MU-NLPC/Calc-aqua_rat huggingface dataset:
Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?  Choices:
A) 2(10)
B) 2(9)
C) 3 * 2(8)
D) 3 * 2(9)
E) None of these

Solution: Explanatory Answer   When a coin is tossed once, there are two outcomes. It can turn up a head or a tail.   When 10 coins are tossed simultaneously, the total number of outcomes = 210   Out of these, if the third coin has to turn up a head, then the number of possibilities for the third coin is only 1 as the outcome is fixed as head.   We need to find out what happens to the remaining 9 coins?   The remaining 9 coins can turn up either a head or a tail. Each of the 9 coins has 2 possibilities.   Number of outcomes for the remaining 9 coins = 2(9)   ∴ the number of outcomes in which the 3rd coin turns a head = 1 * 2(9) = 2(9).   Choice 3 * 2(9)
Answer: D
How many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution?	Choose the correct option
A) 2  B) 4  C) 6  D) 10  E) 20

Solution: 3% sugar solution means that currently there are 1.5 Liters of sugar and this amount must be 5% of a reduced final amount (50-x)   1.5=0.05*(50-x)   0.05x=1   x=20   Answer 20
Answer: E
12*18*6 is the volume of some material. How many cubes of edge 3 can be insert into it?	Select:
A) 48	B) 49	C) 50	D) 51	E) 52

Solution: no. of such cubes = volume of material / volume of one cube    (12*18*6)/(3*3*3)= 
 (12*18*6)/(3*3*3) = 48
48   48NSWER:48
Answer: A
The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (10,0) and (10,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?  Answers.
A) 1/2
B) 1/3
C) 1/4
D) 1/5
E) 1/6

Solution: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.   The center of the rectangle is the point (5,2).   The slope of line passing through points (1,1) and (5,2) = (2-1)/(5-1) = 1/4   The answer is 1/4.
Answer: C
A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(10)?	Choose the correct answer
A) 89/55
B) 91/57
C) 93/59
D) 95/61
E) 97/63

Solution: 89/55(n+1)=1+(1/89/55(n))   89/55(1) = 1   89/55(2) = 2   89/55(3) = 3/2   89/55(4) = 5/3   89/55(5) = 8/5   89/55(6) = 13/8   89/55(7) = 21/13   89/55(8) = 34/21   89/55(9) = 55/34   89/55(10) = 89/55   The answer is 89/55.
Answer: A
Eleven people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?	Choose the correct option
A) 1/10	B) 1/9	C) 1/8	D) 11/10	E) 10/9

Solution: Let P = total cost of the rental van.   The original share per person is P/11.   The new share per person is P/10.   P/10 = P/11 * 11/10 = (1 + 1/10)*original share   The answer is 1/10.
Answer: A
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 6 different offices?
Pick one
A) 501
B) 60
C) 117
D) 110
E) 216

Solution: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 6*6*6=6^3=216.   Answer: 216.
Answer: E
Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71 ___?	Choose the correct choice from the following
A) 35	B) 36	C) 37	D) 84	E) 99

Solution: The numbers increase at a somewhat steady rate, so you have to figure out how much   you have to add to each number to produce the next in the sequence:  3 + 5= 
 3 + 5 = 8
8; 8 + 6= 14;    14 + 7= 
 14 + 7 = 21
21; 21 + 8= 29, and so on. The rule for the sequence is to add successively larger   numbers to each number; therefore, the next number is   71 + 13= 
  71 + 13 = 84
84.   correct answer 84)84
Answer: D
The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?	Answers:	A) 5100	B) 5120	C) 5200	D) 5400	E) 5500

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8000 × 80/100 × 80/100 = 5120   5120)
Answer: B
A bat is bought for Rs.200 and sold at a gain of 20% find its selling price Pick:
A) A)Rs.460/- B) B)Rs.270/- C) C)Rs.280/- D) D)Rs.240/- E) E)Rs.520/-

