MU-NLPC/Calc-aqua_rat huggingface dataset:
Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is	Choose the most appropriate option.
A) 1/5  B) 1/7  C) 1/0  D) 1/2  E) 1/3

Solution: A leap year has 52 weeks and two days   Total number of cases = 7   Number of favourable cases = 1   i.e., {Saturday, Sunday}   Required Probability = 1/7   Answer:1/7
Answer: B
The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 70
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
Choose one: A) 51 B) 88 C) 90 D) 125 E) 108

Solution: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics   No. of total students = 70 + (35-15) + (40-10-12) = 70+20+18= 
70+20+18 = 108
108   Hence, Answer will be 108.
Answer: E
A can do a work in 4 days. B can do the same work in 12 days. If both A & B are working together in how many days they will finish the work? Choose the correct option:	A) 3	B) 5	C) 4	D) 2	E) 6

Solution: 3 rate = 1/4   B rate = 1/16   (3+B) rate = (1/4)+(1/12) = 1/3   3 & B finish the work in 3days   correct option is 3
Answer: A
In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 20 per square m?
Choose the correct choice from the following options:
A) s.43000  B) s.19000  C) s.57000  D) s.60000  E) s.62000

Solution: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m   Total area of the hall to be covered with mat = 2(lb + bh + hl)   = 2(20 * 15 + 15 * 5 + 5 * 20)   =2(300 + 75 + 100)   = 2 * 475= 
2 * 475 = 950
950 sq. m   Total expenditure= 20 * 950   = Rs.19000   s.19000
Answer: B
The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary? Choose the correct choice:
A) 2277  B) 2999  C) 1000  D) 2651  E) 1971

Solution: X * (110/100) * (95/100) = 1045   X * (11/10) * (1/100) = 11   X = 1000   Answer: 1000
Answer: C
Convert the following unit:
4 hectares in mÂ² Pick:
A) 50000 mÂ²  B) 40000 mÂ²  C) 60000 mÂ²  D) 45000 mÂ²  E) 55000 mÂ²

Solution: 4 hectares in mÂ²   1 hectare = 10000 mÂ²   Therefore, 4 hectares = 4 Ã— 10000 mÂ²   = 40000 mÂ²   ANSWER : OPTION 40000 mÂ²
Answer: B
When 242 is divided by a certain divisor the remainder obtained is 6. When 698 is divided by the same divisor the remainder obtained is 13. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 5. What is the value of the divisor?  Choose the correct answer:
A) 11 B) 14 C) 18 D) 23 E) None of these

Solution: let that divisor be x   since remainder is 6 or 13 it means divisor is greater than 13.   now  242-6= 
 242-6 = 236
236=kx (k is an integer and 234 is divisble by x)   similarly  698-13= 
 698-13 = 685
685= lx (l is an integer and 689 is divisible by x)   adding both 698 and 242   = (236+685)+6+13   =x(k+l) + 19   when we divide this number by x then remainder will be equal to remainder of (19 divided by x) = 5 hence x = 19-5= 
19-5 = 14
14   hence 14
Answer: B
Robinson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded? Choose the correct choice from the following answers:
A) 0.49
B) 0.52
C) 0.48
D) 0.6
E) 0.45

Solution: probability of adams approval = 0.7   baker approval =0.5   corfu approval=0.4   proabability of approval is must adam approval and atleast one approval   = adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+   adam approval*baker not approval*coffu approval( atleast one remaining approval   = 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4   =0.14+0.21+0.14= 
0.14+0.21+0.14 = 0.49
0.49   0.49
Answer: A
In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 112 of the workers of that company are men, how many of the workers are women?
Choose the correct answer:
A) 80
B) 98
C) 105
D) 120
E) 210

Solution: Set up equation:   x = total number of workers   112 = 0,4 * 2/3 * x + 0,8 * 1/3 * x   112 = 16/30 x   x = 210   210 - 112= 
210 - 112 = 98
98   Answer 98
Answer: B
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?	Select the correct option:
A) 17 hours B) 95 hours C) 14 hours D) 19 hours E) 18 hours

