RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Two trains 140 m and 190 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
A.17.9 sec
B.11.88 sec
C.27.7 sec
D.10.8 sec
Answer: B.11.88 sec
Explanation: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 190 = 330 m.
Required time = 330 * 9/250 = 11.88 sec.
Answer: B
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $38. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
A.180xy
B.180/(xy)
C.20xy
D.342/(xy)
Answer: D.342/(xy)
Explanation: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 38 / (xy/9) = 342/(xy).
The answer is D.
Question: A store sells a certain product at a fixed price per unit. At the product's current price, f units cost a total of exactly $300. If the price were lowered by $5 from its current value, then f + 2n units would cost exactly $300; if the price were raised by $5, then f – n units would cost exactly $300. What is the value of f?
A.10
B.15
C.20
D.25
Answer: C.20
Explanation: It got too complicated when I used algebra. Using plugging in, it was quite fast.
Price Quantity total value
p f pf = 300
p-5 f+2n (p-5)(f+2n) = 300
p+5 f-n (p+5)(f-n) = 300
Solving three equations for three unknowns. Tough!!
Plugging in, I always start with C. C was the answer here, so saved calculation!
Putting values in above equations:
Price Quantity total value
15 20 300
10 20+2n 300 -> 10(20 + 2n)=300 -> 200 +20n = 300 -> 20n = 100 -> n =5
20 15 300
So f = 20 satisfies all equations!!
Question: If x-y=8, which of the following must be true?
I. If x is positive, y must be positive
II. If x is negative, y must be negative
III. Both x and y are positive
A.I only
B.II only
C.III only
D.I and II
Answer: B.II only
Explanation: The best way to approach such questions is to plug in values for x and y
Given: x-y=8
III. Both x and y are positive:
Let x=10 and y=2
x-y=8
But,
Let x=6 and y=-2
x-y=8
Therefore, NOT TRUE
III. If x is positive, y must be positive
Let x=10 and y=2
x-y=8
But,
Let x = 6 and y=-2
x-y=8
Therefore, NOT TRUE
II. If x is negative, y must be negative
If x is negative, for the expression x-y=8 to be true, y must be a -ve number. Otherwise, the sum of two negative numbers will yield another negative number!
Therefore, TRUE
Ans: 'B'
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containg 17% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?
A.1/3
B.2/3
C.2/5
D.3/5
Answer: C.2/5
Explanation: Let us assume the total original amount of whiskey = 10 ml ---> 4 ml alcohol and 6 ml non-alcohol.
Let x ml be the amount removed ---> total alcohol left = 4-0.4x
New quantity of whiskey added = x ml out of which 0.19 is the alcohol.
Thus, the final quantity of alcohol = 4-0.4x+0.19x ----> (4-0.21x)/ 10 = 0.26 ---> x = 20/3 ml.
Per the question, you need to find the x ml removed as a ratio of the initial volume ---> (20/3)/10 = 2/5.
Hence, C is the correct answer.
Question: Find the number which when multiplied by 15 is increased by 196
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: Explanation:
Let the number be x.
Then, 15x = x + 196
=› 14 x= 196
=› x = 14.
Answer: Option C
Question: The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.
A.1400
B.1500
C.1600
D.1700
Answer: B.1500
Explanation: Solution:
If the sum of two numbers is x and their difference is y, then the difference of their squares is xy.
Here x= 75 and y = 20
75 × 20 = 1500
Answer B
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
A.13
B.14
C.18
D.11
Answer: D.11
Explanation: (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer:D
Question: If each side of a square is increased by 50%, the ratio of the area of the resulting square to the area of the given square is:
A.5:4
B.9:4
C.4:5
D.4:9
Answer: B.9:4
Explanation: Let, each side=a. Then, original area= a2.
New side= 150a/100= 3a/2. New area= 9a2/4.
