divelab/Sys2Bench huggingface dataset:
Question: In covering a distance of 40 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Options:
A)5 km/h
B)6.7 km/h
C)10 km/h
D)15 km/h
E)20 km/h
Rationale: Let A's speed be X km/hr.
Then, 40/x - 40/2x = 3
20/x = 3
x = 6.7 km/hr.
Answer : B
Answer: B
Question: A car travelling with 5/7 km of its actual speed covers 42km in 1hr 40 min 48 sec find the actual speed of the car?
Options:
A)78kmph
B)85kmph
C)35kmph
D)24kmph
E)74kmph
Rationale: time taken =1hr 40 min 48 sec=126/75hrs
let the actual speed be x kmph
then 5/7 x*126/75=42
x=(42*7*75)/5*126=35kmph
Answer (C)
Answer: C
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 68?
Options:
A)68
B)69
C)138
D)68^2
E)68·69
Rationale: In order to get the lowest LCM, we have to take the first number as 69 and the next number as its multiple.
So, I can take 69 and 138 as two distinct numbers, such that Lowest LCM = 138.
Answer should be C.
Answer: C
Question: Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys? (Assume that the probability of having a boy is the same as the probability of having a girl.
Options:
A)1/4
B)3/8
C)5/11
D)1/2
E)6/11
Rationale: Assume that there are 4 Ms. Barton's children in a row: 1-2-3-4. Let show all possible combinations of them being girl(G) or boy(B) giving that there at least two girls. We are seeing each child 1,2,3,4 a s a unique(so, we distinguish between them)
BBGG
BGBG
GBBG
BGGB
GBGB
GGBB
BGGG
GBGG
GGBG
GGGB
GGGG
Overall 11 variants. 6 of them satisfy the condition of 2 boys exactly (they are highlighted in bold)
Therefore the probability is 6/11
Answer:E
Answer: E
Question: What was the principal , if at 12% per annum the interest after 3 years amounted to Rs.5888 less than the sum lent?
Options:
A)9000
B)3000
C)5000
D)1300
E)9200
Rationale: P - 2336 = (P*12*3)/100
P = 9200
Answer: E
Answer: E
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.4. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
Options:
A)(0.4)^5
B)2(0.4)^4
C)3(0.4)^4
D)4(0.4)^4(0.6) + (0.4)^5
E)5(0.4)^4(0.6) + (0.4)^5
Rationale: P(5 heads) = (0.4)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.4)^4(0.6)
The answer is E.
Answer: E
Question: For each color copy, Print Shop X charges $1.25 and Print Shop Y charges $2.75. How much greater is the charge for 60 color copies at Print Shop Y than at Print Shop X?
Options:
A)$80
B)$90
C)$100
D)$110
E)$120
Rationale: The difference in the two prices is $2.75 - $1.25 = $1.50 for each color copy.
Each color copy will cost an extra $1.50 at Print Shop Y.
60*$1.50 = $90
The answer is B.
Answer: B
Question: A box contains 3 white balls, 2 black balls and 6 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw?
Options:
A)52
B)69
C)73
D)47
E)81
Rationale: We may have (1 black and 2 non black) or (2 black and 1 non black)
Required number of ways = 2C1*9C2+1*9C1 = 81
Answer is E
Answer: E
Question: Calculate the circumference of a circular field whose radius is 8 centimeters.
Options:
A)18 π cm
B)1 π cm
C)8 π cm
D)19 π cm
E)28 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*9 = 18 π cm
Answer: A
Answer: A
Question: A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the president?
Options:
A) 1/720
B) 1/5
C) 1/10
D) 1/9
E) 1/6
Rationale: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the president is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the president is 1/10+1/10=2/10.
Answer: B
Answer: B
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of Qis?
Options:
A)A)Rs.4078
B)B)Rs.6100
C)C)Rs.4029
D)D)Rs.4027
E)E)Rs.4020
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv)
Subtracting (iii) from (iv), we get, P = 6100.
P's monthly income = Rs.6100.
Answer: B
Answer: B
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 32 kmph. Of how many minutes does the train stop per hour?
Options:
A)E982
B)27
C)17.3
D)121
E)28
Rationale: Explanation:
T = 13/45 * 60 = 17.3
Answer: Option C
Answer: C
Question: The sum of five numbers is 400. The average of the first two numbers is 50 and the third number is 60. Find the average of the two numbers?
