divelab/Sys2Bench huggingface dataset:
Question: In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
Options:
A)7⁄19
B)2⁄3
C)3⁄4
D)9⁄21
E)None of these
Rationale: If the drawn ball is neither red nor green, then it must be blue, which can be picked in 7C1 = 7 ways. One ball can be picked from the total(8 + 7 + 6 = 21) in 21C1 = 21 ways.
∴ Reqd probability = 7⁄21 = 1⁄3
Answer E
Answer: E
Question: A tank is filled by 3 pipes with uniform flow. The first two pipes operating simultaneously fill the tan in the same time during which the tank is filled by the third pipe alone. The 2nd pipe fills the tank 5 hours faster than first pipe and 4 hours slower than third pipe. The time required by first pipe is
Options:
A)13 hours
B)45 hours
C)15 hours
D)12 hours
E)11 hours
Rationale: If first pipe fills tank in x hrs, then second pipe fills tank in x-5 hrs and 3rd pipe fills tank in x-9 hrs, then
as per given condition
1/x +1/(x-5) = 1/(x-9)
solving it, we get x= 15 hrs
ANSWER:C
Answer: C
Question: A and B can finish a work in 16 days while A alone can do the same work in 32 days. In how many days B alone will complete the work?
Options:
A)76 days
B)48 days
C)98 days
D)32 days
E)22 days
Rationale: B = 1/16 – 1/32 = 1/32 => 32 days
Answer: D
Answer: D
Question: Convert 2/5 to a decimal
Options:
A)0.1
B)0.2
C)0.3
D)0.4
E)0.5
Rationale: Divide 2 by 5: 2 / 5 = 0.4
Answer: 2/5 = 0.4 (D)
Answer: D
Question: Last year 28 members of a certain club traveled to England, 28 members traveled to France, and 30 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
Options:
A)52
B)69
C)71
D)73
E)79
Rationale: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)
n(E or F or I) = 28+ 28 + 30 - 0 - 11 - 6 + 0
Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.
n(E or F or I) = 69
Answer (B)
Answer: B
Question: The batting average of a particular batsman is 62 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
Options:
A)179
B)208
C)210
D)225
E)229
Rationale: Explanation:
Total runs scored by the batsman = 62*46 = 2852 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2852 – 2552 = 300 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 300
2x = 450
x = 225 runs
ANSWER D
Answer: D
Question: A person bought 118 glass bowls at a rate of Rs. 12 per bowl. He sold 102 of them at Rs. 15 and the remaining broke. What is the percentage gain for A?
Options:
A)40
B)300/11
C)243/7
D)475/59
E)279/8
Rationale: CP=118*12=1416 and SP=102*15=1530
Gain %= 100*(1530-1416)/1100= 11400/1416=475/59
ANSWER:D
Answer: D
Question: There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability T that all three secretary are assigned at least one report?
Options:
A)8/9
B)64/81
C)4/9
D)16/81
E)5/9
Rationale: I got the same answer: Here's my reasoning
First Report you have 3 choices
Second Report you have 2 choices
Third Report you have 1 choice
Fourth report 3 choices again
Then total number of ways is: 3*2*1*3=3^2*2
This is not correct. You have assumed that the 4th report must go to someone who already has a report. There is no such constraint. You can easily give the 1st and 2nd reports to secretary 1, 3rd report to secretary 2 and 4th report to secretary 3. But you have ignored all such cases.
The number of ways of ensuring at least one report goes to each secretary is 4C2 (select 2 reports out of 4 which go to the same person)*3C1 (select the person who must type 2 reports)*2! (since you have 2 reports left which you must distribute to the 2 remaining people such that each person gets one) = 36
Required probability T= 36/81.C
Answer: C
Question: A bike covers a certain distance at the speed of 64km/h in 8 hrs. If the bike was to cover the same distance in approximately 6 hrs, at what approximate speed should the bike travel?
Options:
A)80.56 km/h
B)85.34 km/h
C)95.05 km/h
D)98 km/h
E)99.56 km/h
Rationale: Ans.(B)
Sol. Total distance = 64 × 8 = 512 km
Now speed = 512/6 = 85.34 km/h
Answer: B
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)34
B)56
C)72
D)35
E)32
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: Option C
Answer: C
Question: Peter invested a certain sum of money in a simple interest bond whose value grew to $400 at the end of 4 years and to $ 500 at the end of another 2 years. What was the rate of interest in which he invested his sum?
