mathewhe/aqua_rat huggingface dataset:
Question: M is the sum of the reciprocals of the consecutive integers from 401 to 500, inclusive. Which of the following is true?
(A) 1/3 < M < 1/2
(B) 1/5 < M < 1/4
(C) 1/7 < M < 1/5
(D) 1/9 < M < 1/7
(E) 1/12 < M < 1/9
Rationale: M = 1/401 + 1/4+ 1/403 + ...... + 1/500
If we replace the first 99 terms by 1/500, then we get a sum = 100/500 = 1/5. Since the actual terms are larger than 1/500, the sum is larger than 1/5.
If we replace the all the 100 terms by 1/400, we get a sum = 100/400 = 1/4. Since the actual terms are smaller than 1/400, the sum is less than 1/4.
Therefore 1/5 < M < 1/4
Choice B
Answer: (B) 1/5 < M < 1/4
Question: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 2 such machines to perform the same job?
(A) 2.25 hours
(B) 8.75 hours
(C) 12 hours
(D) 24 hours
(E) 16 hours
Rationale: Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.
Now this 48 Units of total work must be done by 2 machines
2 units of work(2 machines) ---> 1 hour
for 48 Units of work
2*24 ---> 1*24 hours
D 24 hours
Answer: (D) 24 hours
Question: Working at constant rate, pump X pumped out half of the water in a flooded basement in 6 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?
(A) a. 10
(B) b. 12
(C) c. 14
(D) d. 28
(E) e. 24
Rationale: rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
28 hours
D
Answer: (D) d. 28
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
(A) 10
(B) 12
(C) 7
(D) 8
(E) 9
Rationale: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
ANSWER A
Answer: (A) 10
Question: Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
(A) 1/7
(B) 2/9
(C) 3/10
(D) 3/11
(E) 3/14
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
Answer: (C) 3/10
Question: A can do a work in 8 days. B can do the same work in 24 days. If both A & B are working together in how many days they will finish the work?
(A) 3
(B) 5
(C) 4
(D) 2
(E) 6
Rationale: A rate = 1/8
B rate = 1/24
(A+B) rate = (1/8)+(1/24) = 1/6
A & B finish the work in 6days
correct option is E
Answer: (E) 6
Question: Ten students in a computer skills company can touch-type and the other 15 can use a particular word processing program. If 13 of the students can neither use the program nor touch-type, then how many students are in the class?
(A) 46
(B) 42
(C) 38
(D) 34
(E) 19
Rationale: the neither = 13 , the minimum number of students in any or both = 15 , thus 19 is out
the maximum number of students (given 13 is in neither ) in any or both could reach = 25 thus 42 and 46 are out
now the answer is b or c both could be the answer
if the intersection between the 2 groups = 0 thus total = 13+15+10 = 38
if the intersection between the 2 groups = 4 thus total = 15+6+13 or 11+10+13 = 34
ANSWER:D
Answer: (D) 34
Question: A certain furniture can be repaired for $15.50 and will last for 1 year. A same kind of furniture can be purchased new for $40.00 and will last for 2 years. The average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes?
(A) 28.9
(B) 31.4
(C) 27.8
(D) 29.03
(E) 30
Rationale: 1) Cost of repairing = 15.5 ( for one year ), Therefore for 2 years it would be$ 31.
2) Cost of new furniture which will last for 2 years is$ 40.
Percentage change formula =( Final value - Initial value ) / ( Initial Value ) * 100. In this case the final value would be the price of new furniture value would be the cost of repairing the old shoe.
I.e ( 40 - 31 ) / ( 31 ) * 100 = 29.03 %.
Ans is D.
Answer: (D) 29.03
Question: What is the tens digit of 6^10?
(A) 7
(B) 3
(C) 5
(D) 1
(E) 9
Rationale: (6^2)=6*6 = 36
(6^3)= 36*6 = .16
(6^4)= .16*6 = ..96
(6^5) = ..96*6 = ..76
(6^6) = ..76*6 = ...56
(6^7) = ....56*6 = ....36
If you see there is a pattern here in tens digits 3,1,9,7,5,3,1 and so on...
Continue the pattern up to 6^10 ( dont actually calculate full values) and answer is A: 7
Answer: (A) 7
Question: The sum of the mean, the median, and the range of the set {5,6,7} equals which one of the following values?
