RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being 13. The rate of interest obtained is:
A.27%
B.87%
C.15%
D.66%
Answer: C.15%
Explanation: Investment = Rs. [20 x (50 - 5)] = Rs. 900.
Face value = Rs. (50 x 20) = Rs. 1000.
Dividend = Rs. 27	x	1000 = Rs. 135.
2	100
Interest obtained = 135	x 100	%	= 15%
900
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Answer: C
Question: w,x,y,z is an arithmetic sequence, which of the following options also qualifies as an arithmetiv sequence?
I. w-6,x-6,y-6,z-6
II. 5w,2x,3y,5z
III. 5w,5x,5y,5z
A.II and III
B.III only
C.I and III
D.I and II
Answer: A.II and III
Explanation: lets look at the three choices...
I. w-6,x-6,y-6,z-6
since the difference is constant, it is an arithmetic sequence...
II. 5w,2x,3y,5z
since the difference is not constant, it is not an arithmetic sequence
III. 5w,5x,5y,5z
since the difference is constant it is an arithmetic sequence...
Answer is A)
Question: At what rate percent on simple interest will a sum of money double itself in 30 years?
A.3 1/3%
B.3 1/7%
C.3 9/3%
D.3 5/3%
Answer: A.3 1/3%
Explanation: P = (P*30*R)/100
R = 3 1/3%
Answer: A
Question: An empty fuel tank with a capacity of 208 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
A.160
B.150
C.82
D.80
Answer: C.82
Explanation: Say there are A gallons of fuel A in the tank, then there would be 208-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 208-A gallons of fuel B is 0.16(208-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(208-A)=30 --> A=82.
Answer: C.
Question: What is the greatest value of m such that 4^m is a factor of 27! ?
A.5
B.7
C.6
D.8
Answer: D.8
Explanation: Pretty simple, really.
If m = 8, then 4m = 32, which is 16x2, both of which are included in 27!
Since 8 is the largest number here, its the answer.
Answer is D
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
A.21 ½ days
B.22 ½ days
C.23 ½ days
D.12 ½ days
Answer: B.22 ½ days
Explanation: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 ¼ *2 = 22 ½ days
ANSWER:B
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
A.288
B.2778
C.299
D.400
Answer: D.400
Explanation: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
27. A and B start a busin. Answer: D
Question: Which of the following fractions is greater than 3 /4 and less than 5 / 6 ?
A.4/8
B.4/5
C.4/6
D.4/1
Answer: B.4/5
Explanation: Explanation:
3 /4 = 0.75, 5/6 = 0.833, 1/2 = .5, 2/3 = 0.66, 4/5 = 0.8, 9/10 = 0.9.
clearly 0.8 lies between 0.75 and .833.
4/5 lies between 3/4 and 5/6..
Answer: B) 4 / 5
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
A.42, 33
B.43, 33
C.42, 38
D.43, 39
Answer: A.42, 33
Explanation: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
A)
Question: The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?
A.67.4kg
B.57.75kg
C.58.85kg
D.49.4kg
Answer: C.58.85kg
Explanation: Actual total weight is (20 Ã— 58.4 - 56 + 65) = 1177 Kgs
Actual average weight is 1177/20 = 58.85kgs
ANSWER IS C
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
A.8
B.76
C.17
D.7
Answer: A.8
Explanation: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Question: A train crosses a pole in 10 sec and a 200m long platform in 20 sec. What is the length of the train?
A.100m
B.200m
C.250m
D.300m
Answer: B.200m
Explanation: Let the length of train be x meter and speed be y m/sec
Therefore, time taken to cross the pole = x/y sec
and time taken to cross the platform = ( Length of train + Length of platform) / speed of train
Therefore x/y = 10
And, (x+200) / y = 20
⇒ 10y + 200 = 20 y
∴ speed of train, y = 20 m/sec
And length of rain = x = 10y = 200m ANSWER : B
Question: Three candidates contested in an election and received 3136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
A.45%
B.49%
C.52%
D.51%
Answer: C.52%
Explanation: Total number of votes polled = 3136+7636+11628 = 22400
Required percentage = 11628*100/22400 = 52%
Answer is C
Question: For every $20 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $2. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
A.1 :2 : 200
B.1 : 4 : 100
C.20 : 4 : 1
D.100 : 4 : 1
Answer: A.1 :2 : 200
Explanation: millionaire 20 cents = 1/5 dollar ..therefore 1 dollar M = 100 dollar of B
therefore 4 dollar M = 400 dollar of B also 2 dollar Y
Y:M:B = 2:4:400
= 1:2:200
A
Question: Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'?
