/85 = x   Q = (85/24)*x   The answer is (85/24)*x.
Answer: C
If the population of a certain country increases at the rate of 10 person every 60 seconds, by how many persons does the population increase in 1 hour? Pick one:
A) 100	B) 200	C) 600	D) 800	E) 1000

Solution: Answer = 10 * 60(1 hour = 60 minutes)= 600   Answer = 600
Answer: C
252 can be expressed as a product of prime as Choose the correct option:
A) 2 x 2 x 3 x 3 x 7	B) 2 x 2 x 2 x 3 x 7	C) 3 x 3 x 3 x 3 x 7	D) 2 x 3 x 3 x 3 x 7	E) None

Solution: Solution   Clearly, 252 =2 x 2 x 3 x 3 x 7   2 x 2 x 3 x 3 x 7nswer 2 x 2 x 3 x 3 x 7
Answer: A
In a T.V. factory, an average of 62 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily avg for the month to 58 sets/day . The average production per day for day last 5 days is ?
Pick:  A) 35  B) 38  C) 48  D) 50  E) 52

Solution: Production during these 5 days = Total production in a month - production in first 25 days.   = 30 x 58 - 25 x 62   = 19   âˆ´ Average for last 5 days = 190 / 5= 
190 / 5 = 38
38   38
Answer: B
There are three departments having students 70,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
Select:	A) 73	B) 74	C) 75	D) 76	E) 77

Solution: WE NEED TO TAKE GCD WHICH IS 2   THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT   1) 70/2 = 35   2) 58/2 = 29   3) 24/2 = 12   TOTAL NO. OF MIN ROOMS REQ76 = 35+12+29= 
35+12+29 = 76
76   ANSWER:76
Answer: D
The cost of 16 apples and 8 mangos is $352 and the cost of 4 apples and 4 mangos is $96. Find the cost of each apple? Pick one
A) 40  B) 20  C) 30  D) 35  E) 28

Solution: B   20   Let the cost of each apple and mango be 'p' and 'q' respectively.   16p + 8q = 352 --- (1)   4p + 4q = 96   8p + 8q = 192 --- (2)   (1) - (2) => 8p = 160   => p = 20
Answer: B
If 0.4 of a number is equal to 0.06 of another number, the ratio of the numbers i
Pick one: A) 2 : 3 B) 3 : 4 C) 3 : 20 D) 20 : 3 E) None

Solution: Sol.   0.4A = 0.06 B ⇔ A / B = 0.06 / 0.40 = 6/40 = 3/20.   ∴ A : B = 3 : 20.   Answer 3 : 20
Answer: C
Population of a city in 20004 was 1000000. If in 2005 there isan increment of 10% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007  Choices.
A) 976374	B) 979923	C) 980241	D) 1036750	E) 1083875

Solution: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)   = P (1 + 10/100)(1 - 35/100)(1 + 45/100)   = 1036750   1036750
Answer: D
List all the even integers between 1 and 11. Find the lowest positive interger that can be divided by each of those numbers. Choose the correct choice from the following choices:	A) 120	B) 234	C) 231	D) 183	E) 123

Solution: The even numbers between 1 and 11 are 2,4,6,8,10,   To get the least positive integer that can be divided by each of these numbers 1,2,3,4,5,6,7,8,9,10 you calculate the lowest common denominator of all the numbers. Express each number as a product of their prime factors and multiply the set of prime numbers from each set with the highest exponent value.   LCM=2^3*3*5   The answer is 120)
Answer: A
jerry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving jerry a third of her cards. jerry plays next, and Michelle follows. Then the game ends. jerry ended up with 14 more cards than Michelle. How many cards did each player have originally?  Pick one:
A) 27	B) 30	C) 34	D) 36	E) 38

Solution: Game Michelle Jerry michelle   Initially 2727 assume   After game 1 1836   After game 2 3024   After game 3 2034   Now jerry has 14 cards more than Michelle.   So the answer is 27
Answer: A
Using all the letters of the word "ANOTHER", how many words can be formed, which begin with A and end with R?  Pick one
A) 80  B) 90  C) 110  D) 120  E) 100

Solution: There are seven letters in the given word.   Consider 7 blanks ....   The first blank and last blank must be filled with A and R all the remaining five blanks can be filled with the remaining 5 letters in 5! ways.   The number of words = 5! = 120.   ANSWER:120
Answer: D
In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. What is the length of the garden?  Choose the correct choice from the following answers:
A) 22 B) 24 C) 26 D) 28 E) 30

Solution: Between the 12 mango trees, there are 11 gaps and each gap has 2 meter length   Also, 1 meter is left from all sides of the boundary of the garden.   Hence, length of the garden = (11 × 2) + 1 + 1 = 24 meter   Answer is 24.
Answer: B
Each month a retailer sells 100 identical items. On each item he makes a profit of $30 that constitutes 16% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
Select the correct option.
A) 157
B) 213
C) 221
D) 223
E) 226

Solution: For this question, we'll need the following formula:   Sell Price = Cost + Profit   We're told that the profit on 1 item is $20 and that this represents 16% of the cost:   Sell Price = Cost + $20   Sell Price = $125 + $20   Thus, the Sell Price is $145 for each item. Selling all 100 items gives the retailer...   100($20) = $2,000 of profit   If the retailer offers a 5% discount on the sell price, then the equation changes...   5%(145) = $7.25 discount   $137.75 = $125 + $12.75   Now, the retailer makes a profit of just $12.75 per item sold.   To earn $2,000 in profit, the retailer must sell....   $12.75(X) = $2,000   X = 2,000/12.75   X = 156.8627 =157 items   157
Answer: A
A bag has 1, 3, 5, 7, 9,11 and 13 cm sticks. Find the probability that they they will form a triangle if 3
sticks are drawn?
Choices.
A) 13 / 35 B) 14 / 35 C) 1 / 2 D) 5 / 6 E) 5 / 5

Solution: Explanation :   Total Cases: =7C3=35   Favourable Cases: (3,5,7),(3,7,9),(3,9,11),(3,11,13),(5,7,9),(5,7,11),(5,9,11),(5,9,13),(5,11,13),   (7,9,11),(7,9,13),(7,11,13),(9,11,13)=total 13.   [Others are rejected because to form a triangle it is necessary that the sum of 2 small   sides must be greater than the third greatest side.]   Hence (A) is correct answer.   13 / 35nswer : 13 / 35
Answer: A
Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Answers.
A) 67 B) 26 C) 87 D) 26 E) 75

Solution: Average   = (76 + 65 + 82 + 67 + 85)/5   = 375/5= 
375/5 = 75
75.   Answer: 75
Answer: E