MU-NLPC/Calc-aqua_rat huggingface dataset:
A bag contains a certain number of 50 paise coins, 20 paise coins and 10 paise coins inthe ratio 3:4:5. If the total value of all the coins in the bag is Rs.350, find the number of 50 paise coins ?	Choose the correct choice:
A) 498  B) 488  C) 375  D) 528  E) 418

Solution: 50*3k + 20*4k + 10*5k = 35000   280k = 35000 => k = 125   50p coins = 3k = 3*125= 
3*125 = 375
375   ANSWER:375
Answer: C
The cost price of three varieties of oranges namely A, B and C is Rs 20/kg, Rs 40/kg and Rs 50/kg. Find the selling price of one kg of orange in which these three varieties of oranges are mixed in the ratio of 2 : 3 : 5 such that there is a net profit of 20%?	Choose the correct choice from the following answers.
A) Rs 48	B) Rs 48.6	C) Rs 49.2	D) Rs 49.8	E) Rs 48.8

Solution: Rs 49.2ost price of one kg of orange in which the three varieties of oranges are mixed in the ratio 2 : 3 : 5 is equal to S where   S = 0.2 x 20 + 0.3 x 40 + 0.5 × 50   = 4 + 12 + 25= 
4 + 12 + 25 = 41
Rs 41   Selling price per kg of oranges to ensure there is a net profit of 20%= 1.2 x 41   = Rs 49.2   ANSWER:Rs 49.2
Answer: C
A certain class of students is being divided into teams. The class can either be divided into 8 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) 24 E) 72

Solution: Let total no of students in the class be N   So, we are told that N is divisible by both 8 24   So, Lets find the least common multiple of 8 24 , ie 24   So our answer is (24) 24
Answer: D
The compound ratio of 5:6, 3:4 and 4:5? Choose the correct choice from the following choices.
A) 1:1
B) 1:87
C) 1:6
D) 1:9
E) 1:2

Solution: 5/6 * 3/4 * 4/5 = 1/2   1:2   Answer: 1:2
Answer: E
A 8000 liter tank, half-full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes. At the same time, the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes. How many minutes does it take to fill the tank completely? Choose the correct choice from the following: A) 8 B) 12 C) 18 D) 24 E) 48

Solution: In: we have: 1,000/2min = 500 litres per minute   Out: we have: 1,000/4 + 1,000/6   Then do: IN - OUT to figure out the net inflow per minute (you get 83.3). Then divide the total number of litres you need (4,000 by that net inflow to get the minutes) - 48 min. Answer 48.
Answer: E
Find the simple interest on $2500 for 3 years at 10% per annum? Choose the correct choice from the following: A) $250 B) $300 C) $750 D) $600 E) $1000

Solution: SI = PTR/100   = 2500*3*10/100= 
2500*3*10/100 = 750
$750   Answer is $750
Answer: C
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is	Select the correct option: A) 2 mph B) 2.5 mph C) 3 mph D) 4 mph E) 5 mph

Solution: Let the speed of the stream x mph.   Speed downstream = (10 + x) mph.   Speed upstream = (10 - x) mph.   36/(10-x)-36/(10+x)=90/60   72x x 60 = 90(100-x2)   x2+48x-100 = 0   (x+ 50)(x - 2) = 0   x = 2 mph.   2 mphNSWER:2 mph
Answer: A
What is the remainder when 6990990900032 is divided by 32 ?	Select the correct option:  A) 5  B) 0  C) 4  D) 2  E) 3

Solution: Though i was unaware of the divisibility test for 32 but i guessed the pattern!!   divisibility rule for 4- last two digits must be divisible by 4   divisibility rule for 8- last three digits must be divisible by 8   similarly, divisibility rule for 32 - last five digits must be divisible by 32   Hence, Ans 0
Answer: B
Which of the following points is closest to line y=x	Pick:
A) (2, -1)  B) (2, 4)  C) (-1, 1)  D) (1, 2)  E) (-2, 0)

Solution: Attachment:   m12-20.pngAs you can see point (1, 2) is the closest to line y=x.   Answer: (1, 2).
Answer: D
What is the greatest integer that will always evenly divide the sum of three consecutive integers?
Pick one.
A) 2  B) 3  C) 4  D) 6  E) 12

Solution: Let the three consecutive integers be x , x + 1 , x + 2   Sum = x + x + 1 + x + 2   = 3x+3 = 3(x+1)   Therefore , 3 will always be a factor .   Answer 3
Answer: B
A delegation of 5 members has to be formed from 3 ladies and 5 gentlemen. In how many ways the delegation can be formed, if 2 particular ladies are always included in the delegation?	Pick:
A) 20	B) 82	C) 82	D) 25	E) 27