Solution: 100 % ------> 200 (100 * 2 = 200)   120 % ------> 240 (120 * 2 = 240)   Selling price = Rs.240/-   Answer : Rs.240/-
Answer: D
To reach her destination, Jeanette must drive 90 miles. If she drives 3 miles every 7 minutes, how much time will it take her to reach her destination?	Choose one
A) 2 hours and 2 minutes B) 54 minutes C) 2 hours and 10 minutes D) 2 hours and 12 minutes E) 2 hours and 15 minutes

Solution: 3 minute for 5 miles how much for 90? minutes for 1(3/5) mile multiplied by 90 miles.   3*90/5= 
3*90/5 = 54
54> 54 min answer is 54 minutes
Answer: B
Find the smallest number of six digits exactly divisible by 25,35,45 and 15.
Select the correct option
A) 100555 B) 100775 C) 100885 D) 100995 E) 100665

Solution: Smallest number of six digits is 100000.   Required number must be divisible by L.C.M. of 25,35,45,15 i.e 1575,   On dividing 100000 by 1575,we get 800 as remainder.   Therefore, Required number = 100000 +( 1575 â€“ 800 ) = 100775.   Answer is 100775.
Answer: B
Convert 500 miles to KM?	Select:  A) 600KM  B) 700KM  C) 800KM  D) 900KM  E) 1000KM

Solution: 800KM     500*1.6= 
  500*1.6 = 800
800   Answer:800KM
Answer: C
The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 180 m, its area is? Choose the correct choice from the following choices.
A) 90	B) 882	C) 277	D) 261	E) 281

Solution: 5x + 12x + 13x = 180 => x = 6   a = 30, b = 72, c = 78   S = (30 + 72 + 78)/2= 
(30 + 72 + 78)/2 = 90
90   90nswer: 90
Answer: A
A is twice as good workman as B, and together they complete a work in 12 days. In how many days can the work be complete by B alone?	Choose the most appropriate option: A) 36 days B) 65 days C) 45 days D) 75 days E) 95 days

Solution: B=336 days   36 days   36 days
Answer: A
On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number T of races we need to conduct to get the top 3 fastest horses?	Pick one
A) 5
B) 7
C) 8
D) 10
E) 11

Solution: T=7 is the correct answer.   Good solution 7uneul.7
Answer: B
The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :  Choose the correct choice from the following.
A) Rs. 110.75	B) Rs. 115.75	C) Rs. 124.75	D) Rs. 125	E) Rs. 126

Solution: For an income of Rs.756, investment = Rs.9000   For an income of Rs., investment = = Rs.125   For a Rs.100 stock, investment = Rs.125.   Market value of Rs. 100 stock = = Rs. 124.75   Rs. 124.75
Answer: C
How much time does a train 225 metres long running at 90 km/hr take to pass a pole?  Choose the correct choice from the following answers
A) 7.9s
B) 2.5s
C) 7.5s
D) 9s
E) 7.4s

Solution: Explanation:   90 km/hr = 90 * 5/18= 
90 * 5/18 = 25
25 m/s   Speed= distance/time; v = d/t   25 = 225/t   t = 9s   ANSWER: 9s
Answer: D
X is an even number and( Y +2) is a positive odd number. Which of the following expressions cannot be even?
Choose one
A) X^5
B) X^4
C) X^3
D) X^2
E) Y+2

Solution: Y+2 WILL BY+2 ODD   Y+2
Answer: E
John has exactly 31 pens, and each pen is either bule, black, or red. If he has 5 more black pens than red pens, and twice as many blue pens as black pens, how many blue pens does john has ?
Choose the correct choice:
A) 15 B) 18 C) 20 D) 22 E) 17

Solution: x = the number of blue pens   y = the number of black pens   z = the number of red pens   From the first sentence we have   Equation #1: x + y + z = 31   ...he has 5 more black pens than red pens...   Equation #2: y = 5 + z   ...twice as many blue pens as black pens...   Equation #3: x = 2y   Solve equation #1 for z: z = y - 5   Now, we can replace both x and z with y in Equation #1   2y + y + (y - 5) = 31   4y - 5 = 31   4y = 36   y = 9   There are 9 black pens. This is 5 more than the number of red pens, so z = 4. Hence the answer is. x = 18, and just for check   18 + 9 + 4= 
  18 + 9 + 4 = 31
31.   Answer= 18,(18)
Answer: B
A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Choose the correct choice from the following options
A) 16%  B) 87%  C) 40%  D) 17%  E) 18%

