RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Of the 20 members of a kitchen crew in traditional Japanese, 17 can prepare sushi, 18 can prepare noodle, and 15 can prepare both. If one member is chosen at random, what is the probability that the member chosen will be someone who can not prepare either dish?
A.a) 1/7
B.b) 1/5
C.c) 1/4
D.d) 0
Answer: D.d) 0
Explanation: You know how to solve for Total number of people who can use at least one machine:
Total = n(A) + n(B) - n(A and B)
Total people who can prepare at least one dish = 17 + 18 - 15 = 20
So all 20 people know how to prepare at least one dish. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to prepare any dish
Answer (D)
Question: When w is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when w + y is divided by 5?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: In my view the answer should be C
w/5 has Remainder=3 -> w = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Question: List R contains five numbers that have an average value of 65. If the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number, what is the smallest possible value in the list?
A.25
B.31
C.35
D.39
Answer: B.31
Explanation: The middle number is 65.
Let the smallest number be x. Then the largest number is 2x+20.
To make x as small as possible, let's make the remaining numbers as large as possible.
So the second largest = the largest = 2x+20.
The second smallest should be equal to the median.
The numbers are x, 65, 65, 2x+20, 2x+20.
x + 65 + 65 + 2x + 20 + 2x + 20 = 5*65 = 325
5x = 155
x = 31
The answer is B.
Question: In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?
A.5760
B.14400
C.480
D.56
Answer: B.14400
Explanation: Consider the following arrangement:
*B*B*B*B*B*
Now, if girls occupy the places of 6 stars no girls will be together.
# of ways 3 girls can occupy the places of these 6 stars is C36=20;
# of ways 3 girls can be arranged on these places is 3!=6
# of ways 5 boys can be arranged is 5!=120
So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20∗6∗120=14,400
ANS:B
Question: Bradley owns b video game cartridges. If Bradleyâ€™s total is quarter the total owned by Andrew and four times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
A.16/3)b
B.17/4)b
C.13/4)b
D.21/4)b
Answer: D.21/4)b
Explanation: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlieâ€™s values in relation to Bradleyâ€™s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradleyâ€™s total
4b = Andrewâ€™s total
(1/4)b = Charlieâ€™s total
Add each total
b + 4b+ (1/4)b = 5b + (1/4)b = (20/4)b + (1/4)b = (21/4)b
Therefore,choose D.
Question: If x is an even integer and y is an odd integer, which of the following must be an even integer?
A.y/x
B.x+y
C.3x + 2y
D.3(x + y)
Answer: C.3x + 2y
Explanation: x is even and y is odd
Check the options
Option A. y/x - Nothing can be said about whether this will be an integer or not INCORRECT
Option B. x+y - Even + odd = Odd INCORRECT
C. 3x + 2y - 3*even + 2*odd = even + even = even - CORRECT
D. 3(x + y) 3*(even + odd) = 3*odd = odd - INCORRECT
E. 2y/x - Nothing can be said about whether this will be an integer or not INCORRECT
ANSWER:C
Question: When 24 is divided by the positive integer b, the remainder is 4. Which of the following statements about b must be true?
I. b is even
II. b is a multiple of 5
III. b is a factor of 20
A.III only
B.I and II only
C.I and III only
D.II and III only
Answer: D.II and III only
Explanation: 24= m*b + 4
m*b=20
put values of m
m=1 b=20
m=2 b=10
m=4 b=5
I. not true
II. true
III. true
D. correct
Question: What is the place value of 0 in the numeral 2074?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: Note : The place value of zero (0) is always 0. It may hold any place in a number,
its value is always 0.
A
Question: Sudesh was standing in the garden early in the morning after sunrise. His sister Gauri, who was coming from the opposite directions, saw that Sudesh's shadow had fallen to his right. Which directions was Gauri facing?
A.North
B.South
C.South-West
D.North-East
Answer: B.South
Explanation: as sun rises from east so the boy's shadow must be fall behind him that means toward west ......if the boy is facing towards north then and only then his sister is able to see a shadow had fallen to his right side
ANSWER:B
Question: C individuals pledged to pay equal contributions so that a charity’s goal of $F could be reached. If d of the contributors failed to pay their share, which of the following represents the additional number of dollars that each of the remaining individuals would have to pay in order to allow the charity to reach its goal?
