divelab/Sys2Bench huggingface dataset:
Question: A part-time employee whose hourly wage was increased by 10 percent decided to reduce the number of hours worked per week so that the employee's total weekly income would remain unchanged. By what percent should the number of hours worked be reduced?
Options:
A)9.09
B)10
C)11
D)12
E)13
Rationale: Let original hourly wage be x and let the no of hours worked be y
Total wage will be =x*y
After the increment the wage will be=1.1 x
Now we need to find number of hours worked so that
x*y=1.1x*z i.e z=x* y/1.1x= 1/1.1 y
%decrease = (y-1/1.1y)/y *100= 1-1/1.1 *100 =9.09%
Thus my answer is A.
Answer: A
Question: Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 4?
Options:
A)7
B)8
C)10
D)11
E)12
Rationale: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p +4 is 6 + 4 = 10.
Answer:C.
Answer: C
Question: The ratio between the radii of two spheres is 1:3. Find the ratio between their volumes?
Options:
A)27:1
B)1:27
C)1:9
D)9:1
E)1:2
Rationale: r1 : r2 = 1:3
r13 : r23 = 1:27
ANSWER:B
Answer: B
Question: Which of the following is a prime number
Options:
A)67
B)68
C)69
D)70
E)72
Rationale: Clearly, 67 is a prime number.
Option A
Answer: A
Question: What will come in place of the x in the following Number series? 6, 12, 21, 33 , 48 , 66 , 87, x
Options:
A)33
B)35
C)39
D)111
E)42
Rationale: The pattern is + 6, + 9, + 12, +15 + 18 +21 + 24 â€¦â€¦â€¦..
So the missing term is = 87 + 24 = 111
Answer : D
Answer: D
Question: What will be the day of the week on 15th August,2010 ?
Options:
A)Sunday
B)Monday
C)Tuesday
D)Friday
E)None of these
Rationale: Solution
15th August,2010 = (2009 years + Period from 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years +7 ordinary years)
= (2 x 2 + 7 x 1)= 11 odd days = 4 odd days
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) =227 days
=(32 weeks + 3 days)=3 odd days.
Total number of odd days =(0 + 0 + 4 + 3)=7 = 0 odd days.
Given day is Sunday . Answer A
Answer: A
Question: n a 1000m race, if A gives B a start of 40m, A wing by 19sec. But if A gives B start of 30sec, B wins by 40m.
Find the time taken by B to run 2000m race?
Options:
A)300
B)250
C)400
D)450
E)500
Rationale: then 960/B -1000/A = 19 => 24/B - 25/A = 19/40
and 1000/B - 960/A = 30 => 25/B - 24/A = 30/40
solving equation A speed =8 and B=20/3
for 1000m b will take 2000/20/3= 250 sec
B
Answer: B
Question: 9, 16, 21, 25, 36,49
Options:
A)9
B)16
C)21
D)25
E)36
Rationale: Each of the numbers except 21, is perfect square.
Answer: Option C
Answer: C
Question: If the distance between A and B is 100m and that of B and C is 500. Then what is the distance between A and C ?
Options:
A)600m
B)more than 600m
C)Between 500m and 600m
D)700m
E)800m
Rationale: those options r not valid for all conditions.
because if A,B,C are on a straight line then the distance between A and C is may be minimum 400m or maximum 600m
ANSWER:A
Answer: A
Question: In an apartment building that has 490 units, 4 out of every 7 units are currently rented, including 1/3 of the one-bedroom units. If, of the rented apartments, there is a 6:1 ratio of two-bedroom units to one-bedroom units, and the building only consists of two-bedroom and one-bedroom units, how many two-bedroom units are not rented?
Options:
A)50
B)70
C)100
D)130
E)140
Rationale: Rented = 4/7*490 = 280.
Rented two-bedroom = 6/7*280 = 240;
Rented one-bedroom = 1/7*280 = 40 (or 280-240=40).
Rented one-bedroom units are 1/3 of all one-bedroom: 1/3*{All one bedroom} = 40 --> {All one-bedroom} = 120
{All two-bedroom} = 490 - 120 = 370.
Two-bedroom not rented = 370 - 240 =130
Answer: D.
Answer: D
Question: How many positive integers less than 5,000 are evenly divisible by neither 18 nor 21?
Options:
A)4,514
B)4,475
C)4,521
D)4,428
E)4,349
Rationale: integers less than 5000 divisible by 18 5000/18 =333.something , so 333
integers less than 5000 divisible by 21 5000/21 = 238.## , so 238
we have double counted some, so take LCM of 18 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 18 and 21 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4428 answer D.
