divelab/Sys2Bench huggingface dataset:
Question: Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 5:00 am and Pipe B at 6:00 am, at what time will the pool be full?
Options:
A)13:00
B)14:00
C)15:00
D)17:00
E)16:00
Rationale: Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 5:00 a.m and Pipe B at 6:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 6:00 a.m
Pool filled after 1 hour with both the pipes on : 1/12
Pool filled after 9 hours with both pipes on : 9/12
Pool filled in 1 hour + Pool filled in 9 hours = 3/12 +9/12 =1
Therefore, it takes 10 hrs to fill the pool
As Pipe A started at 5:00 a.m, pool is full at 15:00 hrs
Answer : C
Answer: C
Question: we have 7 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 15 kg one of 20 kg by using only five weight how many weight u can weight
Options:
A)19
B)18
C)24
D)21
E)32
Rationale: select 5 weight out of 7, 7C5=21
ANSWER:D
Answer: D
Question: Obra drove 140π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
Options:
A)6.67%
B)12.5%
C)18.75%
D)29.16%
E)33.3%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 140π/480π =29.16%
Hence, answer is D.
Answer: D
Question: A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
Options:
A)120
B)288
C)277
D)126
E)221
Rationale: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A
Answer: A
Question: Walking at 5/6th of its usual speed a cab is 8mnts late. Find its usual time to cover the journey?
Options:
A)25m
B)45m
C)40m
D)50m
E)62m
Rationale: New speed = 5/6th of usual speed
New time = 6/5th of usual time
6/5 UT - UT = 8m
UT/5 = 8m
UT = 40m
Answer is C
Answer: C
Question: A rectangular grass field is 70 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)s.1350
B)s.1300
C)s.1328
D)s.1397
E)s.1927
Rationale: Area = (l + b +2d) 2d
= (70 + 55 +2.5 * 2) 2*2.5 => 650
650 * 2 = Rs.1300
Answer: B
Answer: B
Question: The numerator of a fraction is 1 less than twice the denominator. If the numerator and denominator are both increased by \
1, the fraction becomes 3/5. Find the fraction?
Options:
A)A)5/3
B)B)3/5
C)C)4/7
D)D)5/9
E)of these
Rationale: Let the numerator and denominator of the fraction be 'n' and 'd' respectively.
n = 2d - 1
(n + 1)/(d + 1) = 3/5
5n + 5 = 3d + 3
5n + 5 = 3(2n - 1) + 3 => n = 5
n = 2d - 1 => d = 3
Hence the fraction is : 5/3
ANSWER:A
Answer: A
Question: Ravi can do a piece of work in 15 days while Prakash can do it in 30 days. In how many days will they finish it together?
Options:
A)11 days
B)9 days
C)8 days
D)12 days
E)10 days
Rationale: 1/15 + 1/30 = 3/30
10/1 = 10 days
ANSWER:E
Answer: E
Question: The product of three consecutive numbers is 336. Then the sum of the smallest two numbers is ?
Options:
A)13
B)15
C)20
D)38
E)56
Rationale: Product of three numbers = 336
336 = 6*7*8.
So, the three numbers are 6, 7 and 8.
And Sum of smallest of these two = 6+7 = 13.
ANSWER : OPTION A
Answer: A
Question: The edges of a cuboid are respectively 3cm, 4cm and 12 cm. Find the length of the diagonal of cuboid?
