divelab/Sys2Bench huggingface dataset:
Question: Find the number of factors E of 180 that are in the form (4*k + 2), where k is a non-negative integer?
Options:
A)1
B)2
C)3
D)4
E)E=6
Rationale: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 E(=2^2*3^2*5) = 18. So listing the factors gives us:
1, 180
2, 90
3, 60
4, 45
5, 36
6, 30
9, 20
10, 18
12, 15
As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with
2,4,6,10,12,18,20,30,36,60,90,180
For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.
For checking any particular factor whether they conform to the form 4k+2---> do the following
4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.
E is thus the correct answer.
Answer: E
Question: A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 3% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or doubled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $20,000 in property taxes, but did not pay until October 15th?
Options:
A)$1,400
B)$1,800
C)$2,400
D)$21,400
E)$22,800
Rationale: Original amount = 20,000
Fine for July = 20,000 * 3% = 600
Fine for August = lesser of the 2 , 600+600= 1200 or 600*2=1200 . Pick 1200
Fine for September = 1200+600=1800 or 1200*2 = 2400. Pick 1800
Fine for October = 1800+600=2400 or 1800*2 = 3600. Pick 2400.
The wording of the question should be have been clearer as total fines should be = 2400+1800+1200+400 = 5800 and NOT 2400.
2400 is the fine ONLY for the month of October!
C
Answer: C
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 20. Find the sum :
Options:
A)4500
B)7500
C)5000
D)8000
E)None of these
Rationale: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2100=10100×5×2100=10
and CI = 100(1+5100)2−100100(1+5100)2−100
∴ =100×21×2120×20−100=414=100×21×2120×20−100=414
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 20, the sum
= 400 × 20 = 8000 Answer D
Answer: D
Question: In an intercollegiate competition that lasted for 3 days, 185 students took part on day 1, 150 on day 2 and 200 on day 3. If 100 took part on day 1 and day 2 and 110 took part on day 2 and day 3 and 50 took part on all three days, how many students took part only on day 3?
Options:
A)45
B)35
C)55
D)30
E)40
Rationale: Day 1&2 = 100; Only Day 1&2 (100-50) = 50,
Day 2&3 = 110; Only Day 2&3 (110-50) = 60,
Only Day 3 = 200 - (50+60+50) = 40
Answer:E
Answer: E
Question: Difference between the length &breadth of a rectangle is 20 m. If its perimeter is 206 m, then its area is?
Options:
A)2400 m^2
B)2500 m^2
C)2400 m^2
D)2560 m^2
E)2580 m^2
Rationale: Solving the two equations, we get: l = 60 and b = 40.
Area = (l x b) = (60 x 40) m2 = 2400 m^2
C
Answer: C
Question: The sum of ages of 4 girls born at the intervals of 3 years each is 50 years. What is the age of the youngest girl?
Options:
A)years
B)years
C)years
D)years
E)years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) years.
Then, x + (x + 3) + (x + 6) + (x + 9) = 50
4x = 32
x = 8.
Age of the youngest child = x = 4 years.
A)
Answer: A
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)1
B)3
C)4
D)2
E)5
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D
Answer: D
Question: In one day, Juan sends Keith three times as many messages as he sends Laurence, and Laurence sends Missy 5 times as many messages as he receives from Juan. If Missy received 25 messages from Laurence, how many messages does Keith receive from Juan?
Options:
A)3
B)12
C)15
D)18
E)56
Rationale: Juan --> Laurence = x messages;
Juan --> Keith = 3x messages (Juan sends Keith three times as many messages as he sends Laurence);
Laurence --> Missy = 5x =25 (Laurence sends Missy 5 times as many messages as he receives from Juan).
5x =25 --> x = 5 --> 3x = 15.
Answer: C.
Answer: C
Question: 6 women can do 75 unit of work in 8 days by working 5hr/day in how many days 4 women do 30 units of work by working 8hr/day
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: (6x8x5)/75=(Ax4x8)/30
A=3
ANSWER:A
Answer: A
Question: In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 25% of the people who do not have the job of their choice have a university diploma. If 20% of the people have the job of their choice, what percent of the people have a university diploma?
