mathewhe/aqua_rat huggingface dataset:
Question: When 2/3 of the garments in the shipment were inspected, 27 of the garments passed inspection and the remaining 3 garments failed. How many of the uninspected garments must pass inspection in order that 90 percent of the garments in the shipment pass?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 14
Rationale: 2/3x= 30
x=45
for 90% approval we need 41 garments approved.
already approved = 27
we need 14 more.
Answer : E
Answer: (E) 14
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
(E) 10
Rationale: (5 + x)/20 + 5/25 = 1 => x = 11 days
Answer:D
Answer: (D) 11
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
(E) 1:2
Rationale: 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
Answer: (B) 9:4
Question: Simplfy
2b - [b -(a+b) - {b - (b - a+b)} + 2a]
(A) a
(B) 2a
(C) 4a
(D) b
(E) 1
Rationale: 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
Answer: (D) b
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
(E) 400
Rationale: 1/10 % of 4000 = 4
1/10 of 4000 = 400
400-4 = 396
Ans:C
Answer: (C) 396
Question: The captain of a cricket team of 11 members is 29 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 20 years
(B) 21 years
(C) 22 years
(D) 23 years
(E) 26 years
Rationale: Explanation:
Let the average age of the whole team by x years.
11x â€“ (29 + 32) = 9(x -1)
11x â€“ 9x = 52
2x = 52
x = 26.
So, average age of the team is 26 years.
Answer E
Answer: (E) 26 years
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
(E) 1635
Rationale: 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
Answer: (B) 1647
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
(E) 75.6
Rationale: 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..
Answer: (B) 38.4
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
(E) 6500 lbs.-8 Trips
Rationale: Add: 1500 4,500 ÷ 500 = 9
2500
+ 500
4500
Answer 1: 4500 lbs. (Total) Answer 2: 9 Trips
correct answer B
Answer: (B) 4500 lbs.-9 Trips
Question: Solve x2 â€“ 3x â€“ 4 = 0.
(A) 1,4
(B) -1,4
(C) 2,3
(D) 2,-3
(E) 3,4
Rationale: 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
Answer: (B) -1,4
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)
(E) 500p / (625 - p)
Rationale: 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 ,...
Answer: (D) 400r / (500 - r)
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
(E) 64/125
Rationale: 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
Answer: (C) 1
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
(E) 81 : 182
Rationale: Explanation:
Ratio of the sides = ³√2744 : ³√1331 = 14 : 11
Ratio of surface areas = 14^2 : 11^2 = 196 : 121
Answer: Option A
Answer: (A) 196 : 121
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
(E) 65
Rationale: number of pens = 1200
number of pencils = 820
Required number of students = H.C.F. of 1200 and 820 = 20
Answer is B
Answer: (B) 20
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
(E) 18
Rationale: 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.
Answer: (C) 14
Question: The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 299
(B) 266
(C) 299
(D) 750
(E) 600
Rationale: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 => x = 20 * 60 / 2 = 600
Answer: E
Answer: (E) 600
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
(E) 2 hours and 20 minutes
Rationale: 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
Answer: (B) 2 hours and 12 minutes.
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%
(E) 12%
Rationale: 950 --- 50
100 --- ? => 5.26%
Answer: D
Answer: (D) 5.26%
Question: (469 + 174)2 - (469 - 174)2	/(469 x 174)=?
(A) 2
(B) 4
(C) 295
(D) 643
(E) 125
Rationale: Explanation:
Given exp. =	(a + b)2 - (a - b)2/ab
=	4ab/ab
= 4 (where a = 469, b = 174.)
ANSWER IS B
Answer: (B) 4
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.
(E) -2.
Rationale: 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...
Answer: (D) 6.
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
(E) 15
Rationale: 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
Answer: (B) 13
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
(E) $7
Rationale: S.I= $[(1200*10*1)/100]= $120.
C.I= $[1200*(1+(5/100)^2)-1200]= $123.
Difference= $(123-120) =$3.
Answer(D)
Answer: (D) $3
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
(E) 45
Rationale: 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
Answer: (B) 40
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
(E) 64
Rationale: 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
Answer: (C) 18
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
(E) 12
Rationale: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec.Answer: C
Answer: (C) 25
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
(E) -410
Rationale: 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
Answer: (A) -324
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%
(E) 8.3%
Rationale: 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.
Answer: (B) E=2.8%
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
(E) 58 min
Rationale: Distance = Speed * time
8*3 = 24km
New Speed = 16 kmph
Therefore time = D/S = 24/16 = 1.5hr.
Answer : C.
Answer: (C) 1.5 hr
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
(E) 13
Rationale: 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)
Answer: (D) 5
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
(E) 20
Rationale: 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
Answer: (D) 19
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
(E) 15/40
Rationale: 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
Answer: (A) 11/40
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
(E) 3 * 2^10
Rationale: 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
Answer: (A) 2^9
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
(E) None
Rationale: 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
Answer: (D) 11 p.m
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
(E) 700
Rationale: 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
Answer: (B) 540
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
(E) Rs.21.69
Rationale: 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
Answer: (A) Rs.21.60
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
(E) 22
Rationale: 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
Answer: (B) 75
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
(E) 13
Rationale: 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.
Answer: (A) 9
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
(E) 17m
Rationale: 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
Answer: (C) 15m
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
(E) 37
Rationale: D
97
From the given alternatives,
97 × 98 = 9506
∴ Smaller number = 97
Answer: (D) 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
(E) 10
Rationale: 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.
Answer: (A) 1
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
(E)  10
Rationale: Mother has a fixed place and father, so there are 4! ways to arrange the children, hence D
Answer: (D)  24
Question: If x and d are integers and 2x–d= 11, then 4x+ d CANNOT be
(A)  –5
(B)  1
(C)  13
(D)  17
(E)  551
Rationale: 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
Answer: (D)  17
Question: If x = 3 + 5n and y = 2n - 3, then for what value of n, x is double of y (x = 2y) ?
(A) 0
(B) 2
(C) -2
(D) 9
(E) -9
Rationale: Explanation:
x = 2y <=> 3 + 5n = 2(2n - 3) <=> 3 + 5n = 4n - 6 <=> n = -9.
Answer: E
Answer: (E) -9
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
(E) 432
Rationale: 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.
Answer: (A) 54
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
(E) 150
Rationale: 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
Answer: (A) 100
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
(E) 4336.91
Rationale: 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
Answer: (A) 4336.93
Question: A man rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. What is his average speed for the entire trip approximately?
(A) 10.9
(B) 10.2
(C) 10.7
(D) 10.8
(E) 10.1
Rationale: Total distance travelled = 10 + 12 = 22 kmTime taken to travel 10 km at an average speed of 12 km/hr = distancespeed=1012 hrTime taken to travel 12 km at an average speed of 10 km/hr = distancespeed=1210 hrTotal time taken =1012+1210 hrAverage speed = distancetime=22(1012+1210)=22×120(10×10)+(12×12)22×120244=11×120122=11×6061=66061=10.8 kmph
Answer :D
Answer: (D) 10.8
Question: Calculate the area of a triangle, if the sides of are 65 cm, 60 cm and 25 cm, what is its area?
(A) 850 cm2
(B) 750 cm2
(C) 450 cm2
(D) 550 cm2
(E) 650 cm2
Rationale: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.
Area of the triangle = 1/2 * 60 * 25 = 750 cm2
Answer: B
Answer: (B) 750 cm2