Solution: Explanation:   There are three ladies and five gentlemen and a committee of 5 members to be formed.   Number of ways such that two ladies are always included in the committee = ⁶C₃ = (6 * 5 * 4)/6= 
(6 * 5 * 4)/6 = 20
20.   20nswer:20
Answer: A
A ship sails out to a mark at the rate of 15 kmph. and sails back at the rate of 10 kmph. The average rate of sailing is ? Choose the correct choice from the following answers.
A) 5 km/hr B) 12 km/hr C) 12.5 km/hr D) 25 km/hr E) None

Solution: Answer   Average = ( 2uv / u +v ) km/hr   = ( 2 x 15 x 10 ) / (15 +10 ) km/hr.   = 12 km/hr.   Correct Option: 12 km/hr
Answer: B
The unit digit in the product (594 * 897* 929 * 462) is:  Select:
A) 2
B) 5
C) 6
D) 4
E) 10

Solution: Explanation:   Unit digit in the given product = Unit 4igit in (4*7*9*2) = 4   ANSWER: 4
Answer: D
A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 18% less than the price each head sold for the day before.what was the gross profit on this shipment?
Choose the correct answer: A) $105 B) $115 C) $125 D) $130 E) $135

Solution: Sol:   1500 heads -> $600   1 head -> $600/1500   1 head -> $(2/5)   25% more of (2/5) -> 125/100 * 2/5 = $(1/2)   He sold   2/3*1500= 
  2/3*1500 = 1_000
1000 heads for $(1/2) per head   Total revenue by selling 1000 heads= 1000 * 1/2= 
1000 * 1/2 = 500
$500   Heads left: 500   Cost per head: 82% of the previous price: 82/100 * 1/2= $(16/39)   Total revenue by selling 500 heads = 16/39 * 500 = 205   Total revenue after selling 1500 cabbage heads - 205+500 = $705   Money spent on the purchase: $600   Profit = 705-600= 
705-600 = 105
$105   $105ns: $105
Answer: A
How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest? Select the correct option:
A) 3 years	B) 4 years	C) 6 years	D) 5 years	E) 7 years

Solution: Time = (100 x 81)/(450 x 4.5) years = 4 years.   answer 4 years
Answer: B
Ramu bought an old car for Rs. 40000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
Pick one:	A) A)14%	B) B)16%	C) C)18%	D) D)21.6%	E) of these

Solution: Total CP = Rs. 40000 + Rs. 13000 = Rs. 53000 and SP = Rs. 64900   Profit(%) = (64900 - 53000)/55000 * 100 = 21.6%   ANSWER:21.6%
Answer: D
If the sum of a set of 5 different positive prime numbers is 94, what is the difference between largest and smallest prime numbers between them?	Choose the correct choice from the following answers
A) 53  B) 51  C) 47  D) 41  E) 31

Solution: All prime numbers apart from 2 are odd.   Even + Even = Even   Odd + Even = Odd   Odd + Odd = Even   We are given 5 different prime numbers, whose sum is 94 i.e even   If we include 2, we will have 4 odd prime numbers and one even.   This sum would be odd   If we exclude 2, we will have 5 odd numbers.   This sum would be even   Hence 2 is included.   The possible 5 no. are = 11+7+2+43+31= 
11+7+2+43+31 = 94
94   the difference between largest and smallest prime numbers between them= 43 - 2= 
43 - 2 = 41
41   Ans - 41
Answer: D
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?	Choose the correct choice:
A) 28  B) 10  C) 288  D) 277  E) 211

Solution: 7*5: 5*x = 7:10   x = 10   Answer: 10
Answer: B
Ms. Mary sold two properties, X and Y, for $40,000 each. She sold property X for 20 % more than she paid for it and sold property Y for 20% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
Choose the correct choice from the following answers
A) $3233.33  B) $3433.33  C) $3333.33  D) $3533.33  E) $3633.33

Solution: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...   Total %Loss = (Common Gain% or Loss%/10)^2   Hence Here Loss% = (20/10)^2 = 4%   which means he recovered only 96% of his investment which amount to a total revenue = 40000 + 40000= 
40000 + 40000 = 80_000
80000   i.e. 96% of cost= 80000   therefore, 4% of cost (Loss) = $3333.33   Answer: $3333.33
Answer: C
In a recent election, Ms. Robbins received 8,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 5 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
Choose the correct choice:	A) 0.06N + 3,200	B) 0.1N + 7,200	C) 0.4N + 7,200	D) 0.1N + 8,000	E) 0.03N + 8,000

