divelab/Sys2Bench huggingface dataset:
Question: If x and y are positive integers such that (3x + 7y ) is a multiple of 11, then which of the following will also be divided by 11?
Options:
A)4x + 6y
B)x + y + 4
C)9x + 4y
D)4x - 9y
E)None of these
Rationale: Keeping y =1, for x = 5, we have
3x + 7y =22
which is divisible by 11.
Now, substitute x =5 and y =1 in each alternative and find out
which expression becomes a multiple of 11?
Now, 4x + 6y = 4 x 5 + 6 = 26
x + y + 4 = 5 + 1 + 4 = 10
9x + 4y = 9 x 5 + 4 = 49
4x - 9y = 4 x 5 -9 = 20 -9 =11
which is divisible by 11
ANSWER:D
Answer: D
Question: What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 120° each?
Options:
A)90 cm
B)108 cm
C)120 cm
D)132 cm
E)144 cm
Rationale: Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 120*n
from here
n = 6
So perimeter becomes 15*6 = 90
answer A
Answer: A
Question: Express a speed of 36 kmph in meters per second?
Options:
A)62kmp
B)73kmp
C)10kmp
D)37kmp
E)73kmp
Rationale: Answer:C
Answer: C
Question: A 270 metres long bullet train running at the speed of 120 kmph crosses another bullet train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other bullet train ?
Options:
A)226
B)230
C)430
D)310
E)260
Rationale: B
230
Relative speed = (120 + 80) km/hr
= 200 x 5/18
= 500/9 m/sec
Then, (x+270)/9 = 500/9
--> x + 270 = 500
--> x = 230.
Answer: B
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
Options:
A)234
B)254
C)364
D)389
E)430
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: C
Question: If average of two positive number is 2 initially and one number is replaced then the average became twice the initial average. What is number replace.
Options:
A)1
B)2
C)3
D)6
E)5
Rationale: Since the average is 2 which gives (x+y)/2 = 2. X+Y = 4
the numbers must be 1+3 so if you replace 1 by 5 then average becomes 4
Answer: 1
Answer: A
Question: S, B, C are three consecutive positive integers (S>B>C). What is the value of the expression 2S +B +3C?
Options:
A)6A+7.
B)5A+1.
C)5A-1.
D)6A-5.
E)6S-7.
Rationale: => S+S+(S-1)+3(S-2)
Ans E. 6S-7.
Answer: E
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 10 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Options:
A)105%
B)80%
C)120%
D)124.2%
E)138%
Rationale: the profit 0f 2009 in terms of 2008 = (0.8*10/10)*100=80%
B
Answer: B
Question: What is the perimeter of a square with area 25p^2/16 ?
Options:
A)3p/4
B)3p^2/4
C)5p
D)3p^2
E)4p/3
Rationale: Area of square, (side)^2 = (5p/4)^2
Therefore side of the square = 5p/4
Perimeter of square = 4*side = 4* (5p/4) = 5p
Answer is C.
Answer: C
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:
Options:
A)14 years
B)18 years
C)20 years
D)22 years
E)23 years
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22.
ANSWER:D
Answer: D
Question: Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 36kmph. For how many minutes does the bus stop per hr
Options:
A)12 min
B)11 min
C)13 min
D)19 min
E)20 min
Rationale: Due to stoppages,it covers 18km less.
time taken to cover 18 km is [18/54 *60] min = 20min
Answer is E.
Answer: E
Question: In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)12 km/hr
B)11 km/hr
C)18 km/hr
D)10 km/hr
E)13 km/hr
Rationale: Speed in still water =1/2(14+8) kmph = 11 kmph.
Answer : Option B
Answer: B
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more
men joined them. How many days will they take to complete the remaining work?
Options:
A)3days
B)4days
C)2days
D)8days
E)5days
Rationale: 1 man's 1 day work = 1/108
12 men's 6 days work = 6/9 = 2/3
remaining work = 1 – 2/3 = 1/3
18 men's 1 days work = 18/108 = 1/6
1/6 work is done by them in 1 day
therefore, 1/3 work is done by them in 6/3 = 2 days.