(A) 18
(B) 14
(C) 16
(D) 12
(E) 10
Rationale: Here Mean => 5+6+7/3 => 6
median => 6
and range => 7-1 => 6
hence sum => 6+6+6=> 18
Answer: A
Answer: (A) 18
Question: The food in a camp lasts for 20 men for 40 days. If ten more men join, the food will last for how many days ?
(A) 40 days
(B) 27 days
(C) 37 days
(D) 50 days
(E) 45 days
Rationale: one man can consume the same food in 20*40 = 800 days.
10 more men join, the total number of men = 20
The number of days the food will last = 800/30 = 27 days.
ANSWER:B
Answer: (B) 27 days
Question: Which of the following CANNOT be the least common multiple of two positive integers x and y
(A) xy
(B) x
(C) y
(D) y - x
(E) x + y
Rationale: The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - y is less than x, it cannot be the LCM of a x and y.
Answer: D
Answer: (D) y - x
Question: In a sports club with 42 members, 20 play badminton and 23 play tennis and 6 do not play either. How many members play both badminton and tennis?
(A) 3
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 20+23=43
but where as total number is 42-6=36
therefore answer is 43-36=7
Hence Answer is D
Answer: (D) 7
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 3 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
(A) 2.5 hours
(B) 4.5 hours
(C) 5.5 hours
(D) 1.5 hour
(E) None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 3 hours, Tank A and B can effectively fill 1⁄12 × 3 = 1⁄4 of the tank.
Time taken to fill the remaining 1−(1/4) = 3/4 of the tank = (3/4)/(1/6) = 4.5 hours. Answer : Option B
Answer: (B) 4.5 hours
Question: The probability that B can shoot a target 3 out of 3 times is 0.25. What is the probability that the target will be missed by B immediately after such two shots?
(A) 0.25
(B) 0.5
(C) 0.4
(D) 0.75
(E) 0.8
Rationale: Suppose there are total 'x' shots.
B shoots 3 out of 3 times. means out of x shots (x>3)
therefore, 3/x = 0.25 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-3) shots.
thus, the probabilty of missing just after 2 shots is (x-3)/x.
(x-3)/x = 1 - 3/x
= 1 - 0.25
= 0.75
Answer : D
Answer: (D) 0.75
Question: A train passes a station platform in 18 seconds and a man standing on the platform in 12 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 100
(B) 150
(C) 96
(D) 88
(E) 90
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 12) m = 180 m.
Let the length of the platform be x meters.
Then, x + 180/ 18 = 15
x + 180 = 270
x = 90 m.
Answer:E
Answer: (E) 90
Question: Of two numbers, 4 times the smaller one is less then 3 times the 1arger one by 5. If the sum of the numbers is larger than 6 times their difference by 6, find the two numbers.
(A) 59 and 43
(B) 55 and 44
(C) 58 and 43
(D) 59 and 42
(E) 57 and 40
Rationale: Let the numbers be x and y, such that x > y
Then, 3x - 4y = 5 ...(i) and (x + y) - 6 (x - y) = 6 => -5x + 7y = 6 …(ii)
Solving (i) and (ii), we get: x = 59 and y = 43.
Hence, the required numbers are 59 and 43.
Answer is A.
Answer: (A) 59 and 43
Question: If the height of a cone is increased by 140% then its volume is increased by?
(A) 100
(B) 140
(C) 998
(D) 729
(E) 2879
Rationale: 140%
Answer:B
Answer: (B) 140
Question: How many times do the hands of a clock coincide in a day?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.
Answer: Option C
Answer: (C) 22
Question: The distance between Delhi and Mathura is 125 kms. A starts from Delhi with a speed of 25 kmph at 9 a.m. for Mathura and B starts from Mathura with a speed of 35 kmph at 10 a.m. from Delhi. When will they meet?
(A) 11 1/2
(B) 77 2/3
(C) 16 3/4
(D) 10
(E) 98
Rationale: D = 125 – 25 = 100
RS = 35 + 25 = 60
T = 100/60 = 1.6 hours
10 a.m. + 1.6 = 11 1/2a.m..Answer: A
Answer: (A) 11 1/2
Question: A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes john can make using this recipe?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.
Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.
Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.
answer is A
Answer: (A) 5
Question: Find the 10th term of an arithmetic progression whose first term is 8 and the common difference is 2.
(A) 45
(B) 26
(C) 44
(D) 40
(E) 46
Rationale: n th term of A.P = a +(n-1) *d
= 8+(10-1)*2 , = 8 + 18 = 26.
ANSWER:B
Answer: (B) 26
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 13:9
(B) 12:2
(C) 19:3
(D) 19:5
(E) 19:7
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
Answer:D
Answer: (D) 19:5
Question: A container holds 4 quarts of alcohol and 4 quarts of water. How many quarts of water must be added to the container to create a mixture that is 3 parts alcohol to 5 parts water by volume?
(A) 4/3
(B) 5/3
(C) 7/3
(D) 8/3
(E) 10/3
Rationale: Let the number of quarts that should be added to get the required ratio = x
So total quarts of water = (x + 4)
But the original number of quarts of alcohol remains the same, so we have :
4/(x+4) = 3/5
Cross-multiply:
Now we have 20 = 3x + 12
=> 3x = 20 -12
=> x = 8/3
Answer - D
Answer: (D) 8/3
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 14 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: The class borrowed a total of 40*2 = 80 books.
The 28 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 14*2 = 40.
To maximize the number of books borrowed by 1 student, let's assume that 11 students borrowed 3 books and 1 student borrowed the rest.
80 - 40 - 3*11 = 7
The maximum number of books borrowed by any student is 7.
The answer is E.
Answer: (E) 7
Question: Nona is one-third as old as her mother. Five years ago, she was only one-fifth of the age of her mother. How old is Nona now?
(A) 11.5
(B) 12.5
(C) 13.5
(D) 14.5
(E) 15.5
Rationale: mother age be x
nona age bcomes 1/3(x)
1/3(x)-5=1/5(x)
by solving we get,
x=37.5
and nona is 12.5
ANSWER:B
Answer: (B) 12.5
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
Answer:A
Answer: (A) 20
Question: If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 20 days. If he works at reduced efficiency, he can work without break and finish that same job in 20 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?
(A) 7/3
(B) 5/2
(C) 6/5
(D) 1/5
(E) 9/5
Rationale: We're told that there are 2 ways for Dale to complete a job:
1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 20 days.
2) Reduced Efficiency: 20 straight days with no days off.
Working at Full Efficiency creates the following pattern:
2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2+1+2+1+2+1+2+1+2= 20 days
Totals: 14 days on, 6 days off
Reduced Efficiency means that Dale will do 14 days of work in 20 days, thus those Reduceddaysare 14/6=7/3 of Full Efficiency.
Answer : A
Answer: (A) 7/3
Question: The length of a train and that of a platform are equal. If with a speed of 126 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 757
(B) 758
(C) 1050
(D) 750
(E) 738
Rationale: Speed = [126 * 5/18] m/sec = 35 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 35 è x = 35 * 60 / 2
=1050
Answer:C
Answer: (C) 1050
Question: At a certain conference, 32% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 50% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  64.0%
(E)  82.0%
Rationale: Refer to the table in the attachment:
Let x= No. of members who have paid in Full
50 % members paid in full and did not register in advance = 0.5x
32 % registerd in advance and paid in full.
So if total No. of members = 100, then 32 members paid Full and registered in advance.
Hence total members who paid full amount = 0.5x + 32 =x
0.5x =32
Hence x = 64
i.e. 64 out of 100 or 64 %
Ans. D
Answer: (D)  64.0%
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.32, the number of 25 paisa coins is?
(A) 30
(B) 31
(C) 32
(D) 34
(E) 38
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 3200
600x = 3200
x = 5.33 => 6x = 32
ANSWER:C
Answer: (C) 32
Question: Whats the next number in this number series ?
18, 46, 94, 63, 52, ?
(A) 44
(B) 34
(C) 45
(D) 65
(E) 61
Rationale: E
61
Reversed digits of squares of number in descending order.
Answer: (E) 61
Question: In the xy-plane, a line has slope 4 and x-intercept 3. What is the y-intercept of the line?
