RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The average of 6 observations is 13. A new observation is included and the new average is decreased by 1. The seventh observation is?
A.1
B.3
C.5
D.6
Answer: D.6
Explanation: Let seventh observation = X.
Then, according to the question we have
=> (78 + X) / 7 = 12
=> X = 6.
Hence, the seventh observation is 6.
ANSWER:D
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 39° is?
A.40m2
B.45m2
C.49m2
D.51m2
Answer: C.49m2
Explanation: 39/360 * 22/7 * 12 * 12
= 49m2
Answer:C
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
A.3:4
B.3:0
C.3:1
D.3:2
Answer: C.3:1
Explanation: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1.Answer: C
Question: c can run a kilometer race in 4 1/2 min while d can run same race in 5 min. How many meters start can c give d in a kilometer race, so that the race mat end in a dead heat?
A.m
B.m
C.m
D.m
Answer: D.m
Explanation: c can give d (5 min - 4 1/2 min) = 30 sec start.
The distance covered by d in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
c can give d 100m start.
ANSWER:D
Question: A marketing firm determined that, of 200 households surveyed, 80 used neither Brand E nor Brand B soap, 60 used only Brand E soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
A. 15
B. 20
C. 30
D. 40
Answer: D. 40
Explanation: SOLUTION FOR SOAP E AND SOAP B
(D) 40
Question: A customer pays 40 dollars for a coffee maker after a discount of 20 dollars
What is the original price of the coffe maker?
A.50
B.40
C.70
D.60
Answer: D.60
Explanation: Let x be the original price.
x - 20 = 40
x - 20 + 20 = 40 + 20
x + 0 = 60
x = 60
Answer is D
Question: The speed of a train is 90 kmph. What is the distance covered by it in 20 minutes?
A.15
B.66
C.77
D.30
Answer: D.30
Explanation: 90 * 20/60 = 30 kmph
Answer:D
Question: A tour group of 25 people paid a total of $735 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
A.$22
B.$23.94
C.$28
D.$25.20
Answer: C.$28
Explanation: Soln:-
735/25=x+0.05x
735/25=1.05x
x=28
ANSWER:C
Question: A boy can reach a certain place in 15 hours. If he reduces his speed by 1/30th, he goes 5 km less in that time. Find his speed.
A.4 km/hr.
B.6 km/hr
C.8 km/hr
D.10 km/hr
Answer: D.10 km/hr
Explanation: Explanation :
Solution: Let the speed be x km/hr. then,
15x - (15 * 29x/30) = 5
=> 30x-29x = 5*2
=> x =10 km/hr.
Answer : D
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
A.3630
B.3637
C.3630
D.3631
Answer: A.3630
Explanation: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
A.2 2 8/2
B.2 2 1/9
C.2 9 1/2
D.2 2 1/2
Answer: D.2 2 1/2
Explanation: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2kmph
Answer:D
Question: A bag contains 6 white balls, 6 black balls, and 3 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red?
A.0.2
B.0.15
C.0.35
D.0.45
Answer: A.0.2
Explanation: Each ball has an equal probability of being the third ball drawn.
P(3rd ball is red) = 3/15 = 0.2
The answer is A.
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the children stand together?
A.12
B.24
C.50
D.48
Answer: D.48
Explanation: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C1 and C2 are always together.
Consider F and M to be one unit, then we would have total of four units: {F), {M}, {C1C2}, {D}. The number of arrangements of these four units is 4!, but C1 and C2 within their unit can be arranged in 2 ways: {c1c2} or {c2c1}, so total number of arrangements is 4!*2=48.
Answer: D.
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
A.57%
B.82%
C.52%
D.22%
Answer: A.57%
Explanation: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
Answer:A
Question: Express of the following as a fraction:
25%
A.1/4
B.1/8
C.2/9
D.3/6
Answer: A.1/4
Explanation: 25% = 25/100= 1/4.
Answer is A.