Solution: I will go with option E   According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 8000 votes from independent voters and 5 percent from registered voters (i.e 0.05 * 0.6 * N = 0.03N). Hence total votes = 8000 + 0.03N ....option 0.03N + 8,000
Answer: E
The jogging track in a sports complex is 850 m in circumference. Rakesh and his wife start from the same point and walk in opposite directions at 4.2 km/hr and 3.3 km/hr respectively. They will meet for the first time in?  Choices
A) 5.9 min  B) 6.8 min  C) 7.2 min  D) 8.5 min  E) 9.0 min

Solution: Clearly, the two will meet when they are 850m apart.   To be (4.2 + 3.3)= 
(4.2 + 3.3) = 7.5
7.5 km apart, they take 1 hour.   To be 850 m apart, they take= (850/7500 * 60)= 
(850/7500 * 60) = 34/5 = around 6.8
6.8 min.   Answer: 6.8 min
Answer: B
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?  Choose one:  A) 5 : 7 : 8  B) 20 : 49 : 64  C) 38 : 28 : 21  D) 3:7:9  E) None of these

Solution: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.   Then, 14x : 8y : 7z = 5 : 7 : 8.   Now,	14x/8y=5/7   then 98x = 40y   then y =	49/20x   And,	14x/7z=5/8   then112x= 35z   and z =(112/35 )x =(16/5 )x.   x : y : z = x :	(49/20)x	:(16/20)x	= 20 : 49 : 64   ANSWER:20 : 49 : 64
Answer: B
A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. If he sold all of them at a uniform profit of 15%, then he would have got Rs. 40 less. The cost price of each clock is?  Choose the correct choice from the following answers:
A) 26
B) 28
C) 80
D) 26
E) 21

Solution: Let C.P. of clock be Rs. x.   Then, C.P. of 90 clocks = Rs. 90x.   [(110% of 40x) + (120% of 50x)] - (115% of 90x) = 40   44x + 60x - 103.5x = 40   0.5x = 40 => x = 80   Answer: 80
Answer: C
A and B together can complete work in 6 days. A alone starts working and leaves it after working for 3 days completing only half of the work. In how many days it can be completed if the remaining job is undertaken by B? Select:
A) 3
B) 8
C) 5
D) 6
E) 7

Solution: Explanation:   (3+B) one day work =1/6   now 3 does half of the work in 3 days so 3 can complete the whole work in 6 days   3’s one day work =1/6   B’s one day work=1/6 - 1/6= 1/6   B alone can complete the work in 6 days so half of the work in 3 days   3nswer: Option 3
Answer: A
If TEAR is coded as 4657 and BOX is coded as 125. How is BETA coded?  Choose the correct answer
A) 1465	B) 1645	C) 1654	D) 1456	E) 1546

Solution: e=6 t-4 a-5 from the code TEAR, b-1 from the code 1645OX, ANSWER:1645
Answer: B
If 20 typists can type 44 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
Choose the correct choice from the following options:
A) 63	B) 72	C) 198	D) 216	E) 400

Solution: 20 typists can type 44 letters, so 30 typists can type = 44*30/20   44*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 44*30*60/20*20= 198   198 is the answer
Answer: C
What is the 29th digit to the right of the decimal point in the decimal form of 4/11? Choices:  A) 1  B) 2  C) 3  D) 4  E) 5

Solution: 4/11 = 0.363636...   The odd numbered positions in the decimal expansion are all 3.   The answer is 3.
Answer: C
20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres. How many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres? Choose one:
A) 30 B) 32 C) 60 D) Data inadequate E) None of these

Solution: Capacity of the tank = 20 × 13.5= 270 litres   When the capacity of each bucket = 9 litres, then the required no. of buckets   = 270⁄9 = 30   30nswer 30
Answer: A
Mane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Mane or Thomas is to be selected?	Pick:
A) 28
B) 46
C) 55
D) 63
E) 70

Solution: Ans:55   Solution:   M+T+6 = total 8 ,   we need to select at least one of the M and T or both= total 4 out of 8 - 4 out of 6   8554 - 6554   =55
Answer: C
There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 855. How many houses are there?	Select
A) 155	B) 161	C) 154	D) 156	E) 158

Solution: So it starts from 545 and goes like 547, 549,...... 855. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.   i.e., ([855-545][/2]+1 = 156   Ans 156
Answer: D
Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed musthe travel to reach A at 1 PM? Pick one
A) 8 kmph  B) 10 kmph  C) 12 kmph  D) 14 kmph  E) 16 kmph

