divelab/Sys2Bench huggingface dataset:
Question: How many of the following numbers are divisible by 3 but not by 9?
2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276
Options:
A)5
B)6
C)7
D)8
E)None of these
Rationale: Taking the sum of the digits, we have:
S1=9, S2=12, S3=18, S4= 9, S5=21, S6= 12, S7=18, S8=21, S9=15, S10=24.
Clearly S2, S5, S6, S8, S9, S10 are all divisible by 3 but not by 9. So, the number of required numbers= 6.
Answer:B
Answer: B
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg
Options:
A)2:0
B)2:3
C)2:1
D)2:2
E)2:8
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 60 : 90 = 2 : 3
Answer: B
Answer: B
Question: if price of t.v set is reduced by 25%, then its sale increases by 75%, find net effect on sale value
Options:
A)31
B)32
C)46
D)47
E)48
Rationale: - a + b + ((-a)(b)/100)
= -25+75+(-25*75)/100
= -25+75-19
=31
ANSWER:A
Answer: A
Question: 5000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?
Options:
A)10600
B)11600
C)12600
D)10680
E)20600
Rationale: (x*3*1)/100 + [(5000 - x)*5*1]/100 = 144
3x/100 +( 25000 – 5x)/100 = 144
=> x = 10600
ANSWER:A
Answer: A
Question: If a person walks at 12 km/hr instead of 8 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
Options:
A)50 km
B)58 km
C)60 km
D)40 km
E)65 km
Rationale: Let the actual distance traveled be x km. Then,
x/8 = (x + 20)/12
3x - 2x = 40 =>x = 40 km.
Answer :D
Answer: D
Question: Find the least number must be added to 433124 so that remaining no.is divisible by 17?
Options:
A)3
B)2
C)5
D)6
E)1
Rationale: On dividing 433124 by 17 we get the remainder 15, so 2 should be added
B
Answer: B
Question: Tom planted vegetables in a rectangular garden that was 22 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
Options:
A)154 sq. ft.
B)156 sq. ft.
C)157 sq. ft.
D)158 sq. ft.
E)159 sq. ft.
Rationale: area of garden is 22 x 15 = 330 sq. ft.
1/3 x 330 = 110 sq. ft. for corn
1/5 x 330 = 66 sq. ft. for peas
110 + 66 = 176 sq. ft. used
330 - 176 = 154 sq. ft. left over
correct answer A
Answer: A
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did Mary pick?
Options:
A)12
B)24
C)48
D)52
E)37
Rationale: Let x be the amount Peter picked. Then Mary and Lucy picked 2x and x+2x, respectively. So
x+2x+x+2=26
4x=24
x=6
so 2x=2*6=12
correct answer is A) 12
Answer: A
Question: A corporation paid $10 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
Options:
A) 0%
B) 14%
C) 20%
D) 23%
E) 43%
Rationale: Difference in Ratios = (30/150) - (10/50) = 0
% Change = 0%
Answer - A
Answer: A
Question: Reema took a loan of Rs 1800 with simple interest for as many years as the rate of interest. If she paid Rs. 632 as interest at the end of the loan period, what was the rate of interest.
Options:
A)5.925%
B)5.253%
C)7%
D)6.52%
E)5.200%
Rationale: Explanation:
Let rate = R% then Time = R years.
=>1800∗R∗R /100=632
=>R2=35.11
=>R=5.925%
Option A
Answer: A
Question: The measure of the side of a square is tripled. If x represents the perimeter of the original square, what is the value of the new perimeter?
Options:
A)3x
B)4x
C)9x
D)12x
E)27x
Rationale: Original perimeter = x
Hence original side = x/4
New side = 3x/4
New perimeter = 4*3x/4 = 3x
Correct Option: A
Answer: A
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio Q of men to women?
Options:
A) 5:2
B) 5:1
C) 4:3
D) 4:1
E) 3:1
Rationale: (A) Q=184 x 5 + 170 x 2 = 1260.A
Answer: A
Question: If [M] denotes the least integer greater than or equal to M and [M] = 0, which of the following statements must be true?
