MU-NLPC/Calc-aqua_rat huggingface dataset:
The average weight of a group of boys is 30 kg. After a boy of weight 33 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?  Pick:
A) 4  B) 8  C) 5  D) 2  E) 9

Solution: Let the number off boys in the group originally be x.   Total weight of the boys = 30x   After the boy weighing 33 kg joins the group, total weight of boys = 30x + 33   So 30x + 33 + 31(x + 1) = > x = 2.   Answer: 2
Answer: D
A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Choices
A) 1.3 B) 1.2 C) 1.9 D) 1.5 E) 1.1

Solution: M = 4.5   S = x   1.5S = 4.5 + x   US = 4.5 + x   4.5 + x = (4.5 - x)2   4.5 + x = 9 -2x   3x = 4.5   x = 1.5   Answer:1.5
Answer: D
Which of the following lines has x-intercept and y-intercept that are integers Q?	Answers:
A) y=3x+1
B) y=√x+1
C) y=-2/x
D) y=x^2-1
E) xy=1

Solution: Values that satisfy y=x^2-1 are (x,y)=(-1,0),(1,0),(0,-1). Hence, they are all integers Q and the correct answer is y=x^2-1.
Answer: D
if a^2+b^2=177and ab=54 then find the value of a+b/a-b?
Select
A) 5 B) 15 C) 6 D) 3 E) 7

Solution: (a+b)^2=a^2+b^2+2ab=117+2*24=225   a+b=15   (a-b)^2=a^2+b^2-2ab=117-2*54   a-b=3   a+b/a-b=15/3= 
15/3 = 5
5   Option 5
Answer: A
A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to
Rs. 206. Find the number of coins of each type.  Choose the correct choice from the following answers
A) 165  B) 174  C) 160  D) 163  E) 135

Solution: Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.   (5x/2)+( 9x/ 4)+(4x/10)=20650x + 45x + 8x = 41201O3x = 4120 x=40.   Number of 50 p coins = (5 x 40) = 200; Number of 25 p coins = (9 x 40) = 360;   Number of 10 p coins = (4 x 40) = 160.   ANSWER 160 160
Answer: C
The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Options
A) 17 B) 27 C) 19 D) 16 E) 87

Solution: Sum of the 10 numbers = 230   If each number is increased by 4, the total increase =   4 * 10= 
4 * 10 = 40
40   The new sum= 230 + 40= 
230 + 40 = 270
270 The new average= 270/10= 
270/10 = 27
27.   Answer:27
Answer: B
Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 5 of the slips are the drawn, without replacement, what is the probability that all 5 have a even number written on it?	Choose one: A) 1/252 B) 1/10 C) 1/8 D) 1/2 E) 5/9

Solution: Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same)   P(+ on 1st pick) = 5/10   P(+ on 2nd pick) = 4/9   P(+ on 3rd pick) = 3/8   P(+ on 4rd pick) = 2/7   P(+ on 5rd pick) = 1/6   5/10*4/9*3/8*2/7*1/6=1/252   1/252
Answer: A
The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?	Answers.
A) 81 : 121  B) 81 : 128  C) 81 : 120  D) 81 : 125  E) 81 : 122

Solution: Ratio of the sides = 3√729 : 3√1331 = 9 : 11   Ratio of surface areas = 92 : 112 = 81 : 121   81 : 121nswer: 81 : 121
Answer: A
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 15% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above? Choose the correct choice from the following options
A) 5%	B) 10%	C) 15%	D) 25%	E) 30%

Solution: 60-(x+15+z) + 50-(x+15+y) + 35-(z+15+y) + x + +y + z +15 = 100   where x = people who bought MilkChicken   y = people who bought chickenApples   z= people who bought Milk and Apples   x+y+z= the number of people who bought just exactly two products.   Hence solving the above equation we get,   115 -(x+y+z) = 100   Thus, x+y+z= 15   Answer: 15%
Answer: C
Ayesha’s father was 38 years of age when she was born while her mother was 34 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?	Choose one
A) 2 years  B) 4 years  C) 6 years  D) 8 years  E) None

