divelab/Sys2Bench huggingface dataset:
Question: An urn contains 5 red, 6 blue and 8 green balls. 4 balls are randomly selected from the urn, find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ?
Options:
A)20/323
B)40/323
C)60/273
D)50/373
E)40/373
Rationale: Sample space = no. of ways 4 balls were drawn from urn = 19C4 = 3876
No. ways 1 blue and 2 red and 1 green balls were drawn from bag = 6C1 * 5C2 * 8C1 = 480
Probability = 480 / 3876 = 40/323
Ans - B
Answer: B
Question: In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. If the total number of trees in that garden is n, then :
Options:
A)n is a perfect square
B)n is an odd number
C)n is an even number
D)n is a perfect cube.
E)none
Rationale: If there are, for example, 4 rows of trees, each row would have 4 trees. The total would be 4*4=16, which is a perfect square.
Answer: A
Answer: A
Question: A glucose molecule contains 6 carbon, 12 hydrogen and 6 oxygen atoms. During photosynthesis, green plants create glucose daily. If, over a period of 15 days, an eucalyptus plant (a green plant) creates 15,000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day?
Options:
A)60,000
B)6,000
C)2,500
D)250
E)0
Rationale: Solution:
We know that 15,000 glucose molecules are created over a period of 15 days. Therefore 15,000/15 = 1,000 glucose molecules are created on average per day.
Each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms. So 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms. The difference is 12,000 – 6,000 = 6,000.
The correct answer is B.
Answer: B
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)24
C)27
D)28
E)30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: A
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word CAREER could be arranged to create a six-letter code?
Options:
A)6!
B)6! − (3! + 2!)
C)6! − (3! × 2!)
D)6!/(3! + 2!)
E)6!/(2! × 2!)
Rationale: Number of letters in word 'CAREER' = 6.
The letters 'R' and 'E' appear 2 times and 2 times respectively in the word 'CAREER'.
Therefore the mathematical solution for number of ways that the letters of the word CAREER can be arranged to create six-letter code
= 6!/(2!*2!)
Answer:E
Answer: E
Question: Out of 470 students of a school, 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket ?
Options:
A)80
B)150
C)100
D)180
E)220
Rationale: n(A)=325,n(B)=175,n(AuB)=470-50=420.
Required number = n(AnB)=n (A)+n (B)-n(AuB)=325+175-420=80.
Answer is A
Answer: A
Question: A meeting has to be conducted with 6 managers. Find the number of ways in which the managers may be selected from among 9 managers, if there are 2 managers who refuse to attend the meeting together.
Options:
A)36
B)40
C)42
D)45
E)49
Rationale: The total number of ways to choose 6 managers is 9C6 = 84
We need to subtract the number of groups which include the two managers, which is 7C4 = 35.
84 - 35 = 49
The answer is E.
Answer: E
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability T that the integer drawn is divisible by 8?
* A solution will be posted in two days.
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,T two out of three can be divided and the answer is D.
Answer: D
Question: 8 people decided to split the restaurant bill evenly. If the bill was $314.12 dollars, how much money did they 1 cent is the smallest unit?
Options:
A)$314.16
B)$314.17
C)$314.18
D)$314.19
E)$314.20
Rationale: If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8
the last 3 digit 412 not divisible by a
Hence, we need to add 4 to this number for it to be divisible by 8
Correct Option: A
Answer: A
Question: The sum Q of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Qn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
Options:
A)4345
B)4302
C)4258
D)4214
E)4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum Q of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: D
Question: A company hired a printer to produce a total of x + 1 envelopes. The job consisted of two types of envelopes, 4¢ envelopes and 7¢ envelopes. If the company requested 3 more 4¢ envelopes than 7¢ envelopes, which of the following expressions denotes the cost, in cents, of the total x + 1 envelopes ?
