MU-NLPC/Calc-aqua_rat huggingface dataset:
Two cylinders are of the same height. Their radii are in the ratio 1: 3. If the volume of the first cylinder is 40 cc. Find the volume of the second cylinder? Pick one.
A) 360 cc	B) 60 cc	C) 300 cc	D) 36 cc	E) 39 cc

Solution: r1 = x r2 = 3x   Π * x2 * h = 40   Π9 x2h = 40 * 9= 
40 * 9 = 360
360   360 ccNSWER:360 cc
Answer: A
Tough and Tricky questions: Number Properties.
If (z + 3)/7 is an integer, what is remainder when z is divided by 7? Choose the correct choice from the following answers:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: Assume the answer choices as the value of z   7/7= 
7/7 = 1
1   Ans 5
Answer: D
K and L are each four-digit positive integers with thousands, hundreds, tens, and units digits defined as a, b, c, and d, respectively, for the number K, and p, q, r, and s, respectively, for the number L. For numbers K and L, the function W is defined as 5^a*2^b*7^c*3^d ÷ 5^p*2^q*7^r*3^s. The function Z is defined as (K – L) ÷ 10. If W = 16, what is the value of Z?  Answers:
A) 16  B) 20  C) 25  D) 40  E) It cannot be determined from the information given.

Solution: K = 1000a + 100b + 10c + d   L = 1000p + 100q + 10r + s   also W = 16 = 2^4 now when u equate this value   u will get a=p c=r d=s and b-q = 4 as u will have to equate the powers.   now put that in value of z you will get  10*4= 
 10*4 = 40
40   ANSWER:40
Answer: D
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?	Choose the correct choice:
A) 1 years
B) 7 years
C) 6 years
D) 8 years
E) 9 years

Solution: Mother's age when Ayesha's brother was born = 36 years.   Father's age when Ayesha's brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 36)= 
(42 - 36) = 6
6 years.   Answer: 6 years
Answer: C
What is the sum of all possible solutions to |x - 3|^2 + |x - 3| = 30 ? Choose the correct choice.
A) 4
B) 5
C) 3
D) 2
E) 1

Solution: Denote |x - 3| as y: y^2 + y = 30 --> y = -6 or y = 5. Discard the first solution since y = |x - 3|, so it's an absolute value and thus cannot be negative.   y = |x - 3| = 5 --> x = 8 or x = -3. The sum = 5.   Answer: 5.
Answer: B
A collection of books went on sale, and 2/3 of them were sold for $4.25 each. If none of the 30 remaining books were sold, what was the total amount received for the books that were sold?
Pick.
A) $260  B) $255  C) $285  D) $290  E) $275

Solution: If 30 books constitute 1/3rd of the total, then 2/3rd of the total = 60 books   Amount received for sold books = 60 * 4.25= 
60 * 4.25 = 255
$255   Answer : $255
Answer: B
Two members of a certain club are selected to speak at the next club meeting. If there are 36 different possible selections of the 2 club members, how many members does the club have?
Choose the most appropriate option.
A) 5
B) 6
C) 7
D) 8
E) 9

Solution: Let, Total members = n   @n=2, no. of ways to select 2 out of 2(A,B) = (AB) = 1   @n=3, no. of ways to select 2 out of 3(A,B,C) = (AB, AC, BC) = 2+1= 
2+1 = 3
3   @n=4, no. of ways to select 2 out of 4(A,B,C,D) = (AB, AC, AD, BC, BD, CD) = 3+2+1= 
3+2+1 = 6
6   i.e. @n=5, Total Selection of 2 = 4+3+2+1= 
4+3+2+1 = 10
10   i.e. @n=6, Total Selection of 2 = 5+4+3+2+1= 
5+4+3+2+1 = 15
15   i.e. @n=7, Total Selection of 2 = 6+5+4+3+2+1= 
6+5+4+3+2+1 = 21
21   i.e. @n=8, Total Selection of 2 = 7+6+5+4+3+2+1= 
7+6+5+4+3+2+1 = 28
28   i.e. @n=9, Total Selection of 2 = 8+7+6+5+4+3+2+1= 
8+7+6+5+4+3+2+1 = 36
36   Answer: Option 9
Answer: E
If abc ≠ 3 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =  Choose one:  A) (1 + bc)/(b + c)  B) (1 – bc)/(b + c)  C) (1 + b + c)/(bc)  D) (1 – b – c)/(bc)  E) (1 – b – c)/(b + c)