Solution: EXPLANATION   Mother’s age when Ayesha’s brother was born = 34 years.   Father’s age when Ayesha’s brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 – 34) years = 8 years.   Answer 8 years
Answer: D
The ratio of boarders to day students at a school was originally 2 to 5. However, after a number of new boarders join the initial 60 boarders, the ratio changed to 1 to 2. If no boarders became day students and vice versa, and no students left the school, how many new boarders joined the school? Choose the correct choice from the following answers:  A) 12  B) 15  C) 20  D) 24  E) 30

Solution: Let x be the number of new boarders.   The ratio changed from 2:5 = 4:10 up to 1:2 = 5:10.   60 / (60+x) = 4/5   x = 15   The answer is 15.
Answer: B
Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $100 and $105 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings? Choose the correct option.
A) 600  B) 720  C) 1000  D) 1200  E) 1440

Solution: $100 for 2 years = $50 per year.   Extra $5 yearned with the compound interest is the percent yearned on percent. So, $5 is yearned on $50, which means that the interest = 10%.   This on the other hand means that half of the savings = 50*10= 
50*10 = 500
$500. Twice of that= $1,000.   Answer: 1000.
Answer: C
The cost price of a radio is Rs.1500 and it was sold for Rs.1305, find the loss %?  Choose the correct choice from the following options.
A) 13% B) 16% C) 17% D) 78% E) 28%

Solution: 1500 ---- 195   100 ---- ? => 13%   13%nswer:13%
Answer: A
Solve below question 2x + 1 = -19 Pick:  A) -8  B) -9  C) 9  D) 8  E) -10

Solution: 2x + 1 = -19   x = -10   -10
Answer: E
Tom invested Rs. 15000 @ 8% per annum for two years. If the interest is compounded half-yearly, then the amount received by Tom at the end of the year will be? Options:
A) 17,546.75  B) 17,547.40  C) 17,547.88  D) 17,548.32  E) 17,548.80

Solution: P = Rs. 15000; R = 8% p.a. = 4% per half-year; T = 2 years = 4 half-year   Amount = [15000 * (1 + 4/100)4]   = (15000 * (1.04)4) = Rs. 17547.88   Answer: 17,547.88
Answer: C
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 $45000 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?  Pick one:
A) 5 B) 6 C) 9 D) 10 E) 15

Solution: Since the starting point is given as the $4000 scholarship,   Assume $4000 scholarships to be x   6y the given information, $2500 scholarships = 2x   and $1250 scholarships = 6x   Gievn: Total $1250 scholarships = $45000   6x*1250 = 45000   Solve for x = 6   Option 6
Answer: B
There are 9 points marked on the circumference of a circle. How many hexagons can be formed by connecting 6 points of the 9 points?  Choose the correct answer.
A) 84 B) 86 C) 88 D) 90 E) 92

Solution: 9C6=84   The answer is 84.
Answer: A
To prepare cake of type A, it requires 4 eggs. While to prepare cake of type B, it requires 6 eggs. If there are 30 eggs available, and at least one cake of each type needs to be prepared, maximum how many cakes can be prepared of type B?  Choose the correct choice from the following choices: A) 1 B) 2 C) 3 D) 4 E) 5

Solution: If a number of type A cakes are prepared, and b number of type B cakes are prepared. Based on total number of eggs used, 4a + 6b = 30.   => 6b = 30 - 4a   => b = 5 - (4/6)a = 5 - (2/3)a   To maximize b, we have to minimize a, and a has to be a multiple of 3. Also, since at least one cake of each type is to be prepared, a >= 1.   => a = 3.   b = 5 - (2/3)3 = 3.   Answer: 3
Answer: C
A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?  Choose the correct choice from the following answers.
A) 16  B) 11  C) 36  D) 17  E) 12

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 240 + 120= 
240 + 120 = 360
360 m.   Time taken= 360/10= 
360/10 = 36
36 sec.   Answer:36
Answer: C
A thief goes away with a SANTRO car at a speed of 30 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?	Choose the correct choice from the following choices
A) 1 hours B) 2 hours C) 2/3 hours D) 1/3 hours E) 2/5 hours

