MU-NLPC/Calc-aqua_rat huggingface dataset:
4 letters have to be put into their 4 respective envelopes. If the letters are inserted randomly into the envelopes, what is the probability that all the letters go into their respective envelopes?	Select the correct option:
A) 1/30
B) 1/64
C) 1/120
D) 1/240
E) 3/5

Solution: A-B-C-D-E (envelopes)   a-b-c-d-e (letters)   4 letters (a, b, c, d, and e) can be assigned to 4 envelopes (arranged) in 4! ways, out of which only one will be correct, thus the probability is 1/4! = 1/64.   Answer: 1/64.
Answer: B
Two trains 200 m and 800 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?  Pick:
A) 10.6
B) 10.9
C) 36
D) 10.8
E) 10.1

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 200 + 800= 
200 + 800 = 1_000
1000 m.   Required time= 1000 * 9/250= 
1000 * 9/250 = 36
36 sec.   Answer: 36
Answer: C
Three different containers contain 50 litres, 100 litres and 150 litres of mixture of milk and water respectively. What is the biggest measure can measure all the different quantities exactly ?  Choose the correct choice from the following options.
A) 120 litres B) 57 litres C) 60 litres D) 50 litres E) 100 litres

Solution: M1 = 50 litres   M2 = 100 litres   M3 = 150 litres   Required measurement = H.C.F. of M1,M2,M3 = 50 litres   Answer is 50 litres
Answer: D
Amber works 30 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?  Choose the correct option:	A) m/(20d)	B) 20d	C) 10md/6	D) 20d/m	E) 30d

Solution: ANSW30dR: 30d The passage states that she works 30 days a month at d dollars per day, so 30 d is her monthly pay
Answer: E
Insert the missing number
5, -15, 45, -135, (....)
Options:
A) 350
B) -405
C) 405
D) -350
E) 0

Solution: 5*-3=-15   -15*-3= 
-15*-3 = 45
45   45*-3=-135   -135*-3= 
-135*-3 = 405
405   ANSWER:405
Answer: C
A fellow borrowed a certain sum of money at 8% per annum at simple interest and in 8 years the interest amounted to Rs.900 less than the sum lent. What was the sum lent?
Choose the correct choice from the following options:
A) 1050
B) 1220
C) 2500
D) 1060
E) 1110

Solution: P - 900 = (P*8*8)/100   P = 2500   Answer: 2500
Answer: C
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What isthe probability that first is white and second is black?  Choose the correct answer
A) 31/111  B) 36/145  C) 21/115  D) 11/154  E) None of these

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   36/145
Answer: B
In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?  Options:
A) 1/3
B) 2/3
C) 2/5
D) 2/7
E) 2/9

Solution: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10   P (E or H) = P (E U H)   = P (E) + P (H) - P (E ∩ H)   = (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5   2/5
Answer: C
A math teacher has 26 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
Choose the most appropriate option:  A) 9  B) 10  C) 11  D) 12  E) 13

Solution: a square is a special kind of rhombus (sides are perpendicular)   a square is a special kind of rectangles (sides with same length)   Among the 26 cards with have:   15 rectangles   10 rhombus   8 squares   Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.   Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.   We have 8 squares.   So the minimum different cards that represent a square, a rhombus or a rectangle is   2 + 7 + 8= 
  2 + 7 + 8 = 17
17   Which means that the maximum number of circles that you could have is  26 - 17= 
 26 - 17 = 9
9   9nswer (9)
Answer: A
Sunanth is 22 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Choose the correct choice
A) 20 years B) 23 years C) 21 years D) 22 years E) 24 years

Solution: Let present age of the son =c years   Then, present age of the sunanth =(c+22) years   Given that, in 2 years, sunanth's age will be twice the age of his son   =>(c+22)+2=2(c+2)   =>x=20   20 yearsNSWER:20 years
Answer: A
A constructor estimates that 3 people can paint Mr. Gokhle's house in 10 days. If he uses 5 people instead of 3,how long will they take to complete the job?
Select the correct option:
A) 6  B) 5  C) 10  D) 5  E) 4

Solution: Explanation:   Use formula For a work Members Ã— days = constant   3 Ã— 10 = 5Ã— a   a = 6   so answer is 6days   6nswer:6
Answer: A
Due to construction, the speed limit along an 10-mile section of highway is reduced from 55 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? Choose the correct answer.
A) A) 6.24	B) B) 4.1	C) C) 10	D) D) 15	E) E) 24