(A) -12
(B) -3
(C) 0
(D) 3
(E) 9
Rationale: Let the line be represented by a general equation y=mx+b, where m = slope (4) and b=y intercept. We are also given the value of x-intercept 3.
Theory : y intercept represents the point on the line where the x=0, and x intercept represents the point on the line where the y=0.
Putting these values in the equation : 0 = 4*3 + b => b = -12. Hence A.
Answer: (A) -12
Question: The average (arithmetic mean) of six numbers is 8. If 3 is subtracted from each of four of the numbers, what is the new average?
(A) 6
(B) 2
(C) 3
(D) 4
(E) 4.5
Rationale: Sum of 6 numbers = 6*8 =48
If 3 is subtracted from each of four of the numbers , we subtract 3*4=12 from the total sum
Sum of 6 number after subtracting 3 from each of four of the numbers = 48 - 12 = 36
New average = 36/6 = 6
Answer A
Answer: (A) 6
Question: The average of first five multiples of 5 is?
(A) 6
(B) 8
(C) 9
(D) 15
(E) 7
Rationale: Average = 5(1 + 2 + 3 + 4 + 5)/5
= 75/5
= 15.
Answer:D
Answer: (D) 15
Question: Two numbers are in the ratio of 5:7. If 20 is subtracted from each number, they are in the ratio of 5:9. What are the two numbers?
(A) 35, 49
(B) 40, 56
(C) 45, 63
(D) 50, 70
(E) 55, 77
Rationale: (5x-20):(7x-20) = 5y:9y
5x - 20 = 5y
7x - 20 = 9y
140-100 = 45y - 35y
40 = 10y
y = 4
5x-20 = 20
x = 8
The two numbers are 5x and 7x which are 40 and 56.
The answer is B.
Answer: (B) 40, 56
Question: Three dwarves and three elves sit down in a row of six chairs. If no dwarf will sit next to another dwarf and no elf wil sit next to another elf, in how many different ways can the elves and dwarves sit?
(A) 16
(B) 26
(C) 36
(D) 63
(E) 72
Rationale: For the first chair, we select any one person of the 6 in 6C1 ways.
For the second chair, we select any one from the 3 in 3C1 ways (e.g. if an elf is sitting on the first chair, we need to choose out of the 3 dwarves only)
For the third chair, we select one of the leftover 2 (e.g. one elf is already sitting in first chair) in 2C1 ways
For the fourth chair, we select one of the leftover 2 (e.g. one dwarf is already sitting in the second chair and we need to choose of the remaining 2) in 2C1 ways
For the fifth and sixth chairs, there is only one choice each.
Answer: 6C1 * 3C1 * 2C1 * 2C1 = 6*3*2*2 = 72
ANS:E
Answer: (E) 72
Question: For positive integers q and r, which of the following can be written as r^2?
(A) q^2-12
(B) q^2-11
(C) q^2-10
(D) q^2-9
(E) q^2-14
Rationale: Plug values: if q=5, then 5^2-9=4
The question asks which of the following CAN be written as r^2. If q=16, then q^2-9 CAN be written as 2^2.
Answer: D
Answer: (D) q^2-9
Question: What is the area of a square field whose diagonal of length 20 m?
(A) 238
(B) 379
(C) 200
(D) 328
(E) 397
Rationale: d2/2 = (20 * 20)/2
= 200
Answer:C
Answer: (C) 200
Question: sue has 3 apples. Billy has 12 apples. If billy steals all of sues apples and eats 4 how many does he have left?
(A) 11
(B) 10
(C) 7
(D) 9
(E) 8
Rationale: 11 A
Answer: (A) 11
Question: Calculate how many days it will take for 7 boys to wash a 35 m long wall if 5 boys can wash a 25 m long wall in 4 days,
(A) 6 days
(B) 3 days
(C) 4 days
(D) 2 days
(E) 5 days
Rationale: The length of wall painted by one boy in one day = 25 / 5 * 1/4 = 1.25 m
No. of days required to paint 50 m cloth by 8 boys = 35/ 7 *1/ 1.25 = 4 days.
