divelab/Sys2Bench huggingface dataset:
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Options:
A)104 kmph
B)187 kmph
C)164 kmph
D)175 kmph
E)106 kmph
Rationale: 624/6
= 104 kmph
Answer: A
Answer: A
Question: Lexy walks 5 miles from point A to point Q in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Options:
A)40
B)80
C)120
D)160
E)180
Rationale: Lexy walks 5 miles from point A to point Q in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Average speed = total distance/total time
We know the total distance is 5+5 (going from A to Q then from Q to A)
Time = distance/speed
Time = 5/15
Time = 1/3 hour
Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.
This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.
Answer: D). 160
Answer: D
Question: If a - b = 3 and a^2 + b^2 = 33, find the value of ab.
Options:
A)12
B)15
C)10
D)18
E)13
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 33 - 9 = 24
ab = 12.
Answer is A.
Answer: A
Question: A car travels from A to B at an average speed of 50 km/hour. At what average speed would it have to travel from B to A to average 60 km/hour for the whole trip?
Options:
A)55 km/h
B)65 km/h
C)85 km/h
D)75 km/h
E)90 km/h
Rationale: Let d be the distance bewteen A and B
T1 = d / 50 : travel time from A to B
Let S be the speed from B to A
T2 = d/S : travel time from B to A
60 = 2d/(T1 + T2) : average speed for the whole trip
60 = 2d/(d/50 + d/S) : substitute T1 and T2
S = 75 km/hour : solve the above equation for S.
correct answer is D)75 km/h
Answer: D
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)1.9 sec
C)8.9 sec
D)6.9 sec
E)2.9 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Answer: A
Question: The current birth rate per thousand is 32, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by?
Options:
A)2.1%
B)3.2%
C)3.9%
D)4%
E)5.1%
Rationale: Net growth on 1000 = 32-11 = 21
Net growth on 100 = 21*100/1000 = 2.1%
Answer is A
Answer: A
Question: An amount of Rs.80,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
Options:
A)2378
B)20000
C)2697
D)5000
E)6971
Rationale: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 80,000
Thus we get, 2Q + Q + Q + 4Q = 80,000
8Q = 80,000 or Q = Rs. 10000
Thus, R = Rs. 10000, P = 20000 & S = Rs. 40000
Hence, the required difference = (S – P) = (40000 – 20000) = Rs. 20000
ANSWER:B
Answer: B
Question: A man bought a horse and a carriage for 3000. He sold the horse at a gain of 20% and the carriage at a loss 10%, there by gaining 2% on the whole. Find the cost of the horse.
Options:
A)1000
B)1200
C)1500
D)1700
E)None of these
Rationale: Let the C.P. of horse = x
Then the C.P. of carriage = (3000 – x)
20% of x – 10% of (3000 – x) = 2% of 3000
⇒ x⁄5 - (3000−x)/10=60
⇒ 2x - 3000 + x = 600
⇒ 3x = 3600 ⇒ x = 1200
Answer B
Answer: B
Question: Noelle walks from point A to point B at an average speed of 3 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 5 kilometers per hour?
Options:
A)15
B)12.5
C)10
D)8
E)7.75
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
5= 2*3*x/3+x
x= 15
A is the answer
Answer: A
Question: A 6% stock yields 8%. The market value of the stock is:
Options:
A)48
B)75
C)55
D)46
E)57
Rationale: For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.100
---- x 6	= Rs. 75.
8
Market value of Rs. 100 stock = Rs. 75.
Answer: Option B
Answer: B
Question: The price of 3 chudi and 6 tops is Rs. 1500. With the same money one can buy 1 chudi and 12 tops. If one wants to buy 5 tops, how much shall she have to pay ?
Options:
A)500
B)1000
C)1200
D)1300
E)1500
Rationale: Let the price of a chudi and a top be Rs. x and Rs. y respectively.
Then, 3x + 6y = 1500 .... (i)
and x + 12y = 1500 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 500. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 1500 (-)
x + 2y = 500
----------------
10y = 1000
----------------
cost of 5 tops = 5*100 = 500
Answer : A
Answer: A
Question: 20 people with two sisters among them want to sit around a round table such that the two sisters are exactly separated by one person sitting in between them. Find the probability.
Options:
A)1/19
B)2/29
C)3/29
D)4/29
E)5/29
Rationale: 20 people in which 2 sisters are there and the condition is that 2 sisters should be seperated by 1 person
(s1 p s2) be 1 set
then 20-3 persons => 17 persons + 1 set= 18
18 can be arranged in 17! ways bcz it is circular permutuation
the 2 sis can be arranged in 2! ways
and the p place can be filled in 18 ways
and the total permutations are 19!
probability is = (2!*18*17!)/(19!)