Solution: -----------30--------------------|   60 30   D = 30   RS = 60 â€“ 30 = 30   T = 30/30= 
30/30 = 1
1 hours   1 hoursNSWER:1 hours
Answer: A
The ratio of two quantities is 10 : 7. If each of the quantities is increased by 2, their ratio changes to 15:11 then the greatest number is? Pick:
A) 10  B) 12  C) 15  D) 16  E) 20

Solution: Let the numbers be 10x and 7x   Then 10x+2 / 7x+2 = 15/11   110x+22 = 105x+30   5x = 8   x = 1.6   Greatest number = 10*1.6= 
10*1.6 = 16
16   Answer is 16
Answer: D
The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:	Answers
A) 74 B) 94 C) 184 D) 364 E) 512

Solution: L.C.M. of 6, 9, 15 and 18 is 90.   Let required number be 90k + 4, which is multiple of 7.   Least value of k for which (90k + 4) is divisible by 7 is k = 4.   Required number = (90 x 4) + 4 = 364.   Answer: Option 364
Answer: D
College T has 1000 students. Of the 300 students majoring in one or more of the sciences,150 are majoring in Chemistry and 180 are majoring in Biology. If at least 60 of the students are not majoring in either Chemistry or Biology, then the number of students majoring in both Chemistry and Biology could be any number from?
Choose the correct choice from the following options:	A) 110 to 150	B) 60 to 150	C) 30 to 150	D) 60 to 140	E) 70 to 130

Solution: Total = Chemistry + Biology - Both + Neither   300 = 150 + 180 - Both + N   We know that N (Neither) must be at least 30, so set N=30 and solve:   300 = 150 + 180 - Both + 60   300 = 330 - Both   Both = 30   Even if you're not sure whether 150 is the highest or lowest Both could possibly be, it doesn't matter, because you know it's a boundary point of the range,   Both can not be greater than 150, because even if every chemistry major was also a biology major, there are only 130 chemistry majors total. 30 to 150 the solution.
Answer: C
A certain class of students is being divided into teams. The class can either be divided into 18 teams with an equal number of players on each team or 24 teams with an equal number of players on each team. What is the lowest possible number of students in the class? Choose the correct choice from the following answers
A) 6
B) 36
C) 48
D) 60
E) 72

Solution: Prime factorization of 18 = 2*3^2   Prime factorization of 24 = 2^3 *3   LCM of the given numbers = 2^3 *3^2   =72   Answer 72
Answer: E
Sukhbir is taller than Randhir but not as tall as Ajit. If Manoj is taller than Nitin, who is shorter than Ajit, then who among them is the shortest?
Select the correct option: A) Nitin B) Sukhbir C) Manoj D) Data inadequate E) None of these

Solution: Data Inadequate. As No relation is given among Randhir and Nitin.   ANSWER:Data inadequate
Answer: D
Students are in clubs as follows: Science-20, Drama-30, and Band-12. No student is in all three clubs, but 8 are in both Science and Drama, 6 are in both Science and Band, and 4 are in Drama and Band.
How many different students are in at least one of the three clubs?
Pick:
A) 36 B) 38 C) 42 D) 44 E) 48

Solution: Total students = S + 44 + B - (sum of 2-group overlaps) + (all three)   Total students = 20 + 30 + 12 - (6 + 8 + 4) + 0= 
20 + 30 + 12 - (6 + 8 + 4) + 0 = 44
44 students.answer is 44
Answer: D
Find the odd man out.
8, 20, 14, 21, 16, 28, 32 Answers
A) 16
B) 21
C) 8
D) 28
E) 14

Solution: Explanation:   Each of the numbers except 21 is a even numbers.   Answer: 21) 21
Answer: B
Find the odd man out. 21, 28, 35, 42, 49, 51, 56
Choose the most appropriate option.
A) 21
B) 28
C) 35
D) 42
E) 51

Solution: All numbers except 51 are multiples of 7   Answer is 51
Answer: E
A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:
Choose the most appropriate option:  A) 3:4  B) 3:5  C) 4:5  D) 16:15  E) 12:13