ANSWER C 2days
Answer: C
Question: A can do a piece of work in 8 days. B can do it in 6 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)8.7 days
B)2.0 days
C)6.6 days
D)7.7 days
E)4.8 days
Rationale: C = 1/2 - 1/8 - 1/8 = 5/24
=> 4.8 days
Answer: E
Answer: E
Question: Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 20 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
Options:
A)20
B)40
C)60
D)80
E)100
Rationale: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
Sam rides 1 km every 5 minutes.
In the next 20 minutes, Sam rides 4 km so Sam will be 2 km ahead.
It will take Annie 40 minutes to catch Sam.
The answer is B.
Answer: B
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
Options:
A)235 cm2
B)265 cm2
C)285 cm2
D)295 cm2
E)284 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Answer: C
Question: Myra drove at an average speed of 30 miles per hour for the first 30 miles of a trip & then at an average speed of 60 miles/hr for the remaining 30 miles of the trip. If she made no stops during the trip what was her average speed in miles/hr for the entire trip?
Options:
A)The average speed is 35 miles per hour.
B)The average speed is 40 miles per hour.
C)The average speed is 55 miles per hour.
D)The average speed is 66 miles per hour.
E)The average speed is 45 miles per hour.
Rationale: Here, distance for which Myra traveled at the two speeds is same.
Average Speed = 2ab/(a+b) = 2*30*60/(30 + 60) = 40 mph
Answer (B)
Answer: B
Question: In a particular 100 meter race, 5 athletes are participating that are numbered 1-5. In how many ways can athlete #5 finish ahead of #2 provided there's no tie among the athletes?
Options:
A)60
B)100
C)120
D)180
E)240
Rationale: The total number of ways for the athletes to finish is 5! = 120.
#5 will be ahead of #2 in exactly half of these possibilities.
120/2 = 60
The answer is A.
Answer: A
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.22,000 earned at the end of 2years from the startingof the business?
Options:
A)s. 5,000
B)s. 5,500
C)s. 5,700
D)s. 6,600
E)s. 7,500
Rationale: A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 22000 x	3/10	= Rs. 6,600.
D
Answer: D
Question: Walking 9/8 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Options:
A)22
B)99
C)27
D)36
E)20
Rationale: Speed Ratio = 1:9/8 = 8:9
Time Ratio = 9:8
1 -------- 9
4 --------- ? 36 m.Answer:D
Answer: D
Question: In a group of 80 people, 45 have visited Iceland and 33 have visited Norway. If 41 people have visited both Iceland and Norway, how many people have visited neither country?
Options:
A)30
B)31
C)32
D)33
E)34
Rationale: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
80= 45 + 33 - 41 + (# in Neither Group)
=33
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D
Answer: D
Question: A boy wanted to calculate his speed on his bike. His starting point was 350 meters from the turning point. He made the round trip 5 times in 30 minutes. What was the boy's speed in kilometers per hour?
Options:
A)1.75
B)1
C)2.25
D)2.4
E)3.2
Rationale: The distance between the the starting point and the turning point was 350 meters.
The boy made the round trip 5 times so that was 10 times he traveled 350 meters.
10 * 350 = 3500 meters or 3.5 km.
30 minutes is half of an hour.
Divide the 3500 meters in half to put in the right time interval
3500/2 = 1750 meters or 1.75 km
Correct answer is A
Answer: A
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 300 that is both a prime and a palindrome. What is the sum of the digits of p?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Given that p is smallest integer greater than 300 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
D
Answer: D
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
Options:
A)1/9
B)1/4
C)1/5
D)1/3
E)1/7
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability
= 3!4!/6! = 1/5
Answer:C
Answer: C
Question: A sum fetched a total simple interest of $4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Options:
A)$8829
B)$2840
C)$6578
D)$7782
E)$8925
Rationale: E
8925
Principal
= $100 x 4016.25/9 x 5
= $401625/45
= $8925.
Answer: E
Question: A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 2 a.m.?
Options:
A)23 Minutes
B)21 Minutes
C)25 Minutes
D)26 Minutes
E)None of these
Rationale: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-2:00 a.m =10*2=20 total=21
ANSWER:B
Answer: B
Question: If 30% of (x-y) = 20% of (x+y), then what percent of x is y?