Solution: Part filled in 2 hours = 2/6 = 1/3.   Remaining part = 1 - 1/3 = 2/3   (A + B)'s 1 hour work = 2/21   C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]   = (1/6 - 2/21) = 1/14   C alone can fill the tank in 14 hours.   Answer:14 hours
Answer: C
Of the 6 distinguishable wires that lead into an apartment, 2 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?	Choose the correct choice from the following options:
A) 6 B) 7 C) 8 D) 9 E) 10

Solution: Given:   Total number of wires = 6   Number of cable wires = 2   Number of telephone wires = 3   To find:   Number of combination which has at least one cable wires   Solution:   No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2   Since it is a combination of wires, the arrangement is not important   Approach 1:   Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)   Selection 1   Number of ways of selecting one cable wire = 281 = 2   Number of ways of selecting 2 telephone wires = 382 = 3   Total = 281 * 382 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in 8ombinatorics)   Selection 2   Number of ways of selecting one cable wire = 282 = 1   Number of ways of selecting 2 telephone wires = 381 = 3   Total = 282 * 381 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in 8ombinatorics)   Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire   Approach 2   Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)   Total number of ways of selecting 3 wires out of 5 = 582 = 10   Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 383 ( 3 telephone wires and we are selecting all the three at once) = 1   Selection X - Selection Y = 8   Answer is Option 8
Answer: C
What will be the fraction of 12%
Pick one.
A) 1/20 B) 1/50 C) 1/75 D) 3/25 E) None of these

Solution: Explanation:   12*1/100 = 3/25.   Option 3/25
Answer: D
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area n square inches. Which of the following equations must be true?  Choose the correct choice from the following choices:	A) w^2 + pw + n = 0	B) w^2 - pw + 2n = 0	C) 2w^2 + pw + 2n = 0	D) 2w^2 - pw - 2n = 0	E) 2w^2 - pw + 2n = 0

Solution: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.   Now, assume:   Width =w = 1 inchand length = 1 inch;   Perimeter =p = 4 inches;   Area =n = 1 square inches.   Plug the values of w, p, and n into the answer choices: only for E 2w^2 - pw  + 2= 
 + 2 = 2
2 - 4 + 2= 
2 - 4 + 2 = 0
0.   Answer: 2w^2 - pw + 2n= 0.
Answer: E
A dishonest milkman sells a 40 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 10 liters of the mixture and replaces it with an equal amount of milk. He then takes out 20 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?
Choices:
A) 2:5  B) 3:5  C) 2:3  D) 3:2  E) 7:13

Solution: ............................... Milk ............... Water ....................... Total   Initial ...................... 24 .................... 16 .............................. 40   10 Lts mix. taken out 24-6 ............... 16-4 ........................... 40-10   10 Lts milk added..... 18+10 ................ 12 .............................. 40   20 Lts mix. taken out 28-14 ............... 12-6 ........................... 40-20   20 Lts water added..... 14................ 6+20 .............................. 40   New ratio = 14:26 = 7:13   7:13
Answer: E
How many positive integers less than 5,000 are evenly divisible by neither 16 nor 21? Choose the correct option
A) 4,514	B) 4,475	C) 4,521	D) 4,428	E) 4,349

Solution: integers less than 5000 divisible by 16 5000/16 =333.something , so 333   integers less than 5000 divisible by 21 5000/21 = 238.## , so 238   we have double counted some, so take LCM of 16 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 16 and 21 = 333 +238 -47= 
333 +238 -47 = 524
524   now subtract that from 4999. 4999- 524= 4514 answer 4,514.
Answer: A
A special municipal payroll tax charges not tax on a payroll less than $250,000 and only 0.1% on a company’s payroll above $250,000. If Belfried Industries paid $200 in this special municipal payroll tax, then they must have had a payroll of Choose the correct choice from the following options.
A) $450,000  B) $202,000  C) $220,000  D) $400,000  E) $2,200,000

