mathewhe/aqua_rat huggingface dataset:
Question: Four of the five parts numbered (a),(b),(c),(d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
(A) 45 × 120 + 5(2) × 10
(B) 113 × 25 × 2
(C) 27 × 25 × 8 + 15 × 6 + 4 × 40
(D) 226 × 5 + 113 × 45 =
(E) 50(2) × 2 + 13 × 50
Rationale: Others equal 5650.
Answer D
Answer: (D) 226 × 5 + 113 × 45 =
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 2777
(C) 9999
(D) 2777
(E) 2661
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000
Answer: a
Answer: (A) 1000
Question: A baseball card decreased in value 20% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 30%
(C) 32%
(D) 36%
(E) 72%
Rationale: Let the initial value of baseball card = 100
After first year , value of baseball card = (1- 20/100)* 100 = 80
After second year , value of baseball card =(1 - 10/100)* 80 = 72
total percent decrease of the card's value over the two years = (100-72)/100 *100%
=28%
Answer A
Answer: (A) 28%
Question: 1, 8, 27, 64,...
(A) 25
(B) 48
(C) 59
(D) 63
(E) 125
Rationale: Explanation:
Numbers are
1^3=1
2^3=8
3^3=27
4^3=17
5^3=125
ANSWER:E
Answer: (E) 125
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 11 consecutive spaces in a random direction, what is the probability the piece ends no more than 11 spaces from the square numbered 49?
(A) 23%
(B) 24%
(C) 25%
(D) 26%
(E) 27%
Rationale: No more than 11 spaces from 49 means in the rangefrom 49-11=38 to 49+11=60, inclusive. Total numbers in this range 60-38+1=23, the probability favorable/total=23/100
Answer: A
Answer: (A) 23%
Question: A block of wood has dimensions 10cm x 10cm x 90cm. The block is painted red and then cut evenly at the 45 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red?
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: The area of each half is 100+4(450)+100 = 2000
The area that is not painted is 100.
The fraction that is not painted is 100/2000 = 1/20 = 5%
The answer is A.
Answer: (A) 5%
Question: Ashok secured average of 78 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 38
(B) 98
(C) 99
(D) 17
(E) 80
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 78
Therefore total marks in 6 subjects = 78 * 6 = 468
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 468 – 370 = 98
ANSWER: B
Answer: (B) 98
Question: The cost of 20 packets of sugar, each weighing 900 grams is Rs. 28. What will be the cost of 27 packets, if each packet weighs 1 kg?
(A) Rs 42
(B) Rs 56
(C) Rs 58.50
(D) Rs 64.75
(E) None of these
Rationale: Explanation :
Let the required cost be Rs. x. Then,
More packets, More cost (Direct Proportion)
More weight, More cost (Direct Proportion)
Packets 20 : 27
Weight 900 : 1000 :: 28 : x
(20 x 900 x x) = (27 x 1000 x 28)
x = (27 x 1000 x 28) /20 x 900
=42
Answer A
Answer: (A) Rs 42
Question: 4, 5, 7, 11, 19, (...)
(A) 22
(B) 35
(C) 27
(D) 32
(E) 25
Rationale: Explanation :
4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer : Option B
Answer: (B) 35
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After two year A removed his money; B and C continued the business for one more year. If the net profit after 3 years be Rs.4800, then A's share in the profit is?
(A) 600
(B) 400
(C) 678
(D) 867
(E) 768
Rationale: 2*24 : 3*36 : 4*36
4: 9: 12
4/25 * 4800 = 768
Answer: E
Answer: (E) 768
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
(A) 1800
(B) 900
(C) 2500
(D) 2700
(E) 2900
Rationale: Explanation:
Let required number of bottles be xx
More machines, more bottles (direct proportion)
More minutes, more bottles(direct proportion)
Hence we can write as
(machines) 6:10
(minutes) 1:4}::270:x
⇒6×1×x=10×4×270
⇒x=10×4×270/6
=10×4×90/2
=10×4×45=1800
Answer: Option A
Answer: (A) 1800
Question: A student committee that must consists of 6 members is to be formed from a pool of 9 candidates. How many different committees are possible
(A) 5
(B) 8
(C) 40
(D) 56
(E) 84
Rationale: Out of 9 people, any 6 can be selected for a committee. So 9c6 = 84 is the answer.