Options:
A)50.5%
B)44.4%
C)22.2%
D)33.3%
E)20%
Rationale: 30% of (x-y) = 20% of (x+y)
30/100 (x-y) = 20/100 (x+y)
x = 5y
Required percentage = y/x *100 = y/5y * 100 = 20%
Answer is E
Answer: E
Question: Find the fraction which has the same ratio to 2/5 that 3/7 has to 6/5
Options:
A)2/4
B)6/78
C)4/7
D)3/5
E)1/7
Rationale: P : 2/5= 3/7 : 6/5
As the product of the means is equal to the product of the extremes.
P*6/5 = 2/5 * 3/7
P*6/5 = 6/35
P = 1/7 => P = 1/7
ANSWER:E
Answer: E
Question: Find the middle one when The sum of three consecutive even numbers is 36?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: B
Question: A six digit number which is consisting of only one digitseither 1, 2, 3, 4, 5, 6, 7, 8 or 9, e.g., 111111, 222222... etc.This number is always divisible by :
Options:
A)7
B)11
C)13
D)All of these
E)None of these
Rationale: Solution
Since the 7, 11 and 13 all are the factors of such a number.
Answer D
Answer: D
Question: Circles X and Y are concentric. If the radius of circle X is five times that of circle Y, what is the probability that a point selected inside circle X at random will be outside circle Y?
Options:
A)13
B)Pi/3
C)Pi/2
D)5/6
E)24/25
Rationale: Small circle radius = a, so area = PI a ^ 2
Large circle radius = 5a, so area = 9. PI a ^ 2
Area of shaded region = 25PI a^2 - PI a^2 = 24 PI a^2
So, probability = ( 24 PI a^2 ) / (25 PI a^2 )
= 24/25 = Answer = E
Answer: E
Question: $8,000 is deposited in a savings account that pays 12% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?
Options:
A)$8288.55
B)$8985.10
C)$8988.80
D)$8977.14
E)$8964.95
Rationale: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=12/2=6%
Now,
CA=8000(1+6/100)^2=$8988.80
Hence answer is C
Answer: C
Question: In a bag, there are seven 6-sided dice (numbered 1 to 6), three 12-sided dice (numbered 1 to 12), and two 20-sided dice (numbered 1 to 20). If four of these dice are selected at random from the bag, and then the four are rolled and we find the sum of numbers showing on the four dice, how many different possible totals are there for this sum?
Options:
A)46
B)60
C)42
D)61
E)96
Rationale: As 'complex-looking' as this question might appear, it's actually rather simple. Pay careful attention to what the specific questions asks for - the number of DIFFERENT possible SUMS from 4 dice. Since we're dealing with some 'special' dice (some 12-sided and 20-sided dice), we have to adjust out math accordingly, but the possibilities are rather limited:
1) The minimum number on any given die is 1
2) The maximum possible sum would only occur if we took the 4 biggest possible dice and rolled the highest possible number on each.
With 4 dice, we could end up with any SUM between:
4 (if we rolled 1s on all 4 dice)
to
64 (if we rolled two 20s on the 20-sided dice and two 12s on the 12-sided dice).
Thus, there are only 61 possible sums.
D
Answer: D
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/5%
B)16 8/3%
C)16 2/7%
D)16 2/3%
E)12 2/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: The Salary of a Labourer increase consistently by 40% per year. If his present salary is Rs. 3000 then what will his salary be after 3 years ?
Options:
A)8232
B)3282
C)4282
D)8242
E)2382
Rationale: Explanation :
Salary = 3000 x 1.4 x 1.4 x 1.4 = 8232
Answer : Option A
Answer: A
Question: The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 2500 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?
Options:
A)500
B)625
C)1,000
D)1,500
E)2,500
Rationale: X13: (t, d, s)
Y14: (t, 3d, s+2500mi/hour)
Z15: (t+2 seconds, s, 5d)
d=?