C
Answer: (C) 4 days
Question: What are the last two digits of (301*402*503*604*646*547*448*349)^2
(A) 96
(B) 76
(C) 56
(D) 36
(E) 16
Rationale: ((301*402*503*604*646)*(547*448*349))^2
If you observe above digits, last digit are: 1,2,3,4,6,7,8,9; 5 is missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,03,04,46 and final three as 47*48*49.
Solving for only last two digits and multiplying them we get:( (06*04*46)(56*49))^2 = (44*44)^2=36^2=76
Hence answer is B
Answer: (B) 76
Question: If the simple interest on a sum of money at twelve percent per annum for two years is Rs.3800, compound interest on the same sum for the same period at the same rate of interest is
(A) Rs.4028
(B) Rs.4100
(C) Rs.4128
(D) Rs.4228
(E) Rs.4328
Rationale: S I for 2 years = 3800 ie for one year =1900
The compound interest for Rs.1900 for the second year = 1900*12/100 =228
The CI for two years 3800+228 = 4028
ANSWER:A
Answer: (A) Rs.4028
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.600, find the original price per kg?
(A) s.11
(B) s.14
(C) s.15
(D) s.21
(E) s.29
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
600 --- 80
? --- 2 => Rs.15
Answer:C
Answer: (C) s.15
Question: In how many years Rs 200 will produce the same interest at 10% as Rs. 400 produce in 5 years at 12%
(A) 16
(B) 13
(C) 12
(D) 14
(E) 15
Rationale: Explanation:
Clue:
Firstly we need to calculate the SI with prinical 400,Time 5 years and Rate 12%, it will be Rs. 240
Then we can get the Time as
Time = (100*240)/(200*10) = 12
Option C
Answer: (C) 12
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 22000
(C) 24000
(D) 26000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: A merchant marks his goods up by 30% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
(A) 8%
(B) 10%
(C) 21%
(D) 15%
(E) 17%
Rationale: Let the price be 100.
The price becomes 130 after a 30% markup.
Now a discount of 10% on 130.
Profit=117-100
17%
answer E
Answer: (E) 17%
Question: What is the remainder when 10^49 + 2 is divided by 11?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 7
Rationale: With exponent-based problems and huge numbers, it's often helpful to try to establish a pattern using small numbers. On this problem, while 1049+2 is a massive number that you'd never want to try to perform calculations with, you can start by using smaller numbers to get a feel for what it would look like:
10^2+2=102, which when divided by 11 produces a remainder of 3 (as 9 * 11 = 99, leaving 3 left over)
10^3+2=1002, which when divided by 11 produces a remainder of 1 (as 9 * 110 = 990, and when you add one more 11 to that you get to 1001, leaving one left)
10^4+2=10002, which when divided by 11 produces a remainder of 3 (as you can get to 9999 as a multiple of 11, which would leave 3 left over)
10^5+2=100002, which when divided by 11 produces a remainder of 1 (as you can get to 99990 and then add 11 more, bringing you to 100001 leaving one left over).
By this point, you should see that the pattern will repeat, meaning that when 10 has an even exponent the remainder is 3 and when it has an odd exponent the remainder is 1. Therefore, since 10 has an odd exponent in the problem, the remainder will be 1.
answer is A
Answer: (A) 1
Question: How many positive integers less than 400 can be formed using the numbers 1, 2, 3 and 5 for the digits?
(A)  48
(B)  52
(C)  66
(D)  84
(E)  68
Rationale: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
3 5 5
Number of possibilities = 4*4*4 = 64.
Then, just add up the number of 1 digits numbers = 4, so total is 64+4 = 68.
Answer: E
Answer: (E)  68
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 2388
(C) 2798
(D) 2666
(E) 1081
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer:A
Answer: (A) 2000
Question: Which of the following is closest to (-5/6)^199？
(A) -1
(B) -1/2
(C) 0
(D) 1
(E) 2
Rationale: (-5/6)^4 = 625/1296 which is already less than 1/2.
For larger exponents, the expression will get closer and closer to zero.
The answer is C.
Answer: (C) 0
Question: In a group of 4 boys and 6 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?
(A) 185
(B) 197
(C) 209
(D) 221
(E) 233
Rationale: The total number of ways to choose 4 children is 10C4 = 210
The number of ways to choose only boys is 4C4 = 1
The number of groups which include at least one girl is 209.
The answer is C.
Answer: (C) 209