E
Answer: (E) 84
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 12 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
(A) A)11
(B) B)23
(C) C)24
(D) D)29
(E) D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 12..
so total who won N = 11+12 = 23..
B
Answer: (B) B)23
Question: A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?
(A) 150
(B) 240
(C) 108
(D) 369
(E) 879
Rationale: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.
Answer: C
Answer: (C) 108
Question: 396, 462, 572, 427, 671, 264
(A) 396
(B) 427
(C) 671
(D) 264
(E) 572
Rationale: In each number except 427, the middle digit is the sum of other two.
Answer :B
Answer: (B) 427
Question: 8900 ÷ 6 ÷ 4 = ?
(A) 370.837
(B) 370.835
(C) 370.832
(D) 370.833
(E) 370.831
Rationale: Explanation:
Given Exp. 8900 * 1/6 * 1/4
= 370.833
ANSWER: D
Answer: (D) 370.833
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.70/10 sq.metre, whose base & perpendicular distance from the other side being 84m & 24m respectively?
(A) s.2400
(B) s.2016
(C) s. 1400
(D) s. 3480
(E) s. 2000
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 84 * 24 = 2016 m.
Total cost of levelling = Rs. 2016
B
Answer: (B) s.2016
Question: A certain bag contains 60 balls — 22 white, 18 green, 8 yellow, 5 red, and 7 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.09
(B) 0.15
(C) 0.54
(D) 0.8
(E) 0.91
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 18 + 8)/60 = 48/60 = 0.8.
Answer: D.
Answer: (D) 0.8
Question: If a and b are both prime numbers greater than 10, which of the following CANNOT be true?
I. ab is an even number.
II. a - b = 117.
III. The sum of a and b is even.
(A) I and II only
(B)  I only
(C)  I and III only
(D)  II and III only
(E)  I, II and III
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
Since a and b are both prime numbers greater than 10, they must both be odd. Therefore ab must be an odd number, so Statement I cannot be true. Similarly, if a and b are both odd, then a - b cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since a and b are both odd, a + b must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,the correct answer is (A).
Answer : A
Answer: (A) I and II only
Question: The respective ages of father and his son are 40 and 16 years. In how many years will the father be twice as old as his son ?
(A) 19 years
(B) 8 years
(C) 10 years
(D) 15 years
(E) 12 years
Rationale: Suppose x years later the father will be twice as old as his son.
x + 40 = 2 (x + 16)
x = 40 - 32 = 8 years
answer : B
Answer: (B) 8 years
Question: Sonia's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 8 Years
(B) 6 Years
(C) 4 Years
(D) 2 Years
(E) None
Rationale: Explanation:
Mother's age when Sonia's brother was born = 36 years.
Father's age when Sonia's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.
Answer: B
Answer: (B) 6 Years
Question: If Jan 1, 2006 was a Sunday, What was the day of the week Jan 1, 2010?
(A) Friday
(B) Thursday
(C) Tuesday
(D) Saturday
(E) Monday
Rationale: Explanation:
Given that Jan 1 2006 was a Sunday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Sunday + 5 odd days) = Friday
Answer: Option A
Answer: (A) Friday
Question: A warehouse is labeling computer inventory with 5-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 5-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used.
The manager wants to measure the magnitude of the number of 5-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
(A) 981
(B) 1000
(C) 1011
(D) 10000
(E) 1110
Rationale: The number of codes possible if leading zero is allowed = 10*10*10*10*10=10^5
The number of codes possible if leading zero is NOT allowed = 9*10*10*10*10=9*10^4
The difference = 10^5 - 9*10^4 = 10^4(10-9) = 10^4.
Answer: D.
Similar questions to practice:
Hope it helps.
Answer: (D) 10000
Question: The smallest prime number is?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The smallest prime number is 2.
B)
Answer: (B) 2
Question: The average age of 40 students in a class is 15 years. If the age of teacher is also included, the average becomes 16 years, find the age of the teacher.