Distance = Speed*Time
x13: d = s*t
x14: 3d = (s+2500)*t ===> 3d = ts+2500t
z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st
3d = 5d - 2st + 2500t
-2d = -2st + 2500t
2d = 2st - 2500t
d = st - 1250t
x13: d = s*t
st - 1250t = s*t
s - 1250 = s
-625 = s
I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!
The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)
S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?
ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 2500 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 2500
2 = 1250
d=s*t
d=1250*(1/2)
d=625
ANSWER: B
Answer: B
Question: How many ways are there to select a subcommittee of 7 members from among a committee of 17?
Options:
A)22888
B)19448
C)28791
D)27711
E)12111
Rationale: Explanation:
Since it does not matter what order the committee members are chosen in, the combination formula is used.
Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.
C(17,7)= 19,448
Answer: B) 19448
Answer: B
Question: A man is walking at a speed of 10 km per hour. After every kilometre, he takes rest for 5 minutes. How much time will be take to cover a distance of 5 kilometres?
Options:
A)48 min.
B)50 min.
C)45 min.
D)55 min.
E)None of these
Rationale: Rest time = Number of rest × Time for each rest
= 4 × 5 = 20 minutes
Total time to cover 5km
= (5⁄10 × 60)minutes + 20 minutes = 50 minutes
Answer B
Answer: B
Question: In what ratio should a variety of wheat costing Rs. 3 per kg be mixed with another variety of wheat costing Rs. 6.25 per kg to obtain a mixture costing Rs. 4.50 per kg?
Options:
A)8 : 6
B)7 : 6
C)5 : 6
D)7 : 5
E)6 : 7
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (6.25 - 4.50) / (4.50 - 3) = 7/6
ANSWER:B
Answer: B
Question: Two circular signs are to be painted. If the radius of the larger sign is five times that of the smaller sign, how many times more paint is needed to paint the larger sign? (We can assume that a given amount of paint covers the same area on both signs.)
Options:
A)5
B)15
C)25
D)35
E)45
Rationale: Let R be the radius of the smaller sign.
The area A of the smaller sign is A = piR^2.
The area of the larger sign is pi(5R)^2=25piR^2=25A.
Since the area is 25 times larger, we need 25 times more paint for the larger sign.
The answer is C.
Answer: C
Question: What is the last digit of 13^35?
Options:
A)5
B)7
C)6
D)8
E)9
Rationale: explanation:
Let’s begin by looking for a pattern as we increase the exponent.
13^1 = 13 (units digit is 3)
13^2 = 169 (units digit is 9)
13^3 = 2197 (units digit is 7)
Notice that a nice pattern emerges. We get: 3-9-7-1-3-9-7-1-3-9-7-1-…
Whenever n is a multiple of 4, the units digit of 13^n is 1
The units digit of 13^35 is 7
Answer is B
Answer: B
Question: Philip is going with 6 friends on a trip to London for spring break. Airfare and hotel costs a total of $2800.00 for the group of 7 friends. How much does each person have to pay for their hotel and airfare?
Options:
A)$100
B)$200
C)$300
D)$400
E)$500
Rationale: Answer= D
The total cost of the trip ($2800.00) divided by 7 equals $400.00.
Answer: D
Question: A small island country of 5000 people has an emigration and immigration statistic per 500 persons of 50.4 and 15.4 respectively. How long will it take for the population to be half of its current number.
Options:
A)6.8
B)8.5
C)6.1
D)9.1
E)7.14
Rationale: Annual decrease is (500 +15.4 - 50.4)*10=4650
Hence every year there is a decrease of 350
for the population to become half 2500 must emigrate
therefore 2500/350=133.3
correct option is E)7.14
Answer: E
Question: John started driving on a highway at a constant speed of R miles per hour at 13:00. Then, 2 hours later, Tom started driving on the same highway at a constant speed of 5R/4 miles per hour at 15:00. If both drivers maintained their speed, how many miles had John driven on the highway when Tom caught up with John?
Options:
A)6R
B)8R
C)10R
D)12R
E)14R
Rationale: In 2 hours, John drove 2R miles.
Tom can catch John at a rate of 5R/4 - R = R/4 miles per hour.
The time it takes Tom to catch John is 2R / (R/4) = 8 hours.
