mathewhe/aqua_rat huggingface dataset:
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 12 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: To get 40 points as end of season we need another 28 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
hence option B-7
Answer: (B) 7
Question: 5, 11, 17, 25, 33, 43, ?
(A) 44
(B) 26
(C) 58
(D) 59
(E) 53
Rationale: E
53
The sequence is +6, +6, +8, +8, +10, ....
Answer: (E) 53
Question: A letter lock consists of three rings each marked with thirteen different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
(A) 1773
(B) 2196
(C) 2153
(D) 1683
(E) 1673
Rationale: Since each ring consists of thirteen different letters, the total number of attempts possible with the three rings is
= 13*13*13 = 2197. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 2197 - 1
= 2196.
Answer: B
Answer: (B) 2196
Question: Victor gets 95 % marks in examinations. If these are 285 marks, find the maximum marks.
(A) 334
(B) 500
(C) 376
(D) 288
(E) 300
Rationale: Let the maximum marks be m
Then 95 % of m = 285
⇒ 95/100 × m = 285
⇒ m = (285 × 100)/95
⇒ m = 28500/95
⇒ m = 300
Therefore, maximum marks in the examinations are 300.
Answer:E
Answer: (E) 300
Question: Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3669
(A) 3669
(B) 9654
(C) 5945
(D) 7963
(E) 8216
Rationale: The product of first two digits in a number equals the last two digits, except in 3669. Hence, it is the odd one.
The answer is 3669.
ANSWER:A
Answer: (A) 3669
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 20
(B) 80
(C) 100
(D) 200
(E) 250
Rationale: Explanation:
Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: C
Answer: (C) 100
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) Rs.4538
(B) Rs.4518
(C) Rs.4518
(D) Rs.4530
(E) Rs.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs.4530
Answer: D
Answer: (D) Rs.4530
Question: Uncle Bruce is baking chocolate chip cookies. He has 40 ounces of dough (with no chocolate) and 20 ounces of chocolate. How much chocolate is left over if he uses all the dough but only wants the cookies to consist of 25% chocolate?
(A) 8.5
(B) 9.5
(C) 10.5
(D) 6.7
(E) 6.5
Rationale: First, you must find the total weight of the mixture given that 80% of it will be dough.
75%*Total = 40 => (75/100)Total=40 => Total=4000/75=> Total=53.33oz,
From there, you must find 25% of the total 53.33 oz of the mixture.
25%*Total => (25/100)(53.33)= 13.33 oz choclate used,
Not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate. 20-13.3 = 6.7 oz chocolate left over.
Answer : D
Answer: (D) 6.7
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 7 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
(A) 18
(B) 23
(C) 38
(D) 53
(E) 68
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 7.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 8, 23, 38, 53, 68,...
The answer is A.
Answer: (A) 18
Question: y = 248 - 198x
Which of the following values of x gives the greatest value of y in the equation above?
(A)  200
(B)  100
(C)  0.5
(D)  -5
(E)  4
Rationale: Clearly, the negative value of x will result in maximum value of y.
Don't even look at the rest of the answer choices as only one negative value is being present.
Answer is D
Answer: (D)  -5
Question: A number when divided by 45, gives 30 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 15
(A) A)0
(B) B)3
(C) C)4
(D) D)6
(E) E)7
Rationale: Explanation:
P ÷ 45 = 30
=> P = 30 * 45 = 1350
P / 15 = 1350 / 15 = 90, remainder = 0
Answer: Option A
Answer: (A) A)0
Question: If 525/999=0.525, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
(A) -1
(B) 0
(C) 3
(D) 4
(E) 5
Rationale: 0.[u]125[/u = 0.525525525.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: (E) 5
Question: Car Dealership X, the total profit from sales increased by 8 percent over the previous years, while the number of cars sold decreased by 8 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
(A) 17.39%
(B) 20%
(C) 22%
(D) 23%
(E) 25%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.08x / 0.92 y = 108/92 (x/y)
Increase in profit per car = ((16/92) (x/y)) / (x/y) * 100 = 17.39%
Answer = A
Answer: (A) 17.39%
Question: A cashier mentally reversed the digits of one customer's correct amount of change and thus gave the customer an incorrect amount of change. If the cash register contained 9 cents more than it should have as a result of this error, which of the following could have been the correct amount of change in cents?
(A) 14
(B) 45
(C) 54
(D) 65
(E) 32
Rationale: Just check the answers and reverse the numbers until you get 9.
32 - 23 = 9
Answer E
Answer: (E) 32
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.964 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
(A) 22200
(B) 31897
(C) 38799
(D) 40000
(E) 42782
Rationale: P(11/10)^4 - P(6/5)^2 = 964
P = 40000
Answer: D
Answer: (D) 40000
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
(A) 26
(B) 50
(C) 100
(D) 1000
(E) 90
Rationale: 1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ‘n’.