Options:
A)28 m3
B)27 m3
C)60 m3
D)18 m3
E)61 m3
Rationale: lb = 20 ; lh = 15 ; fh
= 12
(lbh)2 = 20 * 15 * 12 => lbh
= 60 m3
Answer: C
Answer: C
Question: When a student Joe, weighing 44 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
Options:
A)5.5 kg
B)11 kg
C)30 kg
D)36.5 kg
E)7 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 44+30 = 74
So, the average the two persons = 37
That gives the answer 44-37 = 7
Answer E
Answer: E
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
Options:
A)1000
B)756
C)480
D)660
E)520
Rationale: Total Men = 7
Total Women = 6
Persons in committee = 5
No. of ways to select at least 3 men = 7C5 + 7C4 * 6C1 + 7C3*6C2
= 756
Ans - B
Answer: B
Question: Consider the sets Tn= {n, n + 1, n + 2, n + 3, n + 4), where n = 1, 2, 3, … , 96. How many of these sets contain 6 or any integral multiple thereof (i.e., any one of the numbers 6, 12, 18, …)?
Options:
A)80
B)81
C)82
D)83
E)84
Rationale: Explanation :
If n = 1, then the set T1 = {1,2,3,4,5}, and it does not have 6 or any multiples.
n = 2 to n = 6 has 6 in the set.
n = 7, has the set T7 = {7,8,9,10,11}, and no 6 or multiples.
So 1 in every 6 members do not have 6 or multiples of 6.
So, till n = 96, there are 16 sets of “6 members” (16*6 = 96) and 16 sets do not have 6 or its multiples, while the remaining 80 sets have.
Answer : A
Answer: A
Question: On a partly cloudy day, Derek decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction T of the total distance did he cover while the sun was shining on him?
Options:
A)1/4
B)4/5
C)1/5
D)1/6
E)1/7
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is T=2/14 = 1/7. Answer: E
Answer: E
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corner, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is
Options:
A)6420
B)8960
C)5120
D)4830
E)None
Rationale: Sol.
Clearly, l = (48 - 16) m = 32 m,
b = (36 - 16) m = 20 m,
h= 8 m.
∴ Volume of the box = (32 x 20 x 8) m3 = 5120 m3
Answer C
Answer: C
Question: Rajeswari went to the stationers and bought things worth Rs. 100, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 10%. then what was the cost of the tax free items?
Options:
A)Rs. 90.50
B)Rs. 89.50
C)Rs. 94.00
D)Rs. 99.50
E)Rs. 94.50
Rationale: Solution
Let the amount of taxable purchases be Rs.x.
Then, 10% of x	= 50/100
x ‹=› (50/100×100/10)
= 5
Cost of tax free items	= Rs.[100 - (5 + 0.50)]
= Rs. 94.50
Answer E
Answer: E
Question: f(x) is a function such that f(2x + 1) = 2f(x) + 1 for all real numbers x and f(0) = 2. Find the value of f(3).
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: f(2x + 1) = 2f(x) + 1 : given
f(3) = 2f(1) + 1 : x = 1 in A
f(1) = 2f(0) + 1 : x = 0 in A
f(3) = 11 : substitute
correct answer B
Answer: B
Question: How many triples (a, b, c) of real numbers satisfy the equations
ab = c, ac = b, and bc = a ?
Options:
A)2
B)4
C)5
D)6
E)8
Rationale: Observe that (0, 0, 0) is a triple as in the problem. Now, if one of a, b and c is 0, then the given
equations imply each of them is 0. So we suppose next that each is non-zero. The equations ab = c
and ac = b imply a2bc = bc so that a2 = 1. Hence, a 2 {1,−1}. Similarly, b 2 {1,−1} and
c 2 {1,−1}. One checks that these imply that either (a, b, c) = (1, 1, 1) or exactly one of a, b and
c is 1 and the other two are −1. These observations lead to the total number of tuples being 5.
correct answer C
Answer: C
Question: An office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 3 notebooks of the same size and the same color or 3 notebooks of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
Options:
A)15
B)20
C)24
D)30
E)36
Rationale: First let's consider the small notebooks.
There are 5 ways to choose 3 notebooks of the same color.
The number of ways to choose 3 notebooks with different colors is 5C3=10.
There are 15 different packages we can make with the small notebooks.
We can use the same process to find 15 different packages with large notebooks.
The total number of different packages is 30.
The answer is D.
Answer: D
Question: 445, 221, 109, 53,...
