MU-NLPC/Calc-aqua_rat huggingface dataset:
Three hundred gallons of fuel are purchased at $0.90 per gallon. The fuel is consumed at a rate of $0.50 worth of fuel per hour. At this rate, how many hours are required to consume the 300 gallons of fuel?  Choose one
A) 510
B) 520
C) 530
D) 540
E) 550

Solution: The fuel is consumed at this rate: $0.50/$0.90 = 5/9 gallons per hour.   The time it takes to consume 300 gallons is:  300 / (5/9)= 
 300 / (5/9) = 540
540 hours.   The answer is 540.
Answer: D
An epidemic is reported to have broken out in Florida. The number of detected instances of a certain disease is reported to have increased by 85% in the last year. What is the lowest number of newly detected instances possible?	Choose one
A) 1	B) 5	C) 11	D) 15	E) 17

Solution: Can (85/100 * n) be 1? No because in that case, n will not be an integer.   Can (85/100 * n) be 5? No because in that case, n will not be an integer.   Notice that 85 = 5*17.   So 85/100 = 17/20   (17/20 * n) = 17   n = 20 (an integer)   We will not get n as integer in any of the other options.   ANSW17R:17
Answer: E
The value of ((x – y)³ + (y - z)³ + (z – x)³)/(9 (x – y) (y – z) (z – x))
is equal to :	Answers:	A) 0	B) 1/12	C) 1	D) 1/4	E) 1/3

Solution: Since (x – y) + (y – z) + (z – x) = 0,   so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).   (3 (x – y) (y – z) (z – x))/(9(x – y) (y – z) (z – x)) = 1/3.   ANSW1/3R:1/3
Answer: E
The least common multiple of positive integer d and 3-digit integer n is 690. If n is not divisible by 3 and d is not divisible by 2, what is the value of n?
Select.
A) 115	B) 230	C) 460	D) 575	E) 690

Solution: The LCM of n and d is 690 = 2*3*5*23.   d is not divisible by 2, thus 2 goes to n   n is not divisible by 3, thus 3 goes to d.   From above:   n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23= 
2*5*23 = 230
230.   Answer: 230.
Answer: B
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Pick: A) 18 a.m B) 10 a.m C) 167 a.m D) 18 a.m E) 11 a.m

Solution: Suppose they meet x hours after 7 a.m.   Distance covered by A in x hours = 20x km.   Distance covered by B in (x - 1) hours = 25(x - 1) km.   Therefore 20x + 25(x - 1) = 110   45x = 135   x = 3.   So, they meet at 10 a.m.   Answer:10 a.m
Answer: B
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.157. Find the unknown rate of two blankets? Select:
A) 420 B) 550 C) 490 D) 450 E) 520

Solution: 10 * 157= 
10 * 157 = 1_570
1570   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1570 – 1050= 520   Answer:520
Answer: E
A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is? Choices.
A) 1 kmph  B) 3 kmph  C) 8 kmph  D) 7 kmph  E) 5 kmph

Solution: DS = 6   US = 4   S = ?   S = (6 - 4)/2= 
(6 - 4)/2 = 1
1 kmph   1 kmphnswer: 1 kmph
Answer: A
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?  Choose the correct choice from the following choices:
A) 79.7	B) 79.8	C) 76.2	D) 79.2	E) 29.2

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer:79.2
Answer: D
Three faces of a fair die are Yellow, two faces red and two blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is  Pick one.
A) 1/36 B) 1/18 C) 1/32 D) 1/37 E) None of these

Solution: Probability of getting yellow color = P(Y) = 3/6 = 1/2   Probability of getting red color = P(R) = 2/6 = 1/3   Probability of getting blue color = P(1/18) = 2/6=1/3   So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ 1/18) = P(Y) x P(R) x P(1/18) = 1/2 x 1/3 x 1/3 = 1/18   ANSWER:1/18
Answer: B
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 81 more than n. What is y in terms of x ?  Options:
A) 10 - x B) 9 - x C) x + 9 D) x - 1 E) x + 1

Solution: Original Digits=xy i.e. Number=10x+y   After reversing the digits:   Digits=yx i.e. Number=10y+x   10y+x is 9 more than 10x+y   10x+y+81=10y+x   10x-x+81=10y-y   9x+81=9y   x+9=y   OR   y=x+9   Ans:x + 9
Answer: C
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:	Choose the correct choice from the following answers.
A) No profit, no loss B) 5% C) 8% D) 10% E) none of the above