Options:
A)30%
B)45%
C)55%
D)65%
E)75%
Rationale: Setting up a matrix is how I solve this one.
Diploma No Diploma Totals
Job of Choice w/Diploma
Job of Choice w/o Diploma = 10%
Job of Choice Total = 20%
Not Job of Choice with Diploma =.25X
Not Job of Choice w/o Diploma= .75X
Total Not Job of Choice = X
Total with Diploma
Total without Diploma
Total citizen = 100
If 20% of people have their job of choice, then 80% of people do NOT have their job of choice. 25% of 80% = 20%. We can also see that 10% of the people have their job of choice and a diploma (20%-10%=10%). 10% + 20% = 30%. Therefore 30% of the people in Country Z have a diploma.
Ans A
Answer: A
Question: The average height of 6 people is 67 inches. When Robert's height is included, the average increases by 2 inches. How tall is Robert in inches?
Options:
A)81
B)72
C)69
D)84
E)67
Rationale: Total height of 6 people = 6*67 = 402
Total height of 7 people = 7*69 = 483
Robert's height = 483-402 = 81 inches
Answer is A
Answer: A
Question: A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 7 points if you must draw exactly 5 “low” cards?
Options:
A)6
B)2
C)3
D)4
E)5
Rationale: Great question Ravih. This is a permutations problem (order matters) with repeating elements. Given thatlowcards are worth 1 pt andhigh cards2 pts, and you must draw 3 low cards, we know that you must also draw 1 high card. The formula for permutations problems with repeating elements isN!/A!B!...where N represents the number of elements in the group and A, B, etc. represent the number of times that repeating elements are repeated. Here there are 4 elements and thelowcard is repeated 3 times. As a result, the formula is:
6!/5! which represents (6*5*4*3*2*1)/(5*4*3*2*1) which simplifies to just 6, giving you answer A.
Answer: A
Question: Lewis must answer 7 out of 10 questions on an examination. If at least 3 of the first 5 questions must be answered, how many possible combinations of 7 questions are available to lewis?
Options:
A)110
B)100
C)90
D)120
E)130
Rationale: as there is ONLY one possiblity of choosing 7 out of 10, while choosing less than 3 in first five
choose 2 in first 5 and all 5 from later half..
ways = 5C2 = 10..
total ways = 10C3 = 120
ans = 120-10 = 110
A
Answer: A
Question: A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?
Options:
A)5
B)4
C)3
D)26
E)87
Rationale: US = 25
DS = 35
M = (35 - 25)/2 = 5
Answer: A
Answer: A
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/8%
B)16 1/3%
C)96 2/3%
D)16 2/3%
E)16 3/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
Options:
A)1/4
B)7/12
C)2/3
D)7/8
E)8/7
Rationale: Let there be g geese, of which 0.3g are male and 0.7g are female
Lets say m geese migrated, 0.2m are male and 0.8m are female
Migration Rate Male = 0.2m / 0.3g = (2/3)*(m/g)
Migration Rate Female = 0.8m / 0.7g = (8/7)*(m/g)
Ratio of migration rates = (2/3) / (8/7) = 7/12
Answer is (B)
Answer: B
Question: In a certain game, a player begins with a bag containing tiles numbered 3 through 10, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
Options:
A)5/18
B)13/36
C)3/8
D)5/8
E)23/36
Rationale: player begins with containing tiles 1 to 10 and have equal probability of selecting means
Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.
Next , player draws one title , if number is even player stops or otherwise title is odd without replacement
player draws second title.
If second title is even , player stops or title is odd without replacement player draws third title.
in third title , without replacement of first and second title, player draws and stops it.
the sum of tilte probability is odd. here two conditions are possible.
1st condition is
1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.
Here are we are not selecting 1st condition as even stops because sum of tile is odd.
Here 5 odd numbers are there we can select 1out of 5 odd numbers.
without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.
here we are selecting one number out of remaining 9 numbers. so probability is 5/18.
we are selecting 1 even number out of 5.
2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.
Then probability is 5/10*4/9*3/8=1/12.
Finally sum of probability of two conditions is 5/18+1/12
=5/18.
so option A is correct.
