divelab/Sys2Bench huggingface dataset:
Question: A is a working and B is sleeping partners in a business. A puts in Rs. 5000 and B puts in Rs.6000. A receives % of the profit for managing the business and the rest is divided in proportion to their capital. What does each get out of a profit of Rs. 880?
Options:
A)770
B)266
C)297
D)260
E)277
Rationale: Total profit = Rs. 880
A's share for managing the business i.e
\inline 12\frac{1}{2} % = \inline \frac{25\times 880}{200}=Rs.110
Remaining profit of A and B as per their capital = 880 - 110 = Rs. 770
Ratio of amounts = 5000 : 6000 = 5 : 6
Sum of ratios = 5 + 6 = 11
A's share = \inline 770\times \frac{5}{11}= Rs.350
A's total share = 350 + 110 = Rs. 460
B's share = \inline 770\times \frac{6}{11}=Rs.420
Answer:A
Answer: A
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
Options:
A)1/3
B)1/5
C)4/7
D)3/5
E)4/9
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
C)
Answer: C
Question: A contract is to be completed in 56 days if 104 persons work, each working at 8 hours a day. After 30 days, 2/5 of the work is completed. How many additional persons should be deployed so that the work will be completed in the scheduled time, each person’s now working 9 hours a day.
Options:
A)160
B)150
C)24
D)56
E)75
Rationale: Explanation:
Persons worked = 104
Number of hours each person worked per day = 8
Number of days they worked = 30
Work completed =25
Remaining days = 56 - 30 = 26
Remaining Work to be completed =1−2/5=3/5
Let the total number of persons who do the remaining work =x
Number of hours each person needs to be work per day = 9
More days, less persons (indirect proportion)
More hours, less persons (indirect proportion)
More work, more persons (direct proportion)
Hence we can write as
(days)30:26
(hours)8:9
(work)35:25 }::x:104
⇒30×8×35×104 =26×9×2/5 × x
⇒x=30×8×3/5×104/26×9×2/5
=30×8×3×104/26×9×2
=30×8×104/26×3×2
=30×8×4/3×2
=5×8×4=160
Number of additional persons required = 160 - 104 = 56
Answer: Option D
Answer: D
Question: A Ball is dropped from 8 m height.it rebounds to half the height when it hits the ground. What is the distance travelled by the ball before it hits the ground?
Options:
A)20m
B)21m
C)22m
D)24m
E)28m
Rationale: distance travelled by the ball before coming to rest = 8+4+4+2+2+1+1+(1/2)+(1/2)+(1/4)+(1/4)+...upto infinity
=8+2*[4+2+1+(1/2)+(1/4)+...]
=8+2*[4/(1-1/2)]
=8+2*8
=24 m
ANSWER:D
Answer: D
Question: Raviraj invested an amount of 1000000000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?
Options:
A)12,310000
B)13,210
C)13,3200000
D)13,120
E)1331000000
Rationale: Amount = 1000000000(1 + 10⁄100)3
= 1000000000 × 11⁄10 × 11⁄10 × 11⁄10
= 1331000000
Answer E
Answer: E
Question: If at least 150 dollar is to be divided equally among 12 beneficiaries, how much more the donor needs to add to his dollar balance in order to meet the equal distribution criteria.
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: The donor when left with 150 dollar can either distribute either 12 dollar (12x12=144) or 13 dollar (13x12=156) meeting criteria of equal distribution. As the donor has to distribute at least 150 dollar, he or she needs to add 6 dollar more to the balance. Answer: B
Answer: B
Question: What number would replace the question mark in this quite difficult number sequence ?
21 32 54 87 131 ?
Options:
A)300
B)125
C)450
D)340
E)186
Rationale: E
186
Explanation :
21+11*1 => 32
32+11*2 => 54
54+11*3 => 87
87+11*4 => 131
131+11*5 => 186
Answer: E
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.