Options:
A)8
B)7
C)42
D)25
E)63
Rationale: Explanation :
To obtain next number, subtract 3 from the previous number and divide the result by 2
445
(445-3)/2=221
(221-3)/2=109
(109-3)/2=53
(53-3)/2=25
ANSWER:D
Answer: D
Question: You have to send 3,000 grapes 1,000 kilometers from grapecity to appleland. Your truck can carry 1,000 grapes at a time. Every time you travel a kilometer towards appleland you must pay a tax of 1 grape but you pay nothing when going in the other direction (towards grapecity).
What is highest number of grapes you can get to appleland?
Options:
A)833
B)765
C)665
D)679
E)874
Rationale: Step one: First you want to make 3 trips of 1,000 grapes 333 kilometers. You will be left with 2,001 grapes and 667 kilometers to go.
Step two: Next you want to take 2 trips of 1,000 grapes 500 kilometers. You will be left with 1,000 grapes and 167 kilometers to go (you have to leave a grape behind).
Step three: Finally, you travel the last 167 kilometers with one load of 1,000 grapes and are left with 833 grapes in appleland.
correct answer is A)833
Answer: A
Question: A shepherd had n goats in the year 2000. In 2001 the no. of goats increased by 40%. In 2002 the no. of goats declined to 70%. In 2003 the no. of goats grew up 30%. In 2004, he sold 10% goats and then he had only 34,398 goats. The percentage increase of the no. of goats in this duration was :
Options:
A)16.66%
B)14.66%
C)11.33%
D)20%
E)None
Rationale: Solution: There is no need of the number of goats given i.e. 34,398.
Initially, let there be 100 goats. Then
100 == 40% ↑==> 140 ==30%↓(declined to 70%)==> 98 ==30%↑ ==> 127.4 ==10%↓(sold)==> 114.66
Hence, % increase = 14.66% [As 100 becomes 114.66].
Answer: Option B
Answer: B
Question: On a track for remote controlled racing cars, racing car A completes the track in 58 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
Options:
A)275
B)325
C)2030
D)425
E)None of these
Rationale: Time required in seconds will be LCM ( 35, 58 ) = 2030
Hence, answer will be (C) 2030
Answer: C
Question: If f(x) = 5 - 2x, then f -1(-3) = ?
Options:
A)1
B)8
C)6
D)4
E)3
Rationale: Find f -1(x) and then Find f -1(- 3)
y = 5 - 2x , given
x = 5 - 2y , interchange x and y
2y = 5 - x , y = log2(5 - x) , solve for y
f -1(x) = log2(5 - x) , inverse function
f -1(- 3) = log2(5 + 3)
= log2(23) = 3
correct answer E
Answer: E
Question: A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 20 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
Options:
A)64
B)130
C)140
D)160
E)120
Rationale: White:Yellow = x:(x+20) = 8:13 --> 13x = 8x + 160 --> x = 32.
The total # of balls originally x + x = 32 + 32 = 64.
Answer: A.
Answer: A
Question: The sum of ages of 5 children born at the intervals of 3 years each is
50 years. Find out the age of the youngest child?
Options:
A)6 years
B)5 years
C)4 years
D)2 years
E)1 year
Rationale: Let the age of the youngest child =x
Then, the ages of 5 children can be written as x,(x+3),(x+6),(x+9) and (x+12)
x+(x+3)+(x+6)+(x+9)x+(x+3)+(x+12)=50
5x+30=50
5x=20
x=20/5=4 Answer: Option C
Answer: C
Question: If w and y are different prime numbers less than ten, what must be true about the sum of w and y?