Solution: Answer is (1 – b – c)/(bc) though it took me around 4 minutes to get that.
Answer: D
Ashley and Vity work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashley and Vity will be chosen?  Select the correct option:
A) 1/10  B) 3/28  C) 2/9  D) 1/4  E) 1/2

Solution: I did slightly different and hence obviously ended up with the answer 2/9.   I assumed that because Ashley and Vity have to be chosen, the remaining selection is 3 people from 8.   8C3/10C5= 2/9. Option 2/9.
Answer: C
A women purchased a sofa and a bed for Rs. 12000 &Rs. 8000 respectively. He sold the sofa at a loss of 9% and the bed at a profit of 14%. Overall how much he make a profit.
Choose the correct choice.
A) 20 B) 10 C) 30 D) 50 E) 40

Solution: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.   r = 12000(1 - 9/100) = 12000 - 1080   m = 8000(1 + 14/100) = 8000 + 1120   Total SP - Total CP = r + m - (12000 + 8000) = -1080 + 1120 = Rs.40   As this is positive, an overall profit of Rs. 40 was made.   10
Answer: B
An order was placed for a carpet whose length and width were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and width were in the ratio 4 : 1 but were was no change in its perimeter. What is the ratio of the areas of the carpets?
Pick:
A) 5:8  B) 3:2  C) 6:1  D) 8:7  E) 5:6

Solution: Let the length and width of one carpet be 3x and 2x.   Let the length and width of the other carpet be 4y and y.   2(3x + 2x) = 2(4y + y)   5x = 5y   x = y   The ratio of the areas of the carpet in both cases:   = 3x * 2x : 4y * y   = 6x^2 : 4y^2   = 6x^2 : 4x^2   = 6 : 4   = 3 : 2   The answer is 3:2.
Answer: B
A boy has Rs. 160 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Choose the correct choice from the following choices
A) 30  B) 110  C) 140  D) 130  E) 120

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 160   16x = 160   x = 10.   Hence, total number of notes = 3x = 30.   30
Answer: A
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? Pick.
A) 30%
B) 35%
C) 40%
D) 45%
E) None of these

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
How many multiples of 9 are there between 18 and 270 ?  Choose the correct answer:
A) 12	B) 27	C) 42	D) 61	E) 60

Solution: It should be mentioned whether 18 and 270 are inclusive.   If 18 and 270 are inclusive, then the answer is   (270-18)/9+1= 
  (270-18)/9+1 = 29
29.   If 18 and 270 are NOT inclusive, then the answer is   (261-27)/9+1= 
  (261-27)/9+1 = 27
27.   Since OA is 27, then we have NOT inclusive case.
Answer: B
Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?	Choose the correct choice:  A) 113 miles  B) 432 miles  C) 456miles  D) 887 miles  E) 767 miles

Solution: The number of miles to drive to finish his journey is given by   1200 - 768= 
1200 - 768 = 432
432 miles   correct answer 432 miles
Answer: B
A train covers a distance in 50 min ,if it runs at a speed
of 48kmph on an average.The speed at which the train must run
to reduce the time of journey to 40min will be.  Answers:
A) 60kmph  B) 63kmph  C) 57kmph  D) 70kmph  E) 61kmph