Options:
A)390 km
B)340 km
C)380 km
D)360 km
E)320 km
Rationale: A
390 km
The total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in AP whose first term is 30 and last term is 48 = 10/2 [30 + 48] = 390 km
Answer: A
Question: In a sports club with 30 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
Options:
A)3
B)5
C)6
D)7
E)8
Rationale: 17+19=36
but where as total number is 30-2=28
therefore answer is 36-28=8
Hence Answer is E
Answer: E
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
Options:
A)25/42
B)25/47
C)25/17
D)25/19
E)25/98
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer: A
Answer: A
Question: If two projectiles are launched at the same moment from 1386 km apart and travel directly towards each other at 445 km per hour and 545 km per hour respectively, how many minutes will it take for them to meet?
Options:
A)80
B)82
C)84
D)86
E)88
Rationale: The projectiles travel a total of 990 km per hour.
The time to meet is 1386/990=1.4 hours = 84 minutes
The answer is C.
Answer: C
Question: Two trains are running at 40km/hr and 20km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
Options:
A) 23 m
B) 23 2/9 m
C) 27 7/9 m
D) 29 m
E) 28 m
Rationale: SOLUTION:
Relative speed =(40-20)km/hr=(20*5/18)m/sec=(50/9)m/sec.
Therefore length of faster train = ((50/9)*5)m=250/9 m = 27 7/9 m.
Answer: C
Answer: C
Question: Ravi and sunil are partners in a business. Ravi invests Rs.9,000 for 8 months and Sunil invested Rs.12000 for 9 months then after one year ratio of their profits will be
Options:
A)1:3
B)2:3
C)3:2
D)3:1
E)3:4
Rationale: =(9000*8):(15000*8)
=72000:108000
=2:3
ANSWER:B
Answer: B
Question: Rs. 120 are divided among A, B, C such that A's share is Rs. 20 more than B's and Rs. 20 less than C's. What is B's share
Options:
A)Rs 10
B)Rs 20
C)Rs 24
D)Rs 28
E)Rs 29
Rationale: Explanation:
Let C = x. Then A = (x—20) and B = (x—40).
x + x - 20 + x - 40 = 120 Or x=60.
A:B:C = 40:20:60 = 2:1 :3.
B's share = Rs. 120*(1/6) = Rs. 20
Option B
Answer: B
Question: A tourist purchased a total of $1,200 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
Options:
A)$1,430
B)$1,310
C)$1,290
D)$1,270
E)$970
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1200 - 230 = 970 hence answer is E
Answer: E
Question: You are having 31kg of rice. You are provided with a 1kg stone for weighing. In how many weights the 31kg of rice can be weighed. ?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: in 1st weight 1kg stone and 1 kg rice.. rice weighed = 1kg.
2nd weighing 2kg of (stone +rice) and 2 kg of rice.. rice weighed = 3kg.
3rd weighing 4kg of (stone +rice) and 4 kg of rice.. rice weighed = 7kg.
4th weighing 8kg of (stone +rice) and 8 kg of rice.. rice weighed = 15kg.
5th weighing 16kg of (stone +rice) and 16 kg of rice.. rice weighed = 31kg.
Therefore 5 weights
ANSWER:C
Answer: C
Question: Find the wrong number below mentioned series
7,30,80,250,550
Options:
A)7
B)30
C)80
D)250
E)550
Rationale: 7 is the only prime number or odd number in the series.
ANSWER:A
Answer: A
Question: If the equation x^2−x=k has at least one solution, which of the following must be true?
Options:
A)k ≥-1/4
B)k < −9
C)k = 9
D)k ≤ 9
E)k ≥ −9
Rationale: x^2−x=k
=> x^2−x - k = 0
For a quadratic equation to have at least one solution, its discriminant (b^2-4ac) should be non-negative.
b^2-4ac ≥0
=> 1- 4*1*(-k) ≥0
=>1 + 4k ≥0
=> k ≥ -14
Answer A
Answer: A
Question: The product of all the prime numbers less than 14 is closest to which of the following powers of 10 ?
Options:
A)10^5
B)10^8
C)10^7
D)10^6
E)10^9
Rationale: Product of Prime numbers less than 14 is 2*3*5*7*11*13
2*5=10 .
10*11*3*7*13 = 10*10*3*10*10 (approximately) ~ Product will be >10^4 <10^6 i.e. 10^5
A is the answer
Answer: A
Question: In a box of 9 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
Options:
A)5/12
B)1/15
C)2/13
D)2/15
E)1/17
Rationale: First, there are 7C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 9C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 7C3/9C3=35/84 = 5/12
Answer is A
Answer: A
Question: 12,31,68,129,220,?