Solution: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP   = Rs. 31150   Profit(%) = (31150 - 22250)/22250 * 100= 
(31150 - 22250)/22250 * 100 = 40
40%   Answer:40%
Answer: C
If x is an integer and |1-x|<2 then which of the following must be true?	Choose the correct choice from the following choices: A) x is not a prime number B) x^2+x is not a prime number C) x is positive D) Number of distinct positive factors of x+2 is a prime number E) x is not a multiple of an odd prime number

Solution: 1−x|<2 = -2<(1-x)<2   = -3<-x<1   = 3>x>-1   So x can hold values of 0,1 & 2 to satisfy the condition. Now we can evaluate the choices.   A) 1 & 2 primes, so incorrect   B) 1^2+1=2 is a prime, so incorrect   C) 0 is not +ve, So incorrect   D) x+2= 2,3,or 4, here 2 has 2 factor(prime), 3 has 2 factor (prime) & 4 has 3 factors (prime). Hence correct choice.   E) 2 is multiple of 1. So incorrect.   Hence Answer Number of distinct positive factors of x+2 is a prime number.
Answer: D
From the integer n, if n*n*n is odd, then what is true from below options?  Choices:
A) n is odd and n*n is even
B) n is odd
C) n*n is even
D) n*n is odd
E) n is even

Solution: n is odd and n*n is even   Option n is odd and n*n is even
Answer: A
If four students are made to sit in a row, then 6 don't have seats. If 6 students are made to sit in a row, then one row is empty. How many students have to sit a row such that each row has equal number of students and all students are seated? Pick one:
A) 0 B) 1 C) 4 D) 5 E) 9

Solution: Let there be a rows.   Then 4a + 6 = 6(a-1) [equating the number of students]   => a= 6   and total number of students = 30   Therefore 5 students much sit in each row such that each row has an equal number of students and all students are seated.   Option (5)
Answer: D
At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers wage is $10.50 per hour, how much less than a manager does a chef earn each hour?	Choose the correct choice from the following answers:
A) $1.40 B) $2.40 C) $3.40 D) $4.40 E) $4.30

Solution: Manager wages per hour = $10.50   Dishwasher wages per hour = half of manager's wages. = 1/2($10.50) ==> $5.25   Chef wages per hour = 20% greater than Dishwasher wages   --> 20% of $5.25 = (20*($5.25)) /100   --> ($95)/100   --> $0.95   Therefore,   Chef wages per hour = $5.25 + $0.95 ==> $6.20   Difference of wages between manager and chef = $10.50 - $6.20 ==> $4.30   ANSW$4.30R:$4.30
Answer: E
A person can walk at a constant rate of 8mph and can bike at a rate of 32mph. If he wants to travel 80 miles in 4 hours using bike and walking at their constant rates, how much distance would he require to walk? Pick
A) 20 B) 30 C) 48 D) 60 E) 72

Solution: Total distance = 80   Distance = Speed * Time   Walking speed = s1 = 8   Walking time = t1   Bike speed = s2 = 32   Time traveled in bike = t2   d1 + d2 = 80   s1t1 + s2t2 = 80   8*t1 + 32*t2 = 80   t1 + 4*t2 = 10 ----- (1)   Given: t1 + t2 =4 ----- (2)   (1) - (2) -->3 t2 = 6 , t2=2 and t1 = 8 - 2= 
8 - 2 = 6
6   Walking distance= s1*t1 = 8*6= 
8*6 = 48
48   Answer: 48
Answer: C
The slant height of a cone is 14 cm and radius of the base is 12cm, find the curved surface of the cone.  Options
A) 150 B) 170 C) 48 D) 528 E) 600