Required ratio= 9a2/4:a2= 9:4
ANSWER:B
Question: Simplfy
2b - [b -(a+b) - {b - (b - a+b)} + 2a]
A.a
B.2a
C.4a
D.b
Answer: D.b
Explanation: Explanation:
2b-[b-(a+b)-{b-(b-a+b)}+2a]
=2b-[b-a-b-{b-(2b-a)}+2a]
=2b-[-a-{b-2b+a}+2a]
=2b-[-a-{-b+a}+2a]
=2b-[-a+b-a+2a]
=2b-[-2a+b+2a]
=2b-b
=b
Option D
Question: When 1/10% of 4,000 is subtracted from 1/10 of 4,000, the difference is
A.50
B.200
C.396
D.398
Answer: C.396
Explanation: 1/10 % of 4000 = 4
1/10 of 4000 = 400
400-4 = 396
Ans:C
Question: Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
A.1254
B.1647
C.1456
D.1555
Answer: B.1647
Explanation: Let the smaller number be x. Then larger number = (x + 1375).
x + 1375 = 6x + 15
5x = 1360
x = 272
Large number = 272+1375 = 1647
B
Question: A set has an average (arithmetic mean) of 42 and a standard deviation of 1.8. Which of the following values is two standard deviations away from the mean?
A.36
B.38.4
C.40.2
D.43.8
Answer: B.38.4
Explanation: AM is 42 and SD is 1.8...
Now, we need to count all numbers greater than 42+2(1.8) = 45.6 or 42-2(1.8) = 38.4 (we are asked to find the value that is two SD away from the mean..so multiply the SD by 2)
Only B is in the list..
Answer: option B is correct answer..
Question: Each truck from Jones Removal Company can haul 500 pounds of trash at a time.
On Wednesday the company has jobs to remove 1,500 pounds of trash from one
site, 500 from another site, and 2,500 from a third site. How many total pounds of
trash will be moved by Jones Company that day? How many trips will it take for the
Jones Company to remove all of the trash?
A.5500 lbs.-2 Trips
B.4500 lbs.-9 Trips
C.2500 lbs.-3 Trips
D.3500 lbs.-7 Trips
Answer: B.4500 lbs.-9 Trips
Explanation: Add: 1500 4,500 ÷ 500 = 9
2500
+ 500
4500
Answer 1: 4500 lbs. (Total) Answer 2: 9 Trips
correct answer B
Question: Solve x2 â€“ 3x â€“ 4 = 0.
A.1,4
B.-1,4
C.2,3
D.2,-3
Answer: B.-1,4
Explanation: This one factors easily:
x2 â€“ 3x â€“ 4 = 0
(x + 1)(x â€“ 4) = 0
x + 1 = 0 or x â€“ 4 = 0
x = â€“1 or x = 4
The solution is x = â€“1, 4
ANSWER B
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspapers sales was from Newspaper A and if r percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of r?
A.100p / (125 - p)
B.150p / (250 - p)
C.300p / (375 - p)
D.400r / (500 - r)
Answer: D.400r / (500 - r)
Explanation: I have just started with qunats section .. I solved this by making two equations and got the answer ... However it was long way of doing it ...
I got the answer as : 100r /(125 - .25 r)...
Multiply this equation by 4 and you get D as the answer ,...
Question: If 4a = 5b and ab ≠0, what is the ratio of a/5 to b/4?
A.125/64
B.25/16
C.1
D.4/5
Answer: C.1
Explanation: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 4a = 5b
Here's one pair: a =5 and b =4
What is the ratio of a/5 to b/4?
In other words, what is the value of (a/5)/(b/4)?
Plug in values to get: (a/5)/(b/4) = (5/5)/(4/4)
= 1/1
= 1
C
Question: The ratio of the volumes of two cubes is 2744 : 1331. What is the ratio of their total surface areas?