Solution: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.   S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680   Gain = (80/1600 * 100)= 
(80/1600 * 100) = 5
5%   Answer= 5%
Answer: B
how many such letters pairs r in word FRONTIER having same no. of letters left between them in the word as they have in the series  Choose one.
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: the no of letters between the specific two letters when we write in the alphabetical order should be same as the number of letters between those two letters in the given word   two are possible   1)letters 'o' and 'n'   2)'n' and 'r'......( middle letters are o,p,q i.e 3 letters in alphabetical order & in the given word t,i,e i.e 3 letters)   so 2 such pairs are possible   ANSWER:2
Answer: B
convert 100 miles into inches?  Choose the correct answer
A) 6336000
B) 6542000
C) 5462300
D) 6213000
E) 6120330

Solution: 1 feet = 12 inches   1 mile = 5280 feet   100 mile = 5280*12*100= 
5280*12*100 = 6_336_000
6336000   6336000ns: 6336000
Answer: A
curie bakes 5 cookies for 5 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?  Choose the correct choice from the following:
A) 1
B) 2
C) 3
D) 4
E) 5

Solution: curie made 5*5= 
5*5 = 25
25 cookies. 2 friends eat 3 cookies, leaving 9 remaining for 2 friends.   9 is not divisible by 2. The 2 friends ate a cumulative number of cookies less than 9 that must be divisible by 2, because the number is the same.   The nearest multiple of 2 is 8.   9-8= 
9-8 = 1
1   1 is the correct answer
Answer: A
A person want to give his money of $12000 to his 5 children A,B,C,D,E in the ratio 2:4:3:1:5. What is the D+E share?
Answers:
A) $1800	B) $2800	C) $3800	D) $5800	E) $4800

Solution: D's share = 12000*1/15= 
12000*1/15 = 800
$800   D's share= 12000*5/15= 
12000*5/15 = 4_000
$4000   A+D= $4800   Answer is $4800
Answer: E
Albert invested amount of 12000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit	Pick one
A) Rs. 8510  B) Rs. 8620  C) Rs. 8730  D) Rs. 13230  E) None of these

Solution: Explanation:   =>(12000×(1+5/100)2)   =>12000×21/20×21/20   =>13230   Option Rs. 13230
Answer: D
The H.C.F of two numbers is 23 and the other two factors of their L.C.M are 11 and 12. The larger of the two numbers is: Pick.
A) 338  B) 276  C) 322  D) 231  E) 121

Solution: Clearly, the numbers are (23 * 11) and (23 * 12). Larger number   = (23 * 12)= 
(23 * 12) = 276
276.   Answer: 276
Answer: B
The ratio of buses to cars on River Road is 1 to 3. If there are 20 fewer buses than cars on River Road, how many cars are on River Road?  Choose the correct choice from the following answers
A) 100  B) 120  C) 140  D) 30  E) 150

Solution: B/C=1/3   C-B=20.........> B=C-20   (C-20)/C=1/3   Testing answers. Clearly Eliminate ABCE   Put C=30.........> (30-20)/30=10/30=1/3   Answer: 30
Answer: D
A man can row downstream at 16 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
Choose the correct choice from the following answers
A) 3 B) 5 C) 6 D) 4 E) 9

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 16 --- (1)   and x - y = 10 --- (2)   From (1) & (2) 2x = 26=> x = 13, y = 3. 3nswer: 3
Answer: A
Agatha has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have? Choose the correct choice from the following choices:
A) 32 B) 30 C) 29 D) 28 E) 27

Solution: 5n + 10m = 460   n > m   Pick an easy number to work with.   suppose n=30.   Then you have 150.   You need another 310 and that means you need m=31 which is greater than n.   Therefore, n > 30.   The only answer choice where n> 30 is if n = 32.   32 is the answer.
Answer: A
A grocery store bought some mangoes at a rate of 4 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?	Options
A) 1:4  B) 1:5  C) 2:3  D) 1:2  E) 1:2