A.df
B.dF/C(C - d)
C.dFC
D.C-d
Answer: B.dF/C(C - d)
Explanation: Number of individuals = C
Amount paid by each individual = n
Total expected amount = Charity's goal = nC = F
n = F/C
Number of individuals who fail to pay = d
Contribution from individuals who would fail to pay = dF/C --> Additional amount
Number of individuals who are paying = C - d
Additional amount has to be divided among the (C - d) individuals --> dF/C(C - d)
B
Question: How many distinct prime numbers are factors of 33150?
A.Four
B.Five
C.Six
D.Seven
Answer: B.Five
Explanation: Start with the prime factorization:
33150 = 50*663 = (2*5*5)*3*221 = (2)*(3)*(5^2)*(13)*(17)
There are five distinct prime factors, {2, 3, 5, 13, and 17}
Answer: B.
Question: Which of the following is the lowest positive integer that is divisible by 5, 6, 7, 8, 9, and 10?
A.2190
B.2360
C.2520
D.2770
Answer: C.2520
Explanation: The number needs to be divisible by 5, 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is C.
Question: A company has two types of machines, type R and type S. Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 4 hours. If the company used the same number of each type of machine to do job in 12 hours,how many machine R were used?
A.3
B.4
C.9/5
D.9/8
Answer: C.9/5
Explanation: yes there is a typo in the question, I got the same ques on my GMAT PREP last week, and the questions goes as:
A company has two types of machines,type R and type S.Operating at a constant rate a machine of R does a certain job in 36 hours and a machine of type S does the job in 4 hours .If the company used the same number of each type of machine to do job in2 hours,how many machine R were used?
So for a job to be done in 2 hours R = 1/2
R_a(Rate of Machine R) = 1/36
R_s(Rate of Machine S) = 1/4
Lets say x machines are used to attain the desired rate, thus
x/36+x/4 = 1/2 (Desired R =1/2 i.e. to complete the job in 2 hours)
(x+9x)/36 = 1/2
10x/36 = 1/2
x = 9/5.
QA = 9/5 (ANSWER C)
Question: What is greatest positive integer n such that 2^n is a factor of 12^9?
A.a)10
B.b)18
C.c)16
D.d)20
Answer: B.b)18
Explanation: The given number is 12^9
=(2*2*3)^9
=(2^18)*(3^9)
So the greatest possible value for n such that 2^n can be factor of given number is 18.
Answer B
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. five pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
A. 5
B. 12
C. 24
D. 32
Answer: D. 32
Explanation: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 32.
Answer: option D
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
A.7 : 6 : 10
B.12 : 15 : 16
C.42 : 45 : 56
D.Cannot be determined
Answer: B.12 : 15 : 16
Explanation: EXPLANATION
Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.
Answer B
Question: If a quarter kg of onions costs 70 paise, how many paise will 100 gm cost?
A.28 paise
B.65 paise
C.56 paise
D.87 paise
Answer: A.28 paise
Explanation: Explanation:
Let the required cost be x paise.
Less weight, Less cost (Direct proportion)
250 : 100 : : 70 : x
250 * x = (100 * 70)
x = (100 * 70) / 250
x = 28
ANSWER: A
Question: If 16^y = 2^16, what is y?
A.2
B.4
C.8
D.10
Answer: B.4
Explanation: 16^y = 2^4y = 2^16
4y=16
y = 4
The answer is B.
Question: At what rate percent on simple interest will a sum of money double itself in 40 years?
A.3 1/3%
B.2 1/2%
C.3 9/3%
D.3 2/3%
Answer: B.2 1/2%
Explanation: P = (P*40*R)/100
R = 2 1/2%
Answer: B
Question: Two bike riders ride in opposite directions around a circular track, starting at the same time from the same point. Biker A rides at a speed of 16 kmph and biker B rides at a speed of 14 kmph. If the track has a diameter of 40 km, after how much time (in hours) will the two bikers meet?
A.8.18 hrs.
B.6.18 hrs.
C.4.18 hrs.
D.1.18 hrs.
Answer: C.4.18 hrs.
Explanation: Explanation:
Distance to be covered = = 40 km
Relative speed of bikers = 16 + 14 = 30 kmph.