Therefore, using ‘n’ alphabets we can form n * n * n = n3 distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n3 different initials = 1 million
i.e. n3 = 106 (1 million = 106)
=> n3 = (102)3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
Option C
Answer: (C) 100
Question: The perimeters of two squares are 44 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
(A) 22 cm
(B) 24 cm
(C) 26 cm
(D) 30 cm
(E) 29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 44/4 = 11 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 11*11 - 8*8
= 57 cm
So side of third square = 7.5 [because area of square = side*side]
Perimeter = 4*Side = 4*7.5 = 30 cm
Answer: Option D
Answer: (D) 30 cm
Question: A housewife has 11 litre of solution that contains sodium carbonate solution and benzene solution in the ratio 3 : 1. She adds 250 ml of 3 : 2 solution of sodium carbonate and benzene solution to it and then uses 250 ml of the combined mixture to make strong organic solution How much of pure sodium carbonate solution is she left with?
(A) 1000 ml
(B) 912.5 ml
(C) 750 ml
(D) 720 ml
(E) 630 ml
Rationale: ln a mixture of 1,000 ml sodium carbonate : benzene solution = 3 : 1.
Hence, sodium carbonate: 750 ml benzene solution 250 ml
A 250 ml of 3 : 2 solution contains 150 ml sodium carbonate solution and l00ml benzene solution.
Total sodium carbonate solution = 900 ml, total benzene solution = 350 ml
After using 250 ml to make strong organic solution , sodium carbonate solution used
= 250/1250 x 900 = 180 ml
pure sodium carbonate solution left = 900 -180 =720ml
ANSWER:D
Answer: (D) 720 ml
Question: Set X consists of the integers from 10 to 15, inclusive, while set Y consists of the integers from 5 to 10, inclusive. How many distinct integers do belong to the both sets at the same time?
(A) 5
(B) 8
(C) 4
(D) 1
(E) 9
Rationale: X= {10, 11, 12,13,14,15}
Y = {5,6, 7, 8, 9, 10}
Common elements = {10} = 1 element
Answer: Option D.
Answer: (D) 1
Question: Which of the following is the Highest Common Factor of 49, 63 and 77?
(A) 8
(B) 10
(C) 7
(D) 14
(E) 12
Rationale: THE HIGHEST COMMON FACTOR IS 7Ans is :C
Answer: (C) 7
Question: A hare and a jackal are running a race. Three leaps of the hare are equal to four leaps of the jackal. For every one leap of the hare, the jackal takes two leaps. Find the ratio of the speed of the hare to the speed of the jackal.
(A) 4:5
(B) 8:5
(C) 5:8
(D) 2:3
(E) 5:3
Rationale: The hare takes 1 leap and the jackal takes 2 leaps.
1 hare leap = 4/3 jackal leaps
Thus the hare's 1 leap = 4/3 jackal leaps.
The ratio of their speeds is 4/3:2 = 4:6 = 2:3.
The answer is D.
Answer: (D) 2:3
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
(A) 720
(B) 740
(C) 760
(D) 780
(E) 790
Rationale: Option 'A'
Answer: (A) 720
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 91/55
(C) 1/495
(D) 1/655
(E) 1/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13) = 1/455.Answer: A
Answer: (A) 1/455
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
(A) 25%
(B) 35%
(C) 45%
(D) 70%
(E) 80%
Rationale: Since the problem doesn't depend on the number of birds in reserve you can suppose that there are 100 birds.
From them 100*0.3=30 are Hawks.So, there are 70 non-Hawks.
There are 0.4*70=28 Paddyfield-Warblers. Therefore, there are 0.25*28=7 Kingfishers.
The total number of birds in the nature reserve that are not Hawks, Paddyfield-Warblers, or Kingfishers is 100-30-28-7=35.
The answer is B
Answer: (B) 35%
Question: A trader purchased on old bicycle for 480. He spent 20% of the cost on its repair. If he wants to earn 144 as net profit on it, how much percentage should he add to the purchase price of the bicycle?
(A) 50%
(B) 48%
(C) 96%
(D) 100%
(E) None of these
Rationale: Purchase price = 480
Repair cost = 20% of 480 = 96
∴ Total cost =480 + 96 = 576
Net profit = 144
∴ Selling price = Total cost + Net
profit= 576 + 144 = 720
Now, Selling price - Purchase price
= 720 – 480 = 240
∴ Reqd percentage = 240⁄280 × 100 = 50%
Answer A
Answer: (A) 50%
Question: The present worth of $169 due in 2 years at 4% per annum compound interest is?