Options:
A)the sum is even
B)the sum is odd
C)the sum is less than ten
D)the sum is greater than ten
E)the sum is less than 13
Rationale: This has to be solved by checking for each option:
Prime numbers less that 10 = 2, 3, 5, 7
A. the sum is even
May or may not be true. w = 3, y, = 5 -> True.
w = 2, y = 3 - True
B. the sum is odd
May or may not be true. w = 3, y, = 5 -> False.
w = 2, y = 3 - True
C. the sum is less than ten
May or may not be true w= 5, y = 7, Sum = 12
w = 2, y = 3. Sum = 5
D. the sum is greater than ten
May or may not be true w= 5, y = 7, Sum = 12
w = 2, y = 3. Sum = 5
E. the sum is less than 13
This will always be true.
Maximum sum = 7 + 5 = 12.
This is always less than 13.
Correct Option: E
Answer: E
Question: Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.?
Options:
A)22
B)88
C)12
D)77
E)99
Rationale: Let the distance traveled be x km.
Then, x/10 - x/15 = 2
3x - 2x = 60 => x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60/10 = 6 hrs.
So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.
Required speed = 60/5 = 12 kmph.
Answer:C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
Options:
A)5/19
B)5/12
C)5/29
D)5/20
E)5/22
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer:B
Answer: B
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1170 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)2388
B)2778
C)1279
D)6150
E)6396
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1170
45k = 1170 => k = 26
246k = 246(26) = Rs. 6396
Thus the total rent paid by all the four agencies is Rs. 6396.
Answer: E
Answer: E
Question: A total of 502 players participated in a single tennis knock out tournament. What is the total number of matches played in the tournament? (Knockout means if a player loses, he is out of the tournament). No match ends in a tie.
Options:
A)501
B)512
C)256
D)255
E)1023
Rationale: There are 502 players, only 1 person wins, 501 players lose. in order to lose, you must have lost a game.
501 games.
ANs- A
Answer: A
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)20
B)70
C)77
D)26
E)12
Rationale: Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer:B
Answer: B
Question: Out of three consecutive odd numbers fifteen times the first number is equal to addition of thrice the third number and adding 15 to six times the second . What is the first number?
Options:
A)11/3
B)12/5
C)13/6
D)13/2
E)18/13
Rationale: Description :
=> 15x=6(x+2)+15+3(x+4)
=> 15x=9x+39
=>6x = 39
X=13/2
Answer D
Answer: D
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)2300 m^2
B)2350 m^2
C)2520 m^2
D)2620 m^2
E)2780 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be
Options:
A)15 years
B)18 years
C)20 years
D)22 years
E)24 years
Rationale: Explanation:
Clue : (60 - x) - 6 = 5(x - 6)
Option C
Answer: C
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)Rs.6119
B)Rs.6129
C)Rs.6115
D)Rs.6150
E)Rs.6118
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs.6150.
Answer: D
Answer: D
Question: 33 1/3% OF 210?
Options:
A)70
B)90
C)110
D)120
E)130
Rationale: 33 1/3 % = 1/3
1/3 × 210 = 70
A)
Answer: A
Question: A 4% stock yield 5%. The market value of the stock is ?
Options:
A)Rs. 125
B)Rs. 80
C)Rs. 99
D)Rs. 109
E)Rs. 101
Rationale: For an income of Rs. 5, investment = Rs. 100
For an income of Rs. 4, investment = Rs. (100/5) x 4 = Rs. 80
Answer : B
Answer: B
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
Options:
A)31
B)86
C)82
D)15
E)10
Rationale: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 =31.
Answer:A
Answer: A
Question: A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 180 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 180 books were paperbacks, the dealer would earn a profit of $360.
Since the actual profit was $400, the dealer must have sold 40 hardbacks.
Then the number of paperbacks sold was 180-40 = 140.
The answer is E.
Answer: E
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Options:
A)129
B)128
C)189
D)187
E)112
Rationale: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36) = Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100] = Rs. 189.
Answer: C
Answer: C
Question: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options:
A)24
B)26
C)42
D)46
E)None of these
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
ANSWER : A
Answer: A
Question: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -1?
