divelab/Sys2Bench huggingface dataset:
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 R in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
Options:
A)25%
B)35%
C)45%
D)70%
E)80%
Rationale: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out R: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Answer: B
Question: A marketing survey of Anytown found that the ratio of trucks to sedans to motorcycles was 3:7:2, respectively. Given that there are 11,200 sedans in Anytown, how many motorcycles are there?
Options:
A)1260
B)2100
C)3600
D)3200
E)5200
Rationale: Let the total number of trucks = 3x
total number of sedans = 7x
total number of motorcycles = 2x
total number of sedans = 11200
=> 7x = 11200
=> x = 1600
total number of motorcycles =2x = 2*1600
=3200
Answer D
Answer: D
Question: Three hundred gallons of fuel are purchased at $0.80 per gallon. The fuel is consumed at a rate of $0.30 worth of fuel per hour. At this rate, how many hours are required to consume the 300 gallons of fuel?
Options:
A)600
B)650
C)700
D)750
E)800
Rationale: The fuel is consumed at this rate: $0.30/$0.80 = 3/8 gallons per hour.
The time it takes to consume 300 gallons is: 300 / (3/8) = 800 hours.
The answer is E.
Answer: E
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2475?
Options:
A)s.800
B)s.810
C)s.825
D)s.900
E)s.920
Rationale: 2475 * 1/3 = 825
Option C
Answer: C
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
A. 5 kmph
Options:
A)5
B)8
C)9
D)3
E)2
Rationale: US = 25
DS = 35
M = (35 - 25)/2
= 5
Answer:A
Answer: A
Question: The decimal 0.1 is how many times greater than the decimal (0.01)^3?
Options:
A)10
B)10^2
C)10^5
D)10^8
E)10^10
Rationale: 0.1 = 10^-1
(0.01)^3 = (10^-2)^3 = 10^-6
10^5 * 10^-6 = 10^-1
The answer is C.
Answer: C
Question: 60% of a number is added to 160, the result is the same number. Find the number?
Options:
A)300
B)400
C)266
D)99
E)121
Rationale: :
(60/100) * X + 160 = X
2X = 800
X = 400
Answer: B
Answer: B
Question: A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random form this box. The probability that at least one of these is defective is:
Options:
A)8/19
B)7/19
C)10/19
D)20/19
E)22/19
Rationale: P(none is defective)=16c2/20c2
=12/19
P( at least one is defective)= 1-12/19
=7/19
ANSWER B
Answer: B
Question: There are 2 sections A and B in a class, consisting of 50 and 50 students respectively. If the average weight of section A is 60kg and that of section B is 80kg, Find the average of the whole class?
Options:
A)50.78kg
B)49.32kg
C)61.67kg
D)70kg
E)70.89kg
Rationale: Total weight of 50+50 students = 50*60 + 50*80 = 3000+4000
Average weight of the class is = 7000/100 =70 kg
Answer is D
Answer: D
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $7. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)90/(xy)
B)90xy
C)xy/90
D)xy/10
E)63/(xy)
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 7/ (xy/9) = 63/(xy).
The answer is E.
Answer: E
Question: Three independent strategies A, B and C have been initiated for cost cutting in a company producing respectively 30%, 30% and 10% savings. Assuming that they operate independently, what is the net saving achieved?
Options:
A)56%
B)64%
C)55.9%
D)68%
E)61%
Rationale: If initial cost is Rs 100, then
Final cost will be 100*0.7*0.7*0.9 = Rs. 44.1
savings = 100-44.1=55.9
so 55.9%
ANSWER:C
Answer: C
Question: John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $20. What is the percent decrease?
Options:
A)20%
B)30%
C)40%
D)70%
E)80%
Rationale: The is always the difference between our starting and ending points. In this case, it’s 100 – 20 = 80. The “original” is our starting point; in this case, it’s 100. (80/100)*100 = (0.8)*100 = 80%.
E
Answer: E
Question: A, B and C rent a pasture. If A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing and the rent of the pasture is Rs. 280, then how much amount should C pay as his share of rent?
Options:
A)35
B)45
C)25
D)72
E)55
Rationale: A : B : C
=10×7:12×5:15×3
=2×7:12×1:3×3
=14:12:9
Amount that C should pay
=280×9/35=8×9=72
Answer is D
Answer: D
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/83 hours
B)30/63 hours
C)39/13 hours
D)30/13 hours
E)10/13 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/26
= 30/13 hours.
