divelab/Sys2Bench huggingface dataset:
Question: During a certain two-week period, 72 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 6 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
Options:
A)1/20 A
B)10 A
C)15 A
D)18 A
E)23 A
Rationale: Movies: 72 % comedies. 28 % remaining genre.
Now in this 28 %, there are only 2 categories. Action movies and Drama Movies.
If Action = x; Drama movies = 6x. Total 7x.
7x = 28; x = 4
Action movies: 4 %
Drama movies: 24 %
we can say that out of 100z,:
comedies: 72z
action: 4z
drama: 24 z
Now action movies were A
This means:
A = 4z.
z = (A/4)
Comedies: 72z = 72 * (A/4)
18 A
D is the answer.
Answer: D
Question: Ashok and Pyarelal invested money together in a business and share a capital of Ashok is 1/9 of that of Pyarelal.if the incur a loss of Rs 1200 then loss of Pyarelal?
Options:
A)600
B)700
C)1080
D)900
E)1000
Rationale: Let the capital of Pyarelal be x, then capital of Ashok=x/9
So ratio of investment of Pyarelal and Ashok = x : x/9 =9x : x
Hence out of the total loss of 1200, loss of Pyarelal= 1200*9x/10x=1080
ANSWER:C
Answer: C
Question: The profit earned by selling an article for 832 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
Options:
A)960
B)1060
C)1,200
D)920
E)None of these
Rationale: Let the profit or loss be x
and 832 – x = 448 + x or, x = 384⁄2 = 192
\ Cost price of the article = 832 – x = 448 + x = 640
\ SP of the article = 640 × 150⁄100 = 960
Answer A
Answer: A
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-sixth of all fruit exports from Country Y are orange exports. If country Y generates $2.5 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
A)$21.25m
B)$75m
C)$106.25m
D)$127.5m
E)$153m
Rationale: 2/10*1/6*(total) = 2.5
1/30*(total) = 2.5
(total) = 2.5*30 = 75
Answer: B.
Answer: B
Question: 8 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
Options:
A)66
B)52
C)58
D)55
E)56
Rationale: Though 2*(8C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 7, so he'll play 14 matches.
Similarly, second guy has to play with the rest of 6 as his 2 games with the first guy are already played. So he plays 12 matches.
This continues like this and the total matches are 14+12+10...+2
14+12+...+2 = 2(7+6+...+1) = 2((7*8)/2) = 7*8 =56.
ANSWER:E
Answer: E
Question: Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 26 have taken the preparatory course and 65 have not taken the course. How many members are there in the swim club?
Options:
A) 60
B) 80
C) 100
D) 130
E) 140
Rationale: 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 65+26=91 members have not passed the test, thus 0.7*Total=91 --> Total=130.
Answer: D.
Answer: D
Question: Set A = {1, 2, 3, 4, 5, 6, e}
Which of the following possible values for e would cause Set A to have the smallest standard deviation?
Options:
A) 1
B) 2.5
C) 3
D) 3.5
E) 7
Rationale: I agree. The mean of the set e 1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Answer: D
Question: 7 people sit at the round table. In how many ways can we sit them so that Bob and Bill don't sit opposing each other?
Options:
A)400
B)420
C)440
D)460
E)480
Rationale: 7 People: Bob,Bill,Red,Blue,White,Pink,Purple
Round Table: T
7 Chairs: 1,2,3,4,5,6,7
Let chairs 1 and 4 be opposite each other;
Bob is sitting on 1 and Bill is sitting on 4;
The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways
Now, Bill and Bob swap their positions;
Bob is sitting on 4 and Bill is sitting on 1;
The rest of the people on 2,3,5,6,7 - can rearrange themselves in 5! ways
Thus total number of ways in which Bob and Bill are sitting opposite each other = 2*5! = 120*2 = 240
We have to find in how many ways they are NOT sitting opposite; subtract 240 from the total number of possible arrangements;
In circular permutation, Total number of arrangements of n people = (n-1)!