Question: The larger interior angle of a parallelogram is 90° more than its smaller interior angle. What is the measure of the smaller interior angle of the parallelogram?
A.90°
B.75°
C.60°
D.45°
Answer: D.45°
Explanation: let smaller be x ,larger becomes x+90... total of all angles=360
so 4x+180=360 and x=45
ANSWER:D
Question: A is twice as good a work man as B and together they finish the work in 6 days. In how many days A alone can finish the work?
A.3
B.9
C.7
D.2
Answer: B.9
Explanation: WC = 2:1
2x + x = 1/6 => x = 1/18
2x = 1/9
A can do the work in 9 days.
Answer: B
Question: In what time will Rs.4600 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
A.7 1/3
B.7 1/6
C.7 1/4
D.7 1/2
Answer: C.7 1/4
Explanation: (4600*3*R)/100 = (5000*5*4)/100
R = 7 1/4
Answer: C
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,70,000 earned at the end of 3 years from the start of the business in 1999?
A.Rs.45,000
B.Rs.50,000
C.Rs.90,000
D.Rs.75,000
Answer: C.Rs.90,000
Explanation: Solution
Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share	=Rs.(270000×2/6)
= Rs.90000.
Answer C
Question: There are 350 snakes at a large zoo. The number of snakes is 5 times the number of all the other animals combined. How many more snakes are there than non snakes animals at the zoo?
A.400
B.360
C.300
D.280
Answer: D.280
Explanation: Answer is D.
Total snakes= 350 = 5 * Other Animals (X)
or X = 70.
So, Difference in snakes and X = 350-70 = 280.
Question: Find the present worth of Rs.930 due 3 years hence at 8% per annum.Aso find the discount?
A.2387
B.180
C.221
D.277
Answer: B.180
Explanation: Explanation:
\inline \fn_jvn P.W = \frac{100\times Amount}{100+(R\times T)}=Rs.\left [ \frac{100\times 930}{100+(8\times 3)} \right ]=Rs.750
T.D = Amount - P.W
= 930 - 750
= Rs.180
Answer: B) 180
Question: In the decimal expansion of (9/10)^4 what is the fourth digit to the right of the decimal point?
A. 2
B. 7
C. 1
D. 0
Answer: C. 1
Explanation: Step 1 Convert fraction to decimal with two decimal places 9/10 = 0.90 then convert to scientific number = 9*10^-1
Step 2 Multiply 9^4 by 10^-4
Step 3 9 has the sequence 9, 81, 729
Answer is C
Question: It takes Avery 3 hours to build a brick wall while Tom can do it in 2 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.20
B.30
C.40
D.50
Answer: A.20
Explanation: Avery takes 3 hours
Tom takes 2 hours
Efficiency of Avery is 1/3 units/hr
Efficiency of Tom is 1/2 units/hr
Combined efficiency of Tom and Avery is 1/3 +1/2 = 5/6 units/hr
Since they worked for 1 hour they completed 5/6 units of work and 1/6 units of work is left which is to be completed by Tom ( Since Avery left )
So Time taken by Tom to complete the remaining work will be 1/6/1/2 hours => 1/3*60 = 20 minutes...
Answer will be (A)
Question: If A speaks the truth 80% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
A.0.8
B.0.48
C.0.6
D.0.14
Answer: B.0.48
Explanation: probability that A speaks truth is 80/100=0.8 probability that B speaks truth is 60/100=0.6 since both A and B are independent of each other so PROBABILITY OF A INTERSECTION B = P(A) *P(B) =0.8 * 0.6 = 0.48
ANSWER:B
Question: How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
A.5(10)
B.10(5)
C.10P5
D.10C5
Answer: A.5(10)
Explanation: Solution:
Each of the 10 letters can be posted in any of the 5 boxes.
So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.
i.e.5 *5 *5 *. . . .*5 (up-to 10 times).