Options:
A)70
B)65
C)85
D)80
E)90
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 400
(P + Q)/2 = 50 and R = 60
P + Q = 100 and R = 60
P + Q + R = 160
S + T = 400 - (P + Q + R) = 240
Average of the last two numbers
= (S + T)/2 = 80
Answer:D
Answer: D
Question: A man buys a cycle for Rs. 2300 and sells it at a loss of 30%. What is the selling price of the cycle?
Options:
A)s. 1690
B)s. 1610
C)s. 1890
D)s. 1602
E)s. 1092
Rationale: S.P. = 70% of Rs. 2300 = Rs.	70	x 2300/100 = Rs. 1610
Answer: Option B
Answer: B
Question: How many 7 in between 1 to 120?
Options:
A)18
B)20
C)22
D)23
E)24
Rationale: 7,17,27,37,47,57,67,
70,71,72,73,74,75,76,77(two 7's),78,79,87,97,107,117
22 7's between 1 to 120
ANSWER:C
Answer: C
Question: If log X/2=log Y/3 = log Z/5, then YZ in terms of X is
Options:
A)X
B)X2
C)X3
D)X4
E)None of these
Rationale: logX/2 = logY/3= logZ/5 = K(say).
=> logX = 2k, logY = 3k, log Z =5K
=> logYZ = 3K + 5K = 8k; logX4 = 8K
Thus, logYZ = logX4
=>YZ = X4
ANSWER:D
Answer: D
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)22
B)24
C)44
D)48
E)52
Rationale: In 12 hr's the hands of the clk will be right angle for 22 times..
as in 1 hr time the hands of the clk will be right angle fot 2 times.
but in (11'o clk - 1'o clk) time it will right angle only twice(2).
so for 12 hrs time 22 times it will be right angle.
for 24 hrs time 44 times it will be right angle..
ANSWER:C
Answer: C
Question: A cask full of milk,'E' liters is removed and water is mixed. This process is repeated and now the ratio in milk to water is 16:9. Then what is the amount of milk in liter.
Options:
A)E+9
B)9E
C)5E
D)8E
E)cant be determined
Rationale: After 'n' operations ,the amount of pure liquid remaining is = [x { ( 1-E/x )^n } ]...where x is original amount of liquid and E is amount of liquid removed..This is standard formula in RS aggarwal...
Now ,in our case the operations is performed twice...
Let the original milk be x liters..
E liters removed twice n = 2,
milk remaining (M) = [ x { (1-E/x)^2 } ]....water is (W) = x - [x { (1-E/x)^2 } ]
M/W = 16/9 Take (1-E/x)^2 = z
now solving we get z = 16/25 that is (1 - E/x)^2 = (4/5)^2
1 - E/x = 4/5
x = 5E
ANSWER:C
Answer: C
Question: The value of log 5 (1/125) is:
Options:
A)3
B)-3
C)1/3
D)-1/3
E)none of these
Rationale: log5(1/125)
=log5(1/5)^3
=3log5(1/5)
=3(log5 1 - log5 5)
=3(0-1)
=-3
ANSWER:B
Answer: B
Question: Find the one which does not belong to that group?
Options:
A)16
B)36
C)27
D)64
E)4
Rationale: Explanation:
16, 36, 64 and 4 are perfect squares but not 27.
Answer:C
Answer: C
Question: 4,25,49,121
Options:
A)149
B)169
C)189
D)209
E)219
Rationale: 13^2= 169 because follow sequence of square of the prime numbers
ANSWER:B
Answer: B
Question: Amy has two decks of 56 cards each: Deck 1 and Deck 2. She takes 8 black cards from Deck 2 and adds them to Deck 1 and shuffles it thoroughly. She now picks a card from the newly formed pack of cards. If the probability of either picking a red ace or a king from the newly formed pack is greater than 1/8, what is the probability that Amy picks a black king or a red Jack from the new pack?
Options:
A)1/6
B)1/8
C)1/9
D)1/10
E)1/13
Rationale: Your solution is correct answer should be 1/13.
E
Answer: E
Question: A certain barrel, which is a right circular cylinder, is filled to capacity with 60 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?
Options:
A)There is no empty capacity
B)100 gallons
C)300 gallons
D)420 gallons
E)840 gallons
Rationale: Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diamter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=60
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=60 in the second cylinder,volume= pie (r^2)*4*2=60*8=480 gallons
Empty capacity=420 gallons
Answer D
Answer: D
Question: The length of a bridge in meters, which a train 80-meters long and traveling at 45 km/hr can cross in 30 seconds is?