Solution: The cost price of a mango = 1/4 dollars.   The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/4 = 1/12 dollars.   The selling price of a mango from the second stack = 1/6 dollars --> the loss from one mango = 1/3 - 1/6 = 1/6 dollars.   The profit from one mango from the first stack is 4 times the loss from one mango from the second stack.   the ratio is 1/12*6/1 = 1/2 =1:2   1:2
Answer: E
The profit obtained by selling an article for Rs. 86 is the same as the loss obtained by selling it for Rs. 42. What is the cost price of the article?	Pick:	A) Rs. 40	B) Rs. 50	C) Rs. 49	D) Rs. 59	E) Rs.64

Solution: S.P 1- C.P = C.P – S.P 2   86 - C.P = C.P - 42   2 C.P = 86 + 42;   C.P = 128/2= 
128/2 = 64
64   ANSWRs.64R:Rs.64
Answer: E
85 80 25 70 55 25 35 ? ?
Choose one:
A) 10 25	B) 25 85	C) 35 25	D) 85 35	E) 25 75

Solution: 85-5= 
85-5 = 80
80   again 25   80-10= 
80-10 = 70
70   70-15= 
70-15 = 55
55   again 25   55-20= 
55-20 = 35
35   35-25= 
35-25 = 10
10   again 25   then answer is 10 ,25   10 25NSWER:10 25
Answer: A
When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
Choose the most appropriate option:
A) 40	B) 50	C) 60	D) 70	E) 80

Solution: Let the number be   2 + 1/2[1/3(a/5)] = a/15   => 2 = a/30 => a = 60   ANSWER:60
Answer: C
x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?  Choose the correct choice.
A) 2 B) 3 C) 5 D) 7 E) 11

Solution: Since smallest possible prime factor is required.   Let x = 2 then --> 2# = 2   x#+7 --  2= 
--  2 = 2
2   x#+7==> 2#+7 = 2+7= 
2+7 = 9
9= 3*3.   Thus 3 is the smallest possible Prime Factor   2 cannot be the possible prime factor because --> x# is always even since it is product of even numbers   Even +7 = Odd. Hence 2 cannot be prime factor of this result   ANSWER:3
Answer: B
Rs. 875 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 875 become in 3 years ?  Choices
A) Rs. 1020.80	B) Rs. 1025	C) Rs. 1061	D) Data inadequate	E) None of these

Solution: Solution   S.I. = Rs.(956-875 )=Rs.81   Rate = (100x81/875x3) = 108/35%   New rate = (108/35 +4)% = 248/35%   New S.I. = Rs.(875 x 248/35 x 3/100) Rs. 186.   ∴ New amount = Rs.(875+186)= Rs. 1061.   Answer Rs. 1061
Answer: C
3/4 of 5/7 of a number is greater than 2/3 of 4/7 of the same number by 26. What is half of that number?
Choose the correct choice from the following answers:	A) 32	B) 78	C) 92	D) 84	E) 96

Solution: Let no. be x   3/4*5/7*x - 2/3*4/7*x = 26   by further solving   15x/28- 8x/21= 26   13x/84= 26   x=168   we have to find x/2   =168/2= 
168/2 = 84
84   ANSWER:84
Answer: D
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:	Choose the correct answer.
A) 14
B) 15
C) 16
D) 18
E) 19

Solution: Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.   Suppose Tanya takes x days to do the work.   5 : 4 :: 20 : x   x = (4 x 20)/5   x = 16 days.   Hence, Tanya takes 16 days to complete the work.   ANSWER:16
Answer: C
The Least Common multiple of 2^6−1 and 2^9−1 is Choose the correct choice from the following choices:
A) 2^12+27*2^9-217
B) 2^ 12 +63*2^3-1
C) 2^12+5^29-1
D) 2^12+9*2^8 -1
E) None of these.

Solution: The best approach in my opinion is what Zarroli has suggested above.   LCM * GCF = Product of the numbers = (2^6−1)∗(2^9−1)=(2^3−1)(2^3+1)∗(2^3−1)(2^6+1+2^3)   Notice that the only common factor between them is (23−1)(23−1) so this must be the GCF. Hence LCM will be the rest of the product.   LCM=(2^3+1)∗(2^3−1)(2^6+1+2^3)=(2^6−1)(2^6+1+2^3)   Now how do you get it in the format in the options? Almost all options have 2^12 and 1 so retain those two and club everything else together.   LCM=2^12−1+(2^6+2^9−2^6−2^3)=2^12−1+2^3(2^6−1)=2^12−1+2^3∗63   Answer (2^ 12 +63*2^3-1)
Answer: B
Of the diplomats who attended a summit conference: 20 spoke Japanese, 32 did not speak Russian and 20% of the diplomats spoke neither Japanese nor Russian. If 10% of the diplomats spoke both Japanese and Russian, then how many diplomats attended the conference?  Choose the correct choice.
A) 70	B) 96	C) 108	D) 120	E) 150

