divelab/Sys2Bench huggingface dataset:
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/3 of an hour late than usual. What is his usual time to reach office?
Options:
A)1
B)4
C)5
D)6
E)7
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/3
3 --------- ? è 1 hour
Answer: A
Answer: A
Question: Rs.500 amounts to Rs.620 in 2 years at simple interest. If the interest is increased by 2%, it would amount to how much?
Options:
A)120
B)25
C)614
D)530
E)210
Rationale: (500*3*2)/100 = 30
500+ 30 = 530
Answer: D
Answer: D
Question: Yearly subscription to professional magazines cost a company $840.00. To Make a 30% cut in the magazine budget, how much less must be spent?
Options:
A)654
B)655
C)656
D)588
E)658
Rationale: total cost 840
840*30/100=252
so the cut in amount is 252
the less amount to be spend is 840-252=588
ANSWER:D
Answer: D
Question: What is the sum of the integers from -190 to 191 inclusive?
Options:
A)0
B)191
C)375
D)875
E)965
Rationale: sum/n= average.
sum=(average)(n)
average=a+b/2=190+191/2=0.5
number of items(n)=B-A+1=191-(-190)+1=195+191=382.
sum=average*n=0.5*382=191.
answer is B
Answer: B
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
Options:
A)6! * 7P6
B)2(6!)
C)6!)2
D)6! * 7
E)7! * 7
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways
= 6! * 7P6
Answer:A:
Answer: A
Question: V is the volume of a cylinder; the radius of the cylinder is 3.5. The height of the cylinder is 650% more than the radius. Which of the following is true?
Options:
A)100 < V < 300
B)300 < V < 500
C)500 < V < 700
D)700 < V < 900
E)900 < V < 1100
Rationale: As we see the answers are in form of range we can use approximation
Volume of cylinder is πr^2h
Given π= 22/7 and r = 3.5 so r^2 ~ 12 and h = 6.5 * 3.5 ~ 23
So 22/7 * 12 * 23 ~ 868
so answer should be
D. 700 < V < 900
Answer : D
Answer: D
Question: If there are 7 pairs of twins, and a committee will be formed with 3 members. In how many ways this committee formed in a way that no siblings in a group?
Options:
A)32
B)24
C)56
D)144
E)280
Rationale: Firstly, there are 7 ways to choose 3 groups from the 4 groups. Hence 7C3.
Next, with the 3 groups chosen, there are 2^3 choices of choosing either one of the siblings.
Hence, the total number of ways are 7C3 * (2^3) = 280
E
Answer: E
Question: Rs 1000 is being charged at 50% per annum. what is the interest for 3rd year at compound interest?
Options:
A)3277
B)2667
C)1125
D)2867
E)9996
Rationale: Explanation:
Total amount for two years = \inline 1000(1.5)^2=2250
Now , interest for third year = \inline \frac{2250\times 50\times 1}{100}=1125
Answer: C) 1125
Answer: C
Question: The total weight of six nougat nuggets is 3 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
Options:
A)0.18 oz.
B)0.5 oz.
C)1.8 oz.
D)5 oz.
E)18 oz
Rationale: Average = Total/Number of items
= 3/6 = 0.5.
Hence, B
Answer: B
Question: A tourist purchased a total of $1,400 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)$1,170
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 1400 - 230 = 1170 hence answer is E
Answer: E
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is?
Options:
A)1/26
B)1/24
C)1/20
D)1/21
E)1/21
Rationale: Let E1 be the event of drawing a red card.
Let E2 be the event of drawing a king .
P(E1 ∩ E2) = P(E1) . P(E2)
(As E1 and E2 are independent)
= 1/2 * 1/13 = 1/26
Answer:A
Answer: A
Question: 223.124 x 11.98 Ã· 6.001 + 11.11 = ?
Options:
A)983.578
B)459.121
C)781.189
D)656.112
E)457.358
Rationale: Explanation:
? = 223.124 x 11.98 Ã· 6.001 + 11.11
â‰ˆ (223.124 x 12/6) + 11.11 â‰ˆ 446.248 + 11.11 â‰ˆ 457.358
Answer: Option E
Answer: E
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 800. How many workers were part of the latter production run?