= 2/19
ANSWER:B
Answer: B
Question: Anna left for city A from city B at 5.20 a.m. She traveled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
Options:
A)10.35 a.m
B)10.15 a.m
C)10.55 a.m
D)10.22 a.m
E)10.25 a.m
Rationale: Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Answer: E
Answer: E
Question: A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
Options:
A)10 sec
B)8 sec
C)6 sec
D)4 sec
E)2 sec
Rationale: Explanation:
Distance = 110 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 110/(110/6) = 6 s
Answer: Option C
Answer: C
Question: Henry solved a certain number of algebra problems in an hour, his older brother Frank solved
four times as many. Together they solved 80. How many were solved by each?
Options:
A)H-12 F-49
B)H-30 F-83
C)H-20 F-90
D)H-16 F-64
E)H-40 F-100
Rationale: I am looking for the number of problems solved by Henry (H) and Frank (F).
Who solved the least number of problems? Hopefully, you said Henry.
So let H = x
Frank solved four times as many, therefore
F = 4x
Read the problem again to find a relationship. Together they solved 80. That means that
H + F = 80 Substituting
x + 4x = 80 Solving for x
5x = 80
x = 16
Therefore Henry solved 16 and Frank solved 4 times 16 of 64 problems.
correct answer D
Answer: D
Question: A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
Options:
A)981
B)1000
C)1011
D)1101
E)1110
Rationale: The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3
The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.=1000
Answer: B.
Answer: B
Question: Jonathan’s grandparents lend $30,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
Options:
A)30,000∗0.1^5
B)30,000∗0.5
C)30,000∗1.5
D)30,000∗1.1^5
E)(30,000∗0.1)^5
Rationale: if you are like me and have used S.I = P x R x T formula in school, while the question is asking for Amount in 5 years. so (c) 30,000∗ 1.5
Ans : C
Answer: C
Question: The sum e of prime numbers that are greater than 60 but less than 70 is
Options:
A) 67
B) 128
C) 191
D) 197
E) 260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum e of 61 and 67 is 128.
Answer B.
Answer: B
Question: If a = 1 and b = -2, then (2a^2 + b)(w + y) + (a + b)(w - y) =
Options:
A)0
B)2x
C)y - w
D)x - y
E)x + y
Rationale: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(w+y)=y-w => Smash C
Answer: C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)11
B)72
C)36
D)99
E)27
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240)/12 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72 km/hr.
Answer: B
Answer: B
Question: What is the largest possible value of cc if 5c+(d−12)^2=235?
Options:
A)17
B)25
C)35
D)42
E)47
Rationale: To maximize c, we should minimize (d-12)^2. (d-12)^2 is a square of a number, thus its smallest possible value is 0 (for d = 12).
In this case we'd have 5c + 0 = 235 --> c = 47.
Answer: E.
Answer: E
Question: The value of (34.31*0.5*1.567)/(0.0673*23.25*7.57) is close to
Options:
A)2
B)1.15
C)2.05
D)2.27
E)2.35
Rationale: (34.31*0.5*1.567)/(0.0673*23.25*7.57) = 26.882/11.845
= 2.27
ANSWER:D
Answer: D
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 8 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
Options:
A)25
B)35
C)75
D)80
E)90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 8 = 76
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 76 + 4 = 80
D
Answer: D
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey?
Options:
A)3.00kmph
B)2.50kmph
C)3.50kmph
D)3.11kmph
E)3.90kmph
Rationale: M = 4.5
S = 2.5
DS = 7
US = 2
AS = (2 * 7 * 2) /9 = 3.11
Answer:D
Answer: D
Question: If a^2bc^2 = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. a^2c^2 = 1
Options:
A)I
B)II
C)III
D)none
E)I&II
Rationale: D
Answer: D
Question: In a ratio which is equal to 4:6, if the antecedent is 30, then the consequent is?
Options:
A)72
B)85
C)64
D)51
E)45
Rationale: We have 4/6 = 30/x
4x = 30*6
x = 45
consequent = 45
Answer is E
Answer: E
Question: How many days will there be from 25th January,1996 to 15th May,1996(both days included)?
Options:
A)112
B)103
C)111
D)120
E)121
Rationale: Explanation:
Number of days from 25-Jan-1996 to 15-May-1996 (both days included)
= 7(Jan) + 29(Feb) + 31 (Mar) + 30(Apr)+ 15(May) = 112
Answer: Option A
Answer: A
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 4 years?