Solution: ANSWER : A , ( with different approach) :   The 200 paid is 0.1% of the additional amount above 250,000. Let it be X   Now 0.1% of X = 200   Therefore X= 200,000   Total = 250,000 + X= 450,000
Answer: A
If (m-8) is a factor of m^2-qm-24, then q=
Select the correct option.
A) 3 B) 5 C) 6 D) 11 E) 16

Solution: (m-8)(m-a)=m^2-qm-24   A=-3   q=8+a=5=5
Answer: B
At a special sale, 6 tickets can be purchased for the price of 3 tickets. If 6 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 6 tickets?	Choose the correct choice from the following:
A) 20%
B) 33.3%
C) 40%
D) 50%
E) 66.6%

Solution: let the price of a ticket be Rs.100, so 3 tickets cost 300 & 6 tickets cost 600   6 tickets purchased at price of 3 tickets ie., for 300, so amount saved s Rs.300,   % of 6 tickets = (300 /600)*100= 
(300 /600)*100 = 50
50 %   ANSWER:50%
Answer: D
X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 3. If X invested Rs. 40,000, the amount invested by Y is
Choose the correct choice from the following answers:	A) 33488	B) 63809	C) 60000	D) 37887	E) 77824

Solution: Explanation:   Suppose Y invested Rs. y. Then 40000/y = 2/3 or y = 60000 .   Answer: 60000) 60000
Answer: C
There are 100 students in a college class of which 36 are boys studying Tamil & 13 girls not studying Tamil. If there are 55 girls in all, then the probability that a boy picked up at random is not studying Tamil, is	Choose one:	A) 1/5	B) 2/3	C) 3/5	D) 4/7	E) 7/11

Solution: There are 55 girls and 45 boys in the college. Out of 45 boys, 36 are studying Tamil and 9 are not studying Tamil. The probability that a boy picked up at random is not studying Tamil= 9/45 = 1/5   1/5
Answer: A
If the three points A, B and C with the coordinates (4, 2), (3, 1) and (2, a) respectively lie on a line, what is the value of a?
Options.
A) 0	B) 1	C) 2	D) 3	E) 4

Solution: The Line will have the same slope irrespective of which two points are taken into account   i.e. Slope of Line using Points (4, 2), (3, 1) = Slope of Line using Points (4, 2), (2, a)   CONCEPT: Slope between two points (a, b) and (c, d) = (d-b)/(c-a)   i.e. (1-2)/(3-4) = (a-2)/(2-4)   i.e. (a-2) = -2   i.e. a = 0   0nswer: option 0
Answer: A
In how many ways CM and Minister be elected from a team of 12 members?  Choose the correct option
A) 128 B) 130 C) 132 D) 139 E) 142

Solution: To do this, if captain is elected first, then we have 12 ways of doing this.   For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 12*11= 
12*11 = 132
132 ways.   132
Answer: C
When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 2/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?	Pick
A) 3/10 B) 2/5 C) 1/2 D) 4 E) 6/5

Solution: Say, the tree grows by x feet every year.   Then, 4 + 6x = (1+2/5)(4+4x)   or, x = 4   Answer 4
Answer: D
A man whose speed is 3.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Pick:
A) 2.0kmph
B) 2.3kmph
C) 2.85kmph
D) 3.0kmph
E) 3.3kmph

Solution: M = 3.5   S = 1.5   DS = 5   US = 2   AS = (2 * 5 * 2) /7 = 2.85   Answer:2.85kmph
Answer: C
If A:B = 1/4: 1/6 B:C = 1/4:1/6 then A:B:C?  Options:	A) 12:14:16	B) 36:24:18	C) 12:24:36	D) 36:24:16	E) 12:36:42

Solution: A:B = 1/4:1/6 = 6:4   B:C = 1/4:1/6 = 6:4   --------------------   A:B:C = 36:24:16   Answer: 36:24:16
Answer: D
The simple interest on 200 for 7 months at 5 paise per rupee per month is
Choose the correct option
A) 70	B) 7	C) 35	D) 30.5	E) None of these

Solution: ∵ Rate = 5 paise per rupee = 5%   ∴ S.I. = 200×5×7/100=70   70nswer 70
Answer: A
A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ? Choose the correct choice from the following.
A) 4 B) 8 C) 12 D) 24 E) 26