A.7
B.5
C.6
D.4
Answer: B.5
Explanation: If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.
Answer: B
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.3 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is?
A.2:6
B.2:3
C.4:5
D.2:1
Answer: C.4:5
Explanation: Let the ratio be k : 1. Then,
k * 16.3 + 1 * 15.4 = (k + 1) * 15.8
= (16.3 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.5 = 4/5
Required ratio = 4/5 : 1 = 4:5.
Answer:C
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
A.228
B.278
C.289
D.500
Answer: D.500
Explanation: P - 340 = (P*4*8)/100
P = 500
Answer: D
Question: By how much is 12% of 24.2 more than 10% of 14.2 ?
A.0.1484
B.14.84
C.1.484
D.2.762
Answer: C.1.484
Explanation: Answer
Required difference = (12 x 24.2) / 100 - (10 x 14.2) / 100
= 2.904 -1.42
= 1.484.
Correct Option: C
Question: In a certain population, there are 3 times as many people aged twenty or under as there are people over twenty. The ratio of those twenty or under to the total population is
A. 1 to 2
B. 3 to 4
C. 1 to 4
D. 2 to 3
Answer: B. 3 to 4
Explanation: Consider the ratio of the under population of 20 to over the 20 as 3:1
therefore 3x:1X
Now the ratio of the under to the whole population becomes 3x/3x+1x
= 3/4
Answer is B
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
A.12/429
B.12/429
C.12/455
D.12/419
Answer: C.12/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer: C
Question: A manufacturer sells a pair of glasses to a wholesale dealer at a profit of 18%. The wholesaler sells the same to retailer at a profit of 20%. The retailer in turn sells them to a customer for Rs. 30.09, there by earning a profit of 25%. The cost price for the manufacturer is?
A.19
B.10
C.17
D.18
Answer: C.17
Explanation: Let the cost price for the manufacturer be Rs. x. Then, 125% of 120% of 118% of x
= 30.09.
125/100 * 120/100 * 118/100 * x
= 3009/100
177/100 x = 3009/100 => x = 17
Answer:C
Question: The average age of 19 boys and the class teacher is 16 years. If the ages of the class teacher and one of the boys are excluded, the average age reduces to 15 years. What is the age of the class teacher ?
A.767
B.26
C.50
D.88
Answer: C.50
Explanation: No. of Persons = 19 boys + 1 class teacher = 20
Average age of 20 people is 16 years.
Therefore, total age of 20 persons = 20 * 16 = 320 years ------ (A)
If the class teacher and one boy are excluded, then the average age is 15 years.
Therefore, total age of 18 boys = 18 * 15 = 270 years ------ (B)
Age of the class teacher and one boy = 320 – 270 = 50 years.
Data is inadequate as the relation between the ages of the boy and the teacher is not provided.
ANSWER: Data Inadequate
Explanation: C
Question: Ramesh can finish a piece of work in 22 days. Rohan is twice as efficient as Ramesh. If they work together how many days will they need to finish the same amount of work?
A.22/3 days
B.9/3 days
C.10/3 days
D.11/3 days
Answer: A.22/3 days
Explanation: Ramesh can finish a piece of work in 22 days. Rohan is twice as efficient as Ramesh.
So Rohan can finish a piece of work in 11 days.
days needed to finish the same amount of work = 1/(1/11+1/22)=22/3 days
ANSWER:A
Question: The average age of 19 students in a group is 17 years. When teacher’s age is included to it, the average increases by one. What is the teacher’s age in years?
A.36
B.37
C.38
D.cannot be determined
Answer: B.37
Explanation: Age of the teacher = (20 × 18 – 19 × 17) years
= 37 years.
Answer B
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.6. The true discount is
A.Rs.72
B.Rs.36
C.Rs.54
D.Rs.50
Answer: D.Rs.50
Explanation: Solution
T.D	= [B.G x 100 / R x T]
= Rs.(6 x 100 / 12 x 1)
= Rs.50.