Options:
A)12%
B)12.5%
C)67%
D)25%
E)33%
Rationale: Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to beRand time as T. We need to find R
Now After a time of 4years the principal P amounts to $400 and after a time of 6years ( question says after another 6years so 4+2) P becomes $500.
Formulating the above data
Amount (A1) at end of 4years
A1= P(1 + 4R/100) = 400
Amount (A2) at end of 6years
A2 = P(1 + 2R/100) = 500
Dividing A2 by A1 we get
(1 + 4R/100)/(1 + 2R/100) = 5/4
after cross multiplication we are left with 4R =100 which gives R = 25%
Option: D
Answer: D
Question: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)42
B)70
C)140
D)196
E)315
Rationale: Ans: 196
7C1 * 8C2
Answer D)
Answer: D
Question: Find the sum of prime numbers lying between 58 and 76?
Options:
A)198
B)201
C)252
D)272
E)331
Rationale: Solution
Required sum	= 59 + 61 + 67 + 71 + 73)
= 331.
Answer E
Answer: E
Question: If a positive integer n is divided by 5 , the remainder is 3. which of the number below yields a remainder of 0 when it is divided by 5
Options:
A)n+3
B)n+2
C)n-2
D)n-1
E)n+1
Rationale: Correct Answer : B
n is divided by 5 , the remainder is 3
n=5k+3 (k is integer)
add 2 to both sides of the above equation
n+2=5k+5
=5(k+1)
n+2 divided by 5 yields a remainder to zero.
Answer: B
Question: On a game show, a contestant spins two different wheels; each wheel is numbered 1 to 15. What is the probability that the contestant will spin all tens?
Options:
A)25
B)64
C)8/7
D)4/6
E)1/225
Rationale: All 15s:
1st wheel = 15 = 1/15
2nd wheel = 15 = 1/15
(1/15)(1/15)= 1/225
Answer: E
Answer: E
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
54.
Options:
A)7-19
B)8-20
C)10-16
D)14-40
E)20-6
Rationale: We are looking for two numbers.
#1 - x
#2 - 3x â€“ 2
The sum is 54. #1 + #2 = 54
Substituting x + 3x â€“ 2 = 54
4x â€“ 2 = 54
4x = 56
x = 14
The first number is 14, the second number is two less than three times 14 or 40.
correct answer D
Answer: D
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $10.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
Options:
A)$4.50
B)$10.2
C)$5.30
D)$5.50
E)$5.60
Rationale: I Tried using Time/Rate approach:-
Initial Price Difference = 10.80 - 3.20 = 7.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x
Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
7.6 = T(5.4x) -> T= (7.6)/5.4X
Final Price = 3.20 + 5X * T -> 3.20 + 5*7.6/5.4 = 10.2
Answer B.
Answer: B
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 40 percent on clothing, 30 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
Options:
A) 2.8%
B) 3.6%
C) 4%
D) 5.2%
E) 6.0%
Rationale: Let amount spent by Jill = 100
Clothing=40, Food=30, others=30
Tax on clothing= 1.6
Tax on others=2.4
Percentage= 4/100= 4%
Answer: C
Answer: C
Question: Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 47 days. On which day of the week in February was the task completed?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Thursday
E)Friday
Rationale: This type of story problem is essentially just about a repeating pattern and a 'remainder.'
We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 47 DAYS. We're asked on what day of the week the task was actually completed on.
Since the task was supposed to be completed on a Wednesday....
A 1 day postponement would be Thursday
A 2 day postponement would be Friday
A 3 day postponement would be Saturday
A 4 day postponement would be Sunday
A 5 day postponement would be Monday
A 6 day postponement would be Tuesday
A 7 day postponement would be Wednesday
A 8 day postponement would be Thursday
Etc.
So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 47 days.
47/7 = 6 remainder 5
This means that there are 6 full weeks AND 5 extra days after a Wednesday....Thus, the task was completed on a Monday.