A.196 : 121
B.81 : 127
C.181 : 196
D.81 : 161
Answer: A.196 : 121
Explanation: Explanation:
Ratio of the sides = ³√2744 : ³√1331 = 14 : 11
Ratio of surface areas = 14^2 : 11^2 = 196 : 121
Answer: Option A
Question: The maximum number of students among them 1200 pens and 820 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
A.40
B.20
C.60
D.80
Answer: B.20
Explanation: number of pens = 1200
number of pencils = 820
Required number of students = H.C.F. of 1200 and 820 = 20
Answer is B
Question: The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 100,000 bacteria
A.10
B.12
C.14
D.16
Answer: C.14
Explanation: The question basically asks how many minutes it takes for a population to increase by factor 100 (100,000 / 1,000 = 100).
Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes:
2^x >= 100, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^7 =128, i.e. the population has to double 7 times.
Since it takes the population 2 minutes to double once it takes 7*2 minutes = 14 minutes to double 7 times.
Thus, solution C = 14 is correct.
Question: It takes Avery 5 hours to build a brick wall while Tom can do it in 4 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?
A.1 hour and 20 minutes.
B.2 hours and 12 minutes.
C.1 hour and 40 minutes.
D.55 minutes
Answer: B.2 hours and 12 minutes.
Explanation: Avery's efficiency is 100/5 = 20%
Tom's = 100/4= 25%
they worked together for 1 hour and finished 45% of the job
remaining = 55 %
Tom will complete 25% in 60 minutes , 50% in 120 minutes and ,
5% in 60*5/25 minutes = 12 minutes
time taken by Tom to finish the remaining on his own = 120+12 = 132 minutes
ANSWER:B
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 950 grams per kg, what is his percent?
A.22%
B.25%
C.77%
D.5.26%
Answer: D.5.26%
Explanation: 950 --- 50
100 --- ? => 5.26%
Answer: D
Question: If (A+B) = 12, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
A.16.
B.8.
C.7.
D.6.
Answer: D.6.
Explanation: Given A+B = 12 => A = 12 - B --> Eq 1
B+C = 9
C+D = 3 => D = 3 - C --> Eq 2
Then Eqs 1 + 2 => A + D = 12 - B + 3 - C
=> 15 - (B+C)
=> 15 - 9 = 6.
Option D...
Question: The average mark of the students of a class in a particular exam is 72. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 92. Find the number of students who wrote the exam?
A.12
B.13
C.14
D.16
Answer: B.13
Explanation: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 92(x - 5)
72x - (5 * 40) = 92(x - 5)
260 = 20x => x = 13
Answer: B
Question: The difference between simple interest and compound interest on $1200 for one year at 10% per annum reckoned half-yearly is:
A.$5
B.$8
C.$9
D.$3
Answer: D.$3
Explanation: S.I= $[(1200*10*1)/100]= $120.
C.I= $[1200*(1+(5/100)^2)-1200]= $123.
Difference= $(123-120) =$3.
Answer(D)
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present
A.38
B.40
C.42
D.44
Answer: B.40
Explanation: Explanation:
Let the mother's present age be x years.
Then, the person's present age = (2/5 x) years.
=> (2/5 x + 8/2) = 1 (x + 8)
=> 2(2x + 40) = 5(x + 8)
=> x = 40
Answer: Option B
Question: A person crosses a 600 m long street in 2 minutes. What is his speed in km per hour?
A.12
B.24
C.18
D.42
Answer: C.18
Explanation: distance = 600 meter
time = 2 minutes = 2 x 60 seconds = 120 seconds
Speed = distance/time=600/120=5 m/s=5 Ã—18/5 km/hr=18 km/hr
Answer :C
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
A.2
B.28
C.25
D.99
Answer: C.25
Explanation: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec.Answer: C
Question: If the operation @ is defined for all a and b by the equation a@b =(a^2*b)*3, then 2@(3@-1) =
A.-324
B.223
C.324
D.-223
Answer: A.-324
Explanation: work within the parenthesis first so solve (3@-1) first
(3@-1)= ((3^2)*-1)*3 = (9*-1)*3= -9*3=-27
now take -3 plug back into equation and solve the rest
2@(-27)=((2^2)*-3)*3 = (4*-27)*3= -324
so -324 is the answer....this question is merely testing order of operations
remember PEMDAS
Option A
Question: Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents E, approximately how much greater is the probability that all three answers are “C” after Raj figures out that statement 1 of the data interpretation problem is also insufficient on its own?