Answer: D
Question: 5 people are sitting in a 4 seat row watching a football game. At halftime they all get up. When they return, they each randomly sit down on one of the 4 chairs. What is the likelihood that none of the 4 end up sitting in the same chair that they sat in during the first half?
Options:
A)3/24
B)9/120
C)15/24
D)18/24
E)21/24
Rationale: Originally seated A B C D
now when after they get up and when they sit back again .
1st- A has option to sit on 3 seats ( apart from his previous seat . thus he now sits on B's seat.)
2nd- Similarly B has option to sit on 3 seats ( because A has already occupied B's previous seat, thus B sits on a's seat.)
3rd- Now C has only 1 option to sit on D's seat . and similarly D also has one option to sit on C's seat.)
hence total favourable outcomes 3*3*1*1=9
and total possible outcomes =5!=120
probability of the favourable outcome= 9/120. B
Answer: B
Question: Three faces of a fair die are Yellow, three faces red and one blue.The die is tossed three
times. The probability that the colours, yellow, red and blue appear in the first, second and
third tosses respectively is
Options:
A)1/36
B)1/24
C)1/32
D)1/37
E)None of these
Rationale: Probability of getting yellow color = P(Y) = 3/6 = 1/2
Probability of getting red color = P(R) = 3/6 = 1/2
Probability of getting blue color = P(B) = 1/6
So, the probability that the colors yellow, red and blue appear in first, second and third toss respectively= P(Y ∩ R ∩ B) = P(Y) x P(R) x P(B) = 1/2 x 1/2 x 1/6 = 1/24
ANSWER:B
Answer: B
Question: Surface area of two spheres are in the ratio 1:4 what is the ratio of their volumes?
Options:
A)1:9
B)1:8
C)1:3
D)1:4
E)1:5
Rationale: 1:8
Answer: B
Answer: B
Question: For positive integers n, the integer part of the nth term of sequence E equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, E_1 = 1.2345678…, while E_2 = 2.4681012… The sum of the first seven terms of sequence E is between:
Options:
A)28 and 29
B)29 and 30
C)30 and 31
D)31 and 32
E)32 and 33
Rationale: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
E_1 = 1.23…
E_2 = 2.46…
E_3 = 3.69…
E_4 = 4.812…
E_5 = 5.10…
E_6 = 6.12…
E_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
Answer: C
Question: A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Options:
A)11 days
B)13 days
C)20 3/17 days
D)21 days
E)None of these
Rationale: Explanation:
Ratio of times taken by A and B = 100:130 = 10:13
Suppose B takes x days to do the work.
x = (23 * 13)/10 = 299/10
A's 1 day work = 1/23; B's 1 day work = 10/299
(A + B)'s 1 day work = (1/23 + 10/299) = 1/13
A and B together can complete the job in 13 days.
ANSWER IS B
Answer: B
Question: Nancy works 3 days per week at a rate of x dollars per day. If Nancy works more than 3 days per week, any extra days are paid at double her normal rate. Nancy worked 2 weeks with no overtime, and then worked 3 more weeks, each with y days of overtime. Which of the following represents Nancy’s total earnings over this period?
Options:
A)a) 3x(2y+5)
B)b) 3x+12y
C)c) 3xy(7x+2)
D)d) 3x(2y+7)
E)e) 4x(y+8)
Rationale: Payment of a week for 3 days a week = $3x
Payment of 4 weeks for 3 days a week = $3x*2 = $6x
Payment of a week for y days overtime a week = $3x+$2xy
Payment of 3 weeks for y days overtime a week = ($3x+$2xy)*3
Total Earnings = $6x + ($3x+$2xy)*3 = 15x+6xy = 3x(2y+5)
Answer: option A
Answer: A
Question: In a race of length L metres, Johnson beats Lewis by Y metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (Y<N)
Options:
A)L(L-N) / L-Y
B)L(N-Y) / L-Y
C)L-N
D)Y-N
E)Y+N
Rationale: As the time is constant, the ratio of distances will be the same as the ratio of speeds.
If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then
Sj/Sl = L/(L-Y)
and Sj/Sg = L/(L-N)
=> Sg/Sl = (L-N)/(L-Y)
Therefore the speeds of Lewis and Greene are in the ratio (L-Y)/(L-N)
When Lewis finishes the race, the time run by him and Greene are same
=> The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.