Answer: A
Question: At a certain amateur bands rock show the ratio of freaks to nerds to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yellsrock on!will be a nerds?
Options:
A)1
B)1/2
C)1/4
D)1/3
E)1/6
Rationale: Another approach is to assign some nice values for the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and 3 geeks for a TOTAL of 6 people.
P(next person who yells rock on!is a nerds) = (# of nerds in the crowd)/(TOTAL # of people in the crowd)
=2/6
= 1/3
Answer:
D
Answer: D
Question: There is one highland where planes get fuel. A plan can cover the half of the world with full tank. A plane can transfer fuel from one plane to the other in the air. How many planes are required to make one plane cover the entire world once. Starting point of the travel is the Highland and coming back to the same Highland. All the other planes giving fuels to this Plane should also come back to the same highland and they don't have to cover the entire world.
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Divide the world as 6 parts.
To cover 1/6 th of the distance 1/3 rd of fuel is required.
1 plane, B, can start in same direction of target flight say A.
It can travel 1/6 th of the distance and give 1/3rd of fuel to A and return home with 1/3rd fuel. Now A can cover 4/6th world with that full tank.
Let C and D start from home at opposite direction.
Let C cover 1/6th dist and give 1/3rd fuel to D. Now D travels 1/3 rd more distance and meets A and gives 1/3rd fuel. Both are now 1/6th distance away from home. Let E take fuel and bring one plane home and F take fuel and bring home A. Now excluding A.. 5 supporting planes are required.
ANSWER:D
Answer: D
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)225 sq.m
B)360 sq.m
C)720 sq.m
D)480 sq.m
E)None of these
Rationale: Explanation:
Consider the rhombus ABCD. Let the diagonals intersect at E. Since
diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = âˆš(625 - 225) = âˆš400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
ANSWER IS E
Answer: E
Question: Given a square of 10cm each side with the four semi circles inside as shown in the above
diagram, find the area of the shaded portion
Options:
A)54
B)55
C)56
D)57
E)58
Rationale: area quadra circle- area of triangle
area of triangle =1/8(area of square)
required area=((pie*5*5/4)-(10*10/8))*8=57
ANSWER:D
Answer: D
Question: A pump can be operated both for filling a tank and for emptying it. The capacity of the tank is 2400 m3. The emptying capacity of the pump is 10m3 per minute higher than its filling capacity. Consequently, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump.
Options:
A)45 m3/min
B)40 m3/min
C)50 m3/min
D)55 m3/min
E)None of these
Rationale: 2400/x - 2400/x+10=8,solving this we get x,
=50m3/min
Answer: C
Answer: C
Question: The total circumference of two circles is 64. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
Options:
A)5.7
B)6.0
C)6.7
D)10.2
E)18.0
Rationale: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 64
where 2r = R
Thus:
2πr + 4πr = 64
6πr = 64
r = approx 3.4
πR + 2Rπ = 64
3πR = 64
R = approx 6.8
r + R = approx 10.2
Answer D
Answer: D
Question: The events A and B are independent. The probability that event A occurs is u and the probability that event B occurs is v. Which of the following is equal to the probability that exactly one of the events A and B occurs?
Options:
A)u − 2uv
B)v − uv
C)u + v − 2uv
D)u + v − uv
E)u + v
Rationale: Probability of A occuring = u , Probability of A NOT occuring = 1-u
Probability of B occuring = v , Probability of B not occurring = 1-v
Probability of atleast of one of A and B occuring = 1-(1-u)(1-v) =u+v -uv
D
Answer: D
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 18, Find x and y ?
Options:
A)x=4,y=8
B)x=4,y=9
C)x=4,y=7
D)x=4,y=64
E)x=5,y=8
Rationale: 4+64=68
when reversed 86
86-68=18
x=4,y=64
ANSWER:D
Answer: D
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
Options:
A)100
B)250
C)260
D)416
E)None
Rationale: Sol.
Let the number of boys and girls be 8x and 5x respectively.
Then, 5x = 160 ⇔ x = 32.
∴ Total number of students = 13x = (13 x 32) = 416.
Answer D
Answer: D
Question: The calendar of the year 2032 can be used again in the year?