Solution: Old time in minutes to cross 10 miles stretch = 10*60/55 = 10*12/11 = 10.9   New time in minutes to cross 10 miles stretch = 10*60/40 = 10*3/2= 
10*3/2 = 15
15   Time difference= 4.1   Ans:4.1
Answer: B
Jim travels the first 3 hours of his journey at 60 mph speed and the remaining 5 hours at 24 mph speed. What is the average speed of Jim's travel in mph?  Answers
A) 37.5 mph
B) 40 mph
C) 50 mph
D) 44 mph
E) None of these

Solution: Explanation :   Average speed=Total Distance/Time.   Total distance travelled by Jim = Distance covered in the first 3 hours + Distance covered in the next 5 hours.   Distance covered in the first 3 hours = 3×60=180 miles   Distance covered in the next 5 hours= 5×24=120 miles   Therefore, total distance travelled = 180+120= 
180+120 = 300
300 miles.   The total time taken= 3+5= 
3+5 = 8
8 hours.   Hence, the average speed= 300/8= 
300/8 = 75/2 = around 37.5
37.5 mph.   37.5 mphnswer : 37.5 mph
Answer: A
Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 18 members of this sequence?
Options:
A) 878  B) 900  C) 788  D) 810  E) 1022

Solution: I would split them up like this.   23 28 33 and so on (9 terms)....the 10th term = 23+8*5= 
23+8*5 = 63
63   27 32 37 and so on (9 terms)......the 9th term= 27+8*5= 
27+8*5 = 67
67   Since the distance between any two numbers is the same we can use arithmetics   first+last/2 times no of numbers= the sum   (23+63)/2 * 9= 
(23+63)/2 * 9 = 387
387   (27+67)/2 * 9= 
(27+67)/2 * 9 = 423
423= 810   810
Answer: D
If A = 2B+1 where A is an Integer then which of the following is true?
Choose the correct choice from the following.
A) A is always Odd
B) A is always Even
C) A is a non multiple of 2
D) A is even if B is a non integer and a multiple of 0.5
E) A=1

Solution: A is even if B is a non integer and a multiple of 0.5
Answer: D
Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?  Select the correct option:
A) Rs.81.60
B) Rs.160
C) Rs.172
D) Rs.727
E) Rs.728

Solution: SI = 40 + 40   CI = 40 + 40 + 1.6= 
40 + 40 + 1.6 = 81.6
81.6   Rs.81.60nswer:Rs.81.60
Answer: A
. A man pays off 3/20 of his debt every month.At the end of 6 months, his remaining debt is $A.How much amount has he cleared off every month?	Choose the correct choice from the following:
A) 3A/20
B) 9A/10
C) A/10
D) 3A/10
E) 3A/2

Solution: Let his total debt be T   Every month he pays off 3/20 of his debt = 3/20∗T3/20∗T   After 6 months he would have paid = 3/20∗6∗T3/20∗6∗T   His remaining debt after 6 months is A.   Hence Total debt = Remaining debt + Paid debt   T=A+3/20∗6∗TT=A+3/20∗6∗T   T−18/20∗T=AT−18/20∗T=A   T∗2/20=AT∗2/20=A   T=10AT=10A   3A/2very month he pays off 3/20 of his debt = 3/20∗T=3/20∗10A=3A/2   Answer : 3A/2
Answer: E
Which of the options is a multiple of 3!+6
Options:	A) 4!-12	B) 4!+2	C) 4!-2	D) 3!+20	E) 4!+20

Solution: When expanded 3!+6 equal (3*2) +6   Therefore (3*2) +6=6+6= 
6+6 = 12
12   Looking at the options the only one that gives a multiple of 12 is option 4!-12)
Answer: A
The cost of 2 chairs and 3 tables is Rs.1300. The cost of 3 chairs and 2 tables is Rs.1200. The cost of each table is more than that of each chair by?  Choose the correct choice from the following:
A) 50
B) 60
C) None of these
D) 70
E) 100

Solution: None of these   100   2None of these + 3T = 1300 --- (1)   3None of these + 3T = 1200 --- (2)   Subtracting 2nd from 1st, we get   -None of these + T = 100 => T - None of these = 100
Answer: C
A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 52000, then the share of B is?
Select.
A) 24007  B) 24000  C) 24028  D) 240011  E) 240121