Solution: Time=50/60 hr=5/6hr   Speed=48mph   distance=S*T=48*5/6= 
48*5/6 = 40
40km   time=40/60hr=2/3hr   New speed = 40* 3/2= 
40* 3/2 = 60
60kmph   60kmphnswer is 60kmph.
Answer: A
Each child has 2 pencils and 13 Skittles. If there are 15 children, how many pencils are there in total?  Select the correct option:
A) 30
B) 12
C) 18
D) 22
E) 08

Solution: 2*15=30.30nswer is 30.
Answer: A
What is the least number which should be added to 2982 so that the sum is exactly divisible by 5, 6, 4, and 3? Choose the correct choice from the following options.
A) 14 B) 18 C) 22 D) 26 E) 30

Solution: L.C.M. of 5, 6, 4 and 3 = 60.   When dividing 2982 by 60, the remainder is 42.   The number to be added = 60 - 42= 
60 - 42 = 18
18.   The answer is 18.
Answer: B
A can finish a work in 18 days and B can do same work in half the time taken by A. then working
together, what part of same work they can finish in a day  Select the correct option:  A) 1\5  B) 1\6  C) 1\7  D) 1\8  E) None of these

Solution: Explanation:   Please note in this quesƟon, we need to answer part of work for a day rather than complete work. It was   worth mentioning here because many do mistake at this point in hurry to solve the question   So lets solve now,   A's 1 day work = 1/18   1\6's 1 day work = 1/9 [because 1\6 take half Ɵme than A]   (A+1\6)'s one day work =   (118+19)=(1+218)=16   So in one day 1/6 work will be done   Answer: 1\6
Answer: B
A and B can do a piece of work in 7 days, B and C in 8 days, C and A in 9 days. How long will C take to do it? Choose one:
A) 14.1 days B) 18.8 days C) 21.4 days D) 24.3 days E) 26.5 days

Solution: 2c = 1/8 + 1/9 – 1/7 = 47/504   c = 47/1008 => 1008/47 = 21.4 days   The answer is 21.4 days.
Answer: C
If the radius of a circle is decreased by 50%, find the percentage decrease
Choose one:
A) 22  B) 099  C) 75  D) 26  E) 18

Solution: Let original radius = R.   New radius = =   Original area = and new area =   Decrease in area = = 75%   Answer: 75
Answer: C
The batting average of a particular batsman is 63 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Choose the correct choice from the following choices.
A) 179 B) 208 C) 210 D) 223 E) 248

Solution: Explanation:   Total runs scored by the batsman = 63*46= 
63*46 = 2_898
2898 runs   Now excluding the two innings the runs scored= 58*44= 
58*44 = 2_552
2552 runs   Hence the runs scored in the two innings= 2898 – 2552 = 346 runs.   Let the highest score be x, hence the lowest score = x – 150   x + (x - 150) = 346   2x = 496   x = 248 runs   ANSW248R 248
Answer: E
At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $203?
Choose the correct answer
A) 1,108	B) 2,100	C) 2,108	D) 2,120	E) 2,256

Solution: I think it should be D.   I can buy 8 250-pack for Rs 22.95*8= 
22.95*8 = 183.6
$183.60   Now, I can buy 6 20-pack for 3.05*5= $18.30   Now, I am left with only $1.15. I cannot but anything with this.   Hence Total Hotdogs = 250*8 + 20*5 = 2120
Answer: D
If the tens digit of positive integer x is 6 and the tens digit of positive integer y is 6, how many possible values of the tens digit of 2(x+y) can there be?  Choose the correct choice from the following.
A) 2 B) 3 C) 4 D) 5 E) 6

Solution: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 60 + p and 60 + q respectively.   2(60+p+60+q)= 240 + 2(p + q).   2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.   Then the tens and ones digits of 2(x+y) can range from 40 up to 76.   There can be 4 possibilities for the tens digit.   The answer is 4.
Answer: C
The sum of two numbers is 25 and their difference is 13. Find their product. Choose the correct choice from the following answers
A) 104 B) 114 C) 315 D) 325 E) 335