Options:
A)A)6
B)B)10
C)C)11
D)D)21
E)E)23.5
Rationale: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1250 .. thus for the current period = 800 -500 = 300
(5n+45)K= 300
k = 300/5n+45........................................2
equate 1 and 2
500/5n+20 = 300 /5n+45
500(5n+45) = 300(5n+20)
2500n + 22500 = 1500n + 6000
1000n = -16500
n = 16
thus n+5 = 21
hence D
Answer: D
Question: If 0 < a < b and k = (2a + 4b)/b , which of the following must be true?
Options:
A)k < 2
B)k < 6
C)k < 9
D)k > 9
E)k > 11
Rationale: Here's another approach:
k = (2a + 4b)/b
= 2a/b + 4b/b
= 2(a/b) + 4
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2.
So, we get k = (some number less than 2) + 4
From here, we can see that k must be less than 6
Answer: B
Answer: B
Question: an operation * is defined by the equation:
a*b=a-b/a+b, for all numbers a and b such that a is not equal to -b, if a is not equal to -e and a*e=0, then e=?
Options:
A)a) -a
B)b) -1/a
C)c) 1/a
D)d)0
E)e)a
Rationale: If a*e=0 and a=-e then a-e = o of a=e, so answer E
Answer: E
Question: A searchlight on top of the watch-tower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds?
Options:
A)1/4
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: 2 revolutions per minute = 1 revolution every 30 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 30 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 5 seconds) = 1 - P (man in dark for max of 5 seconds) = 1 - 5/30 = 1 - 1/6 = 5/6
or the other way would be:
P(man in dark for at least 5 seconds) is like saying he can be in dark for 5,6,7...all the way to 30 seconds because that is the max. In this approach it would be 25/30 seconds = 5/6.
Answer is E
Answer: E
Question: find four consecutive numbers such that the sum of the first three numbers is twelve more than the fourth number ?
Options:
A)7,8,9,10
B)3,4,5,6
C)9,10,11,12
D)6,7,8,9
E)None
Rationale: Let
1st Integer = x
2nd Integer = x+1
3rd Integer = x+2
4th integer = x+3
=======================================
Given
x+x+1+x+2=(x+3)+12
3x+3=x+3+12
3x+3=x+15
3x=x+15-3
3x=x+12
3x-x=12
2x=12
x=12/2
x=6
========================================
1st Integer = x = 6
2nd Integer = x+1 = 6+1 = 7
3rd Integer = x+2 =6+2= 8
4th integer = x+3=6+3=9
Answer D
Answer: D
Question: By selling 16 pencils for a rupee a man loses 28%. How many for a rupee should he sell in order to gain 28%?
Options:
A)8
B)9
C)7
D)6
E)4
Rationale: 72% --- 16
128% --- ?
72/128 * 16 = 9
Answer: B
Answer: B
Question: Find the simple interest on $10000 at 9% per annum for 12 months?
Options:
A)$410
B)$500
C)$650
D)$710
E)$900
Rationale: P = $10000
R = 9%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*9*1/100 = $900
Answer is E
Answer: E
Question: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 200. How much did he have with him in the beginning?
Options:
A)s 200
B)s 500
C)s 300
D)s 450
E)s 550
Rationale: Suppose the amount in the beginning was Rs ’x’
Money spent on clothes = Rs 1x/3 Balance = Rs 2x/3
Money spent on food = 1/5 of 2x/3 = Rs 2x/15
Balance = 2x/3 - 2x/15 = Rs 8x/15
Money spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5
Therefore 2x/5 = 200 = 500
ANSWER:B
Answer: B
Question: A certain junior class has 1000 students and a certain senior class has 800 students. Among these students, there are 40 siblings pairs each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?
Options:
A)3/40000
B)1/3600
C)1/20000
D)1/60
E)1/15
Rationale: Let's see
Pick 40/1000 first
Then we can only pick 1 other pair from the 800
So total will be 40 / 800 *1000
Simplify and you get 1/20000
Answer is C
Answer: C
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 8 : 1 ?
Options:
A)6 months
B)3 months
C)2 months
D)8 months
E)9 months
Rationale: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 8. or x = (85000 * 12) / (42500 * 8) = 3.
So, B joined for 3 months.