Here number of people = 7
Arrangements = (7-1)! = 6!= 720
Number of ways Bob and Bill are NOT sitting opposite = 720-240 = 480.
Answer: E
Answer: E
Question: Johnny makes $6.75 per hour at his work. If he works 10 hours, how much money will he earn?
Options:
A)$67.50
B)$54
C)$28.50
D)$12.50
E)$9.60
Rationale: 6.75*10=67.50. Answer is A.
Answer: A
Question: Veena ranks 44rd from the top in a class of 182. What is her rank from the bottom if 22 students have failed the examination?
Options:
A)88
B)108
C)110
D)90
E)117
Rationale: total student=182
failed=22
paasd student=182-22=160
from bottom her rank is=160-44+1=117
ANSWER:E
Answer: E
Question: In a bag there are a certain number of black balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of black balls to blue balls in the bag
Options:
A)1:2
B)1:4
C)1:1
D)1:5
E)1:6
Rationale: since the probability of drawing a blue ball out of two picks is 1/2.
the ratio of the blue ball to black balls should be 1:1
Answer : C
Answer: C
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)23676
B)19766
C)29172
D)11750
E)11267
Rationale: Explanation:
200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750
Answer:D
Answer: D
Question: Vinay spends 30% of his salary on house rent and 55% of the remaining money on food and clothes. He saves the remaining amount. If he saves ?59724 yearly, how much amount does he spend on food and clothes per month ?
Options:
A)5316
B)4792
C)5817
D)6080
E)6083
Rationale: Let his monthly salary be x.
House rent expenditure = 30/100 x = 3x/10
âˆ´ Remaining = 7x/10
Expense of food = 7x/10 x 55/100 = 77x/200
âˆ´ Remaining = 7x/10 - 77x/200
= 140x - 77x/200 = 63x/200
Monthly saving = 59724/12 = 4977
âˆ´ 63x/200 = 4977 = x = 4977 x 200/63 = 15800
Expenditure on food and clothes = 77x/200
= 6083
Answer: E
Question: If x^2+(1/x^2)=6, x^4+(1/x^4)=?
Options:
A)10
B)11
C)12
D)34
E)15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=6^2-2=34.
Thus, the answer is D.
Answer: D
Question: If the length of a rectangle is doubled and its breadth is tripled, what is the percentage change in its area?
Options:
A)200% increase
B)345% increase
C)400% increase
D)125% increase
E)25% decrease
Rationale: Length is halved.
i.e., length is increased by 200%
Breadth is tripled
i.e., breadth is increased by 200%
Change in area=(−200+200+(200×200)/100)%=400%
i.e., area is increased by 400%
ANSWER:C
Answer: C
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
A)39
B)88
C)3
D)7
E)62
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
\inline \fn_jvn \therefore 16(x-3)+87 = 17x
\inline \fn_jvn \therefore x = 87 - 48 = 39
Answer:A
Answer: A
Question: A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?
Options:
A)0.2
B)0.3
C)0.5
D)0.7
E)0.4
Rationale: color frequency
red 3
green	7
white 10
Let P(E) be the event of getting white marble
P(E) = Frequency for white color / Total frequencies in the above table
= 10 / (3+7+10)
= 10 / 20
= 0.5
My answer is (C)
Answer: C
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 42 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Options:
A)72 sec
B)132 sec
C)192 sec
D)252 sec
E)None
Rationale: Solution
Relative Speed	= (42 - 40 ) Kmph
= 2 kmph
=(2 x 5 / 18)m/sec
= (10 / 18 ) m/sec
Time taken	= (350 x 18 / 10) sec
= 630 sec.
Answer E
Answer: E
Question: Points A, B, C, and D, in that order, lie on a line. If AB = 3 cm, AC = 4 cm, and BD = 8 cm, what is CD, in centimeters?