Options:
A)(9x-12)/2
B)4x+13
C)3x+34
D)6x-4
E)(7x+4)/2
Rationale: We can take
X+1 = 11
X= 10
So 4c envelopes will be 7
and 7c envelopes will be 4
So total cost will be 56
Then that is our target
Plug x =10 in answer choices
Only D works
Correct Answer :D
Answer: D
Question: If six persons sit in a row, then the probability that three particular persons are always together is -
Options:
A)1/9
B)1/7
C)1/5
D)1/1
E)1/3
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: A rower can row 6 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
Options:
A)2.66
B)2.78
C)2.8
D)2.87
E)2.92
Rationale: Let x be the distance to Big Rock.
time = x/5 + x/7 = 1
x = 35/12 = 2.92
The answer is E.
Answer: E
Question: A man is 24 years older than his son.In two years,his age will be twice the age of his son.The present age of the son is:
Options:
A)14 years
B)18 years
C)20 years
D)22 years
E)None of these
Rationale: Solution
Let the son's present age be x years.Then,man's present age =(x + 24)years.
∴ (x + 24)+ 2 =2(x + 2) ⇔ x + 26 =2x + 4 ⇔ x =22. Answer D
Answer: D
Question: Sakshi can do a piece of work in 5 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
Options:
A)4
B)16
C)18
D)25
E)10
Rationale: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 5 : x ⇒ x = (5x4/5) ⇒ x = 4 days.
Hence,Tanya takes 16 days is complete the work.
Answer A
Answer: A
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
Options:
A)2/5
B)4/5
C)5/7
D)7/11
E)7/13
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
A)
Answer: A
Question: Find the rate at Simple interest, at which a sum becomes four Ɵmes of itself in 15 years.
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: Explanation:
Let sum be x and rate be r%
then, (x*r*15)/100 = 3x [important to note here is that simple interest will be 3x not 4x, beause 3x+x =
4x]
=> r = 20%
Answer: B
Answer: B
Question: One day a car rental agency rented 2/3 of its cars, including 3/5 of its cars with CD players. If 3/4 of its cars have CD players, what percent of the cars that were not rented had CD players?
Options:
A)10%
B)35%
C)45%
D)66.7%
E)90%
Rationale: Let us try to solve this by getting some number for total cars.
let there be 3,4 and 5 = 60 cars... ( we have taken denominators of 2/3,3/4 and 3/5 least common number).
2/3(60) = 40 cars ...total rented cars , then 1/3(60) = 20 cars were not rented.
3/4(60) = 45 cars with CD players...total CDP cars
now 3/5(3/4) = 3/5(45) = 27 CDP cars and these are cars that we rented.
Non rented CDP = Total CDP - rented CDP = 45 -27 = 18.
18/20 = 90%.
ANSWER:E
Answer: E
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Options:
A)22
B)88
C)27
D)89
E)287
Rationale: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
Answer: C
Answer: C
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
Options:
A)6 years
B)9 years
C)5 years
D)4 years
E)6 years
Rationale: 4 years
Answer: D
Answer: D
Question: Four rooms of the same type were advertised to be let in a locality. four men made separate applications for a house. What is the probability that each of them applied for the same house.
Options:
A)1/16
B)1/256
C)1/64
D)4/64
E)4/16
Rationale: Each men can choose any of the three houses, hence the total number of ways they can apply is 4^4 = 256.
Each of them to apply for the same house means each of them applying for house A, B or C,D.
P = 4/256 = 1/64.
Answer: C.
Answer: C
Question: A five-character password consists of two letter of the alphabet and three different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
Options:
A)915,040
B)918,720
C)926,000
D)937,440
E)973,440
Rationale: 5 character password: DLDLD
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
Next digit can be chosen in 8 ways.
The letter can be chosen in 25 ways.
This gives us 10*26*9*25*8ways
Now, the letter can also be DDLLD so there will be another 10*9*26*25*8 ways
Total = 10*26*9*25*8*2 = 973,440 ways
E
Answer: E
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.9. 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)(0.9)^5
B)2(0.9)^4
C)3(0.9)^4
D)4(0.9)^4(0.1) + (0.9)^5
E)5(0.9)^4(0.1) + (0.9)^5
Rationale: P(5 heads) = (0.9)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.9)^4(0.1)
The answer is E.