=510
Answer: Option A
Question: A batsman scored 90 runs which included 2 boundaries and 5 sixes. What percent of his total score did he make by running between the wickets.
A.40%
B.50%
C.57%
D.60%
Answer: C.57%
Explanation: Explanation:
Number of runs made by running = 90 - (2 x 4 + 5 x 6)
= 90 - (38
= 52
Now, we need to calculate 38 is what percent of 90.
=> 52/90 * 100 = 57 %
Option C
Question: What percent is 100 gm of 1 kg?
A.25%
B.40%
C.10%
D.8%
Answer: C.10%
Explanation: 1 kg = 1000 gm
100/1000 × 100 = 10000/1000
=10 %
Answer is C
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
A.9
B.8
C.7
D.5
Answer: B.8
Explanation: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:1. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?
A.9:8
B.4:9
C.3:2
D.2:3
Answer: B.4:9
Explanation: The ratio of economy to luxury cars is 3:1 --> E:L = 3:1 = 12:4.
The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9.
Thus, L:S = 4:9.
Answer: B.
Question: When 1/10 percent of 4,000 is subtracted from 1/10 of 4,000, the difference is
A. 0
B. 50
C. 396
D. 495
Answer: C. 396
Explanation: We can break this problem into two parts:
1) What is 1/10 percent of 4,000?
2) What is 1/10 of 4,000?
To calculate 1/10 percent of 4,000 we must first remember to DIVIDE 1/10 BY 100.
So we have: (1/10)/(100)
To divide a number by 100 means to multiply it by 1/100, so we have:
1/10 x 1/100 = 1/1,000
Thus, 1/10 percent of 4,000 = 1/1,000 x 4,000 = 4.
Now let's concentrate on part 2. We need to calculate 1/10 of 4,000. To do this we simply multiply 1/10 by 4,000.
1/10 x 4,000 = 400
The answer to part 1 is 4, and the answer to part 2 is 400. Their difference is 400 – 4= 396.
Answer C.
Question: There are a cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
A.n(n-1)
B.n(n+1)
C.a(a-1)
D.n(n+1)/2
Answer: C.a(a-1)
Explanation: First of all, the possible number of airlines is a. Then, the possible number of airlines departing from one city to another becomes (a-1). Hence, the answer is a(a-1), which makes C
Question: A man rows his boat 110 km downstream and 90 km upstream, taking 3 hours each time. Find the speed of the stream?
A.6
B.5
C.7.5
D.3.5
Answer: D.3.5
Explanation: Speed downstream = d/t = 110/(3) = 37 kmph
Speed upstream = d/t = 90/(3) = 30 kmph
The speed of the stream = (37 - 30)/2 = 3.5 kmph
Answer:D
Question: On a game show, a contestant spins four different wheels; each wheel is numbered 1 to 3. What is the probability that the contestant will spin all tens?
A.87
B.28
C.1/81
D.693
Answer: C.1/81
Explanation: All 3s:
1st wheel = 3 = 1/3
2nd wheel = 3 = 1/3
3rd wheel = 3 = 1/3
4th wheel = 3 = 1/3
(1/3)(1/3)(1/3)(1/3) = 1/81
Answer: C
Question: A merchant has 100 lbs of sugar, part of which he sells at 5% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 5% profit?
A.70 lbs
B.40 lbs
C.30 lbs
D.58 lbs
Answer: D.58 lbs
Explanation: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 5% profit
B = # of pounds sold at 17% profit
A+B = 100 pounds
(.05A + .17B)/(A+B) = .10
.05A + .17B = .1A + .1B
.07B = .05A
7B = 5A
7/5 = A/B
So, for every 7 pounds of A, we have 5 pounds of B.
With 100 pounds total, we have 58 pounds of A and 42 pounds of B.
Option D
Question: If Bill can buy 3 pairs of jeans and 2 shirts for $69 or 2 pairs of jeans and 3 shirts for $66, how much does one shirt cost?