Solution: 2X2 matrix will be the easiest way to calculate this.   Text in black: given statements   Text in red: calculated values   Thus 120=120 is the correct answer
Answer: D
A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is.  Choose the correct choice
A) 1/7
B) 1/2
C) 3/7
D) 2/3
E) 1/3

Solution: Since the coin is a fair coin, every toss is independent of any other toss. Hence, the probability of appearance of tail on the fifth toss is = 1/2   ANSWER:1/2
Answer: B
A train 220 m long passed a pole in 12 sec. How long will it take to pass a platform 600 m long?	Choose the most appropriate option:
A) 80 B) 45 C) 49 D) 50 E) 56

Solution: Speed = 220/12 = 18 m/sec.   Required time = (220 + 600)/18 = 45 sec.   Answer: Option 45
Answer: B
There are 11 baskets numbered from 1 to 11 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
Choose one
A) 180	B) 220	C) 260	D) 300	E) 340

Solution: Each child takes a total of 1+2+3+4+5+6+7+8+9+10+11 = 11*12/2= 
11*12/2 = 66
66 apples.   The total number of apples taken by 10 children is  10*66= 
 10*66 = 660
660   The number of apples left in the end is  1000 - 660= 
 1000 - 660 = 340
340 apples.   The answer is 340.
Answer: E
John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $80. What is the percent decrease?
Choose the correct choice from the following choices:	A) 20%	B) 30%	C) 40%	D) 50%	E) 60%

Solution: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 80 = 20. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (20/100)*100 = (0.2)*100= 
(0.2)*100 = 20
20%.   20%
Answer: A
Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
Select:
A) 4
B) 9
C) 6
D) 10
E) 12

Solution: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and added top and bottom, hence  4+2= 
 4+2 = 6
6.   6
Answer: C
Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,200 nuts and 1,200 bolts?  Select:
A) 1,250 seconds
B) 1,500 seconds
C) 1,800 seconds
D) 2,000 seconds
E) 3,000 seconds

Solution: I used the Rate formula (R=\frac{1}{T})   Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}   Rate of 1st machine = Rate of 2nd machine   After this I got lost.   Please can you help how to approach using algebra?   I wouldn't complicate:   1 machine needs 1,200*1 seconds to produce 1,200 bolts, so 2 need half of that, so 1,200/2 seconds.=600 sec   1 machine needs 1,200*2 seconds to produce 1,200 nuts, so 2 need half of that, so 1,200*2/2 seconds.=1200 sec   total = 1800   1,800 seconds
Answer: C
The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?  Options: A) 48 B) 44 C) 42 D) 40 E) 4

Solution: remaining are divisible by 4   ANSWER:42
Answer: C
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together? Choose the correct choice from the following choices:  A) 6775 ways  B) 1440 ways  C) 1345 ways  D) 1324 ways  E) 1688 ways

Solution: In the word, "MATERIAL" there are three vowels A, I, E.   If all the vowels are together, the arrangement is MTRL'AAEI'.   Consider AAEI as one unit. The arrangement is as follows.   M T R L A A E I   The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.   Number of required ways of arranging the above letters = 5! * 4!/2!   = (120 * 24)/2= 
(120 * 24)/2 = 1_440
1440 ways.   Answer: 1440 ways
Answer: B
A company has 14 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?  Choose the correct option
A) 881 B) 921 C) 961 D) 1001 E) 1041

Solution: 14C4=1001   The answer is 1001.
Answer: D
A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train. Choose the correct answer.
A) 26 B) 16 C) 36 D) 46 E) 13

Solution: Let the speed of the goods train be x kmph.   Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours   10x = 4 x 90 or x =36.   So, speed of goods train = 36kmph.   ANSWER 36
Answer: C
Ten people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?  Select the correct option:
A) 1/9 B) 1/8 C) 1/7 D) 7/8 E) 8/7

Solution: Let P = total cost of the rental van.   The original share per person is P/10.   The new share per person is P/9.   P/9 = P/10 * 10/9 = (1 + 1/9)*original share   The answer is 1/9.
Answer: A
3+3.3+333+33.33=?  Choose the correct option.
A) 362.33 B) 372.63 C) 702.33 D) 702 E) None of them