(A) 22
(B) 27
(C) 28
(D) 26
(E) 56
Rationale: Explanation:
If teacher's age is 15 years, there is no change in the average. But teacher has contributed 1 year to all the students along with maintaining his age at 16.
Age of teacher = Average age of all + Total increase in age
= 16 + (1 x 40 ) = 56 years
Answer:E
Answer: (E) 56
Question: From a group of 14 astronauts that includes 5 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
(A) 175
(B) 190
(C) 165
(D) 180
(E) 200
Rationale: number of astronauts with previous experience = 5
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(5C1)*(9C2)
=5*36= 180
Answer : D
Answer: (D) 180
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 15 minutes. The waste pipe can empty the full cistern in?
(A) A)7
(B) B)6
(C) C)8
(D) D)10
(E) E)5
Rationale: 1/10 + 1/15 - 1/x = 1/15
x = 10
Answer:D
Answer: (D) D)10
Question: 3^(2x/3)=1^(5x)
What is the value of x ?
(A) -1
(B) 2/3
(C) 0
(D) 1/2
(E) 3/4
Rationale: 3^(2x/3)=1
2x/3=0; x=0= ans C
Answer: (C) 0
Question: You have a bucket of jelly beans. Some are red, some are blue, and some green. With your eyes closed, pick out 2 of a like color. How many do you have to grab to be sure you have 2 of the same?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: If you grab 3 it might be all different. So take one extra to make sure you have two of the same.
So, take atleast 4
ANSWER:B
Answer: (B) 4
Question: 11234783131.What are the next three numbers?
(A) 145
(B) 178
(C) 176
(D) 191
(E) 192
Rationale: actually if we split up series then we get,
11,23,47,83,131
from this we see that,
23-11=12,
47-23=24,
83-47=36,
131-83=48,
from option we see that 191-131=60
so,191 is correct option
ANSWER:D
Answer: (D) 191
Question: What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345?
(A) 2345
(B) 2288
(C) 2977
(D) 1280
(E) 1811
Rationale: Explanation:
2000 + 300 + 40 + 5 = 2345
Answer: A
Answer: (A) 2345
Question: In a series of football matches, the probability that Team P wins a match against Team Q is 1/4 and the probability that the match ends in a draw is 1/3. If the two teams play five matches, what is the probability that all five matches end in a draw?
(A) 1/243
(B) 1/81
(C) 1/27
(D) 1/9
(E) 1/3
Rationale: P(5 draws)=(1/3)^5=1/243
The answer is A.
Answer: (A) 1/243
Question: Ayesha’s father was 38 years of age when she was born while her mother was 32 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 10 years
(E) None
Rationale: EXPLANATION
Mother’s age when Ayesha’s brother was born = 32 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 32) years = 10 years.
Answer D
Answer: (D) 10 years
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 767 meters
(B) 426 meters
(C) 500 meters
(D) 165 meters
(E) 156 meters
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: C
Answer: (C) 500 meters
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 80 percent of books that were loaned out are returned and there are 65 books in the special collection at that time, how many books of the special collection were loaned out during that month?
(A) 20
(B) 30
(C) 35
(D) 40
(E) 50
Rationale: there are 10 books less(75-65) which represents 20% of the loaned books (100-80)
So total loaned out books = 50
Answer E
Answer: (E) 50
Question: A batsman scored 120 runs which included 6 boundaries and 4 sixes. What % of his total score did he make by running between the wickets
(A) 40%
(B) 60%
(C) 65%
(D) 70%
(E) 75%
Rationale: Number of runs made by running = 110 - (6 x 4 + 4 x 6)
= 120 - (48)
= 72
Now, we need to calculate 60 is what percent of 120.
=> 72/120 * 100 = 60 %
B
Answer: (B) 60%
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) A)Rs.150
(B) B)Rs.132
(C) C)Rs.100
(D) D)Rs.125
(E) E)Rs.225
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2 = Rs.132
ANSWER:B
Answer: (B) B)Rs.132
Question: N is the greatest number which divides 1305, 4665 and 6905 and gives the same remainder in each case. What is the sum of the digits in N?