Options:
A)x (1+n/100)^5 - x
B)x (1+n/100)^4 - x
C)3x (1+n/100)^4 - x
D)x (1+n/100)^6 - x
E)2x (1+n/100)^4 - x
Rationale: Amount after 4 years compounded yearly = x (1+n/100)^4
Thus profit = Final amount - original principle = x (1+n/100)^4 - x . Answer : B
Answer: B
Question: The ratio of 2 numbers is 2:5 and their H.C.F. is 6. Their L.C.M. is ?
Options:
A)20
B)24
C)52
D)36
E)60
Rationale: Let the numbers be 2x and 5x
Their H.C.F. = 6
so the numbers are 2*6 , 5*6 = 12,30
L.C.M. = 60
Answer is E
Answer: E
Question: If “GREEN” is given number code as 49, what is the difference between the number codes of “VIOLET” and “PINK” ?
Options:
A)33
B)76
C)29
D)10
E)17
Rationale: Explanation:
Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
GREEN = 7 + 18 + 5 + 5 + 14 = 49
Thus we get,
VIOLET = 22 +9 +15+12 + 5 + 20 = 83
PINK = 16 + 9 + 14 + 11 = 50
Thus, difference is 83 – 50 = 33.
ANSWER: A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
Options:
A)150
B)278
C)100
D)776
E)191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter
Answer:C
Answer: C
Question: Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?
Options:
A)5(5/7) days
B)6(5/7) days
C)7(5/7) days
D)5(4/7) days
E)3(5/7) days
Rationale: ram completes 60% of work in 15 days
so ram 1 day work is 60% / 15= 4%
rahim is 50%efficient than ram
so rahim 1 day work is 2%
rachel is 50% efficient than rahim
so rachil 1day work is 1%
total work done by ram rahim and rachel in 1 day is 4%+2%+1%= 7%
7%----- 1 day
40%---------?
40/7
so 5.7=6 days needed to complete the 40%of work
ANSWER:A
Answer: A
Question: Two numbers are in ratio 7:11. If 7 is added to each of the numbers, the ratio becomes 2:3. The smaller number is
Options:
A)39
B)49
C)66
D)77
E)None
Rationale: Solution: Let the numbers be 7x and 11x.
According to question,
(7x+7)/(11x+7) = 2/3;
Or, 22x+14 = 21x+21;
Or, x = 7;
Smaller number = 49.
Answer: Option B
Answer: B
Question: At what rate percent on simple interest will a sum of money double itself in 20 years?
Options:
A)2%
B)6%
C)3%
D)4%
E)5%
Rationale: P = (P*20*R)/100
R = 5%
ANSWER:E
Answer: E
Question: 6x – 5y + 3z = 22
4x + 8y – 11z = 7
5x – 6y + 2z = 12
Given the equations above, x + y + z = ?
Options:
A) 10
B) 12
C) 13
D) 14
E) 15
Rationale: (6x – 5y + 3z) - (5x – 6y + 2z ) = 22-12
or, x+y+z = 10
Option A is the ans
Answer: A
Question: If the two hands in a clock are 8 minutes divisions apart,then the angle between them is
Options:
A)3Â°
B)18Â°
C)24Â°
D)60Â°
E)None of these
Rationale: In a clock, each minute makes 6Â°
âˆ´ 8 minutes will make 6 Ã— 8 = 24Â°
Answer C
Answer: C
Question: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance e before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
Options:
A)25%
B)50%
C)75%
D)100%
E)200%
Rationale: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance e before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.
If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.
ANSWER: A) 25%
Answer: A
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2430 ?
Options:
A)s. 832
B)s. 830
C)s. 822
D)s. 812
E)s. 810
Rationale: Let the total amount in the partnership be 'x'.
Then A's share = x/3
B's share = x/4
C's share = x/5
D's share = x - (x/3 + x/4 +x/5) = 13x/60
A : B : C : D = x/3 : x/4 : x/5 : 13x/60 = 20 : 15 : 12 : 13
A's share in the profit of Rs. 2430 = 20 (2430/60) = Rs. 810.
Answer: E
Answer: E
Question: Josh spends a total of $5.5 buying Q items in the convenience store. If each of the items is either a 5 cents single bubblegum, or a 50 cents bubblegum pack, then Q may be which of the following?
Options:
A)99
B)100
C)101
D)112
E)113
Rationale: Q items in the convenience store $5.5 = 550 cents
550 = 50a + 5b
=>110 = 10a + b
b = 110 - 10a = 10(11-a)
Hence b is even and multiple of 10.
Possible values of b:
b = 10,20,30,40,50,60,70,80,90,100
a = 11,9,8,7,6,5,4,3,2,1
The total (a+b) is 21,29,38,47,56,65,74,83,92,101
The only option is 101. Hence C.