Solution: Let the numbers be x and y.   Then x + y = 25 and x - y = 13.   x = 19; y = 6   xy = 19 * 6= 
19 * 6 = 114
114   ANSWER:114
Answer: B
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 14 members of this sequence?
Choose the correct choice from the following options:
A) 878  B) 900  C) 560  D) 928  E) 1022

Solution: I would split them up like this.   23 28 33 and so on (7 terms)....the 7th term = 23+6*5= 
23+6*5 = 53
53   27 32 37 and so on (7 terms)......the 7th term= 27+6*5= 
27+6*5 = 57
57   Since the distance between any two numbers is the same we can use arithmetics   first+last/2 times no of numbers= the sum   (23+53)/2 * 7= 
(23+53)/2 * 7 = 266
266   (27+57)/2 * 7= 
(27+57)/2 * 7 = 294
294= 560   560
Answer: C
If Jesse flips a coin seven times in a row, what is the probability that the result will not be tails for more than 2 times?	Answers
A) 21/128  B) 29/128  C) 35/128  D) 1/16  E) 1/4

Solution: Not more than 2 times tails = at least 5 times heads   Atleast 5 heads in 7 flip.   The total outcome of flip is = 2^7 = 128   For any Coins problem write the ask in the shown format.   HHHHHTT   HHHHHHT   HHHHHHH   Once you have written in the above mentioned format the answer is pretty straight.   HHHHHTT = [7!]/5!*2! = 21   HHHHHHT = [7!]/6! = 7   HHHHHHH = [7!]/[7!] = 1   Sum 7  / 7= 
7  / 7 = 1
1   Sum= 21+7+1= 
21+7+1 = 29
29/128   Answer - 29/128
Answer: B
In the xy-coordinate system, if (m, n) and (m + 1, n + k) are two points on the line with the equation x = 2y + 5, then k = Choose the correct answer
A) 1/2
B) 1
C) 2
D) 5/2
E) 4

Solution: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+1 =2 *(n+k)+5.   By 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k+4 ---> 5=2k+4 --->k=1/2.   The answer is, therefore, (1/2).
Answer: A
Deepa started a business in 2009 by investing Rs.50,000. She invested Rs. 20,000 as additional amount in 2010 and her friend Sushma joined her with an amount of Rs.70,000. Deepa invested another Rs. 20,000 in 2011 and Avanthi joined them with Rs. 70,000. At the end of these 3 years, they earned a profit of Rs. 3,00,000. Find Sushma's share ?	Choose the correct answer:
A) Rs.1,00,229  B) Rs.1,00,209  C) Rs.1,00,012  D) Rs.1,00,000  E) Rs.1,00,109

Solution: Deepa invested Rs.50,000 for 12 months, Rs.(50000 + 20000) for 12 months and Rs.(50000 + 20000 + 20000) for 12 months.   i.e, she invested Rs.50,000 for 12 months, Rs.70000 for 12 months and Rs.90000 for 12 months.   Sushma invested Rs. 70000 for 2 years; i.e, Rs.70000 for 24 months   And, Avanthi invested Rs.70000 for 1 year; i.e, Rs. 70000 for 12 months.   Their investing ratio:   Deepa : Sushma : Avanthi = (50,000 x 12 + 70000 x 12 + 90000 x 12):(70000 x 24):(70000 x 12)   = (25,20,000):(16,80,000):(8,40,000) = 252:168:84 = 3:2:1   Total profit for 3 years = Rs.3,00,000   Therefore, Sushma's share = Rs.(3,00,000 x 2 /(3+2+1)) = Rs.(3,00,000 x 2/6) = Rs.1,00,000.   Answer: Rs.1,00,000
Answer: D
The ratio of the volumes of two cubes is 8: 27 What is the ratio of their total surface areas? Choices.
A) 2:4	B) 3:6	C) 4:12	D) 4:9	E) 1:3

Solution: Ratio of the sides = Â³âˆš8 : Â³âˆš27   = 2 : 3   Ratio of surface areas =4:9   Answer: 4:9
Answer: D
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.12.60 less, he would have gained 30%. Find the cost of the article.  Choose the correct choice from the following answers:  A) 30  B) 40  C) 50  D) 60  E) 70