(A) 4
(B) 3
(C) 6
(D) 5
(E) 2
Rationale: 6905 - 1305 = 5600
6905 - 4665 = 2240
4665 - 1305 = 3360
Hence, the greatest number which divides 1305, 4665 and 6905 and gives the same remainder, N
= HCF of 5600, 2240, 3360
= 1120
Sum of digits in N
= Sum of digits in 1120
= 1 + 1 + 2 + 0
= 4 Answer: Option A
Answer: (A) 4
Question: Operation#is defined as adding a randomly selected two digit multiple of 12 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?
(A) 0%
(B) 10%
(C) 20%
(D) 30%
(E) 40%
Rationale: Any multiple of 12 is even.
Any two-digit prime number is odd.
(even+odd)/2 is not an integer. Thus # does not yield an integer at all.
Therefore P=0.
Answer: A.
Answer: (A) 0%
Question: John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping?
(A) $62
(B) $92
(C) $32
(D) $22
(E) $82
Rationale: Money spent on drinks
5 ? 4 = $20
Money spent on sandwiches
8 ? 6 = $48
Total money spent
20 + 48 = $68
Money left after shopping
100 - 68 = $32
correct answer C
Answer: (C) $32
Question: mr. depak has $429,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
(A) $1
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+2+9+7+7+4 = 33
If you add 3 , the number is divisible by 6 (33+ 3)
Correct Option : C
Answer: (C) $3
Question: A man and his wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is (1/7) and the probability of wife’s selection is (1/5). What is the probability that only one of them is selected?
(A) 1/7
(B) 4/7
(C) 5/7
(D) 2/7
(E) 9/7
Rationale: P(A)=1/7
P(B)=1/5
P(A’)=6/7
P(B’)4/5
Required probability= P((A and B’) or ( B and A’))
=(1/7x4/5)+(1/5x6/7)
=2/7
ANSWER D
Answer: (D) 2/7
Question: In a rectangular coordinate system, points O (2,2), P (2,6), and Q (10,2) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?
(A) (3,7)
(B) (5,3)
(C) (3,4)
(D) (6,4)
(E) (5,5)
Rationale: All points equidistant from O and Q lie on the line x = 6, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 4, so the fire station should lie on this line.
These two intersect at (6,4) and that will be the point equidistant from all 3 points.
The answer is D.
Answer: (D) (6,4)
Question: 8 friends went to a hotel and decided to pay the bill amount equally. But 7 of them could pay Rs. 80 each as a result 8th has to pay Rs. 70 extra than his share. Find the amount paid by him.
(A) 140
(B) 121
(C) 110
(D) 160
(E) None
Rationale: Explanation:
Average amount paid by 7 persons = Rs. 80
Increase in average due to Rs. 70 paid extra by the 8th men = Rs. 70/7= Rs. 10
Therefore, Average expenditure of 8 friends = Rs. 80 + Rs. 10 = Rs. 90
Therefore, Amount paid by the 11th men = Rs. 90 + Rs. 70 = Rs. 160
Correct Option: D
Answer: (D) 160
Question: Two identical circles intersect such that their centers and the points at which they intersect form a square of side 1 cm. What is the area of the region where the two circles intersect?
(A) pi/2 - 1
(B) pi/4 - 1
(C) 1 - pi/4
(D) pi/8 + 1
(E) 4 - pi
Rationale: Drawing a diagram, we see that the radius of the circle equals the side of the square.
The area of intersection is: pi*r^2/4 - (r^2-pi*r^2/4) = pi*r^2/2 - r^2 = pi/2 - 1
The answer is A.
Answer: (A) pi/2 - 1
Question: The population of a city increases by 8% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
(A) 9%
(B) 9.27%
(C) 22.50%
(D) 12%
(E) None of these
Rationale: Actual increase in population=7%
Let, earlier population=100 then the population after 3 years
=100(1+7/100)^3=122.5043
∴Required percentage=22.50%
ANSWER:C
Answer: (C) 22.50%
Question: There are 25 balls in a jar. You take out 5 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
Rationale: 9 = 5 blue balls + 20/ 5
Answer: B
Answer: (B) 9.
