RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
A.2300
B.600
C.250
D.300
Answer: D.300
Explanation: 1st line - 0 points
2nd line - new 1 point
3td line - new 2 points + old 1 point
4th line - new 3 points + old 2+1 points
5th line - new 4 points + old 3+2+1 points
n-th line - (n-1) points + (n-2) .... 3+2+1
therefore, S=1+2+3...(n-1)
S=(n-1)n/2=24*25/2=300
ANS;D
Question: john bakes 6 cakes for 6 friends. 3 of the friend arrive early and eat 3 cakes each. How many cakes are left over if the other friends all have the same number of cakes?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: john made 6*6 cakes = 36 cakes. 3 friends eat 3 cakes, leaving 27 remaining for 3 friends.
2+7=9, divisible by 3.
27 is divisible by 3. The 3 friends ate a cumulative number of cakes that must be divisible by 3, because the number is the same.
27-27=0
A is the correct answer
Question: Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
A.20%
B.30%
C.40%
D.50%
Answer: B.30%
Explanation: 4C1/(6C3/2)
6C3 = 6!/3!3! = 20 sub committees
Michael will be included in 1/2 or 10 of these
If Michael and Anthony are in a 3 person committee together there is only one spot left and 4 people left to fill it.
4C1 = 4!/3! = 4
4/10 = 40%
Ans:B
Question: The length of the bridge, which a train 170 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
A.876 m
B.157 m
C.205 m
D.156 m
Answer: C.205 m
Explanation: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (170 + x)/30 = 25/2
=> 2(170 + x) = 750 => x
= 205 m.
Answer: C
Question: A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
A.69.5 km/hr
B.70 km/hr
C.79 km/hr
D.79.2 km/hr
Answer: D.79.2 km/hr
Explanation: Let the length of the train is x
x/8=x+264/20
on solving this we get x=176 m
Speed of the train=176/8=22m/sec
22*18/5=396/5=79.2 Kmph
ANSWER:D
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.2:5
B.2:7
C.2:1
D.1:7
Answer: A.2:5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 7), (x, 7)?
A.64
B.121
C.169
D.225
Answer: C.169
Explanation: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 13.
The area is 13*13 = 169.
The answer is C.
Question: If a is 50% greater than b, then a is what % less than b?
A.33.33%
B.50%
C.66.78%
D.70.6%
Answer: A.33.33%
Explanation: if b=150 a=100
150-100=50
75 is 50% of b.
50 is little less than 75 so answer is 33.33%
Answer is A
Question: A batsman in his 12th innings makes a score of 55 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’?
A.42
B.43
C.44
D.45
Answer: C.44
Explanation: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 1) + 55
∴ x = 44
Answer C
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
A.480
B.266
C.287
D.1661
Answer: A.480
Explanation: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
Question: The smallest number which when diminished by 4, is divisible by 12, 16, 18, 21 and 28 is
A.1008
B.1012
C.1022
D.1032
Answer: B.1012
Explanation: Required Number = (L.C.M of 12, 16, 18,21,28)+4
= 1008 + 4
= 1012
Answer: B
Question: A stockiest wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit?
i.	Sell sugar at 10% profit.
ii.	Use 900 g of weight instead of 1 kg.
iii.	Mix 10% impurities in sugar and selling sugar at cost price.
iv.	Increase the price by 5% and reduced weights by 5%.
A.i or ii
B.ii
C.ii, ii and iv
D.Profits are same
Answer: B.ii
Explanation: Solution: Let the CP of 1 kg of sugar be Rs. 100.
Then, CP of 900g sugar = (100*900)/1000 = Rs. 90
Hence, profit % = [(100-90)/90]*100 = 11.11%.
If he add 10% impurity then his CP for 1 kg = (100*1000)/1100 = Rs. 90.9;
And % profit = [(100-90.9)/90.9]*100 = 10.01%
If he reduces weight by 5 % Then, cost price of 950 g = (100*950)/1000 = Rs 95 and SP = 105;
% profit = [(105-95)/95]*100 = 10.25 %.