Solution: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6   Total profit = Rs. 52000   Share of B = 6/13 (52000) = Rs. 24000   Answer:24000
Answer: B
The average of six number is 3.95. The average of two of them is 3.8, while the average of the other two is 3.85. what is the average of the remaining two number ?	Choose the correct option:
A) 4.5  B) 4.2  C) 4.7  D) 4.8  E) None of these

Solution: solution:   Sum of the remaining two numbers = (3.95 × 6) - [(3.8 × 2) + (3.85 ×2)]   =23.70 -(7.6 + 7.7) = 23.70 - 15.3 = 8.4.   ∴ Required average =8.4/2= 
8.4/2 = 4.2
4.2 Answer 4.2
Answer: B
If x/2 years ago Roger was 18 years old and x/2 years from now he will be 4x years old, how old will he be 5x years from now?	Choose the correct choice from the following answers
A) 32 B) 35 C) 30 D) 51 E) 28

Solution: Assume the current age = a   a - x/2 = 18 (i)   a + x/2 = 4x   Or a = 7x/2 (ii)   Putting the value of a from (ii) in (i)   7x/2 - x/2 = 18   Or 6x/2 = 18 Therefore x = 6 and a = 21   5x years from now, age will be  21 + 5*6= 
 21 + 5*6 = 51
51   Option 51
Answer: D
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.  Select the correct option.
A) 224km  B) 233km  C) 277km  D) 256km  E) 297km

Solution: distance = speed x time   Let time taken to travel the first half = x hr   then time taken to travel the second half = (10 - x) hr   Distance covered in the the first half = 21x   Distance covered in the the second half = 24(10 - x)   But distance covered in the the first half = Distance covered in the the second half   => 21x = 24(10 - x)   => 21x = 240 - 24x   => 45x = 240   => 9x = 48   => 3x = 16   ⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km   224kmnswer :224km
Answer: A
The average age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasing theaverage by 4year. Find what was theoriginal strength of class?	Choose the correct choice from the following choices.
A) 11
B) 12
C) 17
D) 19
E) 21

Solution: Let original strength = y   Then , 40y + 12 x 32 = ( y + 12) x 36   ⇒ 40y + 384 = 36y + 432   ⇒ 4y = 48   ∴ y = 12   12
Answer: B
A company has $329,864 in its account. What is the least amount of money (in whole number of dollars) that it must add to the account if the money is paid evenly among 9 of its vendors?  Choose the correct choice: A) $1 B) $2 C) $3 D) $4 E) $6

Solution: To find the least amount that must be added to the Account to split the money evenly among 9 of its vendors,   the total divisible by 9   Simply add the individual digits of the total = 3+2+9+8+6+4= 
3+2+9+8+6+4 = 32
32   If you add 4 , the number is divisible by 9 (32+ 4)   Correct Option : $4
Answer: D
A beekeeper has 600,000 bees living in four beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have? Choose the correct choice from the following answers.
A) 20,000 B) 176470 C) 10000 D) 13000 E) 56600

Solution: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+3*(0.8)*x = 600,000 => 3.4x = 600,000 => x = 176470.   176470 is the answer.
Answer: B
The cross section of a canal is a trapezium in shape. If the canal is 7 metres wide at the top and 9 metres at the bottom and the area of cross-section is 1280 square metres, find the length of the canal.	Choose the correct answer:
A) 160 metres	B) 172 metres	C) 154 metres	D) 165 metres	E) None of these

Solution: None of these   Let the length of canal = h m.   Then,area of canal = 1⁄2 × h(9 + 7)   or 1280 = 1⁄2h(16)   ∴ h = 1280×2/16=160m   160 metresnswer 160 metres
Answer: A
If n is a positive integer, which one of the following numbers must have a remainder of 1 when
divided by any of the numbers 4, 5, and 6?
Choose the correct answer: A) 125n + 1 B) 240n + 1 C) 275n + 1 D) 290n + 1 E) 320n + 1

Solution: The numbers 4, 5, and 6 all divide 240 so they all divide 240n.   When we divide (240n + 1) by 4, 5, or 6, the remainder must be 1.   The answer is 240n + 1.
Answer: B
Find the average of all the numbers between 6 and 34 which are divisible by 5? Choose one.
A) 10  B) 20  C) 34  D) 54  E) 28