Solution: Let C.P=100   Gain=25%   S.P=125   Supposed C.P=80   Gain=30%   S.P=(130*80)/100= 
(130*80)/100 = 104
104   60iff=(125-104)= 
(125-104) = 21
21   60iff 21 when C.P=100   then 60iff 12.60 when C.P=(100*12.60)/21= 
(100*12.60)/21 = 60
60   ANSWER:60
Answer: D
A snooker tournament charges $40.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 300 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?	Choose the correct choice from the following:	A) 190	B) 180	C) 150	D) 200	E) 300

Solution: let no of sits in vip enclosure is x then x*40 +15( 300-x) =7500 or 25x = 7500 -4500 , x = 3000/25= 
3000/25 = 120
120   vip=120 general 200   200
Answer: D
In a sports club with 28 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?  Choices:
A) 7  B) 8  C) 9  D) 10  E) 11

Solution: Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,   (17-x)+(19-x)+x+2=28   38-2x+x=28   38-x=28   x=10   So 8 members play both badminton and tennis.   10
Answer: D
Look at this series: 15, 15, ?, 27, 39, 39, ... What number should fill the blank? Choose the correct choice from the following answers
A) 51 B) 39 C) 27 D) 15 E) None

Solution: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.   Answer: Option 27
Answer: C
Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?	Choose the correct choice from the following choices:
A) 27%	B) 28%	C) 20%	D) 16%	E) 25%

Solution: Rs.1440 - 1200   = Rs.240 is the interest on Rs.1200 for one year.   Rate of interest   = (100 * 240) / (100 * 1)   = 20% p.a   Answer: 20%
Answer: C
A trader sells 20 meters of cloth for Rs. 4500 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?	Pick:
A) Rs. 380 B) Rs. 215 C) Rs. 190 D) Rs. 395 E) None of these

Solution: SP of 1m of cloth = 4500/20= Rs. 225   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 225 - Rs. 10 = Rs. 215.   ANSWER:Rs. 190
Answer: C
A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?  Select.
A) 59000 B) 92828 C) 59282 D) 22888 E) 12991

Solution: Interest received by A from B = 10% of half of Rs.50000 = 10% of Rs. 25000 = Rs.2500.   Amount received by A per annum for being a working partner = 1500 x 12 = Rs.18000   Let 'P' be the part of the remaining profit that A receives as his share.   So,total income of A = (Rs.2500 + Rs.18000 + Rs. P )   Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.   We know that income of A = Twice the income of B   So, (2500 + 18000 + P ) = 2(P)   P = 20500   Thus, the total profit = 2P + Rs.18000   = 2(20500) + 18000 = Rs.59000.   Answer: 12991
Answer: E
A train with 1200m crosses a tree in 120sec, how much time will I take to pass a platform 700m long?	Choose the correct choice:  A) 150sec  B) 130sec  C) 190sec  D) 200sec  E) 100sec

Solution: s=1200/120   s-10m/sec   total length = 1900m   t=d/s   t=1900/10= 
1900/10 = 190
190sec   ANSWER 190sec
Answer: C
When Usha was thrice as old as Nisha, her sister Asha was 25, When Nisha was half as old as Asha, then sister Usha was 34. their ages add to 100. How old is Usha?
Choose the correct option:
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: Asha=25 Nisha =n Usha =3n   Asha=2a Nisha =a Usha =34   The difference of all ages must be same   25-2a=n-a=3n-34   We will get two equation   2n+a=34   n+a=25   From the equation we will get n=9 and a=16   The ages are Asha=2a=32 Nisha =16 and Usha =34   Sum of the ages =100   (32+x)+(16+x)+(34+x)=100   82+3x=100   3x=18   x=6   Age of Usha =34+6= 
34+6 = 40
40   ANSWER:40
Answer: D
A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 3/7th share. How much money is contributed by B?  Choose one:	A) A)Rs.12829	B) B)Rs.12800	C) C)Rs.24000	D) D)Rs.12804	E) E)Rs.12830