Answer: E
Question: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in w hours. In terms of x and w, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
Options:
A)x/(x+y)
B)y/(x+y)
C)xy/(x+y)
D)xy/(x-y)
E)xw/(w-x)
Rationale: Pick some smart numbers for x and w.
Say x=1 hour and w=2 hours (notice that w must be greater than x, since the time for machine A to do the job, which is w hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and w=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
Answer: E
Question: Jim and John are workers in a department that has a total of 8 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
Options:
A)1/25
B)1/14
C)1/28
D)1/7
E)2/19
Rationale: Probability = 2c2/8c2
= 1/28
Answer C
Answer: C
Question: If x>y>0, which of the following must be true:
I. |x|>y
II. x^4 > y^4
III. x^2>y^2
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II and III
Rationale: Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true
Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y
So OA=D
Answer: D
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is
Options:
A)20
B)80
C)100
D)200
E)180
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Correct answer is 100
Answer: C
Question: A can do a piece of work in 24 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)10
B)12
C)13
D)11
E)15
Rationale: 2/24 + 4/15 + x/20 = 1
x = 13 Answer: C
Answer: C
Question: Anup was asked to find the value of 7/12 of a sum of money W. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
Options:
A) 48
B) 89
C) 84
D) 69
E) 49
Rationale: W=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: E
Question: Abby and Bobby type at constant rates of 80 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 400 more words than Bobby?
Options:
A)1:40 PM
B)1:50 PM
C)2:00 PM
D)2:10 PM
E)2:20 PM
Rationale: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 80t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 80t: 600+60t=80t-400 --> t=50.
1:30 PM + 50 minutes = 2:20 PM.
Answer: E.
Answer: E
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5?
Options:
A)148
B)154
C)156
D)158
E)170
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: D
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)5/21
B)5/28
C)5/20
D)5/22
E)5/25
Rationale: Number of ways of (selecting at least two couples among five people selected)
As remaining person can be any one among three couples left.
Required probability
= (10 * 6)/252 = 5/21
Answer: A
Answer: A
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: C) 3
Answer: C
Question: A fair is coin is tossed repeatedly. If head appears on first four tosses then what is the probability of appearance of tail in the fifth toss?
Options:
A)2/3
B)1/2
C)1/8
D)1/0
E)1/6
Rationale: As the given coin is a fair coin, the probability of getting tail on the fifth toss is independent of the out comes in the previous 4 tosses. So probability = 1/2
Answer:B
Answer: B
Question: a is an integer greater than 39 but less than 51, b is an integer greater than 49 but less than 61, what is the range of a/b?
Options:
A)1/4
B)1/3
C)3/4
D)1
E)5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=40 and b=60
So, a/b =2/3
max value of a/b will be when b is lowest and a is highest ---> a=50 and b=50
So, a/b = 1
Range is 1-(2/3) = 1/3.
Answer should be B.
Answer: B
Question: Over a three-week period, the price of an ounce of gold increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks?
Options:
A)0.95G
B)1G
C)1.05G
D)1.1G
E)1.15G
Rationale: Initial price =G
By end of first week increased by 25% => Price =1.25G
By end of second week decreased by 20% => Price= 1.25*0.8G
By end of third week increased by 5% => Price=1.25*0.8*1.05G
=> Price= 1.05G
ANSWER:C
Answer: C
Question: A sum of money deposited at C.I. amounts to Rs.2442 in 2 years and to Rs.2926 in 3 years. Find the rate percent?
Options:
A)11
B)20
C)28
D)24
E)82
Rationale: Explanation:
2420 --- 484
100 --- ? => 20%
Answer: Option B
Answer: B
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
Options:
A)2400
B)2408
C)24028
D)24128
E)2121
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Answer: A
Question: On the xy-plane, each point on circle C has coordinates such
that x 0 and y 0. If the center of circle C is the point (3; 4),
what is the maximum possible area of C?
Options:
A) 6
B) 9
C) 24
D) 32
E) 64
Rationale: I think that theintentof this question is that the circle will have NO CO-ORDINATES that fit the following 2 forms: (0, Y) or (X, 0). In real basic terms, this circle will NEITHER touch (nor cross) the X-axis NOR will it touch (nor cross) the Y-axis.