=> Distance run by Greene when Lewis finishes the race = (L-N)/(L-Y) * L
=> Lewis beats Greene by L - L*(L-N)/(L-Y) = L [ 1 - (L-N)/(L-Y)] = L (N-Y) / (L-Y)
Option (B) is therefore correct.
Answer: B
Question: In how many different ways can the letters of the word 'DEVELOP' be arranged?
Options:
A)10 ways
B)20 ways
C)30 ways
D)2520 ways
E)40 ways
Rationale: Totally there are 7 letters on the word DEVELOP. it contains 1D,2E,1V,1L,1O,1P.
The no of ways is 7!/2!=2520 ways.
ANSWER:D
Answer: D
Question: Frances can complete a job in 10 hours, and Joan can complete the same job in 10 hours. Frances starts the job at 9 a.m., and stops working at 3 p.m. If Joan starts working at 6 p.m. to complete the job, at what time is the job finished?
Options:
A)6 p.m.
B)7 p.m.
C)8 p.m.
D)10 p.m.
E)12 p.m.
Rationale: Let the total work be 24 units.
Frances can complete 2.4 units/hr
Joan can complete 2.4 units/hr
Work done by Frances in 6 hours is 14.4 units ; work left for Joan is 9.6 units ( 24 - 14.4)
Time required by Jones to complete the remaining work will be 14.4/2.4 => 4 hours
Given Jones starts at 6 PM , so she would complete the work at 10 PM
Answer will be (D)
Answer: D
Question: How many multiples of 3 are there between 100 and 300 (both are inclusive)?
Options:
A)67.6
B)1.58
C)2.47
D)3.54
E)6.51
Rationale: the answer is (300-100)/3+1=67.6
Answer is A
Answer: A
Question: If the fractions 2/5, 3/8, 4/9, 5/13 and 6/11 are arranged in ascending order of their values, which one will be the fourth?
Options:
A)4/9
B)2/5
C)3/8
D)5/13
E)6/13
Rationale: Explanation:
2/5 = 0.4, 3/8 = 0.375,
4/9 = 0.44, 5/13 = 0.385 and 6/11 = 0.55
So, 3/8 < 5/13 < 2/5 < 4/9 < 6/11
So, the fourth fraction is = 4/9
Answer: Option A
Answer: A
Question: Sandy bought 65 books for $1380 from one shop and 55 books for $900 from another shop. What is the average price that Sandy paid per book?
Options:
A)$13
B)$15
C)$17
D)$19
E)$21
Rationale: average price per book = (1380 + 900) / (65 + 55) = 2280 / 120 = $19
The answer is D.
Answer: D
Question: 10 people went to a hotel for combine dinner party 8 of them spent Rs. 10 each on their dinner and rest spent 4 more than the average expenditure of all the 10. What was the total money spent by them.
Options:
A)1628.4
B)110
C)1492
D)1496
E)None of these
Rationale: Solution: Let average expenditure of 10 people be x.
then,
10x = 8*10+2*(x+4);
Or, 10x = 10*10+2x+8;
Or, x = 11;
So, total money spent = 11*10 = Rs. 110.
Answer: Option B
Answer: B
Question: Dawson and Henry are in a relay race. Dawson runs the first leg of the course in 38 seconds. Henry runs the second leg of the course in 7 seconds. What was the average time they took to run a leg of the course?
Options:
A)20.5
B)21.5
C)22.5
D)23.5
E)24.5
Rationale: (38 seconds +7 seconds)/2= 22.5 seconds
Correct option is: C
Answer: C
Question: Mangala completes a piece of work in 9 days, Raju completes the same work in 21 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)8 days
B)6 days
C)11 days
D)12 days
E)14 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 = 9× 21/30 = 6 days
B)
Answer: B
Question: 139 persons have signed up for an elimination tournament. All players are to be paired up for the first round, but because 139 is an odd number one player gets a bye, which promotes him to the second round, without actually playing in the first round. The pairing continues on the next round, with a bye to any player left over. If the schedule is planned so that a minimum number of matches is required to determine the champion, the number of matches which must be played is
Options:
A)136
B)137
C)138
D)139
E)None of these
Rationale: Explanation :
This can be logically done in the following manner. There are 139 players in all. We want to determine 1 champion among them.
So all except 1 should lose. Since a player can lose only once and since any match produces only one loser, to produce 138 losers, there should be 138 matches that should be played.