Solution: 3   3.3   333   33.33   ----------   372.63   ----------   Answer is 372.63
Answer: B
How many ways are there to select a subcommittee of 6 members from among a committee of 17? Choose the correct option.
A) 22888	B) 19448	C) 28791	D) 27711	E) 12376

Solution: Explanation:   Since it does not matter what order the committee members are chosen in, the combination formula is used.   Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.   C(17,6)= 12,376   Answer: 12376
Answer: E
A, B and C rents a pasture for Rs.870. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Choose the correct choice from the following answers.
A) 270  B) 278  C) 792  D) 267  E) 721

Solution: 12*8 :16*9 = 18*6   8: 12: 9   9/29 * 870= 
9/29 * 870 = 270
270   270nswer: 270
Answer: A
Martha has 4 dogs and 4 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?  Choose the correct choice from the following choices:
A) 8
B) 9
C) 16
D) 18
E) 20

Solution: 4 dogs, 4 cats; park/barber shop   1 dog - 2 options - either park or barber shop, so, 4 dogs - 8 options and 4 dogs - 8 options.   Total = 16 options.   16
Answer: C
The fourth proportional to 3, 8, 18 is: Choose the correct choice.
A) 42 B) 44 C) 46 D) 48 E) 50

Solution: Let the fourth proportional to 3, 8, 18 be x.   Then, 3 : 8 : 18 : x   3x = (8 x 18)   x =	(8 x 18)/3   x=144/3= 
144/3 = 48
48   Answer: Option 48
Answer: D
The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?	Choose the correct choice from the following options.
A) 100  B) 110  C) 120  D) 140  E) 150

Solution: Sol. x * 4x = 3 * 1200   x = 30   Length = 4 * 30= 
4 * 30 = 120
120   120
Answer: C
Simple interest on a certain sum of money for 3 years at 10% per annum is half the compound interest on Rs. 6500 for 2 years at 14% per annum. The sum placed on simple interest is Choose the correct option.
A) Rs.6500	B) Rs.1947.4	C) Rs.973.7	D) Rs.2000	E) None

Solution: Solution   C.I.	=Rs[6500x(1+14/100)Â²-6500]   Rs.(6500x114/100x114/100-6500)	= Rs.1947.4.   Sum	=Rs. [973.7x100 /3x10]   = Rs.3245.67.   Answer None
Answer: E
two houses of the same type were advertised to be let in a locality. Three men made separate applications for a house. What is the probability that each of them applied for the same house.
Answers
A) 1/3	B) 2/27	C) 3/27	D) 4/27	E) 2/9

Solution: Since each of the house has same probability of getting selected so for each men proability of selecting a house out of 2 houses 1/2   Let us consider case where all 3 men choose House no 1   So for First men it will be 1/2,second men 1/2 and third men also 1/2   So probability of selecting house no 1 is 1/2*1/2*1/2= 1/8   And since there are 2 such house so probability that each men select the same house is 2*1/27   Ans is 2/27
Answer: B
R is the set of positive odd integers less than 100, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?	Choose the correct choice from the following answers:	A) None	B) Two	C) Four	D) Five	E) Seven

Solution: R is the set of positive odd integers less than 100, and S is the set of the squares of the integers in R.   How many elements does the intersection of R and S contain?   R=1,3,5,7,9,11,13,15...   S=1,9,25,49,81...   Numbers: 1, 9, 25, 49, and 81 are odd integers (less than 100) that are in both sets.   Solution: Five   Answer: Five
Answer: D
If XY denotes X is raised to the power Y, Find the last two digits of 19413846+ 19614181	Choose the most appropriate option
A) 67  B) 74  C) 82  D) 98  E) 34

Solution: 1941^3846   unit digit= 1^4=1   10th digit=4*6= 
4*6 = 24
24=2 means last two digit =41   and 1972^4181   unit digit=1   10th digit=7*2= 
7*2 = 14
14 mean last two digit= 41   hence,   41+41= 
41+41 = 82
82
Answer: C
How many digits are in (8×10^14)(10×10^10)?	Options: A) 24 B) 25 C) 26 D) 27 E) 28

Solution: he question simplifies to (8×10^14)(10^11)   => 8*10^25   => Will contain 25 zeros +1 digit 8   =>26   Ans 26
Answer: C