Solution: Average = (10 + 15 + 20 + 25 + 30)/5   = 100/5= 
100/5 = 20
20.   Answer:20
Answer: B
A work could be completed in 100days by x workers. However, due to the absence of 10workers, it was completed in 110days. The original no.of workers was:  Choose the correct choice from the following choices:
A) 90 B) 106 C) 110 D) 120 E) 130

Solution: sax Letlheo g alnumberofworkers hex   x workers can do the wor - 100 days   (x — 10) workers can do the work in 110 days   4 100x 1u1x— 10)   1100 Q x 110   110
Answer: C
In the manufacture of a certain product, 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?	Answers.
A) 0.125%	B) 0.32%	C) 0.8%	D) 1.25%	E) 2.0%

Solution: Percent of defective produced = 8%   Percent of the defective units that are shipped for sale = 4%   Percent of units produced are defective units that are shipped for sale = (4/100)*(8/100)*100%   = (32/10000)*100%   = (32/100)= 
(32/100) = 8/25 = around 0.32
.32 %   Answer 0.32%
Answer: B
If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability Q that N is divisible by 3?  Choose the correct answer
A) 1/3 B) ¼ C) 9/25 D) 5/16 E) 0

Solution: Prime digits are : 2, 3, 5, 7   Total number of 2 digit #s with both digits prime are:   4*4= 
  4*4 = 16
16   out of these numbers divisible by 3= 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.   => prob = 5/16.   Ans D. Took me 3:20 mins.
Answer: D
Find the constant k so that : -x2 - (k + 9)x - 8 = -(x - 2)(x - 4) Choose the correct choice from the following choices
A) 11
B) 12
C) 15
D) 14
E) 19

Solution: -x2 - (k + 9)x - 8 = -(x - 2)(x - 4) : given   -x2 - (k + 9)x - 8 = -x2 + 6x - 8   -(k + 9) = 6 : two polynomials are equal if their corresponding coefficients are equal.   k = -15 : solve the above for k   correct answer 15
Answer: C
A train running at the speed of 48 km/hr crosses a pole in 9 seconds. What is the length of the train?	Choose the correct option
A) 286 B) 120 C) 255 D) 150 E) 287

Solution: Speed=(48 * 5/18) m/sec = (40/3) m/sec Length of the train   = (Speed x Time) = (40/3 * 9)= 
(40/3 * 9) = 120
120 m.   Answer:120
Answer: B
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 45% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above? Pick
A)  5%	B)  10%	C)  15%	D)  35%	E)  30%

Solution: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.   Neither is zero.   Hence 100 = 60 + 50 + 45 - n (Exactly 2 products) - 2*10   100 = 135 - n (Exactly 2 products) => n (Exactly 2 products) = 35.   Answer:  35%
Answer: D
Calculate the time it will take for a train that is 250 meter long to pass a bridge of 150 meter length, if the speed of the train is 35 km/hour ? Pick one
A) 56 seconds	B) 3515 seconds	C) 41.15 seconds	D) 30 seconds	E) 36 seconds

Solution: Speed = 35 Km/hr = 35*(5/18) m/sec = 9.72 m/sec   Total distance = 250+150= 
250+150 = 400
400 meter   Time= Distance/speed   = 400 * (1/9.72) = 41.15 seconds   Answer: 41.15 seconds
Answer: C
In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 20 different models of televisions, what is the minimum number of letters that must be used to make the codes?	Choose the correct choice from the following answers.
A) 5  B) 7  C) 8  D) 9  E) 10

Solution: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥20. The smallest n which fulfills this condition is n = 5.   5nswer 5
Answer: A
what is the smallest number by which 3600 be divided to make it a perfect cube ? Choose the correct option:	A) 9	B) 50	C) 300	D) 450	E) 550

Solution: Solution   3600 = 23 * 52 * 32 * 2.   to make it a perfect cube, it must be divided by 52 * 32 * 2 i.e., 450 .   Answer 450
Answer: D
A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?	Options
A) 1.7  B) 1.4  C) 1.2  D) 1.5  E) 3