Answer: Option B
Question: IF IN A AP SERIES 18TH TERM IS 29 & 29TH TERM IS 18. THEN FIND THE 49TH TERM??
A.0
B.-1
C.-2
D.1
Answer: C.-2
Explanation: 18th term = a + 17d..........(i)
29th term = a + 28d..........(ii)
Solving equation i and ii, we got
d = -1
put d = -1 in any of the above equations and we will get, a = 46
Now, we know 49th term can be written as, a + 48d
now putting the value of a and d in the above equation,
a + 48d = 46 + 48(-1)
= 46 - 48
= -2
ANSWER:C
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 11th and the 20th terms?
A.324
B.335
C.346
D.357
Answer: B.335
Explanation: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 11th term is 11 × 11 – 3 = 118
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 335.
The correct answer is choice (B).
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
A.11
B.10
C.18
D.16
Answer: B.10
Explanation: 7*5: 5*x = 7:10
x = 10
Answer:B
Question: If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
A.7
B.6
C.5
D.4
Answer: A.7
Explanation: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:7
Webs 7:1
1 x 7 x x = 7 x 1 x 7
=> x= 7
Answer is 7
Question: ratio of girl and boys in class is 5:6.if 20 girl leave the class and ratio become 2:3.calculate the no. of boys?
A.100
B.120
C.80
D.90
Answer: B.120
Explanation: girl 5x and boys 6x
5x-20/6x=2/3,15x-60=12x,3x=60,x=20
boys=6x=120
answer B
Question: 1704 x 1704 = ?
A.A)3623216
B.B)2903616
C.C)3624316
D.D)3625116
Answer: B.B)2903616
Explanation: 1704 x 1704 = (1704)2
= (1700 + 4)2
= (1700)2 + (4)2 + (2 x 1700 x 4)
= 2890000 + 16 + 13600.
= 2903616.
B)
Question: Consider the set N = {2, 3, 4, ..., 2n + 1}, where n is a positive integer larger than 10005. If O is the average of the odd integers in N and E is the average of the even integers in N then what is the value of O –E?
A.2
B.1
C.8
D.9
Answer: C.8
Explanation: No need to solve this question. Simply take n = 5. So N = {2, 3, 4, 5, ......11}
Now average of add integers = (3 + 5 + ........11)/5 = 7.
Average of Even integers = (2 + 4 + .....10) / 5 = 6
O - E = 1
Answer:C
Question: A dealer buys dry fruits at the rate of ` 100, ` 80 and ` 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain or no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity?
A.30%
B.40%
C.20%
D.50%
Answer: B.40%
Explanation: Total quantity rate =
(12 * 100 + 15 * 80 + 20 * 60) = 3600
For first 2 qtys, (12 * 100) + (15 * 80) = 2400
But he gets 20% profit = 2400 * 1.2 = 2880
So the third quantity = 3600 – 2880 = 720
Actual third quantity rate = 20  60 = 1200
Loss suffered = (1200 - 720) / 1200
= 480/1200 = 40 %
Answer: B
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 2,450. What was Simran share in the profit?
A.s 9500
B.s 1000
C.s 1,050
D.s 1,100
Answer: C.s 1,050
Explanation: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.2450 x	3/7	= Rs. 1,050.
ANSWER :C
Question: If a, f, and c are consecutive even integers and a < f < c, all of the following must be divisible by 4 EXCEPT
A.a + c
B.f + c
C.ac
D.(bc)/2
Answer: B.f + c
Explanation: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - f + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Question: If 6^t is a factor of (10!)^2, What is the greatest possible value of t ?
A.2
B.4
C.6
D.8
Answer: D.8
Explanation: t 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Question: The successive discounts 20% and 15% are equal to a single discount of?