In 8 hours, John can drive another 8R miles for a total of 10R miles.
The answer is C.
Answer: C
Question: How many three letter words are formed using the letters of the word TWITCH?
Options:
A)65
B)60
C)55
D)50
E)40
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 5P3
= 5 * 4 * 3 = 60.
Answer: B
Answer: B
Question: If x≠y and x·y≠0, which of the following may be true?
Options:
A)x/y=−y/x
B)x^2=−y^2
C)(x−y)^2<0
D)x−y=y−x
E)(x+y)(x−y)=0
Rationale: Answer:	A and B are effectively the same i.e x^2+y^2=0
C square can't be less than 0
D give x = y refuted is question stem
E
Answer: E
Question: P, Q and R have $5000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)2400
B)2403
C)3998
D)2539
E)2000
Rationale: E
2000
Let the amount with R be $ r
r = 2/3 (total amount with P and Q)
r = 2/3(5000 - r) => 3r = 10000 - 2r
=> 5r = 10000 => r = 2000.
Answer: E
Question: What is the least number to be subtracted from 11, 15, 21 and 30 each so that resultant numbers become proportional?
Options:
A)1
B)5
C)3
D)6
E)4
Rationale: Let the least number to be subtracted be x, then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.
<=> (11 - x) : (15 - x) = (21 - x) : (30 - x)
=> (11 - x)(30 - x) = (15 - x)(21 - x)
From the options, when x = 3
=> 8 * 27 = 12 * 18
Answer:C
Answer: C
Question: 1/3 of certain journey is covered at the rate of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the avg speed for the whole journey.
Options:
A)28.5 kmph
B)31 kmph
C)33.333 kmph
D)45.98 kmph
E)98 kmph
Rationale: Average speed = total distance / total time
LCM = 3, 4 = 12
Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)
= 12/ (4/25 + 3/30+ 5/30
= 150*12/54 = 33.333 kmph
C
Answer: C
Question: Out of 7 constants and 4 vowels how many words of 3 consonants and 2 vowels can be formed?
Options:
A)200
B)20000
C)25200
D)2500
E)2000
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= 7C3 * 4C2
= 210
Number of groups each having 3 consonants and 2 vowels = 210
Each group contains 5 letters
Number of ways of arranging 5 letters among themselves
= 5! = (5 * 4 * 3 * 2 * 1)
= 210
Required number of words = (210 * 210)
= 25200
ANSWER C
Answer: C
Question: Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and ten copper coins, how many different sums from 1¢ to 60¢ can he make with a combination of his coins?
Options:
A)30
B)22
C)56
D)44
E)48
Rationale: The total sum is 5*2 + 10*5 = 60¢. If you can make each sum from 1 to 70 (1¢, 2¢, 3¢, ..., 60¢), then the answer would be 60 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 59¢ and 57¢ (since total sum is 60¢ we cannot remove 1¢ or 3¢ to get 59¢ or 57¢).
So, out of 60 sums 4 are for sure not possible, so the answer must be 60 - 4 = 56 sums or less. Only A fits.
Answer: C.
Answer: C
Question: Three numbers are in the ratio 1:3:6 and their H.C.F is 4. The numbers are?
Options:
A)4, 12, 24
B)4, 12, 20
C)4, 12, 22
D)4, 12, 28
E)4, 16, 24
Rationale: Let the required numbers be x, 3x and 6x. Then, their H.C.F = x. So, x = 4.
The numbers are 4, 12, 24.
Answer: A
Answer: A
Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 6 strokes ?
Options:
A)63/64
B)7/8
C)1/4
D)1/8
E)1/16
Rationale: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16
Left After 5th stroke = 1/2 * 1/16 = 1/32
Left After 6th stroke = 1/2 * 1/32 = 1/64
So removed = 1- 1/64 = 63/64
Answer: A
Question: A sum of money deposited at C.I. amounts to Rs.500 in 3 years and to Rs.650 in 4 years. Find the rate percent?
Options:
A)25%
B)30%
C)35%
D)40%
E)45%
Rationale: 500 --- 150
100 --- ? => 30%
Answer: B
Answer: B