Answer D
Question: A group of 6 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
A.x/18
B.x/35
C.3x/70
D.3x/10
Answer: A.x/18
Explanation: cost of boat per day = x
cost per person =x/6
if three more persons afre there, cost =x/9
difference = x/6-x/9
=x/18
Ans A
Question: A scale 6 ft. 8 inches long is divided into 5 equal parts. Find the length of each part.
A.20 inches
B.77 inches
C.16 inches
D.97 inches
Answer: C.16 inches
Explanation: Explanation:
Total length of scale in inches = (6*12) + 8 = 80 inches
Length of each of the 5 parts = 80/5 = 16 inches
ANSWER:C
Question: The average age of a group of 10 students was 20. The average age increased by 4 years when two new students joined the group. What is the average age of the two new students who joined the group?
A.22 years
B.30 years
C.34 years
D.44 years
Answer: D.44 years
Explanation: The total age of 10 students with average 20 = 200
The total age of 12 students with average 24 = 288
The total age of 2 new students = 88
Their average =44
Correct Option D
Question: A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?
A.31 days
B.25 days
C.27 days
D.29 days
Answer: C.27 days
Explanation: If A takes x days to do a work then B takes 2x days to do the same work.
--> 1/x+1/2x = 1/18
--> 3/2x = 1/18
--> x = 27 days.
Hence, A alone can finish the work in 27 days.
Answer : C.
Question: One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either a red card or a king?
A.2/5
B.3/13
C.4/19
D.7/13
Answer: D.7/13
Explanation: Out of 52 cards there will be 26 red cards including 2 kings and 2 more kings. Total 28
probability= 28/52 = 7/13
Answer is D
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
A.46%
B.48%
C.44%
D.49%
Answer: C.44%
Explanation: g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Question: Company C sells a line of 20 products with an average retail price of $1,200. If none of these products sells for less than $400, and exactly 10 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
A.12000
B.11000
C.10000
D.13000
Answer: B.11000
Explanation: The average price of 20 products is $1,200 means that the total price of 20 products is 20*1,200=$24,000.
Next, since exactly 10 of the products sell for less than $1,000, then let's make these 10 items to be at $400 each (min possible).
Now, the remaining 9 items cannot be priced less than $1,000, thus the minimum possible price of each of these 9 items is $1,000.
Thus the minimum possible value of 19 products is 10*400+9*1,000=$13,000.
Therefore, the greatest possible selling price of the most expensive product is $24,000-$13,000=$11,000.
Answer: B.
Question: Find the odd man out. 7, 14, 21, 28, 35, 50, 56
A.50
B.25
C.51
D.90
Answer: A.50
Explanation: Explanation :
All except 50 are multiples of 7
Answer : Option A
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be B's share in the total profit of Rs.25,000 earned at the end of 2 years from the starting of the business?
A.Rs.7500
B.Rs.9000
C.Rs.9500
D.Rs.10,000
Answer: A.Rs.7500
Explanation: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
B's share	=Rs.(25000×3/10)
= Rs.7500.
Answer A
Question: How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
A.A)Rs.6,602.50
B.B)Rs.6,601.50
C.C)Rs.6,603.50
D.D)Rs.6,604.50
Answer: A.A)Rs.6,602.50
Explanation: 20000(11/10)4 - 20000(6/5)2 = 6,602.50
ANSWER:A
Question: Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 56,000 after completion of one year. What will be Madhu's share of profit?
A.Rs. 28,000
B.Rs. 24,000
C.Rs. 30,000
D.Rs. 36,000
Answer: A.Rs. 28,000
Explanation: 30,000 *12=45,000*8
1:1
Madhu's share=1/2*56,000
i.e. Rs. 28,000
ANSWER:A
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $2 per unit. Further, the manufacturer has costs of $16,200 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
A.$28
B.$82
C.$110
D.$190
Answer: D.$190
Explanation: This question can be solved easily using a equation model.
150*p = 16200(fixed cost) + 150*80+150*2.
= 16200+ 12000+300
= 28500
P= $190.
D
Question: Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 8%. What is the approximate interest he pays annually?
A.1500
B.1750
C.2000
D.3500
Answer: D.3500
Explanation: An easy way too attempt this is by approximation:
For the first quarter, he pays 8% of 10,000 which is $800.