Now, = = 4.18 hrs.
Answer:C
Question: Water man has 2 cans of water. The 1st contains 25% water and the rest milk. The 2ndcontains 50% water. How much milk should he mix from each of the containers so as to get 12ltr of water such that the ratio of milk to water is 3 : 5?
A.4 ltr
B.5 ltr
C.6 ltr
D.7 ltr
Answer: C.6 ltr
Explanation: Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3	litre, C.P. of 1 litre mix. in 1st can Re.	3
4	4
Milk in 1 litre mix. in 2nd can =	1	litre, C.P. of 1 litre mix. in 2nd can Re.	1
2	2
Milk in 1 litre of final mix. =	5	litre, Mean price = Re.	5
8	8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
3
4
Mean Price
5
8
1
2
1
8
1
8
Ratio of two mixtures =	1	:	1	= 1 : 1.
8	8
So, quantity of mixture taken from each can = 1	x 12 = 6 ltr.
2
C
Question: Of the three-digit integers greater than 600, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 90
B. 81
C. 80
D. 45
Answer: B. 81
Explanation: To satify the given condition,
required no. of cases = total numbers - numbers with all digits different - numbers when all three digits are same,
number greater than 600;
total numbers = 1*10*10 = 100
numbers with all digits different = 1*9*8 = 72
numbers when all three digits are same (777) = 1
req. = 100- 72 - 1 = 27
considering the numbers between 700999 = 27*3=82
Answer is 81 ('cause 700 can't be included)
Answer (B).
Question: A man whose bowling average is 12.4, takes 7 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
A.143
B.144
C.145
D.146
Answer: C.145
Explanation: 12.4*x+26=(7+x)12
solve equation x=145
ANSWER:C
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 4, respectively, what is the probability that b/a will not be an integer?
A.1/6
B.1/4
C.1/3
D.1/2
Answer: B.1/4
Explanation: a is from the following set {1,2,3,4}
b is from the following set {4,6,8}
Total number of ways of choosing 2 integers, one from each set is = 4* 3 = 12 ways
Now the number of possibilities where b/a is not an integer is for the following outcomes
{b,a} => {4,3},{6,4},{8,3} = 3 ways
Hence probability is = 3/12 = 1/4
ans is B
Question: 16384, 8192, 2048, 256, 16, ?
A.1
B.8
C.2
D.0.5
Answer: D.0.5
Explanation: Explanation :
Terms are continuously divided by 2,4,8,16, and so on
16384
16384 ÷ 2 = 8192
8192 ÷ 4 = 2048
2048 ÷ 8 = 256
256 ÷ 16 = 16
16 ÷ 32 = 0.5
Answer : Option D
Question: Sari and Ken climb up a mountain. At night, they camp together. On the day they are supposed to reach the summit, Sari wakes up at 06:00 and starts climbing at a constant pace. Ken starts climbing only at 08:00, when Sari is already 600 meters ahead of him. Nevertheless, Ken climbs at a constant pace of 500 meters per hour, and reaches the summit before Sari. If Sari is 50 meters behind Ken when he reaches the summit, at what time did Ken reach the summit?
A.13:00
B.11:15
C.14:00
D.15:00
Answer: B.11:15
Explanation: Both Sari and Ken climb in the same direction.
Speed of Sari = 600/2 = 300 meters/hr (since she covers 700 meters in 2 hrs)
Speed of Ken = 500 meters/hr
At 8:00, distance between Ken and Sari is 600 meters. Ken needs to cover this and another 50 meters.
Time he will take = Total distance to be covered/Relative Speed = (600 + 50)/(500 - 300) = 3.25 hrs
Starting from 8:00, in 5 hrs, the time will be 11:15
Answer (B)
Question: If 1.5x=0.04y then the value of (y-x)/(y+x) is
A.730/77
B.73/77
C.7.3/77
D.7.3/770
Answer: B.73/77
Explanation: x/y=0.04/1.5
y/x=1.5/0.04
by componendo dividendo rule
(y+x)/(y-x)=1.54/1.46
(y-x)/(y+x)=1.46/1.54=73/77
ANSWER:B
Question: 5 OUT OF 1500 PARTS OF EARTH IS SULPHUR. WHAT IS THE PERCENTAGE OF SULPHUR IN EARTH
A.11/50
B.2/9
C.1/45
D.1/3
Answer: D.1/3
Explanation: REQUIRED PERCENTAGE=(5/1500*100)%=1/3%
CORRECT OPTIONS: D
Question: In how many different W ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?