Answer: C
Question: A can do a piece of work in 5 hours. B and C together can do it in 4 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
Options:
A)8hr
B)6hr
C)9hr
D)10hr
E)12hr
Rationale: A's 1 hour work = 1/5
B+C 1 hour work = 1/4
A+C 1 hour work = 1/3
A+B+C 1 hour work = 1/5 + 1/4 = 9/20
B's 1 hour work = 9/20 - 1/3 = 7/60 = 9hr (approximately)
B alone will take 9 hours approximately to do the work
Answer is C
Answer: C
Question: If a and b are the roots of the equation x2 - 4x + 4 = 0, then the value of a2 + b2 is:
Options:
A)36
B)24
C)17
D)8
E)5
Rationale: Sol.(b) The sum of roots = a+ b = 4
Product of roots = ab = 4
Now, a2 + b2 = (a + b)2 - 2ab = 16 - 8 = 8
Answer D
Answer: D
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.13600 after a year?
Options:
A)3630
B)9232
C)8828
D)2387
E)4080
Rationale: 6300:4200:10500
3:2:5
3/10 * 13600 = 4080
Answer: E
Answer: E
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 50 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
Options:
A)93%
B)96%
C)100%
D)107%
E)120%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.1 = 33
B = 20*1.5*1.1 = 33
C = 20*1.5*0.4 = 12
D = 20*0.6*1.50 = 18
E = 0
Total 33 + 33 + 12 + 18 = 96.
Answer: B.
Answer: B
Question: The sum of two consecutive integers is 15. Find the numbers.
Options:
A)17, 18
B)7, 8
C)5, 6
D)1, 2
E)8, 9
Rationale: n + (n + 1) = 15
2n + 1 = 15
2n = 14
n = 7
Answer: B
Answer: B
Question: A car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for the rest of the trip. If the average speed for the entire trip is 34 miles per hour, how many hours long is the trip?
Options:
A)6.5
B)7.5
C)8.5
D)9.5
E)10.5
Rationale: Let T be the total time of the trip.
30*5 + 42(T-5) = 34T
8T = 210-150
T = 7.5
The answer is B.
Answer: B
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 2/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
Options:
A)2/35
B)2/3
C)7/35
D)5/7
E)7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 2/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 2/7 x 1/5 = 2/35
ANSWER:A
Answer: A
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
Options:
A)8877
B)3000
C)7787
D)1799
E)1711
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B
Answer: B
Question: A cistern 8 m long and 6 m wide contains water up to a breadth of 1 m 85 cm. Find the total area of the wet surface.
Options:
A)102 m sqaure
B)100 m sqaure
C)152 m sqaure
D)164 m sqaure
E)None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(6*1.85+8*1.85)]+8*6 = 100 m square
Option B
Answer: B
Question: Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown paint and no yellow.
The paint will be namedBrun Xif the paint contains 3 jars of brown paint.
The paint will be namedJaune Xif the paint contains at least 2 jars of yellow.
The paint will be namedJaune Yif the paint contains exactly 1 jar of yellow.
What is the probability W that the new color will be one of theJaunecolors?
Options:
A)5/42
B)37/42
C)1/21
D)4/9
E)5/9
Rationale: I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune W= (40 + 34)/84 = 37/42
Answer: B
Question: Three years ago the average of A and B was 18 Years. With C joining them now, the average becomes 22 years. How old is C now?
Options:
A)24 years
B)27 years
C)28 years
D)30 years
E)32 years
Rationale: (a+b)/2=18
(a+3+b+3+c)/3=22
(3+3+36+c)/3=22
c=24
ANSWER:A
Answer: A
Question: If a Half kg of potato costs 40 paise, how many paise does 400 gm cost?
Options:
A)84 paise
B)44 paise
C)28 paise
D)16 paise
E)18 paise
Rationale: Cost of 1/2 kg potato = 40 Paise
=> Cost of 500 gm potato = 40 Paise
=> Cost of 200 gm potato = (40*200)/500=80/5=16 Paise
ANSWER:D
Answer: D
Question: In what time will a train 100 meters long cross an electric pole, if its speed is 144 km/hr
Options:
A)8.5 seconds
B)2.8 seconds
C)3.5 seconds
D)2.5 seconds
E)2.6 seconds
Rationale: First convert speed into m/sec
Speed = 144*(5/18) = 40 m/sec
Time = Distance/speed
= 100/40 = 2.5 seconds
Answer: D
Answer: D
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Options:
A)Rs.250
B)Rs.256
C)Rs.252
D)Rs.258
E)Rs.253
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? =>
Rs.250
Answer:A
Answer: A
Question: Two stations A and B are 110 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) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: Option B
Answer: B