So for the four quarters in the year, he will approximately play 800*4=3200 over the entire year.
Because of compound interest it will be more than 3200. Approx. option D is correct.
Answer :D
Question: In Jeevans opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Jeevan and he thinks that Jeevans weight is greater than 60 kg but less than 70 kg. His mothers view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Jeevan?
A.67 kg
B.68 kg
C.69 kg
D.None of these
Answer: A.67 kg
Explanation: Explanation :
Let Jeevans weight be X kg.
According to Jeevan, 65 < X < 72.
According to Jeevan's brother, 60 < X < 70.
According to Jeevan's Mother, X <= 68
The Values satisfying all the above conditions are 66, 67 and 68 .
Required average = (66 + 67+68)/3 = 201/3 = 67 kg.
Answer : A
Question: The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:
A.12%
B.13%
C.14%
D.15%
Answer: C.14%
Explanation: S.I. on Rs. 750 = T.D. on Rs. 960.
This means P.W. of Rs. 960 due 2 years hence is Rs. 750.
T.D. = Rs. (960 - 750) = Rs. 210.
Thus, S.I. on R.s 750 for 2 years is Rs. 210.
Rate =(100 x 210)/(750 x 2)%	= 14% ANSWER : C
Question: Jerome anticipated that the WebWeb.com stock price would fall and sold all his WebWeb.com stocks for $5 per stock. He paid $10,000 tax on the revenue. A week later, Jerome became convinced that the WebWeb.com stock price would rise, and he used the money that he had gotten from selling the WebWeb.com stocks to purchase them again, this time at $6 per stock. If Jerome ended up having 5000 WebWeb.com stocks fewer than the number he had before selling them, how many WebWeb.com stocks did he have originally?
A.10,000
B.11,600
C.12,000
D.15,000
Answer: D.15,000
Explanation: Let the number of shares be x.
5*x -10000(money paid in taxes) = 6(x- 5000)
Solving for x, we get the shares as 15000.
Ans :(Option D)
Question: A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.49 kmph
B.50 kmph
C.51 kmph
D.52 kmph
Answer: A.49 kmph
Explanation: Explanation:
Speed of the train relative to man
= (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'x' km/hr.
Then, relative speed = (x - 4) km/hr.
x - 4 = 45 => x = 49 km/hr.
ANSWER IS A
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
A.3387
B.277
C.223
D.992
Answer: D.992
Explanation: (800*3*3)/100 = 72
920 + 72 = 992
Answer: D
Question: If the diameter of circle R is 50% of the diameter of circle S, the area of circle R is what percent of the area of circle S?
A.35%
B.25%
C.20%
D.15%
Answer: B.25%
Explanation: Let diameter of circle R , dr = 50
and diameter of circle S , ds = 100
Radius of circle R , Rr = 25
Radius of circle S , Rs = 50
Area of circle R/ Area of circle S = (pi * Rr ^2 ) /( pi * Rs^2 )
= (25/50)^2 = (5/10)^2
=25%
Answer :B
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another surveyof 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
A.50
B.100
C.150
D.200
Answer: D.200
Explanation: 50% of n people from Eros prefer brand A.
50% of n is 50/100 x n = n/2.
60% of 100 people from Angie prefer brand A.
60% of 100 is 60/100 x 100 = 60.
Of the total n+ 100 people surveyed, n/2 + 60 prefer brand A.
Given that this is 55%,
we have
(n/2+60)/(n+100) x100 =55
Solving the equation
(n/2+60)/(n+100) x100= 55
(n/2+60) = 55/100x(n+100)
(n/2+60) = 11/20n+55
0 = 11n /20 –n/2+55-60
Now subtracting n/2 and 60 from both sides
0=n/20-5
Adding 5 on both sides
5=n/20
n=100
Hence, the total number of people surveyed is
n+ 100 = 100 + 100
= 200.
ANSWER:D
Question: In a certain Parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle?
A.75
B.80
C.85
D.90
Answer: B.80
Explanation: In a parallelogram opposite angles are equal and the angles at each side are supplementary to each other (supplementary angles are two angles that add up to 180°).
Given: x+(x+20)=180 --> x=80.
Answer: B.
Question: In the third grade of Windblown School there are 96 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests?
A.0.
B.6.
C.8.
D.10.