With a center at (3,8), the longest possible radius would ALMOST touch the X-axis, so the radius would be a little less than 3.
If the radius WAS 3 exactly, then the area would be 9pi, which is approximately 28.26
Since the circle CAN'T touch the X-axis, the area has to be LESS than approximately 28.26
As it's written, none of the answers is clearly the correct one.
B
Answer: B
Question: Roger can read a book in k minutes. What part of the book can he read in 7 minutes? (k>8)
Options:
A)8+k
B)k/8
C)7/k
D)(k+ 8)/k
E)(k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer: C
Answer: C
Question: If n = 2×3×5×7×11×13×16, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even
Options:
A)I only
B)II only
C)III only
D)I and III
E)None of the above
Rationale: Statement I: 600 = (2^3)*(3)*(5^2) this is true.
Statement 2 this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (D).
Answer: D
Question: The average monthly salary of 20 employees in an organisation is Rs. 1400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
Options:
A)3600
B)3890
C)88798
D)2789
E)3500
Rationale: Explanation:
Manager's monthly salary Rs. (1500 * 21 - 1400 * 20) = Rs. 3500.
Answer: E
Answer: E
Question: Judges will select 5 finalists from the 8 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
Options:
A)10
B)21
C)210
D)420
E)560
Rationale: First Select 5 from 7 contestants and then select top 3 from those 5 =
8C5*5C3 = 56 * 10 = 560
ANS:E
Answer: E
Question: Let f(x) = 3x2+2x+6. Two distinct lines l1 and l2 exist that are tangent to f(x) and intersect
at the origin. Given that l1 is tangent to f(x) at (x1; f(x1)) and that l2 is tangent to f(x) at
(x2; f(x2)), compute x1x2.
Options:
A)-1
B)-2
C)-3
D)-4
E)-5
Rationale: At any point (x0, y0) in f(x), the slope of the tangent line is
m = 6x0 + 2
Hence, the equation of the tangent line is given by
(y - y0) = m(x- x0)
y - (3x2
0 + 2x0 + 6) = (6x0 + 2)(x - x0)
y = (6x0 + 2)x - 6x2
0- 2x0 + 3x2
0 + 2x0 + 6
y = (6x0 + 2)x- 3x2
0 + 6
For the tangent line to cross the origin, we must have 3x2
0 - 6 = 0. This equation has two
solutions, the product of which is given by 􀀀6
3 = -2 .
correct answer B
Answer: B
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
Options:
A)2888
B)1266
C)1000
D)2779
E)2661
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Answer: C
Question: A certain taxi company charges $3.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
Options:
A)15.6
B)16.0
C)17.5
D)18.7
E)19.1
Rationale: A certain taxi company charges $3.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $3.50 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $3.5 + $15.6 = $18.7.
Answer: E.
Answer: E
Question: B alone can do piece of work in 10 days. A alone can do it in 15 days. If the total wages for the work is Rs 5000, how much should B be paid if they work together for the entire duration of the work?
Options:
A)267
B)7
C)76
D)8
E)82
Rationale: Answer:A
Answer: A
Question: Find the value of y from the given equation. 9^y = 3^12, what is y?
Options:
A)3
B)5
C)7
D)8
E)6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: E
Question: If x and y are both odd prime numbers and x < y, how many distinct positive integer T factors does 2xy have?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: Since 2xy prime T factors are x^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think D would be the correct answer.
Answer: D
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $464,800 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
Options:
A) $1,568,000
B) $448,000
C) $406,000
D) $313,600
E) $116,000
Rationale: My take is D.
(464800*4 + 112000*3)/7 = 313600
Answer: D
Question: A bag contains 40 black balls and 40 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)2/5
B)5/7
C)1/2
D)1/4
E)1/3
Rationale: Total number of balls = 40+40 = 80
no. of white balls = 40
probability of drawing a white ball = 40/80 = 1/2
Answer is C
Answer: C