Options:
A)215
B)235
C)255
D)275
E)295
Rationale: 45 km/h = 45000 m/3600 s = 12.5 m/s
In 30 seconds, the train can go 30(12.5) = 375 meters
Let x be the length of the bridge.
x+80 = 375 meters
x = 295 meters
The answer is E.
Answer: E
Question: Which of the following is the highest fraction?
Options:
A)5⁄7
B)3⁄4
C)2⁄3
D)6⁄7
E)7⁄8
Rationale: Note : If the difference between the numerator and the denominator is constant, then the fraction which has larger value in the numerator is the larger fraction.
Using the above, among the options (a), (c), (d) and (e), (e) has the larger value. Now, compared to option(a), (e) has the larger value.
Answer E
Answer: E
Question: People spend an estimated $75 at the zoo every day, and the total estimated amount for bills every month for the nearest zoo is $200,000. To pay its bills, how many people need to be attending the zoo on a weekly basis? The amount of people needs to be rounded to whole numbers, and a month typically has 4 full weeks.
Options:
A)666
B)667
C)669
D)670
E)665
Rationale: To find out our answer, we must think about how much the zoo makes in a week.
So, we divide 200,000 by 4 to get 50,000
We then divide 50,000 by 75 to get our estimate.
Round the answer to the nearest whole number to get the answer.
Correct Option: B
Answer: B
Question: There are 6 people in the elevator. Their average weight is 156 lbs. Another person enters the elevator, and increases the average weight to 151 lbs. What is the weight of the 7th person.
Options:
A)121
B)168
C)189
D)190
E)200
Rationale: Solution
Average of 7 people after the last one enters = 151 .
âˆ´ Required weight = (7x151)-(6x156)
= 1057- 936
= 121.
Answer A
Answer: A
Question: In how many ways can 4 boys and 3 girls sit around a table in such a way that no two girls sit together?
Options:
A)100
B)144
C)155
D)180
E)190
Rationale: The 4 boys can be seated around a table in 3! Ways. In between them there are 4 places.
The 3 girls can be placed in the 4 places in 4P3 ways.
Therefore, Required number of ways= 3!* 4P3
=6*24
=144
ANSWER:B
Answer: B
Question: Water boils at 212°F or 100°C and ice melts at 32°F or 0°C . If the temperature of a pot of water is 40°C, what is the temperature of the pot of water in °F?
Options:
A)85 °F
B)92 °F
C)96 °F
D)99 °F
E)104 °F
Rationale: Let F and C denote the temperature in Fahrenheit and Celsius respectively.
(F - 32) /(212 - 32) = (C - 0)/(100 - 0)
F = 9C/5 + 32
F = 9(40)/5 + 32 = 104°F
The answer is E.
Answer: E
Question: Marla starts running around a circular track at the same time Nick starts walking around the same circular track. Marla completes 10 laps around the track per hour and Nick completes 5 laps around the track per hour. How many minutes after Marla and Nick begin moving will Marla have completed 4 more laps around the track than Nick?
Options:
A)5
B)48
C)12
D)15
E)20
Rationale: Maria's rate - 10 laps per hour --> 10/60 laps/min
Nick's rate - 5 laps per hour --> 5/60 laps/min
lets set equations:
10/60*t=4 (since Maria had to run 4 laps before Nick would start)
5/60*t=0 (Hick has just started and hasn't run any lap yet)
(10/60-5/60)*t=4-0 (since Nick was chasing Maria)
t=48 min needed Maria to run 4 laps
Answer : B
Answer: B
Question: When x dividedby 288, the remainder is 47. Find the remainder when the same x is divided by 24?
Options:
A)20
B)23
C)25
D)27
E)29
Rationale: 23
Option B
Answer: B
Question: A car covers a distance of 636 km in 6 ½ hours. Find its speed?
Options:
A)104 kmph
B)176 kmph
C)298 kmph
D)106 kmph
E)268 kmph
Rationale: 636/6
= 106 kmph
Answer:D
Answer: D
Question: If the sum of the interior angles of a regular polygon measures up to 1260 degrees, then how many sides does the polygon have?
Options:
A)10
B)9
C)12
D)11
E)14
Rationale: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1260
180n - 360 = 1260
180n = 1620
n = 1620/180 = 9
ANSWER:B
Answer: B
Question: The probability of pulling a black ball out of a glass jar is 1/Q. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
Options:
A)1/(XY)
B)Q/Y
C)Y/X
D)1/(X+Y)
E)1/(X-Y)
Rationale: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/Q
Lets say P of breaking the jar = n
That means 1/Q*n=1/Y
n= Q/Y
B is the answer
Answer: B
Question: A cistern can be filled by 3 pipes in 30, 40 and 60 min and emptied by an escape pipe in half an hour the 3 taps are turned on at noon but the escape pipe is at the same time accidentally left open and not closed for a quarter of an hour at what time will the cistern be full?