Options:
A)129
B)220
C)387
D)347
E)520
Rationale: 2*2*2 + 4 = 12
3*3*3 +4 = 31
4*4*4 + 4 = 68
5*5*5 + 4 = 129
6*6*6 + 4 = 220
7 *7 *7 + 4 = 347
ANSWER : D
Answer: D
Question: The fourth proportional to 5, 8, 15 is:
Options:
A)18
B)24
C)19
D)20
E)22
Rationale: Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
5x = (8 x 15)
x =	(8 x 15)/5
x=120/5 =24
Answer: Option B
Answer: B
Question: Given the equation a^2 +a^(-3)=4.125, which of the following options is the correct value of a?
Options:
A)2
B)1
C)0
D)3
E)5
Rationale: Plugging in the various option into the equation to find out which is correct:
a^2 +a^(-3)= 4.125
2^2 +2^(-3) = 4.125 Ans. A
Answer: A
Question: A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)90
B)67
C)28
D)26
E)27
Rationale: Length = Speed * time
Speed = L/T
S = 500/20
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer:A
Answer: A
Question: #88
A necklace is made by stringing Q no individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then Q could equal
Options:
A)16
B)28
C)41
D)54
E)65
Rationale: You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on...
3+5 = 8
3+5+5 = 13
3+5+5+5=18
3+5+5+5+5=23
So you see it ends in either 8 or 3. Pick an answer that ends in either 8 or 3. Only one answer does, b.
Answer: B
Question: A swimmer jumps from a bridge over a canal and swims one kilometer stream up. After that first kilometer, he passes a floating cork. He continues swimming for half an hour, then turns around, and swims back to the bridge. The swimmer and the cork arrive at the bridge at the same time. The swimmer has been swimming with constant effort. How fast does the water in the canal flow?
Options:
A)3 km/h
B)2 km/h
C)1 km/h
D)4 km/h
E)5 km/h
Rationale: C
1 km/h
If you have written down a full paper of mathematical formulas, you have been thinking too complicatedly...
It is obvious that the cork does not move relatively to the water (i.e. it has the same speed as the water). Therefore, if the swimmer is swimming away from the cork for half an hour (upstream), it will take him another half hour to swim back to the cork again. Because the swimmer is swimming with constant effort, his speed is constant relatively to the speed of the water. You can look at it as if the water in the river does not move, the cork does not move, and the swimmer swims a certain time away from the cork and then back. Consequently, in that one hour time, the cork has floated from 1 kilometer up stream to the bridge.
Conclusion: The water in the canal flows at a speed of 1 km/h.
Answer: C
Question: Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now?
Options:
A)18 years
B)24 years
C)27 years
D)28 years
E)None
Rationale: Solution
Present age of (A+B)	= (18x2+3x2) years
= 42 years.
Present age of (A+B+C)	= (22x3) years
= 66 years.
∴ C's age	= (66 - 42) years
= 24 years.
Answer B
Answer: B
Question: If x+|x|+y=5 and x+|y|-y=6 what is x+y=?
Options:
A)1
B)-1
C)3
D)12
E)13
Rationale: If x<0 and y<0, then we'll have x-x+y=7 and x-y-y=6. From the first equation y=7, so we can discard this case since y is not less than 0.
If x>=0 and y<0, then we'll have x+x+y=7 and x-y-y=6. Solving gives x=4>0 and y=-1<0 --> x+y=3. Since in PS questions only one answer choice can be correct, then the answer is C (so, we can stop here and not even consider other two cases).
Answer: C.
Adding both eqn we get 2x +IxI+IyI = 13
Now considering X <0 and y>0
2x-x +y = 13
we get x+y =12
Hence answer should be D
Answer: D
Question: A man purchases 2 watches for $ 7650. He sells one at 25% profit and the other at a loss of 20%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
Options:
A)$ 3400 and $ 7650
B)$7650and $ 4250
C)$3400 and $4250
D)$7650 and $3400
E)$2240 and $ 3500
Rationale: x + y = 7650 --- (1)
1.25x + 0.8y = 7650 --- (2)
(2) - (1) --> 0.25x - 0.2y = 0
25x = 20y
x/y = 4/5 = (4*850)/(5*850) = 3400/4250
Answer: C
Answer: C
Question: n and p are integers greater than 1;
5n is the square of a number;
75 np is the cube of a number.