A.$10
B.$12
C.$13.20
D.$15
Answer: B.$12
Explanation: Let the price of one shirt be ss and of jeans be j:
3j+2s=69
2j+3s=66
Subtracting the second from the first gives: j−s=3or j=s+3 Plug j in either of the equations and solve for s, which is $12
Answer: B	.
Question: A new savings account offers 4 percent annual interest compounded every 6 months. What would be the total balance in an account after 1 year, if the initial amount in the account were $6000?
A.$80.00
B.$84.40
C.$360.00
D.$6,242.40
Answer: D.$6,242.40
Explanation: The interest is compounded every 6 months. To calculate interest, you must take the principal and multiply it by the interest and the length of time (using the unit used in the interest, typically years). At the end of the first 6 months the interest earned is $6,000(.04) (1/2) = $120. (Note: the 6 months are “1/2” in the equation since 4% is a yearly rate, not a bi-yearly one).
Since the interest is compounded, the second six months of the year are not earning interest on just the original $6,000, but on the interest as well, so they are actually earning interest on $6,120. The interest earned during the final 6 months of the year is $6,120(.04)(1/2) = $122.4. Therefore, the total balance is the original amount ($6000) + $120 + $122.40 = $6,242.40.
The correct answer is D.
Question: A cricket player whose bowling average was 20.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match?
A.64
B.72
C.101
D.111
Answer: C.101
Explanation: Average = Total Runs / Total wickets
Total runs after last match = 20.5w + 52
Total wickets after last match = w + 5
(20.5w + 52) / (w + 5) = 20.5 - 0.5 = 20
w = 96
so total wickets aftr last match = w+5 = 101
ANSWER:C
Question: A work can be finished in 30 days by twenty women. The same work can be finished in fifteen days by 10 men. The ratio between the capacity of a man and a woman is
A.1:3
B.4:1
C.2:3
D.2:1
Answer: B.4:1
Explanation: Work done by 20 women in 1 day = 1/30
Work done by 1 woman in 1 day = 1/(30×20)
Work done by 10 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×10)
Ratio of the capacity of a man and woman =1/(15×10) : 1/(30×20) = 1/150 : 1/600
= 1/1 :1/4 = 4:1
Option B
Question: The length of the bridge, which a train 500 metres long and travelling at 42 km/hr can cross in 60 seconds, is?
A.100 m
B.200 m
C.300 m
D.250 m
Answer: B.200 m
Explanation: Speed = [42 X 5/18] m/sec = [35/3]m/sec
Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/60
35/3 = (130 + x)/60
500+x=700
=>x=200 m
Answer:B
Question: There are five people who can build five houses in just five days. Increase the amount of people to 100. How long would it take these 100 people to build 100 houses?
A.2 days
B.3 days
C.4 days
D.5 days
Answer: D.5 days
Explanation: It will take 5 days for 100 people to build 100 houses.
1 person can build 1 house in 5 days. So, 100 people can build 100 houses in 5 days.
Answer D
Question: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -7?
A.-1
B.7
C.10
D.11
Answer: D.11
Explanation: We know that t1 = 23
So, using the given formula we have:
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26
The same way we find that t2= 20
It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
t8 = 2
t9 = -1
t10 = -4
t11 = -7
So, ourANS is D.
Question: The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 25 percent of the budget?
A. 15 °
B. 36 °
C. 54 °
D. 90 °
Answer: D. 90 °
Explanation: 100 percent = 360 degrees
25 percent = 360*25/100 = 90 degrees
Answer is D.
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
A.8939
B.8383
C.8389
D.4530
Answer: D.4530
Explanation: Explanation:
Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 5 = Rs. 4530
Answer: Option D
Question: A small company reduced its faculty by approximately 15 percent to 195 employees. What was the original number of employees?