Answer:D
Answer: D
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/9 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
Options:
A)1/2
B)2/5
C)3/4
D)4/5
E)5/8
Rationale: Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 3/4 * 4/9 X = 1/3 X
% loaded by day crew = X/(X + 1/3X) = 3/4
Answer C
Answer: C
Question: The sum of two numbers is 33. Five times one number is equal to 6 times the other. The smaller of the two numbers is
Options:
A)10
B)15
C)16
D)22
E)24
Rationale: Sol.
Let the numbers be x and (33 - x).
Then, 5x = 6(33 - x)
⇔ 11x = 198⇔ x = 18.
So, the numbers are 18 and 15.
Answer B
Answer: B
Question: Income and expenditure of a person are in the ratio 5 : 4. If the income of the person is Rs. 19000, then find his savings?
Options:
A)3800
B)3607
C)3608
D)3602
E)3603
Rationale: Let the income and the expenditure of the person be Rs. 5x and Rs. 4x respectively.
Income, 5x = 19000 => x = 3800
Savings = Income - expenditure = 5x - 4x = x
So, savings = Rs. 3800.
Answer:A
Answer: A
Question: In a store, the profit is 320% of the cost. If the cost increases by 25% but the SP remains constant, approximately what %of the sp is the profit?
Options:
A)40%
B)70%
C)80%
D)90%
E)100%
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
B
Answer: B
Question: What is the area of a square field whose sides have a length of 12 meters?
Options:
A)225 sq m
B)126 sq m
C)144 sq m
D)267 sq m
E)231 sq m
Rationale: 12 * 12 = 144 sq m
The answer is C.
Answer: C
Question: If 4x + y = 8 and 3x-4y = 5, then what is the value of 7x - 3y?
Options:
A)23
B)3
C)15
D)52/7
E)60/7
Rationale: 4x+y=8 ...equation 1
3x-4y=5 ...equation 2
adding both the equations
7x- 3y=23
correct answer option A
Answer: A
Question: Rajan borrowed Rs.4000 at 5% p.a compound interest. After 2 years, he repaid Rs.2210 and after 2 more year, the balance with interest. What was the total amount that he paid as interest?
Options:
A)635.50
B)635.55
C)635.590
D)635.52
E)635.51
Rationale: 4000
200 ---- I
200
10 ---- II
---------------
4410
2210
--------
2000
110 ---- III
110
5.50 ---- IV
-----------
2425.50
2210
-----------
4635.50
4000
----------
635.50
Answer: A
Answer: A
Question: On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 40 percent. What was the total rent the motel actually charged for that night ?
Options:
A) $500
B) $800
C) $1,000
D) $1,600
E) $2,400
Rationale: Let total rent the motel charge for all rooms =x
If 10 rooms that were rented for 60 $ had instead been rented for 40 $,
then total difference in prices = 20 $ * 10 = 200 $
Total rent the motel charged would have been reduced by 40 %
.4x = 200
=> x= 500
Answer A
Answer: A
Question: Two express trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)km
B)km
C)km
D)km
E)km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer:B
Answer: B
Question: How much time will take for an amount of Rs. 300 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)5 years
B)6 years
C)7 years
D)12 years
E)15 years
Rationale: Time = (100 * 81) / (300 * 4.5) = 6 years
ANSWER:B
Answer: B
Question: If it takes a tub 5 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
Options:
A)48 seconds
B)1 minute, 12 seconds
C)1 minute, 50 seconds
D)2 minutes, 00 seconds
E)4 minutes, 12 seconds
Rationale: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.
If it takes 5 minutes to drain 5/7 th of tub it takes 5*(7/5) minutes to drain the entire tub and 5*(7/5)*(2/7) min to drain 2/7 th of the tub which is 2 minutes
So answer is D
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 72 km/hr?
Options:
A)2.5
B)5
C)2.4
D)2.8
E)2.1
Rationale: Speed = 72 * 5/18 = 20 m/sec
Time taken = 100/20
= 5 sec.
Answer:B
Answer: B
Question: A train 495 m long is running at a speed of 63 km/hr. In what time will it pass a bridge 240 m long?
Options:
A)39
B)40
C)41
D)42
E)43
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Total distance covered = 495 +240 = 735 m
Required time = 700 * 2/35 = 42 sec
Answer: D
Answer: D
Question: Ram, who is half as efficient as Krish, will take 21 days to complete a task if he worked alone. If Ram and Krish worked together, how long will they take to complete the task?