Options:
A)-1
B)9
C)10
D)14
E)20
Rationale: We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
t8 = 2
t9 = -1
So, ourANS is B.
Answer: B
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
Options:
A)Rs.900
B)Rs.800
C)Rs.500
D)Rs. 400
E)Rs.200
Rationale: Explanation:
441 = P(21/20)2
P =Rs.400
Answer:D
Answer: D
Question: When a random experiment is conducted, the probability that event A occurs is 1/5. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?
Options:
A)16/625
B)56/625
C)96/625
D)126/625
E)156/625
Rationale: One case is: 1/5*1/5*4/5*4/5=16/625
The total number of possible cases is 4C2 = 6
P(event A occurs exactly twice) = 6*(16/625) = 96/625
The answer is C.
Answer: C
Question: The events A and B are independent, the probability that event A occurs is greater than 0, and the probability that event A occurs is twice the probability that event B occurs. The probability that at least one of events A and B occurs is 14 times the probability that both events A and B occur. What is the probability that event A occurs?
Options:
A)77/2
B)1/7
C)78/85
D)1/5
E)47/85
Rationale: Let us say probability of A occuring is a.
Let us say probability of B occuring is b.
a = 2b
Probability (either A or B or both) =14 times Probability (A and B)
a*(1-b) + b*(1-a) + ab = 14*ab
Substituting a=2b in the second equation:
2b*(1-b) + b*(1-2b) + 2b*b = 14*2b*b
3b-2b^2 = 28b^2
3b = 30b^2
b = 3/30 = 1/10
So, a = 2b = 1/5
THE CORRECT ANSWER IS D.
Answer: D
Question: A train travelled from point A to point B at 160 Km/h. On its way back the train travelled at 120 Km/h and therefore the trip back lasted one hour longer. What is the distance (in Km) between A and B?
Options:
A)480.
B)500.
C)510.
D)600.
E)800.
Rationale: distance=speed*time
d1=s1t1
d2=s2t2
The distance from point A to point B is the same for each trip so,
d1=d2 and
t2=t1+1
thus,
s1t1=s2(t1+1)
160t1=120(t1+1)
t1=3
160*3=480
Answer: A
Answer: A
Question: In how many ways 6 boys and 6 girls can be seated in a row so that boys and girls are alternate?
Options:
A)1063800
B)1083600
C)1036800
D)1053800
E)1073600
Rationale: number of ways = 2*6!*6! = 1036800
Answer is C
Answer: C
Question: The cost price of 17 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/15
B)36 2/11
C)45 2/14
D)54 6/11
E)18 2/12
Rationale: 17 CP = 11 SP
11 --- 2 CP
100 --- ? =>54 6/11%.Answer: D
Answer: D
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)4:7
B)4:0
C)4:3
D)4:1
E)4:2
Rationale: 12:9
= 4:3
Answer: C
Answer: C
Question: Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
Options:
A)2304
B)2305
C)2309
D)2310
E)2311
Rationale: Trees increase by 1/4 the number of trees in preceding year. Hence, correct answer must be divisible by 4. Based on divisibility rules, if last 2 digits are divisible by 4 then the number is divisible by 4. Thus, we can eliminate B, C,D,E The answer to be A
Again, trees increase by 1/4 the number of trees in preceding year. Hence, the number of trees increase by 5/4 times the number of trees the preceding year.
If x = initial number of trees = 2304
Year 1 = 5/4x
Year 2 = (5/4)(5/4)x
Year 3 = (5/4)(5/4)(5/4)x
Year 4 = (5/4)(5/4)(5/4)(5/4)x
Only for Answer D: (5/4)(5/4)(5/4)(5/4)2304 = 5625
Hence, correct answer = A
Answer: A
Question: A number exceeds by 35 from its 3/8 part. Then the number is?
Options:
A)A)56
B)B)35
C)C)39
D)D)40
E)E)45
Rationale: x – 3/8 x = 35
x = 56
ANSWER:A
Answer: A