Solution: π * 12*14 =528   Answer:528
Answer: D
4 dice are thrown simultaneously on the board. Find the probability show the same face. Pick
A) 1/114	B) 2/117	C) 1/216	D) 2/111	E) 3/111

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 8:30 a.m. and drives north on the same highway at an average speed of 75 km per hour. Mr. Dinkle will	Choose the correct choice from the following:
A) overtake Mr. Smitherly at 9:30 a.m.
B) overtake Mr. Smitherly at 10:30 a.m.
C) overtake Mr. Smitherly at 11:00 a.m.
D) be 30 miles behind at 8:35 a.m.
E) never overtake Mr. Smitherly

Solution: After thirty minutes, Mr. Smitherly is ahead by 25 km.   Mr. Dinkle gains on Mr. Smitherly 25 km each hour.   1 hour after 8:30 a.m., Mr. Dinkle will catch Mr. Smitherly.   The answer is overtake Mr. Smitherly at 9:30 a.m..
Answer: A
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 15 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
Choose the correct option
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Since (ii) holds for every real number x, it will remain valid if we replace x with   -x. Therefore, f(1-x) = 3+f(-x). Now, from (i), 15 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 15-3= 
15-3 = 12
12. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 12
Answer: E
What's 8 x 600?
Options:  A) 4,800  B) 4,600  C) 4,400  D) 5,400  E) 6,800

Solution: A. 4,800
Answer: A
Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of hydrogen are there in 171 grams of water?  Pick:
A) 11	B) 13	C) 15	D) 17	E) 19

Solution: (2/18)*171= 
(2/18)*171 = 19
19 grams   The answer is 19.
Answer: E
Running at the same constant rate, 6 identical machines can produce a total of 270 pens per minute. At this rate, how many pens could 10 such machines produce in 4 minutes?
Choices
A) 1500  B) 1545.6  C) 1640.33  D) 1800  E) None of these

Solution: Explanation :   Let the required number of bottles be x.   More machines, More bottles (1800irect Proportion)   More minutes, More bottles (1800irect Proportion)   machines 6:10|   |::270:x   time 1:4 |   => 6 * 1 * x = 10 * 4 * 270   => x = (10 * 4 *270)/6   => x = 1800   Answer : 1800
Answer: D
The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 588 sq m, then what is the breadth of the rectangular plot? Select
A) 16
B) 17
C) 18
D) 19
E) 14

Solution: Let the breadth of the plot be b m.   Length of the plot = 3 b m   (3b)(b) = 588   3b2 = 588   b2 = 196   b = 14 m.   Answer: Option 14
Answer: E
At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 5 tickets?
Choose the correct choice from the following answers:
A) 20%
B) 33.3%
C) 40%
D) 60%
E) 66.6%

Solution: let the price of a ticket be Rs.100, so 3 tickets cost 300 & 5 tickets cost 500   5 tickets purchased at price of 3 tickets ie., for 300, so amount saved s Rs.200,   % of 5 tickets = (200 /500)*100= 
(200 /500)*100 = 40
40 %   ANSWER:40%
Answer: C
Arun is travelling on his cycle and has calculated to reach point A at 2 pm if he travels at
10 kmph. He will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?  Pick one:
A) 8 kmph B) 12 kmph C) 10 kmph D) 14 kmph E) 15 kmph

Solution: Let distance be x km   travelling at 10 kmph reach at 2 pm   travelling at 15 kmph reach at 12 noon   =>time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs   x/10 - x/15 = 2   3x-2x*30   x=60   time needed if travelled at 10kmph = 60/10= 
60/10 = 6
6 hrs=>reach at 1 pm => (6-1)= 
(6-1) = 5
5 hrs   req speed= 60/5= 
60/5 = 12
12 kmph   ANSWER 12 kmph
Answer: B
Two trains of length 100 m and 200 m are 70 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?
Choose the correct choice from the following options:
A) 2 sec
B) 32/3 sec
C) 20/7 sec
D) 32/3 sec
E) 53/2 sec