Answer : C
Answer: C
Question: A certain bacteria colony doubles in size every day for 21 days, at which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
Options:
A)6.33
B)7.5
C)20
D)15
E)19
Rationale: If there is one bacteria colony, then it will reach the limit of its habitat in 21 days.
If there are two bacteria colonies, then in order to reach the limit of habitat they would need to double one time less than in case with one colony. Thus colonies need to double 20 times.
Answer: C.
Similar questions to practice:
Hope it helps.
Answer: C
Question: The number of new words that can be formed by rearranging the letters of the word 'RAM' is ?
Options:
A)5
B)10
C)120
D)6
E)8
Rationale: Number of words which can be formed
= 3! - 1 = 6- 1
= 5.
Answer:A
Answer: A
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 50 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
Options:
A)22%
B)24%
C)25%
D)27%
E)31%
Rationale: Total sales =800
Comission = (20/100)*500+ (50/100)*300
=100 + 150
=250
%Comission =(250/800)*100=31.3~ 31%
Answer is E
Answer: E
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)5 kmph
B)6 kmph
C)7 kmph
D)8 kmph
E)9 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
ANSWER:D
Answer: D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
Options:
A)7
B)6
C)8
D)7/20
E)1
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: D
Question: A contractor is engaged for 30days on the condition thathe receives Rs.25 for each day he works &is fined Rs.7.50 for each day is absent. He gets Rs.555 in all. For how many days was he absent?
Options:
A)8
B)10
C)15
D)6
E)19
Rationale: 30 * 25 = 750
455
-----------
195
25 + 7.50 = 32.5
195/32.5 = 6
D
Answer: D
Question: The value of log2 16 is:
A.
1
8
B.	4
C.	8
D.	16
Answer: Option B
Explanation:
Options:
A)2
B)4
C)6
D)8
E)12
Rationale: Let log2 16 = n.
Then, 2n = 16 = 24 n = 4.
log2 16 = 4.
Answer: Option B
Answer: B
Question: Jerry travels 8 miles at an average speed of 40 miles per hour, stops for 11 minutes, and then travels another 20 miles at an average speed of 60 miles per hour. What is Jerry’s average speed, in miles per hour, for this trip?
Options:
A)37
B)42.5
C)44
D)50
E)52.5
Rationale: Total Time taken by jerry = (8/40)*60 Minutes + 11 Minutes + (20/60)*60 Minutes = 45 Minutes
Average Speed = Total Distance / Total Time = (8+20) miles / (45/60)Hours = 28*60 / 45 = 37 Miles per hour
Answer: option A
Answer: A
Question: The volume of a rectangular box is 330 square inches. The length on one side of the top is 11
inches, and the height of the box is 3 inches. What is the area of the top of the box? (A drawing
may help you with this one.)
Options:
A)100
B)130
C)120
D)110
E)101
Rationale: 3 x 11 = 33
V = 33 x missing measure
V is 330
330 ÷ 33 = 10 which is the missing
measure of the side of the box top
10 x 11 = 110 sq. ft. which is area
of the top of the box.
correct answer D
Answer: D
Question: In a room are five chairs to accommodate 3 people. One person to a chair. How many seating arrangements are possible?
Options:
A)45
B)60
C)72
D)90
E)120
Rationale: The first person has 5 options i.e. 5 chairs to choose from
The second person has 4 options i.e. 4 chairs to choose from (first one has already taken a chair)
The third person has 3 options i.e. 3 chairs to choose from (two chairs are already gone)
Total seating arrangements 5*4*3 = 60
ANS:B
Answer: B
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years.What is the sum ?
Options:
A)Rs. 4462.50
B)Rs. 8032.50
C)Rs. 8900
D)Rs. 8925
E)None of these
Rationale: Solution
Principal = Rs. (100x4016.25/9x5)= Rs.401625/25= Rs. 8925.
Answer D
Answer: D
Question: The probability of pulling a black ball out of a glass jar is 1/W. 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)E/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/W
Lets say P of breaking the jar = n
That means 1/W*n=1/Y
n= W/Y
B is the answer
Answer: B
Question: In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 75000*10^(-3) Petri dishes. How many germs live happily in a single dish?
Options:
A)10
B)20
C)30
D)40
E)48
Rationale: 0.036*10^5 can be written as 3600
75000*10^(-3) can be written as 75
Required= 3600/75= 48
ANSWER:E
Answer: E
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 25 times the difference between the two numbers. How many coins did the old man have?