A.15
B.58
C.32
D.27
Answer: C.32
Explanation: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Answer: C
Question: What is the smallest positive integer x, such that 6000x is a perfect cube?
A.4
B.6
C.36
D.12
Answer: C.36
Explanation: Take out the factors of 6000 that will come 2*3*10^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2
C is the answer.
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?
A.0.5908
B.0.5904
C.0.5906
D.0.5904
Answer: B.0.5904
Explanation: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Question: If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 25000 sheets of xerox paper?
A.$1250
B.$1060
C.$1350
D.$900
Answer: B.$1060
Explanation: For first 2000 pages - cost 5 cents/paper
For 2001 - 10000 - cost 4.5 cents/paper
For 10000+ - 4 cents/paper
So Cost = (5 cents * 2000 ) + (4.5 cents * 8000 ) + (4 cents * 15000) = $1060
alternatively, (0.05 x 2000)+(0.045x8000)+(0.04x 15000) = 1,060
ANSWER:B
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 500 nuts and 500 bolts?
A.250 seconds
B.500 seconds
C.750 seconds
D.2,000 seconds
Answer: C.750 seconds
Explanation: To minimize the amount of time, we should make both machines work all the time while producing 500 nuts and 500 bolts.
Two machines to produce 500 bolts will need (500*1)/2 = 250 seconds.
Two machines to produce 500 nuts will need (500*2)/2 = 500 seconds.
Total = 250+500=750.
Answer: C
Question: Two trains, traveling towards each other, left from two stations that are 900 miles apart, at 4 pm. If the rate of the first train is 72 mph and the rate of the second train is 78 mph, at whatt time will they pass each other?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: After t hours, the two trains will have traveled distances D1 and D2 (in miles) given by
D1 = 72 t and D2 = 78 t
After t hours total distance D traveled by the two trains is given by
D = D1 + D2 = 72 t + 78 t = 150 t
When distance D is equal to 900 miles, the two trains pass each other.
150 t = 900
t = 6 hours.
Answer:C
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
A.3377
B.268
C.1200
D.2877
Answer: C.1200
Explanation: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer: C
Question: Find the compound interest on $ 66,000 at 20% per annum for 9 months, compounded quarterly
A.2532.12
B.2552.2
C.9524.32
D.10403.25
Answer: D.10403.25
Explanation: Principal = $ 66000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [66000 x (1+(5/100))^3] = $ 76403.25
CI. = $ (76403.25 - 66000) = $ 10403.25
Answer D.
Question: 10 t-shirts are available to choose. 5 of them are printed, and 5 of them are plain t-shirts. If 3 t-shirts are to be selected at random from the 10, what is the probability that at least one of them is a printed t-shirt.
A.1/12
B.7/12
C.5/12
D.11/12
Answer: D.11/12
Explanation: You have 10 t-shirts. You need to choose 3 of them. You can do this in 10C3 = 10*9*8/3*2*1 = 120 ways.
You have 5 plain t-shirts. You can choose 3 out of them in 5C3 = 5*4/2 = 10 ways.
So you have total 120 ways of picking 3 t-shirts out of 10. In 10 of those ways, you pick all plain t-shirts. So what happens in the rest of the 110 ways? In those, you must be picking up at least one printed t-shirt.
So probability of picking at least one printed t-shirt = 110/120 = 11/12
Answer is D
Question: All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 152 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
A.1216
B.1723
C.1129
D.2613
Answer: A.1216
Explanation: A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 152 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 152 = 3k + 152 => 2k = 304 => k = 152
The initial quantity of milk in A = 8k = 8 * 152 = 1216 liters.
Question: A walks at 10 kmph and 4 hours after his start, B cycles after him at 20 kmph. How far from the start does B catch up with A?