Options:
A)M = 0
B)0 <= M < 1
C)-1 < M <= 0
D)-1 <= M < 0
E)0 < M <= 1
Rationale: The answer for this is0 < = M< = 1
However it is not available in the options. The match to the above is-1 <M <= 0
Answer = C
Answer: C
Question: A photograph measuring 8.5 by 7.5 cm is to be enlarged. If the enlargement of the longer side is 13.6 cm, what is the length of the smaller side?
Options:
A)12 cm
B)10 cm
C)13 cm
D)15 cm
E)19 cm
Rationale: A
12 cm
= (13.6 ÷ 8.5) × 7.5
= 12 cm.
Answer: A
Question: A man can row with a speed of 10 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)A)63kmph
B)B)63kmph
C)C)15kmph
D)D)62kmph
E)E)74kmph
Rationale: Explanation:
M = 10
S = 5
DS = 10 + 5 = 15
Answer: Option C
Answer: C
Question: I have a huge bed-sheet of 1 meter long.
I want to cuts this role into pieces of 20 centimeter long cloth.
How long will it take me to cut the bed sheet if each 20 centimeter cut took me 5 minutes ?
Options:
A)150 Min
B)245 Min
C)185 Min
D)300 Min
E)205 Min
Rationale: B
It will take 49 cuts not 50.
so 49*5 => 245 minutes
Answer: B
Question: The diameters of two spheres are in the ratio 1:2 what is the ratio of their surface area?
Options:
A)1:0
B)1:4
C)1:6
D)1:2
E)1:1
Rationale: 1:4
Answer:B
Answer: B
Question: What will be 40 percent of a number whose 200 percent is 90 ?
Options:
A)144
B)72
C)18
D)None of these
E)Cannot be determined
Rationale: Answer
∵ 200% of N = 90
⇒ N = (90 x 100) / 200 = 45
∴ 40% of N = (40 x 45) / 100 = 18
Correct Option: C
Answer: C
Question: Icarus and three of his friends want to donate money to a family which has 9 members so that they can get $12.00 to buy Chanukkah gifts this year.
Icarus has $35.00, his second friend has $37.00. The third friend has $30.00
How much more money do they need so they can give $12.00 to each of the 9 family members.
Options:
A)$6
B)$9
C)$7
D)$10
E)$5
Rationale: Answer= A
Icarus and his 2 friends have a total of $102.00 ($35 +$37 +$30).
Each of the family members need $12.00.
$12 x 9 = $108
$108 - $102 = $6
Answer= A
Answer: A
Question: The equation (M )/84 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?
Options:
A)(P-7)*6
B)(P-7)*5
C)(P-7)*2
D)(P-7)*3
E)(P-7)*4
Rationale: M/84 =(P-7)/21
M = (P-7)*84/21
=(P-7)*4
E
Answer: E
Question: A shipment of 8 television sets contains 2 black-and-white sets and 7 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
Options:
A)1/7
B)1/4
C)5/14
D)11/28
E)13/28
Rationale: I get 1/4, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(7,2)/C(8/2)=7/28=1/4
B
Answer: B
Question: In a class, 20% of the members own only two cars each, 40% of the remaining own three cars each and the remaining members own only one car each. Which of the following statements is definitely true from the given statements ?
Options:
A)Only 20% of the total members own three cars each.
B)48% of the total members own only one car each.
C)60% of the total members own at least two cars each.
D)80% of the total members own at least one car
E)None of these
Rationale: Explanation:
Let total number of members be 100,
Then, number of members owning only 2 cars = 20.
Number of members owning 3 cars = 40% of 80 = 32.
Number of members owning only 1 car = 100 - (20 + 32) = 48.
Thus, 48% of the total members own one car each.
Answer: Option B
Answer: B
Question: (258% of 1265) ÷6 = ?
Options:
A)A)125
B)B)175
C)C)225
D)D)375
E)E)544
Rationale: Explanation :
? = (258 x 1265/100) ÷ 6 = 326370/600 = 544
Answer : Option E
Answer: E
Question: In Solution P, the proportion of water to alcohol is 5:1. In Solution Q, the proportion of water to alcohol is 2:1. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?
Options:
A)21%
B)23%
C)25%
D)27%
E)29%
Rationale: Let V be the total volume of the new solution.