Solution: M = 9   S = x   DS = 9 + x   US = 9 + x   9 + x = (9 - x)2   9 + x = 18 -2x   3x = 9   x = 3   Answer: 3
Answer: E
If p and q are prime numbers, how many divisors does the product p^4 * q^5 have?  Pick:
A) 30	B) 40	C) 45	D) 50	E) 56

Solution: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)   Therefore, the answer is A. 5*6=30
Answer: A
Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 61.3 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?  Choose the correct choice from the following answers
A) 0.08  B) 1.0  C) 1.1  D) 10.5  E) 1.4

Solution: Change in production of motor vehicles = 61.3 - 3.9= 
61.3 - 3.9 = 57.4
57.4 million in 41 years (1987 - 1946)   average increase per year= 57.4/41= 
57.4/41 = 1.4
1.4 million (apporx.)   Answer (1.4)
Answer: E
Two pipes can fill a tank in 14 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ? Choose the most appropriate option
A) 5.5 Hours  B) 7.5 Hours  C) 8.5 Hours  D) 9.5 Hours  E) 6.5 Hours

Solution: In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19   So fill tank fill up in 19/2= 
19/2 = 19/2 = around 9.5
9.5 Hours   ANSWER:9.5 Hours
Answer: D
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 10 minutes?	Pick: A) 40 B) 100 C) 150 D) 240 E) 300

Solution: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 10 minutes the population increases by 10 x 4 = 40 people.   Answer. 40.
Answer: A
The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? Choose the correct choice from the following.
A) 1.5  B) 2.4  C) 3.6  D) 4.0  E) 4.6

Solution: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]   = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.   Required average = (9.2 / 2) = 4.6.   4.6
Answer: E
remy bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?	Choose the correct option:
A) 50RW/Q  B) 50QR/W.  C) 25RQ/W  D) 25RW/Q  E) RW/(4Q)

Solution: Cost of 1 steaks = W/2Q dollars or 100W/2Q cents   Cost of R steaks at no discount = 100RW/2Q = 50RW/Q   Cost of R steaks at 50% discount 100  /2= 
100  /2 = 50
50RW/Q   Cost of R steaks at 50% discount= 1/2 * 50RW/Q = 25RW/Q   Hence, answer will be 25RW/Q.
Answer: D
In what ratio P:Q should the Mixture P of milk and water in the ratio of 4:1 be mixed with another Mixture Q of milk and water in the ratio 2:3 so that the resultant mixture contains equal quantities of milk and water?	Choose the correct option.
A) 1:3	B) 2:3	C) 1:4	D) 3:4	E) 3:5

Solution: (4/5)*P +(2/5)*Q = (1/5)*P+(3/5)*Q   3P=Q   P/Q = 1/3   The answer is 1:3.
Answer: A
In how many ways the letters of the word RAIMBON be arranged?  Answers:
A) 6468
B) 9667
C) 5040
D) 9865
E) 4687

Solution: Total ways of arranging the letters = 7! = 5040 ways.   5040)
Answer: C
For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6, -5 ?  Options
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: Given sequence: {1, -3, 2, 5, -4, -6}   The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.   1*(-3)=-3=negative;   -3*2=-6=negative;   2*5= 
2*5 = 10
10=positive;   5*(-4)=-20=negative;   (-4)*(-6)= 
(-4)*(-6) = 24
24=positive.   So there are 4 pairs of consecutive terms of the sequence for which the product is negative.   Answer: 4.
Answer: D
A student can select one of 6 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science. Options
A) 22
B) 72
C) 99
D) 37
E) 01

Solution: 6C1×3C1×4C16C1×3C1×4C1 = 6x3x4=72 ways   Answer:72
Answer: B
A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room. Choose the correct answer
A) 6,18,6	B) 6,18,0	C) 6,18,7	D) 6,18,2	E) 6,18,1

Solution: Explanation:   Let breadth = x metres, length = 3x metres, height = H metres.   Area of the floor=(Total cost of carpeting)/(Rate) = (270/5)= 
(270/5) = 54
54   So, breadth= 6 m and length = = 9 m.   Now, papered area = (1720/10)= 
(1720/10) = 172
172   6,18,6rea of 1 door and 2 windows= 8   Total area of 4 walls = (172 + 8)= 
(172 + 8) = 180
180   6,18,6nswer: 6,18,6) b=6;l=18;H=6
Answer: A