A.E=2.3%
B.E=2.8%
C.E=3.3%
D.5.6%
Answer: B.E=2.8%
Explanation: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers, E(1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Question: Walking at the rate of 8 kmph a man cover certain distance in 3 hrs.. Running at a speed of 16 kmph the man will cover the same distance in.
A.1.2 hr
B.2.5 hr
C.1.5 hr
D.48 min
Answer: C.1.5 hr
Explanation: Distance = Speed * time
8*3 = 24km
New Speed = 16 kmph
Therefore time = D/S = 24/16 = 1.5hr.
Answer : C.
Question: Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $12100, how many months will it take Joan to pay back her mortgage?
A.6
B.8
C.10
D.5
Answer: D.5
Explanation: Joan starts off with 100 $ .. which is to be tripled every month
Her monthly payments look like this :
100 , 300 , 900 , 2700 ......... Upto 12100
This can be re written as :
100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 121
So we have 1 , 3 , 9 , 27 ..... 12100 in GP
We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)
Therefore to find the Sum of n terms of a GP we use this formula :
Sn = a (1-r^n) / 1 -r
121 = 1 - 3^n / 1-3 ; 1-3^n / -2
Cross multiplying we get
121 x -2 = 1- 3^n
- 242 = 1 - 3^n
- 243 = - 3 ^n
243 = 3 ^n (negatives cancel out)
243 can also be re written as 3 ^ 5
Therefore ; 3 ^5 = 3 ^n
Thus n = 5 (D)
Question: Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
A.12
B.14
C.18
D.19
Answer: D.19
Explanation: There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, Red) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
ANSWER:D
Question: A group consists of equal number of men and women. Of them 10% of men and 45% of women are unemployed. If a person is randomly selected from the group. Find the probability for the selected person to be an employee
A.11/40
B.12/40
C.13/40
D.14/40
Answer: A.11/40
Explanation: if man is selected then probability of him to be employed = 10/100
similarly if women is selected then probability of her to be employed = 45/100
so probability = (1/2)(10/100)+(1/2)(45/100) = 2/40 + 9/40 = 11/40
ANSWER:A
Question: Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
A.2^9
B.2^10
C.3 * 2^8
D.3 * 2^9
Answer: A.2^9
Explanation: Apart from 3rd toss which needs to be Heads all other outcome are free and independent of each other.
total outcome for remaining 9 toss = 2929
3rd toss out come => 1 way
hence total outcome => 29∗1=2929∗1=29 => A
ANSWER:A
Question: A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?
A.8 p.m
B.9 p.m
C.10 p.m.
D.11 p.m
Answer: D.11 p.m
Explanation: Sol.
Time from 5 a.m. on a day to 10 p.m. on 4th day = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock.
∴ 356/15 hrs of this clock = 24 hours of correct clock.
= 90 hrs of correct clock.
So, the correct time is 11 p.m.
Answer D
Question: A marketing manager is able to manage an average of Rs240 per week during 40h week . But in the final week of the month, his rates are increased by 50%. Then find out the commission the marketing manager makes in that week, if he puts in 60h during that final week?
A.500
B.540
C.520
D.600
Answer: B.540
Explanation: Answer
Average rate per hr = 240/40 = Rs6/hr
In last week, his rate per hour increases by 50%,
so in the last week, his hourly rate = Rs.6 x (1+50%)= Rs.9
Total hour spent in final week = 60h
∴ Total commission = 60h x Rs.9/hr = Rs.540
Correct Option: B
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
A.Rs.21.60
B.Rs.21.61
C.Rs.21.62
D.Rs.21.66
Answer: A.Rs.21.60
Explanation: Explanation:
Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 = Rs.21.60
Answer:A
Question: Three numbers are in the ratio 2 : 3 : 5 and their average is 50. The largest number is :
A.30
B.75
C.27
D.21
Answer: B.75
Explanation: Explanation:
Let the numbers be 2x, 3x and 5x, Then, (2x + 3x + 5x ) / 3 = 50
=> 10x = 150
=> x = 15.