(A) $145.89
(B) $138.62
(C) $156.25
(D) $160.23
(E) $158.95
Rationale: Present worth = 169/ (1 + 4/100)^2 = 169 * 25/26 * 25/26 = $156.25
Answer is C
Answer: (C) $156.25
Question: What least number mustbe subtracted from 427398 so that remaining no.is divisible by 15
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
Answer: Option A
Answer: (A) 3
Question: Here is 15 dots. If you select 3 dots randomly, what is the probability that 3 dots make a triangle?
(A) 412/4228
(B) 412/455
(C) 412/429
(D) 412/418
(E) 412/419
Rationale: I think there seem some problem with this question. Total ways of selecting 3 dots out of 15 is 15C315C3 = 455 If 3 dots are collinear then triangle may not be formed. Now look at the above diagram. If we select any 3 dots from the red lines they may not form a triangle. They are 3 x 5C35C3 = 30. If we select the three letters from blue lines, they may not form a triangle. They are in total 5 ways. Also there are 6 others lines which don't form a triangle. Also another two orange lines. Total = 30 + 5 + 6 + 2 = 43. So we can form a triangle in 455 - 43 = 412. So answer could be 412/455.
\Answer:B
Answer: (B) 412/455
Question: Ten animals of a circus has to be placed inside in ten cages one in each cage. If 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal.
(A) A.464
(B) B.808
(C) C.5024
(D) D.86400
(E) E.302400
Rationale: ways for cages that are too small = 5*4*3*2=120
since we have 6 cages and 6 animal left therefore ways for 6 cages =6!
total ways =120*6!=86400
Answer D
Answer: (D) D.86400
Question: What least number should be added to 1015, so that the sum is completely divisible by 25?
(A) 4
(B) 3
(C) 2
(D) 10
(E) 5
Rationale: 1015 Ã· 25 = 40 with remainder = 15
15 + 10 = 25.
Hence 10 should be added to 1015 so that the sum will be divisible by 25
Answer: Option D
Answer: (D) 10
Question: If Re.250 amounts to Rs.550 over a period of 4 years. What is the rate of simple interest?
(A) 31%
(B) 28%
(C) 25%
(D) 22%
(E) 30%
Rationale: 300 = (250*4*R)/100
R = 30%
Answer:E
Answer: (E) 30%
Question: if x/4-x-3/6=1,then find the value of x.
(A) 12
(B) 10
(C) 8
(D) 6
(E) 4
Rationale: (x /4)-((x-3)/6)=1
(3x-2(x-3) )/12 = 1
3x-2x+6=12
x=6.
Option D
Answer: (D) 6
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.105 only. Menâ€™s wages are?
(A) 6Rs
(B) 7Rs
(C) 8Rs
(D) 4Rs
(E) 1Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 105 Rs.
5M + 5M + 5M ----- 105 Rs.
15M ------ 105 Rs. => 1M = 7Rs.
Answer:B
Answer: (B) 7Rs
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Answer: (B) If x>=y
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction W of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
(A) 1/(3x)
(B) 3x/(x-3)
(C) (x – 3)/(3x)
(D) x/(x-3)
(E) (x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete W=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: (C) (x – 3)/(3x)
Question: In a graduating class, the difference between the highest and lowest salaries is $100,000. The median salary is $50,000 higher than the lowest salary and the average salary is $20,000 higher than the median. What is the minimum number of students Q in the class?
(A) A)10
(B) B)12
(C) C)15
(D) D)20
(E) E)25
Rationale: the difference between the highest and lowest salaries is $100,000.
So there are at least 2 people - say one with salary 0 and the other with 100k. No salary will be outside this range.
Median = 50k more than lowest. So median is right in the center of lowest and highest since lowest and highest differ by 100k. In our example, median = 50k. Since there are more than 2 people, there would probably be a person at 50k.
Mean = 20k more than median so in our example, mean salary = 70k
On the number line,
0........50k (median)........100k
Mean = 70k
So there must be people more toward 100k to bring the mean up to 70k. Since we want to add minimum people, we will add people at 100k to quickly make up the right side deficit. 0 and 50k are (70k + 20k) = 90k away from 70k. 100k is 30k away from 70k. To bring the mean to 70k, we will add two people at 100k each to get:
0....50k.....100k, 100k, 100k
But when we add more people to the right of 70k, the median will shift to the right. We need to keep the median at 50k. So every time we add people to the right of 70k, we need to add people at 50k too to balance the median. 50k is 20k less than 70k while 100k is 30k more than 70k. To keep the mean same, we need to add 2 people at 100k for every 3 people we add at 50k. So if we add 3 people at 50k and 2 people at 100k, we get:
0, ... 50k, 50k, 50k, 50k, ... 100k, 100k, 100k, 100k, 100k
the median is not at 50k yet.