The smallest value for n + p is
Options:
A)14
B)18
C)20
D)30
E)50
Rationale: n>1
p>1
5∗n=x^2
75 np=y3
n+p=?
Well, a square number is usually the result of himself times himself so in the case of n the least value possible (being 5 a prime) is 5*5
n=5
as for p
75∗5∗p=y3
we know 375 is equal = 53∗31 therefore to obtain a cube we need 32 or 9 -> p=9p=9
p+n=14
ANSWER:A
Answer: A
Question: A truck covers a distance of 376 km at a certain speed in 8 hours. How much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?
Options:
A)6 hours
B)5 hours
C)7 hours
D)8 hours
E)None
Rationale: Explanation :
Speed of the truck = Distance/time = 376/8 = 47 kmph
Now, speed of car = (speed of truck + 18) kmph = (47 + 18) = 65 kmph
Distance travelled by car = 376 + 14 = 390 km
Time taken by car = Distance/Speed = 390/65 = 6 hours.
Answer – A
Answer: A
Question: A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
Options:
A)37
B)299
C)72
D).32
E)01
Rationale: Explanation:
Let cost price of lemons be x.
Selling price of lemons becomes CP - loss.
=>SP=x-(20/100)x
=>40=x(80/100)
=>50
So 45 lemons cost Rs 50
Cost of 1 lemon = 50/45 Rs
Cost of 24 lemons = (50/45)*24 =80/3 Rs
Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32
ANSWER:D
Answer: D
Question: What least number should be added to 1021, so that the sum is completely divisible by 25?
Options:
A)4
B)3
C)2
D)0
E)5
Rationale: 1021 Ã· 25 = 40 with remainder = 21
21 + 4 = 25.
Hence 4 should be added to 1021 so that the sum will be divisible by 25
Answer: Option A
Answer: A
Question: A and B put in Rs.300 and Rs.500 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.200 where as B does not. In what ratio should they divide the second year's profit?
Options:
A)39:40
B)39:49
C)15:16
D)14:18
E)39:41
Rationale: Explanation:
3: 5
A = 3/8*200 = 75
375: 400
39:40
Answer:C
Answer: C
Question: Calculate the average mark scored by Nancy if she obtained the following scores in an examination: 65, 78, 89, 51 and 69 marks (out of 100) in English Language, Physics, Mathematics, Chemistry and Biology?
Options:
A)40.4
B)60.4
C)50.4
D)70.4
E)79.4
Rationale: Explanation:
Average mark = 65+78+89+51+69/5=70.4
Answer: Option D
Answer: D
Question: If 183 is divisible by 11, find the value of the smallest natural no. N?
Options:
A)5
B)7
C)9
D)10
E)11
Rationale: In aptitude tests , we get questions on divisibility by 11.
A number is divisible by 11, when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11
The given number is N183.
(Sum of digits at EVEN places) – (sum of digits at ODD places)=0
(8 + N)- (3+1)= 0
(8 + N) - 4 = 0
Here the value of N must be 7
B
Answer: B
Question: The salary of a person was reduced by 35%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
Options:
A)50%
B)32%
C)25%
D)54%
E)29%
Rationale: Let the original salary be $100
New salary = $65
Increase on 65 = 35
increase on 100 = 35/65 *100 = 54%(APPROXIMATELY)
Answer is D
Answer: D
Question: A hostel had provisions for 250 men for 36 days. If 50 men left the hostel, how long will the food last at the same rate?
Options:
A)30
B)45
C)50
D)60
E)65
Rationale: A hostel had provisions for 250 men for 36 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 36
250×36=200x
5×36=4x
x=5×9=45
ANSWER B
Answer: B
Question: The average (arithmetic mean) of 27, 32, and 64 is 6 less than the average of 29, 42, and x. What is x?
Options:
A)62
B)64
C)66
D)68
E)70
Rationale: The average of 27, 32, and 64 is 41.