Solution: They are moving in opposite directions, relative speed is equal to the sum of their speeds.   Relative speed = (54 + 72)*5/18 = 7*5= 
7*5 = 35
35 mps.   The time required= d/s = 70/35= 
70/35 = 2
2 sec.   2 secnswer:a
Answer: A
rahul played weel in this season.his current batting averagge is 52.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.	Choose the correct choice from the following options:
A) 8  B) 12  C) 9  D) 6  E) 5

Solution: 52x+78=54(x+1)   =>2x=24   =>x=12   ANSWER:12
Answer: B
How many 7-letter words can be formed using the letters of the English alphabet that contain 3 different vowels and 4 different consonants?  Choose the correct option:	A) 5!*5c2 *21c2	B) 4!*5c2 *21c2	C) 4!*5c3 *21c2	D) 6!*5c3 *21c2	E) 7!*5c3 *21c4

Solution: combination for 3 vowels out of 5 = 5c3 ways   combination for 4 consonants of 21 = 21c4 ways   Additionally the arrangement can be = 7!   total arrangements =7!*5c3 *21c4   7!*5c3 *21c4
Answer: E
A right triangle ATC has to be constructed in the xy-plane so that the right angle is at A and AT is parallel to x axis. The coordinates of A, T and C are integers and satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. How many different triangles can be constructed with these properties?
Choose the correct answer:	A) 63	B) 336	C) 567	D) 3024	E) 5040

Solution: All the cordinates are integer hence,   possible AT values are   {-1,0}, {-1,1} ....{-1,7}: 8 ways   ....   {7,-1}, {7,0} ......{7,6}: 8 ways     9*8= 
  9*8 = 72
72   for AC values can be   {1,2}, {1,3} .... {1,7} : 6ways   ......   {7,1}, {7,2} ..... {7,6} : 6 ways     7*6= 
  7*6 = 42
42   Total= 72 * 42= 
72 * 42 = 3_024
3024 hence 3024
Answer: D
In the equation g = 36.12f, f and g are integers. If g/f leaves a remainder of r, which of the following must divide into r?	Select:	A) 2	B) 3	C) 4	D) 6	E) 12

Solution: 1) It says it is a equation, so g=36.12f should be 36.12 * f..   2) It says f is an integer, again it means 36.12 * f..   Otherwise f would be just a digit and it would be mentioned..   Although not clearly mentioned that 36.12f is actually 36.12 * f, BUT entire info points towards that..   and that is why I have taken g/f = 36.12
Answer: B
How many positive integers between 100 and 500 are there such that they are multiples of 19?
Choices
A) 10
B) 15
C) 21
D) 18
E) 19

Solution: Multiples of 19 = 114,133,152,-----,494   Number of multiples of 19 => 494-114/19+1= 21   Answer is 21
Answer: C
How many of the factors of 120 are divisible by 2?	Choose the correct choice from the following answers:
A) 4
B) 8
C) 10
D) 12
E) 16

Solution: 120 = 2^3*3*5   The total number of factors is (1+3)(1+1)(1+1) = 16   The odd factors are 1, 3, 5, and 15.   The number of even factors is 16-4= 
16-4 = 12
12   The answer is 12.
Answer: D
A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour. Choose the correct choice from the following answers:  A) 15/7  B) 4/17  C) 7/18  D) 19/6  E) 7/15

Solution: Let S be the sample space   Then n(S)=no of ways of drawing 2 balls out of   (6+4)= 
  (6+4) = 10
10c2=(10*9)/(2*1)= 
(10*9)/(2*1) = 45
45   Let 7/15=event of getting both balls of same colour   Then n(7/15)=no of ways(2 balls out of six) or(2 balls out of 4)   =(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6= 
15+6 = 21
21   P(7/15)=n(7/15)/n(S)=21/45=7/15   Option 7/15
Answer: E
A bag contains 24 purple jellybeans, 16 green jellybeans, and 10 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green? Choices:
A) 15%
B) 20%
C) 25%
D) 32%
E) 35%