A.70
B.288
C.576
D.10,080
Answer: C.576
Explanation: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves
Answer W= (4!)^2 = 576 or C
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 40 different models of televisions, what is the minimum number of letters that must be used to make the codes?
A.6
B.7
C.7
D.9
Answer: C.7
Explanation: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥40. The smallest n which fulfills this condition is n = 7.
Answer C
Question: A car covers a distance of 780 km in 6 ½ hours. Find its speed?
A.104 kmph
B.187 kmph
C.164 kmph
D.130 kmph
Answer: D.130 kmph
Explanation: 780/6
= 130 kmph
Answer: D
Question: Statements: Prime school-going children in urban India have now become avid as well as more regular viewers of TV, even in households without a TV. As a result there has been an alarming decline inthe extent of readership of newspapers. Conclusions: 1) Method of increasing the readership of newspapers should be devised. 2) A team of experts should be sent to other countries to study the impact of TV. on the readership of newspapers.
A.Only conclusion I follows
B.Only conclusion II follows
C.Either I or II follows
D.Neither I nor II follows
Answer: D.Neither I nor II follows
Explanation: The statement concentrates on the increasing viewership of TV. and does not stress either on increasing the readership of newspapers or making studies regarding the same. So, neither I nor II follows.
D
Question: Call a number Guardian if it is composite but not divisible by 2, 3, or 5. The three smallest guardian numbers are 49, 77, and 91. There are 168 prime numbers less than 1000. How many Guardian numbers are there less than 1000?
A.100
B.102
C.104
D.106
Answer: A.100
Explanation: S1 = total number of numbers divisible by 2 from 1-1000 = 500
S2 = total number of numbers divisible by 3 from 1-1000 = 333
S3 = total number of numbers divisible by 5 from 1-1000 = 200
S4 = total number of numbers divisible by 2 and 3 = 166
S5 = total number of numbers divisible by 2 and 5 = 100
S6= total number of numbers divisible by 3 and 5 =66
S7 = total number of numbers divisible by 2,3 and 5 = 33
thus total number of numbers divisible by 2,3 or 5 are = 500 +333+200-166-100-66+33 = 734
now since we have already included 2,3 and 5 while calculating their multiple in the above calculations, hence total number of prime numbers from 1-1000 becomes = 168-3 =165
also, since 1 is neither composite nor prime, hence we will subtract 1 from the final answer.
thus total number of guardian numbers are 1000-734-1-165 = 100
ANSWER:A
Question: add 8% of 24 and 10% of 40.
A.9.5
B.10.5
C.5.5
D.5.9
Answer: D.5.9
Explanation: 8% of 24 + 10% of 40
24*8/100+40*10/100
1.9+4=5.9
answer D
Question: Rajan is sixth from the left end and vinay is tenth from the right end in a row of boys. If there are eight boys between Rajan and Vinay, how many boys are there in the row ?
A.24
B.66
C.88
D.27
Answer: A.24
Explanation: Explanation:
Number of boys in the row = (6 + 10 + 8) = 24
Answer: A) 24
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 74 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
A.8715
B.0152
C.3581
D.5476
Answer: D.5476
Explanation: D
5476
n^1
74 * 74 = 5476 (sum of first 74 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Question: The average (arithmetic mean) of 4 different integers is 68. If the largest integer is 90, what is the least possible value of the smallest integer?
A.5
B.19
C.29
D.30
Answer: A.5
Explanation: Total of Integers=68*4=272
Lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer.
But all integers are distinct. So if the largest integer is 90, then the middle 2 will be 88 and 89
Lowest of least possible integer = 272-(90+89+88)=272-267=5
Answer: A
Question: In an examination, it is required to score 32% of the aggregate marks for a student to pass the examination.Raju has scored 250 marks and was declared failed by 22 marks.Find the aggregate marks?
A.720
B.750
C.800
D.850
Answer: D.850
Explanation: 32% of x =272.
x=850
ANSWER:D
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 13000, then find the annual income of A?