Answer: B
Answer: B
Question: Dhoni weighs twice as much as Nameetha. Nameetha's weight is 55% of Bima's weight. Dravid weighs 35% of Leela's weight. Leela weighs 30% of Dhoni's weight. Who among these 5 persons weighs the least?
Options:
A)Dravid
B)Dhoni
C)Bima
D)Nameetha
E)Leela
Rationale: if
Bima weight = x
we get
Nameetha's weight = 0.55x
Dhoni's weight = 1.1x
Leela's weight = 0.33x
and Dravid's weight = 0.1155x
Answer : A
Answer: A
Question: A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 5% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
Options:
A)3.5
B)3.75
C)4
D)4.25
E)4.5
Rationale: (1000xtx3/100) + (1400xtx5/100) = 350 → t =3.5 answer A
Answer: A
Question: Find the length of the longest pole that can be placed in an indoor stadium 24 m long, 18 m wide and 16 m high
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: sqrt(1156)=34
becoz max length is cuboid diagonal d=sqrt(L^2+B^2+H^2)
where L lenght
B breadth & H height
ANSWER:D
Answer: D
Question: During a given week A programmer spends 1/4 of his time preparing flow chart, 3/8 of his time coding and the rest of the time in debugging the programs. If he works 48 hours during the week , how many hours did he spend debugging the program.
Options:
A)15 hrs
B)16 hrs
C)18 hrs
D)19 hrs
E)17 hrs
Rationale: programmer takes 1/4*48=12 hrs a week to make flowchrt
same way.....18 hrs a week for codin...
so....for debugging=48-(12+18)=18 hrs
ANSWER:C
Answer: C
Question: Priya went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 2%. then what was the cost of the tax free items?
Options:
A)Rs. 175.50
B)Rs. 174.50
C)Rs. 174.00
D)Rs. 170.00
E)Rs. 173.50
Rationale: Solution
Let the amount of taxable purchases be Rs.x.
Then, 2% of x	= 50/100
x ‹=› (50/100×100/2)
= 25
Cost of tax free items	= Rs.[200 - (25 + 0.50)]
= Rs. 174.50
Answer B
Answer: B
Question: 8 friends are living in 8 different flats of an apartment. Each of them was allotted a parking spot to park their cars in the ground floor. But they used to park their cars randomly in any of the 8 parking spots. In how many ways can they park their cars so that exactly 6 people park their cars in the spots allotted to them?
Options:
A)20
B)28
C)36
D)44
E)52
Rationale: 8C6 = 28
The remaining 2 people in each case will be parked in each other's parking spots.
The answer is B.
Answer: B
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/6%
B)16 2/8%
C)16 3/3%
D)16 2/3%
E)14 2/6%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: Find the value of 72519 x 9999 = m?
Options:
A)709115678
B)723417481
C)710017481
D)725117481
E)None
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
A)10
B)26
C)12
D)24
E)48
Rationale: 1/8 + 1/24 = 1/6
6 * 2 = 12
Answer: C
Answer: C
Question: Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 12 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?
Options:
A)42
B)42.5
C)44
D)50
E)52.5
Rationale: Total Time taken by jerry = (8/40)*60 Minutes + 12 Minutes + (20/60)*60 Minutes = 44 Minutes
Average Speed = Total Distance / Total Time = (8+20) miles / (44/60)Hours = 28*60 / 44 = 42 Miles per hour
Answer: option A
Answer: A
Question: In a class composed of x girls and y boys, What part of the class is composed of girls
Options:
A)y/(x + y)
B)x/xy
C)x/(x + y)
D)y/xy
E)1/xy
Rationale: X/(X+Y).... ANSWER:C
Answer: C
Question: While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?
Options:
A)1/2
B)17/36
C)91/216
D)11/36
E)25/216
Rationale: Total outcomes possible: 36
Total outcomes possible with sum 7: 6
Probability to win when rolled once = 6/36
Probability not to win when rolled once = 30/36 = 5/6
Probability to win in three attempts= 1- Probability will not to win in all three attempts
= 1- (5/6* 5/6*5/6)
= 91/216
Answer is C.