Solution: Probability of green beans = 16 / (24 + 16 + 10) = 16/50 = 32%   Answer is 32%
Answer: D
A sum amounts to Rs.3087 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?	Choose the correct choice from the following choices.
A) s.4000
B) s.5000
C) s.4500
D) s.4800
E) s.2800

Solution: CI=3087,R=5,N=2   CI=P[1+R/100]^2   =P[1+5/100]^2   3087=P[21/20]^2   3087[20/21]^2   2800   ANSWs.2800R:s.2800
Answer: E
A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is : Choose the correct choice from the following answers:
A) 8 cm	B) 6 cm	C) 4 cm	D) 3 cm	E) None

Solution: Sol.   Let the height of the cone be h cm. Then,   1/3 ∏ * 6 * 6 * h = 4/3 ∏ * 3 * 3* 3 ⇒   h = [36 * 3 / 36= 
36 * 3 / 36 = 3
3 cm.   Answer 3 cm
Answer: D
If x and y are positive integers, and 3 is not a factor of y, then y may be which of the following?  Choose the correct choice from the following answers
A) (x−1)·x·(x+1)  B) (x−3)·(x−1)·(x+1)  C) (x−2)·x·(x+2)  D) (x−1)·x·(x+2)  E) (x−3)·(x+1)·(x+2)

Solution: Plugged in values :   let x=5   A. (x−1)·x·(x+1) --> divisible by 3   B. (x−3)·(x−1)·(x+1) --> divisible by 3   C. (x−2)·x·(x+2) --> divisible by 3   D. (x−1)·x·(x+2) --> not divisible. Hence the answer.
Answer: D
If y = x^2 + px + q, y is minimum when x is:	Choose the correct choice from the following:
A) p /q	B) -p/q	C) -p/2	D) -q/2	E) q/p

Solution: We're given the equation Y = X^2 + pX + q.   IF.. we use a simple Classic Quadratic....   p = 2   q = 1   Y = X^2 + 2X + 1   We can then go about finding the answer that yields the MINIMUM result when X = ...   Answer A: p/q = 2/1= 
2/1 = 2
2 --> 4+4+1= +9   Answer B: -p/q = -2/1 = -2 --> 4-4+1 = +1   Answer -p/2: -p/2 = -2/2 = -1 --> 1-2+1 = 0   Answer D: -q/2 = -1/2 -->(1/4)-1+1 = +1/4   Answer E: q/p = 1/2 --> (1/4)+1+1 = +2 1/4   From these results, we can see the minimum result:   -p/2
Answer: C
After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?  Choose the correct choice from the following answers
A) 8  B) 0  C) 9  D) 72  E) 4

Solution: Ans: Tricky one but simple. How do you put exactly 1 letter in the wrong envelope? we need minimum two. So answer is 0.   Answer:0
Answer: B
Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 300 envelopes	Options:
A) 6 minutes  B) 5 minutes  C) 7 minutes  D) 3 minutes  E) 4 minutes

Solution: earl takes 1 min. for 36 envelopes.   ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.   so both of them when work together can stuff 36+24= 
36+24 = 60
60 envelopes in 1 min.   for 300 envelopes they will take 300/60 mins. i.e., 5 mins.   ANSWER:5 minutes
Answer: B
The probability that a number selected at random from the first 50 natural numbers is a composite number is? Choose the correct choice from the following choices
A) 17/28 B) 17/25 C) 17/26 D) 17/76 E) 17/22

Solution: The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favourable cases are 34.   Required probability = 34/50 = 17/25.   Answer: 17/25
Answer: B
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 7a then which of the following is c equal to?
Choose the correct choice from the following choices
A) a/12	B) a/8	C) 6a	D) 10a	E) 12a

Solution: The sum of the roots is = -b/a = -7a/a = -7. Let the other root be x. Thus, x-2 = -7   x = -5. Again, the product of the roots is   -2*-5= 
  -2*-5 = 10
10. Thus, c/a= 10. c = 10a.   10a.
Answer: D