Options:
A) 24
B) 26
C) 30
D) 25
E) 40
Rationale: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 25(x - y) --> x + y = 25.
Answer: D.
Answer: D
Question: What is the greatest positive integer n such that 3^n is a factor of 36^100?
Options:
A)100
B)200
C)300
D)600
E)900
Rationale: Prime factorization out is the way to go here!
36 ^100
3^2 times 2^2 and both to the power of 100
[(3^2)*(2^2)]^100
giving you the beautifully simplistic answer of 3^200 and 2^200
Ans is 200
ANSWER:B
Answer: B
Question: Mrs. Stark paid $6,000 for 100 shares of stock A and $4,000 for 100 shares of stock B. She later sold the same shares of both stocks, gaining 3/8 the amount she paid for stock B. If the prices she had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
Options:
A)The same.
B)A loss 1 1/2 times as much.
C)A loss 2 times as much.
D)A loss 9 times as much
E)A gain 1 1/2 times as much
Rationale: A = 6000; B = 4000; Profit = (3/8)*4000 = 1500
After prices are reversed:
A = 4000; B = 6000; Profit = (3/8)*6000 = 2250
2250 = 3/2(1500) --> Gain of 3/2 times 1500
Answer: E
Answer: E
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 25% of all the students at Morse have cars, how many students are in the three lower grades?
Options:
A)500
B)900
C)1200
D)1350
E)1500
Rationale: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.25(x+300)
0.15x = 75
x = 500
The answer is A.
Answer: A
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
Options:
A)26
B)29
C)39
D)42
E)43
Rationale: 39
Option 'C'
Answer: C
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
Options:
A)3 (5/19)
B)3 (5/13)
C)3 (5/11)
D)3 (3/11)
E)33(5/11)
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Answer: C
Answer: C
Question: professor absentminded has a very peculiar problem that he cannot remember number larger than 15. however he tells his wife, i can remember any number up to 100 by remembering the three numbers obtained as remainder when the numbers is divided by 3,7 and 11 respectively. for example (2,3,6)is 17. professor remembers that he had(2,4,8)rupees in the purse, and he paid(2,5,4) rupees to the servant. how much money is left in the purse?
Options:
A)45
B)46
C)47
D)48
E)49
Rationale: find out the common term in those 3 series for (2,4,8)
3N+2=2,5,8,11,14......71,74
7N+4=4,11,18...67,74
11N+8=8,19,30......63,74
find out the common term in those 3 series for (2,5,4)
3N+2=2,5.....23,26
7N+5=5,12,19,26
11N+4=4,15,26
now 74-26=48
ANSWER:D
Answer: D
Question: Two trains, 130 and 110 metres long, while going in the same direction, the faster train takes one minute to pass the other completely. If they are moving in opposite direction, they pass each other completely in 3 seconds. Find the speed of trains.
Options:
A)30 m/s, 40 m/s
B)32 m/s, 48 m/s
C)40 m/s, 44 m/s
D)38 m/s, 42 m/s
E)None of these
Rationale: Let speed of trains are S1 m/s and S2 m/s.
Then, s1 - s2 = 130+110/60=4 ....(i)
and s1 + s2 = 130+110/3=80....(ii)
on solving (i) and (ii), we get
S1 = 42 m/s , S2 = 38 m/s
Answer D
Answer: D
Question: Mike earns $15 per hour and Phil earns $10per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
Options:
A)33.3%
B)32.5%
C)37%
D)37.5%
E)40%
Rationale: What % less of 15is 10
let it be x % less ,then
=15(1-x/100)=10
1-x/100=10/15
x=100/3
x=33.3%
Ans A
Answer: A
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {9, 10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
Options:
A)1/20
B)1/12
C)2/15
D)3/10
E)1/7
Rationale: P(x is prime) = 1/3
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 1/3*1/4 = 1/12
The answer is B.
Answer: B
Question: For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
Options:
A)x + y + z + 1
B)xyz + xz
C)xy + z + 1
D)xyz + 1
E)xyz + 1/2
Rationale: x appetizers,
y + 1 main courses,
z dessert
Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = xC1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}
Hence, number of ways = x(y+1)z = xyz + xz
Correct Option: B
Answer: B
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)72 kmph
B)75 kmph
C)30 kmph
D)80 kmph
E)85 kmph
Rationale: Explanation:
S = (90 + 60)/2 = 75 kmph
ANSWER IS B
Answer: B