Options:
A)60 min
B)90 min
C)120 min
D)150 min
E)170 min
Rationale: Explanation:
Let the total time be x min
x/30 + x/40 + x/60 – x/15 = 1
=> x = 120 min
Answer: Option C
Answer: C
Question: The factorial expression 13!/7! is not divisible by which of the following integers?
Options:
A)3
B)5
C)6
D)7
E)9
Rationale: 13!/7!
= (13*12 * 11 *10 * 9 * 8 * 7!)/7!
= 13*12 * 11 * 10 * 9*8
The given factorial expression is not divisible by 7
Answer D
Answer: D
Question: Rahul travels from A to B a distance of 200 miles in 5 hours. He returns to A in 4 hours. Find his average speed?
Options:
A)52.2mph
B)61.9mph
C)44.4mph
D)35.7mph
E)65.6mph
Rationale: Speed from A to B = 200/5 = 40 mph
Speed from B to A = 200/4 = 50 mph
Average speed = 2*40*50 / 90 = 44.4mph
Answer is C
Answer: C
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
Options:
A)1/3.
B)1/2.
C)3.
D)2.
E)6.
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 9 and L be 3, 9 - 3 = (9 + 3 )/2
C
Answer: C
Question: The function f is defined for all the positive integers h by the following rule: f(h) is the number of positive integers each of which is less than h and has no positive factor in common with h other than 1 . if p is a prime number then f(p)?
Options:
A)p-1
B)p-2
C)(p+1)/2
D)(p-1)/2
E)2
Rationale: The moment you put a prime number in the function f(h), notice that all the numbers lesser than h have no divisor clashing with divisor of h since h is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: A
Question: In 24 minutes, the hour hand of a clock moves through an angle of:
Options:
A)60°
B)24°
C)12°
D)5°
E)None
Rationale: 12 hour = 360˚, 1 hr. = 360/12 = 30˚ 60 min = 30˚, 1 min 30/60 = .5˚ 24 min. = 1/2 ×24 = 12˚
Answer: C
Answer: C
Question: A copying machine "P" can copy 135 pages in 9 minutes, P and Q together can copy 300 pages in 12 minutes. In what time Q can copy 80 pages?
Options:
A)6 minute
B)7 minute
C)9 minute
D)8 minute
E)10 minute
Rationale: P copying 135 pages in 9 minutes.
so in 1 minute P copying=135/9=15 pages
P and Q both copying 300 pages in 12 minute.
so in 12 minute P coying the 12*15=180 pages.
so Q copying alone=300-180=120 pages.
according to question Q takes 12 minute for copying the pages.
so for 1 minute 120/12=10 pages.
because for 10 pages takes 1 minute
so 80 pages it's takes 8 minute
so ans is 8 minute.
ANSWER:D
Answer: D
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
Options:
A)1:2
B)2:5
C)6"2
D)3:1
E)4:7
Rationale: Explanation:
Let speed upstream=x
hen, speed downstream =2x
Speed in still water =2x+x/2
Speed of the stream=2x-x/2
Speed in still water : Speed of the stream=3x/2:x/2=3:1
Answer:D
Answer: D
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)39
B)27
C)30
D)98
E)287
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer: C
Answer: C
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)7!
B)8!
C)9!
D)11!
E)12!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B
Question: If x^2 > x^7> x^5, which of the following could be the value of x?
Options:
A)-9
B)-2
C)-5/8
D)5
E)9
Rationale: x^2 > x^7 > x^5
1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.
This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.
2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.
With this information, we know that x is a negative number between 0 and -1; therefore, C (-5/8) is the only option.
Answer: C
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $8.55 each. One day, she bought 9 t-shirts. How much money did she spend?
Options:
A)$150
B)$248.75
C)$200
D)$171.6
E)$73.1025
Rationale: $8.55*9=$73.1025. Answer is E.
Answer: E
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 40% on his income, while Mindy pays a rate of only 25% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
Options:
A)28%
B)30%
C)32%
D)34%
E)36%
Rationale: Let x be Mork's income, then Mindy's income is 4x.
The total tax paid is 0.4x + 1.0x = 1.4x
1.4x / 5x = 0.28
The answer is A.