Solution: Explanation:   Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.   Answer: 24
Answer: D
Local trains leave from a station at an interval of 14 minutes at a speed of 36 km/h. A man moving in the same direction along the road meets the trains at an interval of 18 minutes. Find the speed of the man.	Choose the correct option:
A) 8 km/h	B) 7 km/h	C) 6 km/h	D) 5.8 km/h	E) None of these

Solution: Let speed of man = S km/h. Then,   36 × 14⁄60 = 18⁄60[36 - S] ⇒ 36 – S = 28 ⇒ S = 8 km/h.   8 km/hnswer 8 km/h
Answer: A
For rs 600 Mr. Karan can buy a max of 24 cups of tea and for rs 1500 he can buy a maximum of 15 cups of coffee. He has 2200 in his pocket and purchase 8 cups of tea what is the max no of cups of coffee he can purchase with the remaining money? Choose the correct option.
A) 20	B) 30	C) 40	D) 50	E) 60

Solution: Explanation:   Let X = Rate of 1 cup of tea.   And Y = Rate of 1cup of coffee.   And Z = Max no of cups of coffee he can purchase with the remaining money.   From question we have,   X = 600/24= 
600/24 = 25
25.   and Y= 1500/15= 
1500/15 = 100
100.   So acc. to the question,=> 8X + ZY = 2200   => 8(25) + 100Z = 2200   => 200 + 100z = 2200   => Z = 20.   20NSWER IS 20
Answer: A
In one hour,a boat goes 21 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is : Select.
A) 3 B) 5 C) 10 D) 9 E) 15

Solution: Solution   Speed in still water =1/2(21+9)kmph.= 15 kmph. Answer 15
Answer: E
A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 300 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?  Choose the correct choice from the following choices:
A) 300
B) 320
C) 330
D) 340
E) 290

Solution: 300nswer 300   300 * T = 1 km => T = 1/360 km/h   V*(T+2/3600) = 1   V (1/360 + 2/3600) = 1 => V = 300 km/h
Answer: A
A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $52500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?  Choose the correct choice from the following: A) 7 B) 6 C) 9 D) 10 E) 15

Solution: Since the starting point is given as the $4000 scholarship,   7ssume $4000 scholarships to be x   By the given information, $2500 scholarships = 2x   and $1250 scholarships = 6x   Gievn: Total $1250 scholarships = $52500   6x*1250 = 52500   Solve for x = 7   Option 7
Answer: A
In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 3/4 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and curved  Pick one:  A) 1/8  B) 1/6  C) 1/4  D) 3/4  E) 7/8

Solution: Good question.   So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).   We're told that 3/4 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/4 are yellow. We're also told there is an equal probability of straight or curved, 1/2.   We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).   So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(curved) = 1/4 * 1/2 = 1/8, or 1/8.
Answer: A
The angles of a triangle are in the ratio 1:3:8. Find the measurement of the three angles of triangle.	Options:	A) 100°	B) 110°	C) 120°	D) 140°	E) 160°

Solution: If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence   x + 3x + 8x = 180   Solve for x   12x = 180   x = 15   The measures of the three angles are   x = 15°   3x = 3 × 15 = 45°   8x = 8 × 15 = 120°   120°
Answer: C
If the first day of a year (other than leap year) was Friday, then which was the last day of that year?
Choose the correct choice from the following choices
A) Saturday
B) Friday
C) Tuesday
D) Monday
E) None of these

Solution: Explanation :   Given that first day of a normal year was Friday   Odd days of the mentioned year = 1 (Since it is an ordinary year)   Hence First day of the next year = (Friday + 1 Odd day) = Saturday   ? Last day of the mentioned year = Friday   Answer : Option Friday
Answer: B
A man in a train travelling at 28km/hr notices that a train going in the opposite direction passes him in 12 sec.If the length of this train is 210m find its speed .	Choose the correct option.
A) 35 km/hr  B) 40 km/hr  C) 50 km/hr  D) 60 km/hr  E) 70 km/hr