Answer: C
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
Options:
A)240
B)388
C)379
D)277
E)122
Rationale: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: A
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)2.2
C)3
D)3.5
E)4
Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
ANSWER:C
Answer: C
Question: At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $2 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?
Options:
A) 7
B) 8
C) 6
D) 10
E) 11
Rationale: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/2<7=~6.
Answer: C.
Answer: C
Question: A batsman has scored an average of 46 runs for a certain number of innings played in England. When he came back to India, he played another two test matches of two innings each and scored at an average of 55 runs. For the innings in England and in India taken together, he has improved his average by 2 runs over the matches played in England.Find the number of innings played in England.
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Let the number of innings played in England be x.
∴ Total runs scored in England = 46x
Total runs scored for innings played in India
= 55 × 4 = 220
(∵ the number of innings played in India = 4)
Also, 46x+220 /x+4 = 48
⇒ 46x + 220 = 48 x + 192
⇒ 2x = 28
⇒ x = 14
Answer C
Answer: C
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
Options:
A)228
B)276
C)199
D)150
E)882
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m. Answer:D
Answer: D
Question: What values of x satisfy the equation x2/3 + x1/3 – 2 ≤ 0 ?
Options:
A)– 8 ≤ x ≤ 1
B)– 1 ≤ x ≤ 8
C)1 ≤ x ≤ 8
D)– 8 ≤ x ≤ 8
E)None of these
Rationale: Explanation :
Let, x1/3 = y. The equation becomes y2 + y – 2 ≤ 0, or y2 + y ≤ 2.
Now, look at the upper limit. We know that y2 + y ≤ 2.
Among the positive numbers, 1 is the biggest number that satisfies the equation. No number greater than 1 can have y2 + y ≤ 2. So the upper limit is 1.
Maximum value of y is 1, hence maximum value of x1/3 is 1, and hence maximum value of x is 1.
This answer is there only for option 1. Hence that is the answer.
Answer : A
Answer: A
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 123, what is the least possible value of n?
Options:
A)37
B)123
C)41
D)52
E)87
Rationale: 123 is 3 * 41, so n needs to be at least 41, so the answer is C.
Answer: C
Question: 2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: (2m + 4b)’s one day’s work = 1/4
(5m + 6b)’s one day’s work = 1/3
=> (8m + 16b)’s one day’s work = (15m + 18b) ’s one day’s work
=> 7 men’s work = 2 boy’s work
So, we should be employ 5 more men to be completed the work.
ANSWER:C
Answer: C
Question: Given that x = 2^b – (8^34 + 16^5), which of the following values for b yields the lowest value for |x|?
Options:
A)101
B)102
C)103
D)104
E)122
Rationale: 8^34 + 16^5 = 2^102 + 2^20
Compared to 2^102, the value of 2^20 is negligible.
2^102 - (2^102 +2^20) will minimize the value of |x|.
The answer is B.
Answer: B
Question: If the length of the sides of two cubes are in the ratio 6:1, what is the ratio of their total surface area?
Options:
A)6:1
B)12:1
C)24:1
D)36:1
E)72:1
Rationale: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(6x)^2=216x^2.
The ratio of surface areas is 36:1.
The answer is D.
Answer: D
Question: A number exceeds by 25 from its 3/8 part. Then the number is?
Options:
A)32
B)35
C)39
D)40
E)45
Rationale: Explanation:
x – 3/8 x = 25
x = 40
ANSWER IS D
Answer: D
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
Options:
A)14
B)16
C)18
D)22
E)24
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
Option A
Answer: A
Question: CONVERT 1.6 hectares in ares
Options:
A)130 ares.
B)160 ares.
C)180 ares.
D)230 ares.
E)250 ares.
Rationale: 1.6 hectares in ares
1 hectare = 100 ares
Therefore, 1.6 hectares = 1.6 × 100 ares
= 160 ares.
ANSWER- B
Answer: B
Question: 20 beavers, working together in a constant pace, can build a dam in 6 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
Options:
A)10.
B)4.
C)5.
D)6
E)8.
Rationale: Total Work = 20*6= 120 Beaver hours
12 Beaver * x =120 Beaver hours
x=120/12=10
ANSWER:A
Answer: A
Question: If both 2^2 and 3^4 are factors of the number a*4^3*6^2*13^11, then what is the smallest possible value of a?