A.100km
B.150km
C.80km
D.120km
Answer: C.80km
Explanation: Suppose after x km from the start B catches up with A. Then, the difference in the time taken by A to cover x km and that taken by B to cover x km is 4 hours.
x/10 - x/20 = 4
x = 80 km
Answer is C
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Thursday at 11 AM, what will be the time at the end of 10 days?
A.11:54:24 AM
B.11:56:24 AM
C.12:16:40 PM
D.11:54:40 AM
Answer: A.11:54:24 AM
Explanation: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 32 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;
Net gain in 10 days = 86.40 - 32 = 54.4 minutes.
11AM + 54.4 minutes = 11:54 and 4/10th of a minute or 24 seconds.
Answer: A
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40
B.56
C.41
D.42
Answer: A.40
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: Option A
Question: If the average marks of three batches of 40, 50 and 60 students respectively is 45, 55, 65, what is the average marks of all the students?
A.56.33
B.34.89
C.23.67
D.54.65
Answer: A.56.33
Explanation: Average marks of batch1 = 45
Students in batch1 = 40
Total marks of batch1 = 40*45
Average marks of batch2 = 55
Students in batch2 = 50
Total marks of batch2 = 50 × 55
Average marks of batch3 = 65
Students in batch3 = 60
Total marks of batch3 = 65 × 60
Total students = 40 + 60 + 50 = 150
Average marks of all the students
=((40*45)+(50×55)+(65×60))/150
=169/3
=56.333
Answer is A.
Question: a, b are positive integers. The remainder of a to be divided by 5 is 2 and the remainder of b to be divided by 7 is 3.
Which is possible to be the remainder of a*b to be divided by 48
A.a) 2
B.b) 6
C.c) 8
D.d) 12
Answer: B.b) 6
Explanation: Two ways to do it...
a=5x+2..
b=7y+3..
1) convenient way..
Take x and y as 0, and you will get a*b as 2*3=6
Answer : B
Question: What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 40 seconds?
A.308
B.320
C.332
D.344
Answer: D.344
Explanation: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 40 seconds, the train can travel 25/2 * 40 = 500 meters
500 = length of train + length of bridge
length of bridge = 500 - 156 = 344 meters
The answer is D.
Question: 10 groups have applied for funding from the rec board. After dividing the budget equally among the 10, the rec board finds that there are 4 dollars left over, as funding allocations must be in whole numbers of dollars.
The next semester, the rec board has 4 times as much money to allocate to the 10 groups. How much money will be left over this semester?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: We can put m=10*k+4.
So 4*m=40*k+16 ---> 40*k+16 = 10*(4*m+1) +6 ---> The remainder is 6.
The answer is, therefore, (C).
Question: Sum of the squares of three numbers is 467 and the sum of their products taken two at a time is 131. Find the sum?
A.20
B.27
C.25
D.27
Answer: B.27
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 467 + 2* 131
a + b + c = √729 = 27
B
Question: A train 140 m long is running at 60 kmph. In how much time wiU it pass a platform 260 m long?
A.21sec
B.22sec
C.23sec
D.24sec
Answer: D.24sec
Explanation: s=d/t
d=140+260=400m
s=60*5/18 m/sec=50/3 m/sec
t=400/(50/3)=1200/50=24sec
ANSWER:D
Question: Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 6 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
A.8 mph
B.5.25 mph
C.3.5 mph
D.4 mph
Answer: C.3.5 mph
Explanation: (1 mph +6 mph)/2 = 3.5 mph
Correct option is: C
Question: A charity is raising Â£1000 for disabled children. If it spends Â£20 for every Â£100 raised, how much money do they need to raise to reach the goal?
A.A - 1200
B.A - 1200
C.A - 1200
D.D - 12
Answer: C.A - 1200
Explanation: His overall steps are +6
take 100 - 6
take 94/6 to lowest divisible number - 90/6
This means that it will take 15 "overall" actions to reach the 90th centimeter. -15*18 steps added later
Set steps at 90. walk 10 steps. fall off - add 10 to total
15*18 + 10 = 280 steps in total
Double checking, 6*15 = 90, meaning that it took 15 forwards and backwards to reach.