Answer: A.0.
Explanation: Total = 96
failed in math = 96/3=32
failed in literature=108/6=16
the least failed in both can be 0
while max can be 16
Answer A
Question: The fourth proportional to 12, 14 and 18 is?
A.21
B.66
C.55
D.88
Answer: A.21
Explanation: (14*18)/12
= 21
Answer:A
Question: A pupil's marks were wrongly entered as 73 instead of 63. Due to the average marks for the class got increased by half. The number of pupils in the class is?
A.18
B.82
C.20
D.27
Answer: C.20
Explanation: Let there be x pupils in the class.
Total increase in marks
= (x * 1/2) = x/2
x/2 = (73 - 63) => x/2
= 10 => x = 20.
Answer: C
Question: Given that G and H are events such that
Q(G)= 0.30
Q(H)=0.9
Q(GnH)=0.9
find Q (G|H) and Q(G|H)
A.1/5
B.1/6
C.1/3
D.1/6
Answer: C.1/3
Explanation: Here, G and H are events
Q(G|H) = Q(GnH)/Q(H) = 0.9/0.9= 1
Q(G|H) = Q(GnH)/Q(G) = 0.9/0.30 = 1/3
Answer is C
Question: How many 2 digits number are there which when subtracted from the number formed by reversing its digits as well as when added to the number formed by reversing its digit, result is a perfect square.
A.63
B.64
C.65
D.66
Answer: C.65
Explanation: If xy is number, then 11(x+y) and 9*(x-y) should be perfect square.
which is possible when
x+y=11 and x-y = 1,4,9
value of x,y is valid only when x-y=1, then x=6,y=5
so number is 65.
ANSWER:C
Question: How many pieces can a square pizza be cut into by making 6 linear cuts?
A.20
B.21
C.22
D.23
Answer: C.22
Explanation: 1 cut makes 2 pieces
a second cut can make 4 pieces by cutting through both pieces
a third cut can make 7 pieces by cutting through 3 of the pieces
a fourth cut can make 11 pieces by cutting through 4 of the pieces
a fifth cut can make 16 pieces by cutting through 5 of the pieces
a sixth cut can make 22 pieces by cutting through 6 of the pieces
C
Question: What is the greatest prime factor of 4^16 - 2^28?
A.2
B.3
C.5
D.7
Answer: C.5
Explanation: I'm happy to help with this.
We know 4 = 2^2, so 4^17 = (2^2)^17 = 2^(2*16) = 2^32
That takes advantage of a law of exponents that says (a^n)^m = a^(n*m)
So, 4^16 - 2^28 = 2^32 - 2^28 = 2^(28 + 4) - 2^28 = (2^28)*(2*4) - 2^28 = (2^4 - 1) *(2^28)
= (16 - 1)*(2^28) = 15*(2^28)
The prime factors of 63 are 3*5, so the largest prime factor is 7, answer choice D.
Here's a blog you may find helpful.
http://magoosh.com/gmat/2012/gmat-math-factors/
Does all that make sense? Please let me know if you have any further questions.
Mike
Wow. I am floored by how great of an explanation you provided. Posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week.
C
Question: A bat is bought for Rs.400 and sold at a gain of 30% find its selling price?
A.s.460/-
B.s.480/-
C.s.500/-
D.s.520/-
Answer: D.s.520/-
Explanation: 100 % ------> 400 (100 * 4 = 400)
130 % ------> 520 (130 * 4 = 520)
Selling price = Rs.520/-
Option 'D'
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
A.40
B.25
C.30
D.35
Answer: A.40
Explanation: Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) = 90 years.
Sum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years.
Husband's present age = (90 - 50) = 40 years.
ANSWER A
Question: Matt gets a $1,000 commission on a big sale. This commission alone raises his average commission by $150. If Matt's new average commission is $550, how many sales has Matt made?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: Let, Average Commission = x
No. of items sold = y
Total Commission = xy
New Commission = xy+1000
New Average = (xy+1000) / (y+1) = 150+x
i.e. (xy+1000) = (y+1)* (150+x)
i.e. (xy+1000) = (xy+x+150y+150)
i.e. (850) = (x+150y)
New Commission = 550 = 150+x
i.e. x=400
i.e. y = 3
New Sales = y+1 = 4
Answer: option B