Solution: For an income of $1 in 9% stock at 96, investment =$(96/9)=32/3   For an income of $1 in 12% stock at 120, investment =$(120/12)= 
(120/12) = 10
$10   Ratio of investment=32/3:10   =16:15   Option 16:15
Answer: D
In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 4720 votes were polled, then how many valid votes did B get?
Pick:
A) 1534 B) 2999 C) 2834 D) 2777 E) 2991

Solution: Let the total number of votes polled in the election be 100k.   Number of valid votes = 100k - 20% (100k) = 80k   Let the number of votes polled in favour of A and B be a and b respectively.   a - b = 15% (100k) => a = b + 15k   => a + b = b + 15k + b   Now, 2b + 15k = 80k and hence b = 32.5k   It is given that 100k = 4720   32.5k = 32.5k/100k * 4720 = 1534   The number of valid votes polled in favour of B is 1534.   1534nswer: 153432.5 /100  * 4720= 
32.5 /100  * 4720 = 1_534
1534   The number of valid votes polled in favour of B is 1534.   1534nswer: 1534
Answer: A
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
Select:
A) 22
B) 28
C) 29
D) 20
E) 21

Solution: Average of 20 numbers = 0   Sum of 20 numbers = (0 * 20)= 
(0 * 20) = 0
0   It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).   Answer: 20
Answer: D
A man invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest of 5% per annum. How much amount will Albert get on maturity of the fixed deposit ? Choose one: A) Rs.8600 B) Rs.8620 C) Rs.8820 D) Rs. 8840 E) Rs. 8940

Solution: Amount = 8000 *1+(5/100)2   = 8000 *21/20 * 21/20   = Rs.8820   ANSWER:Rs.8820
Answer: C
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 $211? Choose the correct choice from the following answers.
A) 1,108	B) 2,100	C) 2,108	D) 2,124	E) 2,180

Solution: I think it should be E.   I can buy 8 250-pack for Rs 22.95*8= 
22.95*8 = 183.6
$183.60   Now, I can buy 9 20-pack for 3.05*9= $15.25   Now, I am left with only $1.15. I cannot but anything with this.   Hence Total Hotdogs = 250*8 + 20*9= 
250*8 + 20*9 = 2_180
2180
Answer: E
Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 5 kg of fresh grapes?
Choose the most appropriate option: A) 2 kg B) 2.4 kg C) 2.5 kg D) 10 kg E) 0.625

Solution: The weight of non-water in 5 kg of fresh grapes (which is 100-90= 
100-90 = 10
10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20= 
100-20 = 80
80% of whole weight), so 5âˆ—0.1=xâˆ—0.8--> x=0.625   Answer: 0.625.
Answer: E
Find the number of shares that can be bought for Rs.8800 if the market value is Rs.20 each with brokerage being 2.5%.	Choose the correct answer:
A) 429.3	B) 270	C) 177	D) 166	E) 111

Solution: Explanation:   Cost of each share = (20 + 2.5% of 20) = Rs.20.5   Therefore, number of shares = 8800/20.5 = 429.3   429.3NSWER:429.3
Answer: A
A fast food restaurant sells chicken in orders of 6, 9, and 20.
What is the largest number of pieces of chicken you cannot order from this restaurant?	Options:
A) 23
B) 33
C) 43
D) 53
E) 63

Solution: 43.   After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).
Answer: C
A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.50. If the company’s latest order required a truck with at least 384,000 cubic inches of storage space in which to ship the hats in their boxes, what was the minimum value of the order?	Choose the most appropriate option
A) $3,000	B) $1,350	C) $1,725	D) $2,050	E) $2,250

Solution: Number of boxes= Total volume/volume of one box= 384,000/ (8*10*12)= 400   One box costs 7.50, so 400 box will cost= 400*7.5= 
400*7.5 = 3_000
3000   $3,000 is the answer
Answer: A
Free notebooks were distributed in a class among all the students. Each student got notebooks which were one-eighth of the number of student. If number of student been half, then each child would have received 16 notebooks in total. Find the total number of books distributed among students?  Choose the correct answer.
A) 435	B) 456	C) 467	D) 489	E) 512

Solution: Let suppose total number of students in class are X.   Then from the question we can conclude it that,   X∗18X=X2∗16=>X=64Total notebooks,=18X2=(18∗64∗64)=512   512
Answer: E
A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?  Choose the correct choice from the following options:
A) 60%  B) 50%  C) 80%  D) 70%  E) 53%