Options:
A)6
B)9
C)12
D)15
E)18
Rationale: The number a must include at least 3^2 = 9
The answer is B.
Answer: B
Question: Three different containers contain 496 litres, 403 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly?
Options:
A)1 litre
B)7 litre
C)31 litre
D)41 litre
E)None
Rationale: Solution
Required measurement	= H.C.F of (496, 403, 713) litres
‹=›31 litres.
Answer C
Answer: C
Question: If both a and b belongs to the set {1,2,3,4 }, then the number of equations of the form ax2 + bx + 1 = 0 having real roots is
Options:
A)10
B)7
C)6
D)12
E)15
Rationale: Explanation :
ax2 + bx + 1 = 0 .
For real roots
=> b2 -4ac ≥ 0 .
i.e b2 - 4a(1) ≥ 0 .
i.e b2 ≥ 4a.
For a = 1, 4a = 4, ∴ b = 2, 3, 4
a = 2, 4a = 8, ∴ b = 3, 4
a = 3, 4a = 12, ∴ b = 4
a = 4, 4a = 16, ∴ b = 4
∴ Number of equations possible = 7.
Harsh Mishra a year ago
0 upvotes
Answer : B
Answer: B
Question: For all numbers a and b, the operationis defined by ab = (a + 2)(b – 3).
If 3y = –30, then y =
Options:
A) –15
B) –6
C) -3
D) 6
E) 15
Rationale: (3+2)(y-3)=-30..
x-3=-6..
x=-3
C
Answer: C
Question: The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
Options:
A)Rs.3000
B)Rs.3300
C)Rs.3600
D)Rs.3900
E)Rs.3800
Rationale: P = 144(100/5)2 => P = 3600
ANSWER:C
Answer: C
Question: The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is?
Options:
A)0.7%
B)8.3%
C)0.3%
D)0.39%
E)2.3%
Rationale: (1500 * R1 * 3)/100 - (1500 * R2 * 3)/100
= 13.50 4500(R1 - R2)
= 1350
R1 - R2 = 0.3%
Answer: C
Answer: C
Question: In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 2 : 3. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony?
Options:
A)A)1:6
B)B)1:1
C)C)1:8
D)D)1:3
E)E)1:9
Rationale: Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 3/7 * 70 = 40.
Number educated women in the colony = 2/5 * 30 = 12.
Number of uneducated women in the colony = 3/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1:3.
Answer:D
Answer: D
Question: How many words can be formed from the letters of the word ‘DIRECTOR’ So that the vowels are always together?
Options:
A)3251
B)2160
C)1203
D)2564
E)5421
Rationale: In the given word, we treat the vowels IEO as one letter.
Thus, we have DRCTR (IEO).
This group has 6 letters of which R occurs 2 times and others are different.
Number of ways of arranging these letters = 6!/2! = 360.
Now 3 vowels can be arranged among themselves in 3! = 6 ways.
Required number of ways = (360x6) = 2160.
Ans: B
Answer: B
Question: In a garden, 26 trees are planted at equal distances along a yard 600 metres long, one tree being at each end of the yard. What is the distance between two consecutive trees?
Options:
A)10
B)8
C)12
D)24
E)16
Rationale: 26 trees have 25 gaps between them.
Length of each gap = 600/25 = 24
i.e., distance between two consecutive trees = 24
Answer is D.
Answer: D
Question: A sum of money becomes 7/6 of itself in 2 years at a certain rate of simple interest. The rate per annum is?
Options:
A)50/9
B)50/7
C)50/6
D)50/8
E)50/3
Rationale: Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 2 years.
Rate = (100 * x) / (x * 6 * 2) = 50/6 %.
Answer:C
Answer: C
Question: Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity W for the round trip?
Options:
A)24 miles per hour
B)48 miles per hour
C)50 miles per hour
D)53 1/3 miles per hour
E)68 miles per hour
Rationale: Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's return speed is (1.5)(40) = 60 miles/hour.
D = (R)(T)
120 = (60)(T)
120/60 = 2 = T
2 hours to drive to SD
Total Distance = 240 miles
Total Time = 3+2 = 5 hours
Average Speed = 240/5 = 48 miles/hour
Final Answer:
B
Answer: B