A.Rs. 420000
B.Rs. 180000
C.Rs. 436800
D.Rs. 504000
Answer: C.Rs. 436800
Explanation: B's monthly income = 13000 * 112/100 = Rs. 14560
B's monthly income = 2 parts ----> Rs. 14560
A's monthly income = 5 parts = 5/2 * 14560 = Rs. 36400
A's annual income = Rs. 36400 * 12 = Rs. 436800
ANSWER:C
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
A.99
B.86
C.21
D.26
Answer: A.99
Explanation: 30 * 33/2 = 5/2 * 2 * x => x
= 99
A
Question: A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in?
A.9
B.9 3/5
C.10
D.11
Answer: B.9 3/5
Explanation: (A + B + C)'s 1 day's work =	1	,
4
A's 1 day's work =	1	,
16
B's 1 day's work =	1	.
12
Therefore C's 1 day's work =	1	-	(	1	+	1	)	=	(	1	-	7	)	=	5	.
4	16	12	4	48	48
So, C alone can do the work in	48	= 9	3	days.
5	5
Answer is B
Question: 5,7,11,19,?,67,131
A.32
B.40
C.30
D.35
Answer: D.35
Explanation: The Pattern is + 2, + 4, +8, +16, ...
19+16=35
Answer :D
Question: A ladder was rested along a wall of height 5m. If ladder slides 2m away from the wall then ladder touches the foot of the wall .What is the height of the ladder.
A.6.25 mtrs
B.7.25 mtrs
C.8.25 mtrs
D.9.25 mtrs
Answer: B.7.25 mtrs
Explanation: suppose , earlier foot of ladder was x mtres away from wall, then
length of ladder = x+2 mtrs
hence
(x+2)^2 = x^2+5^2
x= 21/4 = 5.25 mtrs
length of ladder = 5.25+2= 7.25 mtrs
ANSWER:B
Question: From January 1, 2015, to January 1, 2017, the number of people enrolled in health maintenance organizations increased by 12 percent. The enrollment on January 1, 2017, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 2015 ?
A.38
B.39
C.40
D.41
Answer: C.40
Explanation: Soln:-
12x=45 --> 28/25*x=45 --> x=45*25/28=1125/28=~40
Answer: C.
Question: When x is divided by y, the quotient is q with remainder r. Which of the following is y in terms of r, x, and q? (Assume both y and q are nonzero.)
A.x – r – q
B.(x+r)/q
C.x/q−r
D.(x−r)/q
Answer: D.(x−r)/q
Explanation: Given that when x is divided y, the quotient is q and remainder is r. This implies x-r is divisible by y and yq=(x-r) or y = (x-r)/q.
Answer D.
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 32150. What percentage of profit did he make?
A.22
B.44.5
C.40
D.26
Answer: B.44.5
Explanation: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 32150
Profit(%) = (32150 - 22250)/22250 * 100 = 44.5%.Answer:B
Question: Two persons start running simultaneously around a circular track of length 380 m from the same point at speeds of 24 kmph and 28 kmph. When will they meet for the first time any where on the track if they
are moving in the opposite direction ?
A.144
B.36
C.124
D.26
Answer: D.26
Explanation: Time taken to meet the first time = length of track/relative speed
= 380/ (24 +28) (5/18)
= 380/52 *(18/5) = 26 sec.
Answer : D
Question: The number 341 is equal to the sum of the cubes of two integers. What is the product of those integers?
A.8
B.15
C.21
D.30
Answer: D.30
Explanation: 5^3+6^3= 341 number is 5*6=30
D
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $4,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
A. 11,500
B. 24,500
C. 25,500
D. 26,500
Answer: A. 11,500
Explanation: OFFICIAL SOLUTION:
The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 4,000), and Isabella’s are 0.10x. Set up the equation and solve:
550 + (0.08)(x – 4,000) = 0.10x
Distribute the 0.08:
550 + 0.08x – 320 = 0.10x
Combine terms and subtract 0.08x from both sides:
230 = 0.02x
Divide both sides by 0.02:
11,500 = x
Your answer is A.
Question: What is the 28th digit to the right of the decimal point in the decimal form of 4/11?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: 4/11 = 0.363636...
The even numbered positions in the decimal expansion are all 6.
The answer is D.