A
Answer: A
Question: A certain farmer pays $30 per acre per month to rent farmland. How much does the farmer pay per month to rent a rectangular plot of farmland that is 360 feet by 1210 feet? (43,560 square feet = 1 acre)
Options:
A)$5,330
B)$3,360
C)$1,350
D)$300
E)$150
Rationale: Basically the question an error. 1 acre = 43,560 square feet and if it is then the answer is 300 (D)
Answer: D
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:?
Options:
A)Rs.8467
B)Rs.8428
C)Rs.8400
D)Rs.8429
E)Rs.8420
Rationale: Ratio of their shares
= 22500 : 35000
= 9:14
Deepak's share
= 13800 * 14/23
= Rs.8400.
Answer:C
Answer: C
Question: How many ways are there for 6 males and 3 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
Options:
A)6
B)12
C)72
D)100
E)1440
Rationale: So Mary has her own chair, fixed position. Other two females around the table can sit in 2 ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 6 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 6! different ways, so total 2*6!=1440
Answer E.
Answer: E
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 2 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Options:
A)187 km
B)480 km
C)278 km
D)240 km
E)671 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 2
2x/15 - x/8 = 2 => x = 240 km.
Answer:D
Answer: D
Question: Miguel is 41 years old. He is 5 years older than twice his son’s age. Find the age of his son.
Options:
A)11years
B)12years
C)13years
D)14years
E)18years
Rationale: sons age=x
41-2x=5
x=18years
ANSWER:E
Answer: E
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
Options:
A)2
B)2 1/2
C)3
D)3 1/2
E)4
Rationale: Ratio; white: black: gray = 3: 5: (3+5) = 3: 5: 8
If 2 gallons of the mixture is needed <==> Need 2 gallons of gray paint.
Then,
3: 5: 8 = x: y: 2
3/8 = x/2; x = 3/4
5/8 = y/2; y = 5/4
You need 3/4 gallon of white. You have to buy 1 gallons.
You need 5/4 gallons of black. You have to buy 1 gallon and another 1/2 gallon of black.
The least amount of paint = 1 + 1 + 1/2 = 2.5.
ANSWER:B
Answer: B
Question: A class contains five juniors and five seniors. If one member of the class is assigned at random to present a paper on a certain subject, and another member of the class is randomly assigned to assist him, what is the probability T that both will be juniors?
Options:
A)1/10
B)1/5
C)2/9
D)2/5
E)1/2
Rationale: I think you're right. The other way to do it (but the long way) is to figure out the probability that it is not two Juniors.
2 seniors = P(Senior) * P(Senior) = 2/9
1 Senior and 1 Junior = (1/2) *(5/9)*2 = 5/9
Probability that it is not two Juniors is 5/9+2/9 = 7/9 so the probability T that it is two juniors is 1- (7/9) = 2/9.C
Answer: C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 120km/h, what is the circumference of the tire?
Options:
A)2 meters
B)6 meters
C)5 meters
D)3 meters
E)7 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 120,000 m : C is the circumference
C = 5 meters
correct answer C
Answer: C
Question: A can do a piece of work in 15 days. A does the work for 5 days only and leaves the job. B does the remaining work in 12 days.In how many days B alone can do the work?
Options:
A)5days
B)7 days
C)12 days
D)9 days
E)18 days
Rationale: Explanation:
A’s 5 day work = 5*1/15=1/3
Remaining work = 1-1/3=2/3
B completes 2/3 work in 6 days
B alone can do in x days
2/3*x=12
X=18 days
Answer: Option E
Answer: E
Question: Solve:-
666 x 666 x 666 + 555 x 555 x 555 = ?(666 x 666 - 666 x 555 + 555 x 555)
Options:
A)888
B)333
C)555
D)1221
E)889
Rationale: Given Exp. = (a3 + b3) = (a + b) = (666 + 555) = 1221(a2 - ab + b2)
Answer D
Answer: D
Question: Simplify (212 * 212 + 312 * 312 )
Options:
A)132288
B)142088
C)142188
D)142288
E)142388
Rationale: Explanation:
Trick: Above equation can be solved by using following formula
(a2+b2)=1/2((a+b)2+(a−b)2)
Answer: Option D
Answer: D
Question: Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?