Options:
A) 7
B) 2
C) 3
D) 4
E) 5
Rationale: Putting a value to each point, lets use the following:
A - 0
B - 3 (AB = 3)
C - 4 (AC = 4)
D - 11 (BD = 8)
CD is 11-4 = 7.
Ans A
Answer: A
Question: Find the odd man out.
1, 9, 25, 4, 36, 65, 49
Options:
A)1
B)25
C)9
D)65
E)49
Rationale: Explanation:
Each of the numbers except 65 is a perfect squares.
Answer: D) 65
Answer: D
Question: here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
Options:
A)2100
B)1800
C)1245
D)3210
E)4521
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Ans: B
Answer: B
Question: A train travels from New York to Chicago, a distance of approximately 540 miles, at an average rate of 60 miles per hour and arrives in Chicago at 6:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
Options:
A)3:00
B)4:00
C)5:00
D)6:00
E)10:00
Rationale: 6:00 in evening in Chicago = 7:00 in evening in New York. So, the train was in Chicago 7:00 in the evening, New York time.
The trip took T=D/R=540/60=9 hours. Therefore, the train depart from New York at 7:00 - 9 hours = 10:00 in the morning, New York time.
Answer: E.
Answer: E
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 60 percent of the pack would be outfielder cards?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 60% of toatal Ocards
12-X<.6*12
X>12-7.2
X>4.8
X=5
Ans B
Answer: B
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
A)287 sec
B)288 sec
C)48 sec
D)16 sec
E)17 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer: C
Answer: C
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] + 2 = f(3x – 6)
Options:
A)0
B)4
C)5
D)7
E)13
Rationale: Answer = C = 5
f(x) = 3x – 5
2*[f(x)] + 2 = f(3x – 6)
2(3x-5) + 2 = 3 (3x-6) - 5
6x - 8 = 9x - 23
x = 5
Answer: C
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 21st of September 1990?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Thursday
E)Friday
Rationale: There are 365 days in an ordinary year and 366 days in a leap-year.
365 divided by 7 (a week period) yields a remainder of 1, thus the same date after an ordinary year would fall on the next day of a week;
366 divided by 7 (a week period) yields a remainder of 2, thus the same date after a leap-year would fall two days after in a week;
Thus 3 years, 1988, 1989 and 1990, will accumulate 2+1+1=4 days, plus 2 days of difference between 19th and 21st, which gives total of 6 days of difference (6 days shift). Thus, 21st of September 1990 was Saturday+6 days=Friday.
Answer: E.
Answer: E
Question: Last year, for every 100 million vehicles that travelled on a certain highway, 94 vehicles were involved in accidents. If 3 billion vehicles travelled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Options:
A)288
B)320
C)2,820
D)3,200
E)28,800
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 94 accidents as 3 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 3,000 million rather than 3 billion. Creating a proportion we have:
100/94= 3,000/x
Cross multiplying gives us:
100x = 3,000 * 94
x = 30 * 94 = 2,820
Correct answer is C.
Answer: C
Question: X is able to do a piece of work in 14 days and Y can do the same work in 20 days. If they can work together for 5 days, what is the fraction of work completed?
Options:
A)15/28
B)17/28
C)13/28
D)19/28
E)11/28
Rationale: Explanation :
Amount of work X can do in 1 day = 1/14
Amount of work Y can do in 1 day = 1/20
Amount of work X and Y can do in 1 day = 1/14+ 1/20= 17/140
Amount of work X and Y can together do in 5 days = 5 × (17/140) = 17/28
Answer : Option B
Answer: B
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
Options:
A)1/6
B)1/0
C)1/5
D)1/4
E)1/1
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer: C
Answer: C
Question: #p is defined as 2p+20 for any number p. What is p, if #(#(#p))=12?
Options:
A)–16
B)–44
C)10
D)16
E)18
Rationale: #p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = 12 ---> 8p= -128 ---> p = -16, A is the correct answer.