Options:
A)16 days
B)12 days
C)8 days
D)7 days
E)18 days
Rationale: Number of days taken by Ram to complete task = 21
Since Ram is half as efficient as Krish , Amount of work done by Krish in 1 day = Amount of work done by Ram in 2 days
If total work done by Ram in 24 days is 21w
Amount of work done by Ram in 1 day = w
Amount of work done by Krish in 1 day = 2w
Total amount of work done by Krish and Ram in a day = 3w
Total amount of time needed by Krish and Ram to complete task = 21w/3w = 7 days
Answer D
Answer: D
Question: A palindrome is a number that reads the same forward and backward, such as 343. How many odd, 6-digit numbers are palindromes?
Options:
A)400
B)450
C)500
D)900
E)2500
Rationale: First recognize you only need to consider the first three digits (because the second three are just the first three flipped)
There are 900 possibilities for the first three digits of a 6 digit number, 100-999 inclusive. Everything starting with a 1,3,5,7,9 will be odd, which is 5/9ths of the combinations.
5/9*900 = 500
ANSWER:C
Answer: C
Question: The average (arithmetic mean) of eight numbers is 41.5. If the sum of half of these numbers is 152.4, what is the average of the other half?
Options:
A)35.5
B)38.7
C)41.2
D)44.9
E)47.5
Rationale: The average of this half is 152.4/4 = 38.1
This is 3.4 below the overall average, thus the average of the other half of the numbers must be 3.4 above the overall age, that is 41.5+3.4 = 44.9
The answer is D.
Answer: D
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
Options:
A)338
B)237
C)126
D)140
E)882
Rationale: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
Answer: D
Answer: D
Question: In a class of 230 students, 130 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
Options:
A)80%
B)44%
C)30%
D)20%
E)10%
Rationale: No of students study french= 230- No of students study spanish = 230-130=100
% of the students study french but not spanish = (100/230)*100 % = 44 %
Answer:B
Answer: B
Question: Simple interest on a certain sum at a certain annual rate of interest is 1/9 of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is:
Options:
A)5
B)8
C)3 1/3
D)2 2/3
E)None of these
Rationale: Explanation :
Let sum = x. Then, S.I. = x/9
Let rate = R% and time = R years.
[x * R * R / 100] = x / 9 ? R^2 = 100/9
R = 10/3 = 3 1/3.
Hence, time = 3 1/3 %.
Answer : C
Answer: C
Question: A cistern is normally filled in 4 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
Options:
A)10 hours
B)20 hours
C)30 hours
D)40 hours
E)12 hours
Rationale: If leakage/hour=1/x, then 1/4 -1/x= 1/6, solving 1/x=1/12
So in 12 hours full cistern will be empty.
ANSWER:E
Answer: E
Question: The sum of two number is twice their difference, If one of the number is 10, the other number is ?
31/ 3
Options:
A)3 1/3
B)30
C)1/3
D)4 1/4
E)None of these
Rationale: Answer
Let the other number be x.
Then, 10 + x = 2(x - 10)
⇒ x = 30
Correct Option: B
Answer: B
Question: Jithin bought six books at an average price (arithmetic mean) of 20$. If jithin returned two books to the retailer, at an average price of the remaining book was 14.5$, then what is the average price, in dollar, of the two returned books ?
Options:
A)25
B)26.5
C)27
D)28
E)29
Rationale: Total price of six books = 6*20=120$
Total price of four books = 4*16=64$
Total price of two books = 120-64=56$
Average price of two books = 56/2=28$
Correct option Answer:D
Answer: D
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 50 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
Options:
A)99
B)95
C)98
D)97
E)100
Rationale: The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: A.
Answer: A
Question: Marsha and Wenbao picked strawberries one afternoon. They combined all of their strawberries together and divided them evenly (50/50). If Marsha picked an odd number of strawberries which of the following is true?
Options:
A)Wenbao picked 50 strawberries.
B)Wenbao picked 49 strawberries.
C)Wenbao picked 52 strawberries.
D)Wenbao picked 40 strawberries.
E)Wenbao picked 56 strawberries.
Rationale: From Parity Mathematics Rule: The sum of two odd numbers is even. The sum of and odd number and an even number is odd.
Marsha and Wenbao divided their strawberries evenly (50/50) after adding them together.
Marsha picked an odd number of strawberries, so Wenbao had to have picked an odd number of strawberries.
Answer: B
Answer: B
Question: Seven mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
Options:
A)6
B)2400
C)2520
D)360
E)2540
Rationale: Arrangement of 7=7!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 7!/2=2520.
Answer: C
Answer: C
Question: The sum of ages of 10 children born at the intervals of 1 years each is 105years. What is the age of the youngest child?