Options:
A)2060
B)2050
C)2040
D)2033
E)2034
Rationale: Explanation:
Given year 2032 when divided by 4, leaves a remainder 0.
NOTE: When remainder is 0, 28 is added to the given year to get the result.
So, 2032 + 28 = 2060
Answer: A
Answer: A
Question: Find the perimeter and area of the rectangle of length 19 cm and breadth 13 cm.
Options:
A)71 cm2
B)121 cm2
C)141 cm2
D)171 cm2
E)247 cm2
Rationale: length = 19 cm, breadth = 13 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (19 + 13) cm
= 2 × 32 cm
= 64 cm
We know that the area of rectangle = length × breadth
= (19 × 13) cm22
= 247 cm2
ANSWER : E
Answer: E
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
Options:
A)4 months
B)6 months
C)7 months
D)9 months
E)10 months
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
ANSWER:C
Answer: C
Question: A will states that the estate would be divided among six sons with the remainder donated to charity. One stipulation in the will is that no one among the sons can receive an amount within 12% of another's amount. If one of the beneficiaries received $30,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the six sons?
Options:
A)$4096
B)$14043
C)$7892
D)$17736
E)$15336
Rationale: 1st - 30,000.
2nd - 0.88*30,000 = 26,400
3rd - 0.88*26,400 = 23,232
4th - 0.88*23,232 = 20,444.16
5th - 0.88*20,444.16 = ~17,990.86
6th - 0.88*17,990.86 = ~15,831.96
Range = 30,000 - 15,831 = 14,168
Answer: B.
Answer: B
Question: Every student in a room is either a junior or a senior. There is at least one junior and at least one senior in the room. If 4/5 of the juniors is equal to 1/2 of the seniors, what fraction of the students in the room are juniors?
Options:
A)13/20
B)11/3
C)5/13
D)12/17
E)17/20
Rationale: Let total number of juniors= J
total number of seniors =S
(4/5) J = (1/2) S
=> S = 8/5 J
Total number of students = J+S = (13/5) J
Fraction of the students in the room are juniors = J/(J+S) = J/[(13/5) J]
=5/13
Answer C
Answer: C
Question: 5x + y = 19 , and x + 3y = 1. Find the value of 3x + 2y
Options:
A)20
B)18
C)11
D)10
E)5
Rationale: Add these two equations
6x + 4y = 20
Divide by 2 ( to Get 3x + 2y)
Answer will be D. 10
Answer: D
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of spade or an ace of club is:
Options:
A)1/13
B)1/26
C)2/13
D)1/52
E)1/48
Rationale: Explanation :
Total outcomes = 52
Favourable outcomes (getting a queen of spade or an ace of club) = 2
Probability = 2/52 = 1/26.
Answer : B
Answer: B
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)45 km/hr
B)50 km/hr
C)54 km/hr
D)55 km/hr
E)59 km/hr
Rationale: Speed of the train relative to man =	125	m/sec
10
=	25	m/sec.
2
=	25	x	18	km/hr
2	5
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x = 50 km/hr.
ANSWER:B
Answer: B
Question: There is a train and car. The ratio between the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 320 km in 5 hours. The speed of the bus is 4/5th of the speed of the train. How many kilometers will the car cover in 7 hours?
Options:
A)375
B)425
C)475
D)525
E)575
Rationale: The speed of the bus is 320/5 = 64 km/hr
The speed of the train is (64*5)/4 = 80 km/hr
The speed of the car is 80/16 * 15 = 75 km/hr
The distance covered by the car in 7 hours is 75 × 7 = 525 km
The answer is D.
Answer: D
Question: In a 5 digit ID number, what is the probability of exactly 4 digits are the digit 2?
Options:
A)0.81
B)1
C)11/22500
D)0.0081
E).144
Rationale: Total number of 5 digit numbers = 9 * 10 * 10 * 10 * 10 = 90,000
No. of ways of arranging 4 digits as 2 = 5C4=5.
Arrangements are as follows. Here X can be any digit other than 2
1) 2222X = no. of ways = 9
2) 2X222 = no. of ways = 9
3) 22X22 = no. of ways = 9
4) X2222 = no. of ways = 8
5) 222X2 = no. of ways = 9
Probability = (9+9+9+9+8)/90000
=11/22500
Ans - C
Answer: C
Question: If S = {8, 16, 24, 32, 40, 48}, what is the product of mean and median of the numbers in S?