Solution: 16*8: x*4 = 4:3   x = 24 =>   Rs.2400   Answer: Rs.24000
Answer: C
A shipment of 240 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?  Choices.
A) 1/250	B) 9/74	C) 1/11	D) 1/9	E) 1/3

Solution: Probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = (84/240)   Probability of chosing one defective phone from a lot of 239(we already picked one) which ontains 83(we already picked one) defective phones is = (83/239)   Combined probability of series of events = product of the probabilities = (84/240)*(83/239)   84/240 is close to (7/20) and (83/239)= (25/72)   so answer is (7/20)*(25/72) (9/74)   So, answer will be 9/74
Answer: B
A circular ground whose radius is 15 metres, has a 1.2 metre-broad garden around it. What is the area of the garden in square metres?	Choose the correct choice from the following answers:	A) 118.67	B) 116.67	C) 117.67	D) 120.56	E) 120.57

Solution: Req. area = Ï€[(16.2)2 â€“ (15)2]   = 22â„7 Ã— (31.2 Ã— 1.2)[since a2 - b2 = (a + b)(a - b)]   = (22 Ã— 31.2 Ã— 1.2)/7 = 117.67sq m   Answer 117.67
Answer: C
A 230 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
Options.
A) 230m B) 240m C) 250m D) 260m E) 270m

Solution: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s   time= 9sec   let the lenght of second train is x   total distance covered= 230 + x   therefore, D= speed*time   thus 230 + x = 500/9 * 9= 
500/9 * 9 = 500
500-230= 
500-230 = 270
270 m   ANSW270mR:270m
Answer: E
In how many ways can the letters A, M, A, Z, O, N be arranged so that the two A's are not next to each other?
Choose the correct choice from the following.
A) 36  B) 48  C) 72  D) 96  E) 240

Solution: 2 A   1 M   1 Z   1 O   1 N   Number of ways these letters can be arranged = 6!/2! (2! to account 2 same As) = 360   Consider 2 As as 1 entity and thus the number of arrangements for (AA)MZON = 5! = 120   Total allowed cases = 360-120= 
360-120 = 240
240   240 is the correct answer.
Answer: E
An amount of Rs. 100000 is invested in two types of shares. The first yields an interest of 9% p.a and the second, 11% p.a. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was?
Pick
A) 37507 B) 37500 C) 83887 D) 29978 E) 29912

Solution: Let the sum invested at 9% be Rs. x and that invested at 11% be Rs. (100000 - x). Then,   (x * 9 * 1)/100 + [(100000 - x) * 11 * 1]/100 = (100000 * 39/4 * 1/100)   (9x + 1100000 - 11x)/100 = 39000/4= 
39000/4 = 9_750
9750   x= 62500   Sum invested at 9% = Rs. 62500   Sum invested at 11% = Rs. (100000 - 62500) = Rs. 37500.   Answer:37500
Answer: B
A fair red coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?	Choose the correct choice from the following answers:
A) A)37/256
B) B)56/256
C) C)65/256
D) D)70/256
E) E)81/256

Solution: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.   8!/6!2! = 7*4= 
7*4 = 28
28   8!/7!1!= 8   8!/8! = 1   28 + 8 + 1 8 /8= 
8 /8 = 1
1   28 + 8 + 1= 
28 + 8 + 1 = 37
37/256   ans:37/256
Answer: A
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is?  Choose the correct choice from the following
A) 5/5
B) 5/9
C) 5/1
D) 5/7
E) 5/2

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   Answer: 5/9
Answer: B
A box contains six bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?	Choose the correct choice from the following answers:
A) 21/81 B) 16/81 C) 65/81 D) 2/3 E) 1/2

Solution: Required probability   = 1 - 16/81   = 65/81   Answer: 65/81
Answer: C