Options:
A)33
B)77
C)48
D)99
E)12
Rationale: Sravan's one day's work = 1/25 - 1/75 = 2/75
Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75
Sravan completed 16/75th of total work.
So, his share is 16/75 * 225 = Rs. 48.
Answer: C
Answer: C
Question: If y exceeds x by 30%, then x is less than y by?
Options:
A)16 2/9%
B)16 3/3%
C)16 2/3%
D)23 1/13%
E)16 1/3%
Rationale: X=100	y=130
130------30
100-------? => 23 1/13%
Answer:D
Answer: D
Question: A certain number of men can do a work in 20days. If there were 4 men less it could be finished in 5days more. How many men are there?
Options:
A)10
B)20
C)25
D)30
E)35
Rationale: The original number of men = 4(20+5)/5 = 20men
Answer is B
Answer: B
Question: Janet covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
Options:
A)1 hour 45 minutes
B)2 hours
C)2 hours 30 minutes
D)3 hours
E)None of these
Rationale: Janet covered a distance of 340 miles between city A and city B taking a total of 5 hours. time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)
average speed is 340/5=68
That gives the answer 3:2=D
Answer: D
Question: . A car covers a distance of 742 km in 7 hours. Find its speed?
Options:
A)104
B)55
C)148
D)150
E)159
Rationale: 742/5 = 148 kmph
Answer: C
Answer: C
Question: 5216 x 51 = ?
Options:
A)212016
B)266016
C)266436
D)216314
E)216318
Rationale: Normal way of multiplication may take time. Here are one alternative.
5216 x 51 = (5216 x 50) + 5216 = (5216 x 100)/2 + 5216
= 521600/2 + 5216 = 260800 + 5216 = 266016
Answer is B
Answer: B
Question: A garrison of 400 men had a provision for 31 days. After 27 days 200 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Options:
A)65 days
B)45 days
C)8 days
D)16 days
E)18 days
Rationale: 400 --- 31
400 --- 4
200 --- ?
400*4 = 200*x => x =8 days.
Answer: C
Answer: C
Question: A certain Deep Blue paint contains 45 percent blue pigment and 55 percent red pigment by weight. A certain green paint contains 35 percent blue pigment and 65 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
Options:
A)1.5
B)2.5
C)3.5
D)2.75
E)4.5
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.55 =2.75 Grams of red pigment
Answer: D
Question: the sum of 7th and 23rd term of A.P. is equal to the sum of 8th , 15th and 13 th term . find the term which is 0
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: t7 + t23 = t8 + t15 + t13
=> a+6d + a+22d = a+7d + a+14d + a+12d
=> a +5d = 0
=> t6= 0 i.e. 6th term is zero.
ANSWER: A
Answer: A
Question: Two bullet trains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)11 sec.
B)15 sec.
C)13.3 sec.
D)17 sec.
E)19 sec.
Rationale: Speed of the first bullet train = 120/10 m/sec = 12 m/sec.
Speed of the second bullet train = 120/20 m/sec = 6 m/sec.
Relative speed = (12 + 6) = 18 m/sec.
Required time = (120 + 120)/18 sec = 13.3 sec.
C
Answer: C
Question: A train crosses a pole in 4 sec while travelling at a speed of 135 kmph, what is the length of the train?
Options:
A)135 m
B)140 m
C)145 m
D)150 m
E)155 m
Rationale: Explanation:
D = 135 * 5/18 * 4 = 150 m
Answer: Option D
Answer: D
Question: Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
Options:
A)9/25
B)9/50
C)18/25
D)13/20
E)None of these
Rationale: EXPLANATION:
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25
ANSWER IS A
Answer: A
Question: Mangala completes a piece of work in 10 days, Raju completes the same work in 60 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)60/7 days
B)10 days
C)12 days
D)14 days
E)16 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 Ã— 60/70 = 60/7 days
A)
Answer: A
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage R must x be of z?