Solution: relative speed of trains = 210/12 mtrs/sec = 210*18/(12*5)= 
210*18/(12*5) = 63
63 km/hr   speed of 2nd train= 63-28= 
63-28 = 35
35 km/hr   35 km/hrNSWER:35 km/hr
Answer: A
The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is
Choose one
A) 35.2  B) 36.1  C) 36.2  D) 36.4  E) None

Solution: Solution   Correct sum= (36x50+43-23)   = 1820.   âˆ´ Correct mean= 1820 / 50   = 36.4.   Answer 36.4
Answer: D
Sum of the local value and the face value of 4 in the numeral 153489216 is	Choose the correct answer:
A) 40004 B) 4004 C) 4000004 D) 400004 E) 44

Solution: (Local value of 4) + (Face value of 4) = (400000 + 4)= 
(400000 + 4) = 400_004
400004   400004
Answer: D
Two numbers N and 16 have LCM = 48 and GCF = 8. Find N. Choose the correct answer:
A) 12
B) 32
C) 24
D) 46
E) 57

Solution: The product of two integers is equal to the product of their LCM and GCF. Hence.   16 * N = 48 * 8   N = 48 * 8 / 16= 
48 * 8 / 16 = 24
24   correct answer 24
Answer: C
Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit? Pick one.
A) Rs.2329
B) Rs.2380
C) Rs.2329
D) Rs.2320
E) Rs.2328

Solution: Kamal : Sameer = (9000 * 12) : (8000 * 7)   = 108:56 = 27:14   Sameer's share = 6970 * 14/41 = Rs.2380.   Answer: Rs.2380
Answer: B
P(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point P?	Pick:
A) (1, 2).  B) (2, 0)  C) (0, -2)  D) (-2, 0)  E) (2, 2)

Solution: circle x^2+y^2=4 cuts line y2+  2= 
2+  2 = 4
4 cuts line y=x+2.   so intercept will be x^2+(x+2)^2=4   x(x+1)=0,   x=0 or x=-1.   in the options only c has x=0.   ANSWER:(0, -2)
Answer: C
If one positive integer is greater than another positive integer by 3, and the difference of their cubes is 279, what is their sum? Options
A) 5
B) 7
C) 9
D) 11
E) 13

Solution: 1^3 = 1   2^3 = 8   3^3 = 27   4^3 = 64   5^3 = 125   6^3 = 216   7^3 = 343   The two numbers are 4 and 7.   The answer is 11.
Answer: D
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 {5, 6, 7, 8}, what is the probability that xy will be even?
Options
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 = 1/2.   Answer: 1/2.
Answer: C
How many different 4 digit numbers can be formed from the number 1234 by re-arranging its digits so that the odd digits occupy even position
Pick one
A) 2  B) 8  C) 4  D) 7  E) 3

Solution: There are 2 odd numbers which have to be placed at 2 even places =2!=2 ways   There are 2 even numbers which have to be placed at 2 odd places. So 2! = 2 ways   so total number of ways of arranging all these numbers are  2 * 2= 
 2 * 2 = 4
4 ways   Answer:4
Answer: C
2 men and 2 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)	Choose the correct choice from the following answers.
A) 4 B) 15 C) 18 D) 21 E) 24

Solution: The list should be WMWMW. Hence, from women 2! And men 2!, we get (2!)(2!)=4. Therefore, the correct answer is 4.
Answer: A
How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5? Pick one
A) 6  B) 7  C) 8  D) 9  E) 10

Solution: The numbers should be of the form 5c+3.   The minimum is 3 when c=0.   The maximum is 48 when c=9.   There are 10 such numbers.   The answer is 10.
Answer: E
In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 284. What is the sum of all the integers in the sequence?  Choose the correct choice from the following options
A) 552
B) 568
C) 574
D) 586
E) 600

Solution: let the first term of the sequence be x   since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms)   now,   sum of first 4 terms =284   or,   4x+12=284   x=272/4= 
272/4 = 68
68   Thus the answer can now be calculated by either summing up 68+70+72+... 8th term   or   s=n/2(2a+(n-1)d   =8/2(2*68+(7*2))   =4(136+14)=600   600
Answer: E