Add another 3 people at 50k and another 2 at 100k to get
0, 50k, 50k, 50k, 50k, 50k, 50k, 50k, 100k, 100k, 100k, 100k, 100k, 100k, 100k
Now the median is 50k and mean is 70k.
Total number of people is 15.
Answer (C)
Answer: (C) C)15
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order P? (1 cubic meter = 1,000 liters)
(A) 92
(B) 90
(C) 82
(D) 78
(E) 75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
P=12.5*6 = 75.E
Answer: (E) 75
Question: 12 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
(A) 150
(B) 131
(C) 115
(D) 90
(E) 45
Rationale: there are 12 business exec and in each handshake 2 business execs are involved.
hence 12C2=66
Also, each of 12 exec will shake hand with every 7 other chairmen for total of 84 handshake.
total=66+84=150
ANS: A
Answer: (A) 150
Question: If north becomes south-west ant south-west becomes east and all the directions changed in the same manner,then what will be the direction for south-east?
(A) North-West
(B) North-East
(C) North
(D) West
(E) none
Rationale: North -> South-west
North-east -> West
East -> North-west
South-east -> North
South -> North-east
South-west -> east
West -> South-east
North-west -> south
ANSWER:C
Answer: (C) North
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent Q?
(A) 20%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
Q=[(2 - 1)/1] * 100% = 100%
Answer: (C) 100%
Question: In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points M is in the same quadrant as the fourth vertex of the square?
(A) (-5, -3)
(B) (-5, 3)
(C) (5, -3)
(D) (3, -5)
(E) (3, 5)
Rationale: The question:In the xy-plane, the points M=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?
I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means
Vertex #1 = (c, d) is in QII (that is, negative x and positive y)
Vertex #2 = (c, -d) is in QIII (that is, both xy negative)
Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)
That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.
Answer: (E) (3, 5)
Question: Rs. 925 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. 925 become in 3 years ?
(A) Rs. 1020.80
(B) Rs. 1025
(C) Rs. 1067
(D) Data inadequate
(E) None of these
Rationale: Solution
S.I. = Rs.(956-925 )=Rs.31
Rate = (100x31/925x3) =124/111%
New rate = (124/111 +4)% = 568/111%
New S.I. = Rs.(925 x 568/111 x 3/100) Rs. 142
∴ New amount = Rs.(925+142)= Rs. 1067.
Answer C
Answer: (C) Rs. 1067
Question: If x < y < z and y - x > 5, where x is an even integer and y and z are odd integers, what is the least possible value Q of z - x?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: x<y<z
To find the least possible value for z-x; we need to find the values for z and x that can be closest to each other. If x is some even number, then what could be minimum possible odd z.
If x is some even number
y-x>5; y>x+5; minimum value for y=x+5+2=x+7[Note: x+5 is as even+odd=odd and nearest odd greater than x+5 is x+5+2]
Minimum value for z=y+2=x+7+2=x+9 [Note: z=y+2 because both z and y are odd. Difference between two odd numbers is 2]
Q=z-x = x+9-x= 9
Ans:D
Answer: (D) 9
Question: Find large number from below question The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1254
(B) 1376
(C) 1659
(D) 1555
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Large number = 274+1385 = 1659
C
Answer: (C) 1659
Question: A Mersenne number is a positive integer that is one less than any power of 2. A Mersenne prime is a Mersenne number that also happens to be prime. The largest known prime number, 2^(43112609) - 1, is a Mersenne prime. If the largest known Mersenne prime were multiplied by the smallest Mersenne prime, which of the following would represent the units digit of the product?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: First of all, think which is the smallest Mersenne prime?
The smallest prime 1 less than a power of 2 is 3.
We need the last digit of 2^{43112609} - 1. What will be the last digit of 2^{43112609}?
Recall cyclicity of last digits. After every 4 powers, the last digit repeats itself. Let's look at the last digits of powers of 2.
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6
2^5 = 2
2^6 = 4
and so on...
When 43112609 is divided by 4, you get remainder 1 (divide just the last two digits by 4. Whatever remainder you get will be the remainder when you divide the actual number by 4)
So the last digit of 2^{43112609} is 2
Last digit of 2^{43112609} - 1 is 1
Product of the last digits is 1*3 = 3
Answer (B)
Answer: (B) 3
Question: Two trains of length 200 m and 300 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 87/7 sec
(B) 20 sec
(C) 80/9 sec
(D) 80/5 sec
(E) 20/7 sec
Rationale: Relative speed = (36 + 72)* 5/18 = 6 * 5 = 30 mps.
The time required = d/s = (100 + 200 + 300)/30
= 600/30 = 20 sec.
Answer: B
Answer: (B) 20 sec
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
(A) 0.5919
(B) P(E)=0.5904
(C) 0.5929
(D) 0.5928
(E) 0.594
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: (B) P(E)=0.5904