Largest number 5x = 5*15 = 75
Answer: B
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (3, 0), (6, 3), and (6, -3)?
A.9
B.10
C.11
D.12
Answer: A.9
Explanation: The triangle is symmetric about the x-axis.
The part above the x-axis forms a triangle with a base of 3 and a height of 3.
The area of this part is (1/2)(3)(3).
We can double this to find the area of the whole triangle.
The total area is (2)(1/2)(3)(3) = 9.
The answer is A.
Question: One young and one old man reach a same distance in 20min and 30min respectively. If old starts at 10.00am and youngman starts at 10.05am. When they meet. Pls provide solution
A.12m
B.14m
C.15m
D.16m
Answer: C.15m
Explanation: The real ans is 10:15am
Let the dis be 30 m
Old man travel 1m/min
Young travel 1.5m/min
At 10:05 old man = 5m
young = 0m
At 10:10 old man = 10m
young = 7.5m
At 10:15 old man= 15m
young = 15m
ANSWER:C
Question: The product of two successive numbers is 9506. Which is the smaller of the two numbers?
A.78
B.68
C.88
D.97
Answer: D.97
Explanation: D
97
From the given alternatives,
97 × 98 = 9506
∴ Smaller number = 97
Question: If the following is true, can you find the value of (4 + 9)?
7 + 7 = 2
8 + 8 = 4
8 + 5 = 1
6 + 9 = 3
10 + 11 = 9
A.1
B.5
C.6
D.7
Answer: A.1
Explanation: A
1
Explanation:
4 + 9 = 1
The trick to solve is to assume the first number as the time in AM and the second number is the number of hours you have to add to it. You'll find the time in PM when you do that.
For example
7 AM + 7 hours = 14:00 or 2 PM
4 AM + 9 hours = 13:00 or 1 PM.
Question: A family with 1 mother, 1 father, and 4 children sit in a car with 2 front seats and 4 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other three children on either side of him, how many seating arrangements are possible?
A. 3
B. 4
C. 6
D. 24
Answer: D. 24
Explanation: Mother has a fixed place and father, so there are 4! ways to arrange the children, hence D
Question: If x and d are integers and 2x–d= 11, then 4x+ d CANNOT be
A. –5
B. 1
C. 13
D. 17
Answer: D. 17
Explanation: 2x-d=11....d=2x-11
4x+d=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D
Question: Blaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
A.54
B.72
C.96
D.144
Answer: A.54
Explanation: Blaudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement.2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Question: If the average (arithmetic mean) of x, y, and 40 is 5 greater than the average of x, y, 40, and 60, find the average of x and y.
A.100
B.110
C.120
D.140
Answer: A.100
Explanation: consider the statement "9 is 5 greater than 4": 9 = 4 + 5
similarly,
the average of x, y, and 40 = (the average of x, y, 40, and 60) + 5
(x+y+40)/3 = (x+y+40+60)/4 + 5
(x+y+40)/3 = (x+y+100)/4 + 5
get a common denominator on the right side
(x+y+40)/3 = (x+y+100)/4 + 20/4
(x+y+40)/3 = (x+y+100+20)/4
(x+y+40)/3 = (x+y+120)/4
cross multiply
4(x+y+40) = 3(x+y+120)
4x+4x+160 = 3x+3y+360
collect like terms
4x-3x+4y-3y = 360 - 160
x + y = 200
thus
(x+y)/2 = 200/2
(x+y)/2 = 100
the average of x and y is 100
A
Question: A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly.What amount was paid for the note
A.4336.93
B.4336.99
C.4336.96
D.4336.92
Answer: A.4336.93
Explanation: Explanation:
i=j/m
Maturity value = PV(1 + i)^n
Term = 5 years - 21 months= 3.25 years
Price paid = FV(1+ i )^-n
Answer: A) 4336.93