Options:
A)(n/m)%
B)(m × n)%
C)(100 / [m × n]) %
D)(100 × m/n)%
E)(100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer R is 100n/m %.E
Answer: E
Question: Average of first five multiples of 5 is
Options:
A)9
B)11
C)13
D)15
E)16
Rationale: Explanation:
Average=5(1+2+3+4+5)/5=15
Answer: Option D
Answer: D
Question: Earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and Ellen requires a minutes and half to stuff the same number of envelops.Working together,how long will it take Earl and Ellen to stuff 360 envelopes
Options:
A)6 minutes
B)5 minutes
C)7 minutes
D)3 minutes
E)4 minutes
Rationale: earl takes 1 min. for 36 envelopes.
ellen takes 3/2 mins for the same. so ellen can stuff ((36)/(3/2)) in 1 min. i.e., 24 envlpes a min.
so both of them when work together can stuff 36+24=60 envelopes in 1 min.
for 360 envelopes they will take 360/60 mins. i.e., 6 mins.
ANSWER:A
Answer: A
Question: If y is an integer, then the least possible value of |21 - 5y| is
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: We know that 5y is a multiple of 5, so let’s first look at the multiples of 5 closest to 22. We have “20” and “25”. Let’s subtract both of these from 21 and see which one produces the smallest result. When 5y = 20, y is 4 and when 5y = 25, y is 5. Let’s start with letting y = 4.
|21-5(4)|
|21-20|
|1| = 1
Next, let’s let y equal 5.
|21-5(5)|
|21-25|
|-4| =4
We see that the smallest possible value of |21-5y| is 1.
Answer B.
Answer: B
Question: How many integers from 22 to 160, inclusive, are divisible by 3 but not divisible by 7?
Options:
A)30
B)35
C)40
D)50
E)60
Rationale: We should find # of integers divisible by 3 but not by 3*7=21.
# of multiples of 21 in the range from 22 to 160, inclusive is (147-42)/21+1=6;
46-6=40.
Answer: C.
Answer: C
Question: A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:
Options:
A)12 days
B)18 days
C)24 days
D)30 days
E)None of these
Rationale: Explanation:
A + B = C + D
| | | |
Ratio of efficiency 10x + 5x 9x + 6x
|________| |_________|
15x 15x
Therefore , ratio of efficiency of A:C =10:9
Therefore, ratio of days taken by A:C = 9:10
Therefore, number of days taken by A = 18 days
Answer: B
Answer: B
Question: Consider the equation K = (mv^2)/2.
If v and m are both doubled, by what factor is K increased?
Options:
A)2
B)6
C)8
D)10
E)4
Rationale: We have,
K = (mv^2)/2
On doubling both m and v,
K = [(2m)*(2v)^2]/2
K = (2m*4v^2)/2
K = (8mv^2)/2
K = 8*(mv^2)/2
Initially K = (mv^2)/2. After changing m and v, K = 8*(mv^2)/2
Hence, K increases by 8 times.
Answer = C = 8
Answer: C
Question: Danny is sitting on a rectangular box. The area of the front face of the box is half the area of the top face, and the area of the top face is 1.5 times the area of the side face. If the volume of the box is 1536, what is the area of the side face of the box?
Options:
A)34
B)65
C)88
D)90
E)128
Rationale: Lets suppose length= l, breadth= b, depth= d
Front face area= l*w = 1/2 w*d (l=1/2 d or d=2l)
top face area= w*d
side face area= w*d = 1.5 d*l (w=1.5l)
Volume = l*w*d= 1536
l*1.5l*2l= 1536
l=8
Side face area= l*d= l*2l= 8*2*8=128
E is the answer
Answer: E
Question: Bay is going with 8 friends on a trip to New York for spring break. Airfare and hotel costs a total of $7200.00 for the group of 9 friends. How much does each person have to pay for their hotel and airfare?
Options:
A)$720
B)$800
C)$810
D)$700
E)$750
Rationale: Answer= B
The total cost of the trip ($7200.00) divided by 9 equals $800.00.
Answer: B
Question: The area of a triangle will be when a = 2m, b = 5m, c = 7m, a, b, c being lengths of respective sides?
Options:
A)2
B)7
C)5
D)3
E)4
Rationale: S = (2 + 5 + 7)/2
= 7
Answer: B
Answer: B