Solution: Let the distance travelled by x km.   Then, x - x = 2   10 15   3x - 2x = 60   x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60 hrs = 6 hrs.   10   So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.   Required speed = 60 kmph. = 12 kmph.   5   12 kmph
Answer: C
If the average (arithmetic mean) of x and y is 60, and z – x = 80, what is the average of y and z?
Choose the correct choice from the following choices.
A) 100	B) 120	C) 125	D) 115	E) 90

Solution: x+y/2 = 60   => x+y = 120   x = z - 80...sub this value   z-80+y = 120   =>z+y = 200   =>z+y/2 = 100   100nswer : 100
Answer: A
At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
Choose the correct answer:
A) 16 4/17	B) 16 4/16	C) 16 4/12	D) 16 4/11	E) 16 4/13

Solution: At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.   To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.   15 min. are gained in   = (60/55 x 15)min   =16+4/11   The hands are coincident at 16 + 4/11 min past 3   Answer: 16 4/11
Answer: D
In a shower, 9 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Answers:
A) 75 cu. m
B) 1350 cu. m
C) 7500 cu. m
D) 75000 cu. m
E) 7.50 cu. m

Solution: 1 hectare = 10000 sq mtr   The volume of water that falls on 1.5 hectares of ground = 0.09*1.5*10000= 
0.09*1.5*10000 = 1_350
1350 cub mtr .   ANSWER:1350 cu. m
Answer: B
A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A's share is Rs. 855, what is the total profit?
Answers.
A) 1500	B) 2000	C) 3000	D) 3500	E) 2500

Solution: Profit as x   since 5% and 95% of x will be divided b/w 1500 and B ration 3:2   =>profit 95x/100 * 3/5   given that 1500's share is Rs 855 =>   95x/100 * 3/5 = 855   hence x = 1500   1500NSWER 1500
Answer: A
The price of stock decreased by 5% last year and rose by 10% this year. What is the net percentage change in the price of the stock?	Select:
A) 0.2%  B) 0.8%  C) 1.2%  D) 1.6%  E) 4.5%

Solution: (100% - 5%) * (100% + 10%) = 0.95 * 1.10= 
0.95 * 1.10 = 1.045
1.045= 104.5%.   The net percentage change in the price of the stock is (+) 4.5%   The answer is 4.5%
Answer: E
x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 6
2. (z-x)(y-x+2) = 4
3. xy is odd
Choose the correct choice from the following answers
A) I only
B) II only
C) III only
D) I only
E) I, II, and III

Solution: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1   Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6.   Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+2) = 2*3= 
2*3 = 6
6 So, not true   Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.   So, I is always true and hence answer is   I only.
Answer: D
Concentrated pineapple juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated pineapple juice, at the most, can fit into 3 wooden boxes?  Choose the most appropriate option:
A) 24.
B) 28.
C) 36.
D) 42.
E) 48.

Solution: concentrated pineapple juice since height of a tube is 15 inches , the tubes can fit only in one way .   now, diameter of each tube = 5 inches   therefore, 4*2 can be put in each wooden box   in 3 boxes  3*4*2= 
 3*4*2 = 24
24=24.
Answer: A
Mary works 9 hours per day on Monday, Wednesday and Friday, and 5 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $407 per week. How much does she earn in dollars per hour?	Options.
A) 12 B) 10 C) 9 D) 8 E) 11

Solution: So, she works 27 hours in 3 days   So, she works 10 hours in 2 days   So in a week she works 37 hours ( 27 + 10 ) and earns $407   So, Hourly wage is  407/37= 
 407/37 = 11
> 11   Hence answer will be (11) 11
Answer: E
If x, y, and z are positive integers such that x is a factor of y and y is a factor of z, which of the following is NOT necessarily an integer?
Choose the most appropriate option.
A) (x + y)/z	B) (y + z)/x	C) yz/x	D) (2y + 3z)/x	E) (xy + z)/y

Solution: As per the question, let x = 2, y = 6, and z = 12. Plugging these into the answer choices, only (x + y)/z does not yield an integer.
Answer: A
A sum was put at simple interest at a certain rate for 10 years . Had it been put at 5% higher rate , it would have fetched Rs.300 more. What was the Sum? Choose the correct choice from the following choices:
A) s.1200 B) s.1300 C) s.600 D) s.800 E) s.1200