Options:
A)652
B)589
C)456
D)620
E)784
Rationale: Mean = (8 + 16 +24 + 32 + 40 + 48)/6 = 28
Median = (24+32)/2 = 28
Product = 28*28 = 784
Option E
Answer: E
Question: There are 10 boxes numbered from 1 to 10. Either a red ball or a green ball will be placed in each box in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. How many different ways can this be done?
Options:
A)46
B)49
C)52
D)55
E)58
Rationale: 1 green ball: 10 ways
2 green balls: 9 ways
3 green balls: 8 ways
4 green balls: 7 ways
5 green balls: 6 ways
6 green balls: 5 ways
7 green balls: 4 ways
8 green balls: 3 ways
9 green balls: 2 ways
10 green balls: 1 way
The total number of ways is 10*11/2=55
The answer is D.
Answer: D
Question: If A = x% of y and B = y% of x, then which of the following is true?
Options:
A)None of these
B)A is smaller than B.
C)Relationship between A and B
D)If x is smaller than y, then cannot be determined. A is greater than B.
E)A is greater than B.
Rationale: Explanation :
A = (x/100)y = xy/100.................(Equation 1)
B = (y/100)x = yx/100.................(Equation 2)
From these equations, it is clear that A = B
Answer : Option A
Answer: A
Question: Several students are studying together for an exam. 60% of the students who studied less than 10 hours a week feel unprepared. 80% of students who studied 10 hours or more each week feel prepared. If 75% of the students studied less than 10 hours per week, what percent of the students feel prepared for the exam?
Options:
A)20
B)25
C)30
D)35
E)50
Rationale: Let's say there are 100 students.
Students who studied <10 hrs = 75% = 75
So students who studied =>10hrs = 25
Given: 60% of the students who studied less than 10 hours a week feel unprepared.
So 40% of 75 (=30) feel prepared
Given: 80% of students who studied 10 hours or more each week feel prepared.
So 80% of 25 (= 20) feel prepared
Total (30 + 20) = 50 out of 100 feel prepared. 50% feel prepared
ANSWER:E
Answer: E
Question: Mary charges $8.50 per hour to clean a house. If she works 27 hours, how much
does she earn in one week?
Options:
A)$619.50
B)$122.50
C)$229.50
D)$429.50
E)$312.50
Rationale: Multiply 27 hours x $8.50 =
Answer: $229.50
correct answer C
Answer: C
Question: For 1rs 4p interest
wat will be for 2000rs?
Options:
A)45Rs
B)80Rs
C)40Rs
D)30Rs
E)48Rs
Rationale: For 1rs , 4p interest
for 2000rs, x
x= 2000/1 * 4p ==> 8000 paise
To express in rs, 8000/100 = 80rs
ANSWER:B
Answer: B
Question: Find the total number of divisors of 1728(including 1 and 1728)
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: 1728=2^6*3^3
no. of divisors = (6+1)*(3+1)=28
ANSWER:A
Answer: A
Question: A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?
Options:
A)10 min.
B)40 min.
C)30 min.
D)20 min.
E)15 min.
Rationale: Part filled by (A + B) in 1 minute =1/60+1/40=1/24	.
Suppose the tank is filled in x minutes.
Then,	x /2	(1/24+ 1/40)= 1
x/2 x 1/15=1
x/30=1
x = 30 min.
Answer is C
Answer: C
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2240 less than the principal. What was the principal?
Options:
A)1500
B)2500
C)2507
D)2800
E)11500
Rationale: P - 2240 = (P*5*4)/100
P = 2800
Answer: D
Answer: D
Question: Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 50 years. The age of E is?
Options:
A)50
B)47
C)48
D)49
E)46
Rationale: Solution
5 years ago average age of A,B,C,D = 45 years
=> 5 years ago total age of A, B, C, D = 45 x 4 = 180 years
=> Total present age of A, B, C, D = 180 + 5x4 = 200 years
If E's present age is x years = 200+x/5= 50
x=50 years. Answer A
Answer: A