The amount of alcohol added from Solution P is (1/6)*V/2=(1/12)*V
The amount of alcohol added from Solution Q is (1/3)*V/2=(1/6)*V
The total amount of alcohol in the new solution is (1/12+1/6)*V=(1/4)*V
The alcohol concentration is 1/4=25%
The answer is C.
Answer: C
Question: There are 134 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: IMO 14
Take each answer choice and substract it from 134 and the divided this with 11. E
Answer: E
Question: P is three times as old as Q. In 12 years, P will be twice as old as Q. How old was P three years ago?
Options:
A)21
B)24
C)27
D)30
E)33
Rationale: P = 3Q so Q = P/3
P+12 = 2(Q+12) = 2(P/3+12)
P/3 = 12
P = 36
Three years ago, P was 33.
The answer is E.
Answer: E
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/8 hours to fill the tank. The leak can drain all the water of the tank in?
Options:
A)17 hr
B)19 hr
C)10 hr
D)34 hr
E)36 hr
Rationale: Work done by the tank in 1 hour
= (1/2 -2 1/8)
= 1/34 Leak will empty the tank in 34 hrs.
Answer:D
Answer: D
Question: . A boy has five trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Explanation:
The boy can select one trouser in five ways.
The boy can select one shirt in 10 ways.
The number of ways in which he can select one trouser and one shirt is 5 * 10 = 50 ways.
Answer: Option C
Answer: C
Question: Find the HCF of
22×32×72, 2×34×7
Options:
A)128
B)126
C)146
D)434
E)None of these
Rationale: Explanation:
HCF is Highest common factor, so we need to get the common highest factors among given values. So
we got
2 * 3*3 * 7=126
Answer: Option B
Answer: B
Question: Abigail has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
Options:
A) 32
B) 30
C) 29
D) 28
E) 27
Rationale: 5g + 10h = 460
g > h
Pick an easy number to work with.
suppose g=30.
Then you have 150.
You need another 310 and that means you need h=31 which is greater than g.
Therefore, g > 30.
The only answer choice where g > 30 is if g = 32.
A is the answer.
Answer: A
Question: After striking the floor, a rubber ball rebounds to 4/5th of the height from which it has fallen. Find the total distance that it travels before coming to rest if it has been gently dropped from a height of 120 metres.
Options:
A)540 m
B)960 m
C)1080 m
D)1020 m
E)1120 m
Rationale: Solution: The first drop is 120 metres. After this the ball will rise by 96 metres and fall by 96 metres. This process will continue in the form of infinite GP with common ratio 0.8 and first term 96. The required answer is given by the formula:
a/(1-r)
Now,
[{120/(1/5)}+{96/(1/5)}]
= 1080 m.
Answer C
Answer: C
Question: Rahim bought 40 books for Rs.600 from one shop and 20 books for Rs.240 from another. What is the average price he paid per book ?
Options:
A)s.14
B)s.18
C)s.12
D)s.11
E)s.10
Rationale: Average price per book
= (600 + 240) / (40 + 20) = 840/ 60
= Rs.14
Answer:A
Answer: A
Question: A boat goes 100 km downstream in 10 hours, and 45 km upstream in 15 hours. The speed of the stream is?
Options:
A)4km/h
B)3km/h
C)2km/h
D)3.5 km/h
E)E)None
Rationale: 100 --- 10 DS = 10
? ---- 1
45 ---- 15 US =3
? ----- 1 S = (10 - 3)/2
= 3.5 kmph
ANSWER:D
Answer: D
Question: A collection of 20 coins, each with a face value of either 10 cents or 35 cents, has a total face value of $2.5. How many of the coins have a face value of 10 cents?
Options:
A)24
B)18
C)32
D)16
E)20
Rationale: 0.10(x)+0.35(20-x)=2.5
0.10x+7-0.35x=2.5
so x=18
ans is B
Answer: B
Question: Find the average of the first 25 natural numbers?
Options:
A)8
B)9
C)13
D)11
E)12
Rationale: Average of the first 'n' natural numbers = (n + 1)/2
We get (25 + 1)/2 = 13
ANSWER:C
Answer: C
Question: A group of tourists wants to visit only two of the four cities A, B, C, and D. How many travel itineraries can they make? All cities are connected to one another and please note that visiting the same cities in a different order counts as a different itinerary.