The average of 29, 42 and x is 47.
Then 29 + 42 + x = 141.
x = 70.
The answer is E.
Answer: E
Question: 288 Ã· ? Ã— 15 + 270 = 405
Options:
A)24
B)25
C)32
D)39
E)43
Rationale: Explanation:
288 Ã· ? Ã— 15 = 405 - 270 = 135
(288 Ã— 15)/? = 135
? = (288Ã— 15)/135 = 32
Answer: Option C
Answer: C
Question: Ramesh can finish a piece of work in 14 days. Rohan is twice as efficient as Ramesh.If they work together how many days will they need to finish the same amount of work?
Options:
A)8/3 days
B)9/3 days
C)10/3 days
D)14/3 days
E)7/3 days
Rationale: Ramesh can finish a piece of work in 14 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 7 days.
days needed to finish the same amount of work = 1/(1/7+1/14)=14/3 days
ANSWER:D
Answer: D
Question: If a town of 15,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
Options:
A)a.16000
B)b.17000
C)c.18000
D)d.19000
E)e.20000
Rationale: 1% is quite small and hence the answer is A)
Answer: A
Question: In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day.
Options:
A) 129,500
B) 129,600
C) 129,700
D) 129,800
E) 129,900
Rationale: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 6-3 = 3 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 3 = 129,600. Hence B.
Answer: B
Question: How many seconds will a 600 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)11
B)36
C)99
D)88
E)61
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 600 * 3/50 = 36 sec.
Answer: B
Answer: B
Question: The value of (7x10^7)(7x10^8) is closest to which of the following?
Options:
A)10^11
B)10^12
C)10^17
D)10^14
E)10^18
Rationale: multiplying these we get,
49 x 10^7 x 10^8
= 4.9 x 10^16
which is closer to 10^17
Answer: C
Answer: C
Question: In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (3,-1), (3, 8), (12, 2), (12,-7)?
Options:
A)69
B)75
C)81
D)87
E)93
Rationale: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (9 + 9) × 9 = 81.
The answer is C.
Answer: C
Question: An exam consists of 8 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 80% is a passing grade, what is the probability that Brian passes?
Options:
A)1/16
B)37/256
C)1/2
D)219/256
E)125/256
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 125/256.
E
Answer: E
Question: If the product of two numbers is 51216 and their H.C.F. is 33, find their L.C.M.
Options:
A)600
B)680
C)582
D)560
E)None of these
Rationale: Explanation:
HCF * LCM = 51216, because we know
Product of two numbers = Product of HCF and LCM
LCM = 51216/88 = 582
Option C
Answer: C
Question: A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 2k1,k24, where k represents a digit that occurs twice, how many values could n have?
Options:
A)1
B)2
C)3
D)4
E)10
Rationale: 2k1k24
Taking sum of the numericals = 2 + 1 + 2 + 4 = 9
We require the values of K such that they are also divisible by 3
201024
231324
261624
291924
Answer = 4 =D
Answer: D
Question: The story of Rapunzel is legendary, but do you know how long it took her to grow her hair so long? First of all, her tower was 22 feet high. On average, her hair would grow 2 feet per year. However, she also had to trim her hair occasionally so that it would continue to grow strong enough to hold a man's body weight. These would amount to cutting off 1/2 foot of her hair every 8 months. Assuming she was bald from the beginning and the prince could jump 3 feet up from the ground to grab the hair, how many months of hair growth would Rapunzel need to be united with her prince charming?
Options:
A)211.2
B)132
C)130.29
D)150.86
E)182.4
Rationale: Needed length of hair = 22 feet minus 3 feet (Prince's jump) = 19 feet of hair
Annual growth rate: 2 feet hair growth per year
Annual loss rate calculation: 1/2 foot divided by 8 months = 1/16 monthly, times 12 = 3/4 foot hair loss per year
NET annual growth rate: 2 minus 3/4 = 1.25 feet hair growth per year
YEARS needed to grow: 19 (feet needed) divided by 1.25 (yearly growth) = 15.2 years
MONTHS needed to grow: 15.2 years x 12 months in a year = 182.4 months
The correct option is E) 182.4 months.
Answer: E