Answer: A
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 37 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
Options:
A)36
B)2^4*3
C)24
D)38
E)47
Rationale: Working backward from the day it's covered:
day 37: fully covered
day 36: half covered
So 36 days
ANSWER:A
Answer: A
Question: There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of sections A is 40 kg and that of sections b is 35 kg. Find the average weight of the whole class
Options:
A)36.25
B)37.25
C)38.35
D)39.25
E)None
Rationale: Solution
Total weight of(36+44)Students	= (36x40+44x35)Kg
= 2980 kg.
Average weight of the whole class	= (2980 / 80)
= 37.25.
Answer B
Answer: B
Question: Few years ago on 31st January on her 26th birthday a lady laid a baby. Now what's the sum of their ages?
Options:
A)37
B)38
C)43
D)51
E)52
Rationale: All other options have thier unit place digit odd while we require even digit because before x years she laid a baby. That time she is 26years old
so now sum of thier ages is 26 + 2x. The total should be even number
ANSWER:B
Answer: B
Question: 5,9,16,28,48,__
Options:
A)79
B)80
C)81
D)82
E)83
Rationale: (9+5) +2 = 16
(16+9) +3 = 28
(28+16)+4 = 48
(48+28)+5 = 81
ANSWER:C
Answer: C
Question: Vikas bought a grinder with 15% discount on the labelled price. He sold the grinder for Rs.2880 with 20% profit on the labelled price. At what price did he buy the grinder?
Options:
A)Rs 2000
B)Rs 2040
C)Rs 2240
D)Rs 2400
E)None of these
Rationale: Explanation :
Let the labelled price be Rs.x. Then, 120% of x = 2880
Therefore x=(2880100/120) = 2400.
C.P = 85% of Rs.2400 = Rs(85/100x2400) =Rs.2040.
Answer : B
Answer: B
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
Options:
A)11 1/8%
B)11 8/9%
C)11 1/9%
D)19 1/9%
E)11 1/1%
Rationale: 900 --- 100
100 --- ? => 11 1/9%
Answer: C
Answer: C
Question: It took Malcom 3.5 hours to drive from city A to city B. On his way back to city A, he increased his speed by 20 km per hour and it took him 3 hours.
Find the average speed for the whole journey.
Options:
A)134.9 km/hr
B)129.2 km/hr
C)119.6 km/hr
D)140.5 km/hr
E)155.3 km/hr
Rationale: Let x and x + 20 be the speeds of the car from A to B and then from B to A. Hence the distance from A to B may expressed as 3.5 x and the distance from B to A as 3(x + 20)
The average speed = total distance / total time = (3.5 x + 3 (x + 20)) / (3.5 + 3)
The distance from A to B is equal to the distance from B to A, hence: 3.5 x = 3(x + 20). Solve for x to obtain x = 120 km/hr.
We now substitute x by 120 in the formula for the average speed to obtain.
average speed = 129.2 km/hr
correct answer B)129.2 km/hr
Answer: B
Question: Three dice are thrown together, Find the probability of getting a total of atmost 5?
Options:
A)2/35
B)1/8
C)3/31
D)2/9
E)5/108
Rationale: Three different dice are thrown at the same time.
Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.
Number of events of getting a total of atmost 5 = 10
i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2).
Therefore, probability of getting a total of atmost 5
P(E) = Number of favorable outcomes/Total number of possible outcome
= 10/216
= 5/108
Answer: E
Question: if (64)2 - (36)2 = 10x, then x = ?
Options:
A)200
B)220
C)210
D)280
E)None of these
Rationale: Explanation :
a2−b2=(a−b)(a+b)
(64)2 - (36)2 = (64 - 36)(64 + 36) = 28 × 100
Given that (64)2 - (36)2 = 10x
=> 28 × 100 = 10x
=> x = 280. Answer : Option D
Answer: D
Question: There is rain at a rate of 12 centimeters per hour all over New Jersey. Somewhere downtown in New Jersey a group of students are waiting for the rain to stop. If the rain filled a tank the with a base area of 250 square centimeters and a depth of 6 centimeters, how long did the students wait for the rain to stop?
Options:
A)8 hours
B)4 hours 25 minutes
C)3 hours 15 minutes
D)6 hours
E)2 hours
Rationale: Answer is : E, 4 hours and 30 mins
The volume of the tank is irrelevant and only height matters since rain fell all over the city.
Thus, it takes only . 12 / 6 = 2 hours of rain to fill the tank.
Answer: E