Solution: L.C.M of 15 and 12 = 60   CP of 60 articles = Rs. 100 (25 * 4)   SP of 60 articles = Rs. 150 (30 * 5)   Profit percentage = (150 - 100)/100 * 100= 
(150 - 100)/100 * 100 = 50
50%   Answer: 50%
Answer: B
Two pipes can separately fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is full, a leak develops in the tank through which one-third of water supplied by both the pipes goes out. What is the total time taken to fill the tank?
Select the correct option
A) 18 hrs B) 16 hrs C) 15 hrs D) 12 hrs E) 10 hrs

Solution: Explanation:   1/20 + 1/30 = 1/12   1 + 1/3 = 4/3   1 --- 12   4/3 --- ?     4/3 * 12= 
  4/3 * 12 = 16
16 hrs   ANSWER IS 16 hrs
Answer: B
A & B started one company. They invest Rs. 1,00,000/- each. They deposit the money to Bank. Bank give 1% interest per month. After 2 years B left from company and asked A to return the money with interest. A says it will take time to release the FD and he assure B to give the money withinterest @0.5%. B Agreed this. What is the profit of A? Pick one.
A) 48000	B) 12000	C) 36000	D) 24000	E) 30000

Solution: Total Investment : 100000/-*2=200000/-   Interest rate @ 1%= 200000*1%*12*2= 48000/-   Total : 248000/-   Interest to B : 100000/-*0.5%*12*2 = 12000/-   Paid to B : 100000/- + 12000/- = 112000/-   profit of A : 36000/-   Answer is 36000
Answer: C
At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses T at the restaurant? (Assume that all boxes are filled to capacity.) Select the correct option
A) 96
B) 240
C) T=256
D) T=384
E) T=480

Solution: Most Test Takers would recognize the system of equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....   We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.   This means, at the minimum, we have...   1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272= 
12 + 272 = 284
284 glasses at the MINIMUM   Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....   The difference in the number of boxes MUST be 16 though, so we could have....   2 small boxes and 18 large boxes   3 small boxes and 19 large boxes   etc.   With every additional small box + large box that we add, we add   12+16= 
  12+16 = 28
28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....   284+28= 
284+28 = 312
312   312+28= 
312+28 = 340
340   340+28= 
340+28 = 368
368   368+28= 
368+28 = 396
396   At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....   396+28= 
396+28 = 424
424   424+28= 
424+28 = 452
452   452+28= 
452+28 = 480
480   Final Answer:   T=480
Answer: E
A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 20 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $400 before any discount?	Choose the correct option: A) $230.00 B) $224.00 C) $263.80 D) $282.00 E) $210.00

Solution: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).   We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 20% off of the DISCOUNTED price....   We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):   30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...   The final price of an item that originally cost $400 would be.....   ($400)(.7)(.8) =   ($400)(.56)=224   Final Answer:   $224.00
Answer: B
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 20 hrs and a machine of type S does the same job in 30 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used? Choose the correct choice from the following options:
A) 4 B) 5 C) 6 D) 8 E) 9

Solution: Type R completes 1/20 of the job each hour.   Type S completes 1/30 of the job each hour.   Together R and S complete 1/20 +1/30 = 1/12 of the job each hour.   Let n be the number of each type of machine.   2*n*(1/12) = 1 job completed   n = 6   The answer is 6.
Answer: C
A letter lock consists of three rings each marked with nine different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Choose the correct choice from the following.
A) 176 B) 178 C) 728 D) 789 E) 770

Solution: Since each ring consists of nine different letters, the total number of attempts possible with the three rings is   = 9 * 9 * 9= 
9 * 9 * 9 = 729
729. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 729 - 1= 
729 - 1 = 728
728.   Answer: 728
Answer: C
How many words can be formed using the letters of the word “COMPANY”? Choose the correct choice from the following answers:
A) 1224
B) 2434
C) 3243
D) 3435
E) 5040

Solution: There are ‘7’ different letters of the word “COMPANY”   Number of Permutations taking all the letters at a time = 7P7   7!= 5040   5040
Answer: E