Answer: A
Question: Two motor bikes cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower bike takes 1 hour more than the faster bike ?
Options:
A)860 km
B)870 km
C)960 km
D)260 km
E)840 km
Rationale: Explanation:
60(x + 1) = 64x
X = 15
60 x 16 = 960 km
Answer: C
Answer: C
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 1 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
A)40 gallons
B)100 gallons
C)120 gallons
D)180 gallons
E)130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 1 gallons\
Volume of whole = 1 * 40 = 40 gallons.
ANSWER:A
Answer: A
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.620 in all. For how many days was he absent?
Options:
A)8
B)10
C)15
D)7
E)4
Rationale: 30 * 25 = 750
620
-----------
130
25 + 7.50 = 32.5
130/32.5 = 4
E
Answer: E
Question: If the first day of a year (other than leap year) was Thursday, then which was the last day of that year?
Options:
A)Saturday
B)Thursday
C)Tuesday
D)Monday
E)None of these
Rationale: Explanation :
Given that first day of a normal year was Thursday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Thursday+ 1 Odd day) = Friday
Therefore, last day of the mentioned year = Thursday. Answer : Option B
Answer: B
Question: A sum of money lent out at S.I. amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is?
Options:
A)299
B)600
C)77
D)266
E)222
Rationale: S.I for 5 years = (1020 - 720) = Rs. 300.
S.I. for 2 years = 300/5 * 2 = Rs. 120.
Principal = (720 - 120) = Rs. 600.
Answer: B
Answer: B
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
Options:
A)27
B)29
C)39
D)42
E)45
Rationale: 39
Option 'C'
Answer: C
Question: The mean of 50 observations was 36. It was found later that an observation 28 was wrongly taken as 23. The corrected new mean is :
Options:
A)36.0
B)36.5
C)36.1
D)36.2
E)36.8
Rationale: Explanation:
Correct Sum = (36 * 50 + 28 - 23) = 1825.
Correct mean = = 1805/50 = 36.1
Answer: C) 36.1
Answer: C
Question: There is 7 friends (A1, A2, A3....A7).If A1 have to have shake with all without repeat. How many handshakes possible?
Options:
A)6
B)21
C)28
D)7
E)5
Rationale: a1 with (a2, a3,a4,a5,a6,a7)
6 handshakes
ANSWER:A
Answer: A
Question: A box measuring 27 inches long by 15 inches wide by 6 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Options:
A)90
B)180
C)210
D)240
E)864
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
3 is the biggest number that could divide all three, 27, 15 and 6.
Thus side of cube must be 3, and total number of cubes = 27/3 * 15/3*6/3 = 90
Ans A it is.
Answer: A
Question: If the least common subtraction of two prime numbers x and y is 10, where x < y , then the value of 2x + y is
Options:
A)7
B)9
C)11
D)21
E)31
Rationale: (x-y) = 10 and both x an y are prime.
The only values of x and y can be 7 and 17 (x = 7 and y = 17)
2x + y = 2*7 + 17= 31
Correct Option: E
Answer: E
Question: The difference between a two-digit number and the number obtained by interchanging the digit is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2?
Options:
A)4
B)8
C)16
D)24
E)None of these
Rationale: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let the ten's and unit's digits be 2x and x respectively.
Then, (10 * 2x + x) - (10x + 2x) = 36
9x = 36
x = 4
Required difference = (2x + x) - (2x - x) = 2x = 8.
ANSWER:B
Answer: B
Question: There are 870 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
Options:
A)75
B)100
C)125
D)175
E)145
Rationale: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 870.
Hence, we have m+f= 870
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 870/3 = 290
Solving the three equations yields the solution
f = 290,m= 580, and d= 290.
The number of female democratic participants equals half the female participants equals
290/2 = 145.
ANSWER:E
Answer: E
Question: 12.5 * 4.2 * 8.8 = ?