Question: For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(26)?
(A) 23
(B) 19
(C) 17
(D) 13
(E) 11
Rationale: f(26) = 2*4*6*8*10*12*14*16*18*20*22*24*26
The greatest prime factor in this list is 13.
The answer is D.
Answer: (D) 13
Question: A double decked bus can accomodate 50 passengers,20 in the upper deck and 30 in the lower deck.In how many ways can the passengers be accomodated if 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck?
(A) 1. 85!50!60!/40!45!
(B) 2. 85!/40!45!
(C) 3. 110!/50!60!
(D) 4. 25!/10!15!
(E) 5. 110!/40!45!
Rationale: 50 passengers,20 in the upper deck and 30 in the lower deck.
25 passengers have issues as 15 refuse to be in the upper deck while 10 others refuse to be in the lower deck
So those 15 will be put in lower deck and 10 will be in upper deck
So from the rest 25 passengers(50-25), we need to find 10 people to put into upper deck and the rest go to lower deck
So the ways are: C(25,10) = 25!/10!15! . Answer D
Answer: (D) 4. 25!/10!15!
Question: Three persons A, B and C divide a certain amount of money such that A's share is Rs.4 less than half of the total amount. B's share is Rs.8 more than half of what is left and finally C takes the which is Rs.14. Find the total amount they initially had with them?
(A) 16
(B) 78
(C) 80
(D) 76
(E) 23
Rationale: Let the total amount be Rs.P
Let shares of A and B be Rs.X and Rs.Y respectively.
Given, C's share was Rs.14.
X + Y + 14 = P --- (1)
From the given data, X = P/2 - 4 --- (2)
Remaining amount = P - (P/2 - 4) = P/2 + 4
Y = 1/2(P/2 + 4) + 8
=> P/4 + 10 --- (3)
From (1), (2) and (3)
P/2 - 4 + P/4 + 10 + 14 = P
=> 3P/4 + 20 = P
=> P - 3P/4 = 20
=> P/4 = 20 => P = Rs.80
Answer: C
Answer: (C) 80
Question: There is a cycle race going on in a circular track and 1/5th of the total in front a person and 5/6th of the total behind that person gives up the total number of participants. Total how many participants are there?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: Assume there are x participants in the race.
participants in front of a person wil b x-1 and
that behind him wil b x-1.
so
1/5(x-1) + 5/6(x-1) = x
we get,
x=31
ANSWER:B
Answer: (B) 31
Question: A train of length 250 m crosses a bridge of length 150m in 32 seconds. What is the speed of train?
(A) 33
(B) 27
(C) 25
(D) 22
(E) 45
Rationale: Sol : (length of train+ length of bridge) = speed of train x Time
(250+150) = 32 x Speed
Speed = 400/32= 12.5 m/s =45 km/h
ANSWER=E
Answer: (E) 45
Question: In a room filled with 7 people, 3 people have exactly 1 sibling in the room and 4 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
(A) 5/21
(B) 3/7
(C) 4/7
(D) 5/7
(E) 13/21
Rationale: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 4 people who have exactly 2 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 2 people out of 7 is 7C2=21
first sibling pair----(A and B)--selecting 2 people --2C2=1
second sibling pair (C and D)--selecting 2 people--2C2=1
third sibling pair (E F G)--selecting 2 out of 4 --4C2=6
total= 1+1+6=8
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 2 people who are siblings
=8/21(21 is 7C2)
=1-8/21
=13/21
ANS E
Answer: (E) 13/21
Question: If the sum of one-half, one-third and one-fourth of a number exceeds the number itself by 4, what could be the number ?
(A) 24
(B) 36
(C) 72
(D) None of these
(E) Cannot be determined
Rationale: Answer
Let the number be N
∴ (1/2 + 1/3 + 1/4)N = {(6 +4 +3) x N } / 12
= 13N / 12
According to the question,
13N/12 - N = 4
∴ N = 48
Option: D
Answer: (D) None of these