Options:
A)12
B)16
C)24
D)28
E)32
Rationale: The number of ways to choose two cities is 4C2=6.
The number of itineraries for each pair of 2 cities is 2!.
So the number of itineraries to two cities is 6*2!=12.
The answer is A.
Answer: A
Question: A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is
Options:
A)56 kg
B)36 kg
C)48 kg
D)27 kg
E)None of these
Rationale: Solution : weight = 18/25 *50 = 36 kg Answer B
Answer: B
Question: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint. How many liters of blue paint must be added to 16 liters of Fuchsia to change it to Mauve paint?
Options:
A)9
B)12
C)14
D)16
E)18
Rationale: in 16 liters, Red = 5/8 * 16 = 10 and Blue = 6
so, 10/(6+x) = 3/6
or, x = 14 (Answer C)
Answer: C
Question: Two stations A and B are 155 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)9
B)10
C)11
D)12
E)8
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 155
45x = 180
x = 4.
So, they meet at 11 a.m.
Answer: Option C
Answer: C
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 18 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)565
B)444
C)676
D)767
E)408
Rationale: 1h ----- 2
? ------ 60
12 h
RS = 16 + 18 = 34
T = 12
D = 34 * 12 =408
Answer: E
Answer: E
Question: A first grade teacher uses ten flash cards, each numbered from 1 to10, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '3' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
Options:
A)80
B)40
C)50
D)60
E)70
Rationale: problem of combination 8C4 = 8!/4!*(8-4)! = 8*7*6*5*4!/4!*4! =70
E
Answer: E
Question: On a certain transatlantic crossing, 35 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
Options:
A)33 1/3%
B)87.5%
C)50%
D)60%
E)66 2/3%
Rationale: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 35 => X= 87.5.
Answer B
Answer: B
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 110 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Options:
A)2989
B)2765
C)5600
D)2989
E)9772
Rationale: Total production of salt by the company in that year
= 5000 + 5110 + 5220 + .... + 6210 = 67370.
Average monthly production of salt for that year
= 67370/12
= 5614.
Answer:C
Answer: C
Question: What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
Options:
A)35
B)56
C)46
D)87
E)98
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 .
Answer: C
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)2000
B)3000
C)4000
D)3500
E)4500
Rationale: Capital be x
then 1920 - x/x*100 = 1280
1920-x=x-1280
2x=3200
x=1600
req = 125% of rs 1600 = rs(125/100*1600) = 2000
ANSWER A
Answer: A
Question: x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 6 will be equal to:
Options:
A)3
B)6
C)1/4
D)1/3
E)9
Rationale: Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /6^2 = 1/4
Answer : C
Answer: C
Question: Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 32 percent ryegrass, what percent of the weight of this mixture is X ?
Options:
A) 10%
B) 33.33 %
C) 46.66%
D) 50%
E) 66.66 %
Rationale: ---------------->Ryegrass
X-------------->	40%
Y-------------->	25%
M(mixture)---->32%
0.4X + (M-X)0.25 = 0.32M
0.15X = 0.07M
X = 0.4666M
X = 46.66% of M
C
Answer: C
Question: In the new budget the price of cheese rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
Options:
A)20%
B)9.1%
C)10.9%
D)12.6%
E)15%
Rationale: Reduce in consumption = R/(100+R) *100% = 25/125 *100 =20%
Answer is A
Answer: A
Question: Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $99 dollar, which she typically uses for gifts and charitable causes. What is Jill’s net monthly salary?
Options:
A)$2400
B)$3300
C)$6000
D)$6400
E)$9600
Rationale: let x be the monthly salary
15%of 1/5*x=99
x=3300
answer B
Answer: B
Question: On a purchase of $112, a store offered a payment plan consisting of a $12 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
Options:
A)10.7%
B)11.7%
C)12.7%
D)13.7%
E)14.7%
Rationale: 12*10 + 12 = 132
(12/112)* 100 = 10.7
Answer : A
Answer: A
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Options:
A)440
B)440 * sqrt (2)
C)400 * sqrt (3)
D)450 * sqrt (4)
E)440 * sqrt (5)
Rationale: let the constant be k
F1 = 440
F2 = 440k
F3 = 440 k * k = 440 * k^2
F13= 440 * k^12
we know F13 = 2 *F1 = 2 * 440 = 880
880/440 = k^12
k = twelfth root of 2
for F7...