Options:
A)352
B)435
C)462
D)646
E)742
Rationale: C
462
? = 12.5 * 4.2 * 8.8 = 462
Answer: C
Question: 15 different biology books and 8 different chemistry books lie on a shelf. In how many ways can a student pick 2 books of each type?
Options:
A)80
B)160
C)720
D)2100
E)2940
Rationale: No. of ways of picking 2 biology books(from 15 books) = 15c2 = (15*14)/2 = 105
No. of ways of picking 2 chemistry books(from 8 books) = 8c2 = (8*7)/2 = 28
Total ways of picking 2 books of each type = 105*28 =2940
(Option E)
Answer: E
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)49 sec
B)50 sec
C)48 second
D)43 sec
E)32 sec
Rationale: D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Answer:C
Answer: C
Question: 50% of a number is added to 200, the result is the same number. Find the number?
Options:
A)300
B)288
C)400
D)129
E)281
Rationale: (50/100) * X + 200 = X
x/2 +200 = x
x+400=2x
x=400
Answer : C
Answer: C
Question: What is the probability of getting a number less than 4 when a die is rolled?
Options:
A)1/2
B)1/6
C)1/3
D)1/4
E)1/5
Rationale: Total number of outcomes possible when a die is rolled = 6 (âˆµ any one face out of the 6 faces)
i.e., n(S) = 6
E = Getting a number less than 4 = {1, 2, 3}
Hence, n(E) = 3
P(E) = n(E)/n(S)=3/6=1/2
Answer:A
Answer: A
Question: If the units digit of n^39 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
Options:
A)Only II
B)Only I
C)Only III
D)I and II
E)II and III
Rationale: I tried in this way.
Given n^39 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^39 - then divide 39 by 4 = reminder 3.
Then we have for only 7^3 - we have units digit as 3.
Hence 47^39 = 7 (units).
Option A is correct answer , and with 41^39 we always get 1 as units digit and 43^39 - we get units as 3.
Answer: A
Question: The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number p, what is the largest possible value of p?
Options:
A)97
B)151
C)209
D)211
E)219
Rationale: What is the largest possible sum of these three numbers that we can form? Maximize the first digit: 76+73+71=220=even, so not a prime. Let's try next largest sum, switch digits in 76 and we'll get: 67+73+71=211=prime.
Answer: D.
Answer: D
Question: Worker A takes 7 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)70/17
B)40/9
C)50/9
D)60/9
E)80/9
Rationale: one day work of A = 1/7
one day work of B = 1/10
so one day work of A and B together = 1/7 + 1/10 = 17/70
so total days required = 70/17
ANSWER:A
Answer: A
Question: A rower whose speed is 8 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 4 km/hr. What is the rower's average speed (in km/hr) for the total journey?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: time upstream = d / 4
time downstream = d / 12
total time = d/4 + d/12 = d/3
average speed = 2d / (d/3) = 6 km/hr
The answer is B.
Answer: B
Question: A , B , C started a partnership business by investing Rs 27000 , 72000 , 81000 respectively. At the end of the year , the profit were distributed among them. If C's share of profit is 36000, What is the total profit?
Options:
A)80000
B)90000
C)70000
D)120000
E)None of these
Rationale: Explanation :
A:B:C = 27000:72000:81000
= 3:8:9
Let the total profit= p
Then p * 9/20 = 36000
=> p = 36000*20/9 = 80000. Answer : Option A
Answer: A
Question: Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate J in miles per hour for the entire trip?
Options:
A)26.7
B)J=30.0
C)J=40.0
D)J=53.3
E)60.0
Rationale: VERITAS PREPOFFICIAL SOLUTION
Correct Answer: C
Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.
Answer choice C is correct.
Answer: C
Question: Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 6?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: i'm not sure i got the question right, if it is what i think it is, then 4 should be the right answer
0,1,2, will not have 2 slip sum it 6,add another (either 6,7,8 or 9) and we'll have a pair with sum 6
Ans:B
Answer: B