Options:
A)4
B)5
C)2
D)7
E)6
Rationale: Let the ages of children be x, (x + 1), (x + 2, (x + 3), (x + 4), (x + 5), (x + 6),(x + 7), (x + 8), and (x + 9) years.
Then, x + (x + 1) + (x + 2) + (x + 3) + (x + 4)+ (x + 5) + (x + 6)+ (x + 7) + (x + 8)+(x+9) = 105
10x = 60
x = 6
Age of the youngest child = x = 6 years.
Answer:E
Answer: E
Question: A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is?
Options:
A)3.34 sq m
B)98.8 sq m
C)67.8 sq m
D)27.9 sq m
E)19.9 sq m
Rationale: Area of the path = Area of the outer circle - Area of the inner circle
= ∏{4/2 + 25/100}2 - ∏[4/2]2
= ∏[2.252 - 22] = ∏(0.25)(4.25) { (a2 - b2 = (a - b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16
= 3.34 sq m
Answer: A
Answer: A
Question: Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 1800
Options:
A)30
B)70
C)210
D)300
E)180
Rationale: 27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.
100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.
Then we want to know what is the largest possible GCF of x and 2100.
Well 1800 = 3 * 6 * 10 * 10
We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.
We know x has one factor of 3, but not two factors --- that takes the 3.
We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other
No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.
3*6*10 = 180
If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 1800.
E
Answer: E
Question: Two trains having length of 140 metre and 160 metre long run at the speed of 60 km/hr and
40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is
Options:
A)10.8 sec
B)12 sec
C)9.8 sec
D)8 sec
E)10 sec
Rationale: dist -(140+160) = 300 m = 0.3 km
relative speed = (60+40) = 100 km/hr
req time = 0.3/100 hr
0.3/100 * 3600 sec = 10.8 sec
ANSWER A
Answer: A
Question: The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the maximum distance from A to C?
Options:
A)11
B)8
C)2
D)4
E)5
Rationale: Explanation:
Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5 miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle. The minimum distance will be 1, and maximum 11
Answer: A
Answer: A
Question: A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options:
A)Rs. 1900
B)Rs. 2660
C)Rs. 2800
D)Rs. 2840
E)None of these
Rationale: Explanation:
For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
B's share = Rs.(7030 x	14/37)=Rs. 2660.
ANSWER IS B
Answer: B
Question: How many four-digit positive integers can be formed by using the digits from 1 to 9 so that two digits are equal to each other and the remaining two are also equal to each other but different from the other two ?
.
Options:
A)400
B)1728
C)108
D)216
E)432
Rationale: The number of ways u can chose two digits from 9 digits is 9C2=(9*8)/2.
And the no of ways u can arrange two digits like asked is 4C2=(4*3)/2.
total ways is 36*6=216.
ANSWER:D
Answer: D
Question: 12 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
Options:
A)10
B)3
C)4
D)7
E)5
Rationale: Required number of machines = 12*10/40 = 3
Answer is B
Answer: B
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits S can does Grace have available during her trip?
Options:
A) 2,520
B) 1,260
C) 620
D) 360
E) 120
Rationale: The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you S=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
Answer: B
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 6, 2008?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Friday
E)Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 6 days beyond Monday
Hence, It will be Sunday. answer : E
Answer: E
Question: Robin is traveling from one end of a forest to the other. In order to find his way back, he is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of bap. The pattern repeats after he leaves the morsel of bap. If Robin drops 2,000 morsels of bread, what are the last 3 morsels of bread that he drops?
Options:
A)wheat − wheat − white
B)bap - wheat - wheat
C)white − bap − wheat
D)white − white − white
E)white − white − bap
Rationale: In a single round Robin drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options A, C, D and E can be eliminated
Answer: B
Answer: B
Question: The integer T has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of T and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let T be 67 and y be a8. Then the product of T and y can be written as (60+7)*(10a+8)=600a + 480+70a+56=600a+536+70a. Since 600a dose not affect on the tens digit we can ignore 600a.
So tens digit should be the unit of 3+7a. That means 3+7a =8, 18, 28, 38, 48 or 58 (since 3+7a<=3+7*9=66) --->7a=5, 15, 25, 35, 45, 55. So the only possibility is a=5.
So the answer is (C).
Answer: C
Question: When a random experiment is conducted, the probability that event A occurs is 1/6. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?
Options:
A)17/216
B)19/216
C)23/216
D)25/216
E)35/216
Rationale: One case is: 1/6*1/6*5/6*5/6=25/1296
The total number of possible cases is 4C2 = 6
P(event A occurs exactly twice) = 6*(25/1296) = 25/216
The answer is D.
Answer: D