Solution: At 5% more rate, the increase in S.I for 10 years = Rs.300 (given)   So, at 5% more rate, the increase in SI for 1 year = 300/10 = Rs.30/-   i.e. Rs.30 is 5% of the invested sum   So, 1% of the invested sum = 30/5   Therefore, the invested sum = 30 × 100/5 = Rs.600 Answer: s.600
Answer: C
If y is a given positive integer,.What is the remainder if y is divided by 25, since when y divided by 7 and 12 the remainders are 4 and 3 respectively. Select.
A) 12  B) Between 1 and5, inclusive  C) Between 10 and 15, inclusive  D) Between 6 and 9, inclusive  E) 10

Solution: Given the integer y   7y+4= 12y+3   Start 7y+4 -->11, 18, 25,32,39,...   Of these only 39 fit the description 12y+3. The remainder when divided by 25 is 14. So answer is C).   Answer = Between 10 and 15, inclusive)
Answer: C
If a certain sample of data has a mean of 25.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean? Choose the correct answer.
A) (19.0; 26.5)
B) (14.5; 28.0)
C) (23.0; 28.5)
D) (22.5; 26.0)
E) (19.0; 30.5)

Solution: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.   The values between 20 and 30 are within 2.5 standard deviations from the mean.   The answer is (19.0; 30.5).
Answer: E
Two teams participating in a competition had to take a test in a given time. Team
B chose the easier test with 300 questions, and team A the difficult test with 10%less questions. Team A completed the test 3 hours before schedule while team B completed it 6 hours before schedule. If team B answered 7 questions more than
team A per hour, how many questions did team B answer per hour?  Choose the correct answer:
A) 21  B) 22  C) 23  D) 25  E) 27

Solution: If t hrs is normal time,   then   270/(t-3) + 7 = 300/(t-6)   so t = 18   so Qns done by team A per hour = 270/15= 
270/15 = 18
18 qns.   Qns done by team B per hour= 300/12= 
300/12 = 25
25 qns.   ANSWER:25
Answer: D
A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 44 days, then together ,all will finish the work in :  Choose one.
A) 13 3/3 days
B) 12 1/3 days
C) 15 days
D) 20 days
E) 30 days

Solution: C alone can finish the work in 44 days.   (A + B)can do it in 20 days   (A + B)s 1 days wok = 1/20.   As 1 days work : Bs 1 days Work = 1/2 : 1 = 1:2.   Aâ€™s 1 dayâ€™s work = (1/20) * (1/3) = (1/60). [Divide 1/20 in the raio 1:2] Bs 1 days work = (1/20) * (2/3) = 1/30   (A+B+c)S 1 dayâ€™s work = (1/60) + (1/30) + (1/44) = 1/(13 3/4)   All the three together will finish it in = 13 and 3/4 days.   13 3/3 daysNSWER:13 3/3 days
Answer: A
A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income? Choose one:	A) 900	B) 197	C) 176	D) 107	E) 727

Solution: X * 4/5 * 80/100 = 576   X = 14400/16= 
14400/16 = 900
900   900nswer: 900
Answer: A
Evaluate combination
99C97=99!/(97)!(2)! Choose the correct choice from the following choices.
A) 6170
B) 4851
C) 4171
D) 3170
E) None of these

Solution: Explanation:   nCr=n!/(r)!(n−r)!   99C97=99!/(97)!(2)!   =99∗98∗97!/(97)!(2)!   =99∗98/2∗1   =4851 Option 4851
Answer: B
A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 2 buckles is how many times that of 5 buckles and 6 buttons?
Select
A) 7/15 B) 4/9. C) 6/11 D) 5/9 E) 8/15

Solution: 2 buttons + 2 buckles = 1/3(11 buckles + 3buttons)   6 buttons + 6 buckles = 11 buckles + 3buttons   3buttons = buckles   Weight of 3buttons and buckles = 5buckles + 2buckles = 7buckles   Weight of 6buttons and 5buckles = 10buckles + 5buckles = 15buckles   (3buttons and 2buckles) = x * (6buttons and 5buckles)   7 = x*15   x = 7/15   7/15nswer: 7/15
Answer: A
How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336, 528
Answers:
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: Explanation:   A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.   Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.   Also, 5184 is not divisible by 11.   Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.   Answer: 5
Answer: B
Ram was asked to multiply a number by 441 and he came with an answer 70229. His
Teacher told him that all the digits except the 2’s in his answer are correct. Which of the following could be the correct answer?  Options:
A) 70119	B) 70110	C) 70117	D) 70112	E) 71119

Solution: 441*158= 
441*158 = 69_678
69678   441*159= 
441*159 = 70_119
70119   441*160= 
441*160 = 70_560
70560   441*161= 
441*161 = 71_001
71001   since all the digits except 2 are correct , second number will be 159 and answer= 70119   70119NSWER:70119
Answer: A