It is dangerous to oversimplify so take context. For each average steps, adding 12 each time will ensure that it is a valid process that will not resulting in falling off the meter stick. At 15 overall, he falls off. but at 14, 6*14 = 84, adding 12 we get 96 which does not result in him falling off. It is completely safe to say 15 overall steps do not result in falling off.
From there, take 10 steps an on the 11th, not counted, he falls off since he was at 90.
All that's left is to count the total steps.
each overall step has 18 steps, 12 forward and 6 backward
18*15 = 270
then add the final steps 270 +10 = 280
Answer: C
Question: There are three persons A, B and C when the age of A is added to half of the age of B, the result is equal to C's age. One-third of the age of 'B' is equal to one-fourth of the age of 'C'. If one-fifth of A's age is added to half of B's age, the result is equal to half of C's age. Then what is the age of 'B' ?
A.16 yrs
B.20 yrs
C.24 yrs
D.30 yrs
Answer: C.24 yrs
Explanation: Explanation :
A + B/2 = C .......(i)
B/3 = C/4 ........(ii)
A/5 + B/2 = C/2 ........(iii)
Solving these three eqns, A = 20, B = 24 and C = 32
Answer : Option C
Question: On average, activated yeast cells divide once every 120 minutes; that is, each individual cell divides into two individual cells over that time span. Given that a certain yeast colony consisted of 310,000 cells two hours ago, approximately how many cells will be populating the colony eight hours from now?
A.4,960,000
B.6,860,000
C.9,920,000
D.11,720,000
Answer: C.9,920,000
Explanation: 310,000 × 2 × 2×2×2×2 = 310,000 × 32 = C
Question: A train covered a distance at a uniform speed .if the train had been 6 km/hr faster it would have been 4 hour less than schedule time and if the train were slower by 6 km/hr it would have been 6 hrs more.find the distance.
A.720 km
B.820 km
C.920 km
D.620 km
Answer: A.720 km
Explanation: Let t be the usual time taken by the train to cover the distance
Let d be the distance, s be the usual speed
Usual time taken => d/s = t => d=ts
d/(s+6) = t-4
ts/(s+6) = t-4
ts = ts+6t-4s-24
6t - 4s - 24 = 0 --> (1)
d/(s-6) = t+6
ts = ts-6t+6s-36
-6t + 6s - 36=0 --->(2)
Solving (1) nd (2), v get
s = 30 km/h
t = 24 hrs
d = t * s
d = 30 * 24 = 720 km
ANSWER:A
Question: The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 5 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?
A.25 km
B.30 km
C.40 km
D.50 km
Answer: A.25 km
Explanation: Number of stops in an hour: 60/5 = 12
Distance between stops: 60/12 = 5 km
Distance between Yahya's house and Pinedale Mall: 5 x 5 = 25 km
IMO, correct answer is "A."
Question: Three table runners have a combined area of 220 square inches. By overlapping the runners to cover 80% of a table of area 175 square inches, the area that is covered by exactly two layers of runner is 24 square inches. What is the area of the table that is covered with three layers of runner?
A. 18 square inches
B. 20 square inches
C. 24 square inches
D. 28 square inches
Answer: D. 28 square inches
Explanation: Total = a + b + c - (sum of EXACTLY 2-group overlaps) - 2*(all three) + Neither
80%*175 = 220 - 24 - 2*(all three) + 0
2*(all three) = 220 - 24 - 140
all three = 28
Answer: D
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 4 years older than B the present age of B is
A.37
B.38
C.39
D.34
Answer: D.34
Explanation: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+4
=>2b-b-4 = 30
b=34
so the present age of b is 34 years
ANSWER:D
Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :
A.45
B.46
C.47
D.48
Answer: A.45
Explanation: Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg. Answer : A