A.A)182
B.B)208
C.C)220
D.D)229
Answer: D.D)229
Explanation: If x is the original number of employees, then after 15% reduction in employees number is .85x
but we are given .85x = 195
x = 229
So the original number of employees is 229
Correct Answer - D
Question: A vendor buys 10 t-shirts at an average price of $14 per t-shirt. He then buys 15 more t-shirts at an average price of $11 per t-shirt. What is the average price Q per t-shirt that the vendor paid for these purchases?
A.$12.20
B.$12.50
C.$12.55
D.$12.70
Answer: A.$12.20
Explanation: Correct Answer: A
Explanation: The relevant formula for this problem is Average Q= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, since 11 x 15 = 165. The grand sum is then $140 + $165, which equals $305. The total number of shirts purchased was 25, so to get the average price per shirt, we divide 305 by 25, which equals $12.20. As a result, the correct answer is A.
NOTE: A relative understanding of weighted average offers a shortcut to this problem. Because the true average of 11 and 14 is 12.5, but the vendor sells more shirts at the lower price than at the higher price, the weighted average must be less than $12.50; only answer choice A is a possibility.
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 4 ½ hours if they are walking in the same direction?
A.7 km
B.6 km
C.5 5/8 km
D.9 km
Answer: C.5 5/8 km
Explanation: RS = 5 ¾ - 4 ½ = 1 ¼
T = 4 ½ h.
D = 5/4 * 9/2 = 45/8
= 5 5/8 km
Answer:C
Question: How many prime numbers between 100 to 150?
A.11
B.10
C.13
D.12
Answer: B.10
Explanation: primes are of the form 6n+1 or 6n-1
Put n=17
6n+1=6*17+1=103
for n=17
6n-1=6*17-1=101
for n=18 , ==>107 and 109
for n=19 , ==> 113
for n =20 ==> no prime no.
for n =21 ==> 127
for n =22 ==> 131
for n=23 ==> 137 AND 139
for n =24 ==> no prime number
for n= 25 ==> 149
therefore total number of prime numbers = 10
Ans - B
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
I. ab < 1
III. a/b < 1
A.I only
B.II only
C.III only
D.I and II only
Answer: D.I and II only
Explanation: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
A.3:4
B.3:2
C.3:9
D.3:8
Answer: B.3:2
Explanation: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
6000 : 8000 => 3:4
Answer: B
Question: A 150 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
A.300
B.175
C.360
D.370
Answer: B.175
Explanation: Speed = 150/18 = 25/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 150)/39 = 25/3
=> x = 325 m.
L=325-150 =175 m
Answer: Option B
Question: A book is bought for $60 and sold for $75. What is the profit in percentage?
A.12
B.15
C.20
D.25
Answer: D.25
Explanation: 75/60 = 1.25
The answer is D.
Question: On one side of a coin there is the number 0 and on the other side the number 1. What is the probability that the sum of three coin tosses will be 2?
A.1/8.
B.1/2.
C.1/5.
D.3/8.
Answer: D.3/8.
Explanation: Assume the coin is unbiased.
Possible sums from 3 tosses = 0,1,2,3
O and 3 are possible in only 1 case each. (0,0,0 or 1,1,1)
1 is possible in 3C1 = 3 cases. (1,0,0; 0,1,0 or 0,0,1) or
similarly, 2 is possible in 3C2=3 cases (1,0,1; 1,1,0; 0,1,1)
So answer will be 3/8. Answer :Option D.
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold k bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2k
II. y > k
III. y > 3
A.I only
B.II only
C.I and II
D.II and III
Answer: D.II and III
Explanation: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(k-12) where k is the total number of bikes sold (when k>12). K = cycles sold last week
KS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2KS
lets test all statements with K=0;
KS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with K=1;
KS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with K=6;
KS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Question: A company decreased the price of its main product by 20%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
A.3.0
B.7.0
C.5.0
D.2.0
Answer: C.5.0
Explanation: For the total revenue to remain the same when the price is one fifth, the number of products sold must five times. Therefore increase in the number of products sold is 100%
=> The required ratio = 100%/20% = 5.0
Answer : C