F7 = 440 * k^6 ( as we wrote for F2 and F3)
F7 = 440 * (twelfth root of 2) ^ 6
F7 = 440 * sqrt (2)
Answer B
Answer: B
Question: Machine A can process 6000 envelopes in 3 hours. Machines B and C working together but independently can process the same number of envelopes in 2.5 hours. If Machines A and C working together but independently process 3000 envelopes in 1 hour, then how many hours would it take Machine B to process 2800 envelopes.
Options:
A)2
B)3
C)4
D)6
E)60/7
Rationale: You can either take the amount of work done as the same as Karishma has done or take the work done by each in the same time. I will do the latter
1. Work done in 1 hr by A is 2000 envelopes
2. Work done in 1 hr by A and C is 3000 envelopes
3. So work done in 1 hr by C is 1000 envelopes
4. Work done in 1 hr by B and C is 2400 envelopes
5. So work done in 1 hr by B is 1400 envelopes
6. So to process 2800 envelopes B will take 2800/1400 hrs = 2 hrs
So the answer is choice A
Answer: A
Question: Two numbers are respectively 50% and 20% more than a third number. The percentage that is first of the second is?
Options:
A)125%
B)97%
C)118%
D)52%
E)83%
Rationale: I II III
150 120 100
120----------150
100-----------? => 125%
Answer:A
Answer: A
Question: A carpenter is building a frame for a wall painting. The painting is in the shape of a rectangle. If the sides of the rectangle are in the ratio of 3:2 and the shorter side has a length of 16 inches, how many inches of framing material does the carpenter need to frame the painting?
Options:
A)12
B)22 1/2
C)37 1/2
D)88
E)80
Rationale: (16/2) ( 2+3) * 2 = 80=E
Answer: E
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.855 per pound?
Options:
A)1:3
B)1:2
C)1:1
D)2:1
E)4:5
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.855
0.9 – 0.1x = 0.855
x = 0.45
Thus ratio of both flours is 4:5
E
Answer: E
Question: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?
Options:
A)3510
B)2620
C)1404
D)700
E)635
Rationale: Committee can have either: 2 men and 4 women OR 3 men and 3 women (to meet the condition of at least 2 men and 3 women).
Ways to chose 6 members committee without restriction (two men refuse to server together): C28∗C45+C38∗C35=700C82∗C54+C83∗C53=700
Ways to chose 6 members committee with two particular men serve together: C22∗C45+(C22∗C16)∗C35=5+60=65C22∗C54+(C22∗C61)∗C53=5+60=65
700-65 = 635
Answer: E.
Answer: E
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number W of races we need to conduct to get the top 3 fastest horses?
Options:
A)5
B)7
C)8
D)10
E)11
Rationale: W=7 is the correct answer.
Good solution Buneul.B
Answer: B
Question: When a train travels at a speed of 80kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
Options:
A)25km
B)50km
C)60km
D)85km
E)95km
Rationale: Let x be the time reached with the speed 80km/h
50km/h ----> x+15
Distance is equal so
80(km/h)× xhr = 50(km/h) × (x+15) hr
So
80 x = 50x + 750
So the would be in km
And x = 25
ANSWER:A
Answer: A
Question: Two pipes A and B can fill a tank in 24 and 48 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?
Options:
A)12
B)16
C)19
D)20
E)22
Rationale: Part filled by A in 1 min. = 1/24
Part filled by B in 1 min. = 1/48
part filled by (A + B) in 1 min. = 1/24 + 1/48 = 1/16.
Both the pipes can fill the tank in 16 minutes.
Answer: B
Answer: B
Question: In Lottery,there are 10 prizes and 25 blanks.A lottery is drawn at random.What is the Probability of getting a prize?
Options:
A)1/7
B)2/7
C)3/7
D)4/7
E)1
Rationale: Total number of outcomes possible,n(s)=10+25=35.
Total number of prize,n(e)=10
p(e)=n(e)/n(s)=10/35=2/7
Answer is option B
Answer: B