RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?
A.1/16
B.5/16
C.2/5
D.13/16
Answer: D.13/16
Explanation: Fair coin is tossed 5 times . Hence total number of outcomes = 2^5 = 32.
Problem asks for probability of getting atleast heads twice. Hence if we calculate probability of getting Heads exactly once and probability of not getting Heads at all and subract it from the total probability of the event which is 1 (As total probability of certain event will be always 1) we can get the probability of getting atleast heads twice.
Probability of getting exactly one head and no heads= (Number of possible outcomes [ HTTTT , THTTT, TTHTT, TTTHT, TTTTH , TTTTT] = 6)/ (Total possible outcomes = 32)
=> 6/32 = 3/16
Hence probability of getting atleast heads twice = 1 - (3/16) = 13/16 => Choice [D]
Question: If 8a = 9b and ab ≠0, what is the ratio of a/9 to b/8?
A.64/81
B.8/9
C.1
D.9/8
Answer: C.1
Explanation: if ab ≠0
then a and b has two integer sets of pair
if a=9 then b=8
and if a=-9 then b=-8
also in fraction if a=1/8 then b=1/9
any of the pair we check the ratio 8a/9b=1
ANSWER:C
Question: The avg weight of A,B & C is 70 kg. If D joins the group, the avg weight of the group becomes 70 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 68 kg. What is the weight of A?
A.81
B.65
C.75
D.89
Answer: A.81
Explanation: A + B + C = 3 *70 = 210
A + B + C + D = 4 * 70 = 280 ---- (i)
So, D = 70& E = 70 + 3 = 73
B + C + D +E =68 * 4 = 272 --- (ii)
From Eq. (i) & (ii)
A-E = 280 –272 = 8
A = E +8 = 73 + 8 = 81
Answer : A
Question: How many legs are there if each sheep has 4 legs and there are total 250 of that kind?
A.A)700
B.B)800
C.C)1000
D.D)10000
Answer: C.C)1000
Explanation: Sol.
Total of 250 each has 4 legs
= 250 * 4
= 1000
Answer : C
Question: A garrison of 400 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
A.10 days
B.20 days
C.5 days
D.25 days
Answer: A.10 days
Explanation: 400 --- 31
400 --- 3
120 --- ?
400*3 = 120*x => x =10 days
ANSWER A
Question: If 14 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
A.78 days.
B.154 days.
C.149 days.
D.148 days.
Answer: B.154 days.
Explanation: B
154 days.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (14*6*88/1) = (6*8*d/1)
on solving, d = 154 days.
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
A. 3 4/9 days
A.9 3/7 days
B.9 7/8 days
C.9 3/8 days
D.9 3/8 days
Answer: C.9 3/8 days
Explanation: 1/15 + 1/25 = 8/75
75/8
= 9 3/8 days
Answer:C
Question: . Data sufficiency question:
What will be the percentage profit of selling one liter milk.?
1) 16 liter of milk is sold at cost price after adding 20% water to it.
2) the cost price of one liter milk is Rs.16.
A.23
B.29
C.27
D.1291
Answer: B.29
Explanation: Explanation:
Let us assume one liter costs Rs.1. So C.P = Rs.16
When 20% water is added, then total volume = 20 liters. So SP = 20. Profit can be calculated.
Statement 1 is sufficient.
Statement 2 is not required.
Answer:B
Question: Amy's sells kale at x dollar per pound for the first 20 pounds and .5x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?
A.24
B.25
C.26
D.21.5
Answer: D.21.5
Explanation: For Amy's deal to be better, the cost has to be less or equal to Lucia's
Assuming 'n' is the number of pounds of kale, the equation is
20x + (n-20) (0.5x) <= 14x + (n-14)(0.9x)
Resolve it:
==> 20x + 0.5nx - 10x <= 14x + 0.9nx - 12.6x
==> 8.6x <=0.4nx
==> 21.5x < =nx
==> x (n-21.5) > = 0
as x cannot be 0,
==> n - 21.5>=0
==> n > = 21.5
so the minimum value is 21.5
'D' would be the correct answer
Question: If 12x = 16y = 28z, then what is a possible sum of positive integers x, y, and z?
A.52
B.58
C.122
D.84
Answer: C.122
Explanation: 12x = 16y = 28z
3x = 4y = 7z
3(4*7) = 4(3*7) = 7(3*4)
Addition = 28+21+12 = 61
Answer would be multiple of 61 which is 122
Answer :C
Question: A certain essay consists of 12 paragraphs. Each paragraph contains at least 110 words but not more than 120 words. Which of the following could be the total number of words in the essay?
A.1430
B.1540
C.1640
D.1740
Answer: A.1430
Explanation: lets consider minimum no of words ... 12 * 110 = 1320
Lets consider maximum no of words .... 12*120= 1440
answer should be one of these two values or should lie between these two values ...
only 1 option A - 1430
Question: A square marked 1, 2, 3 and 4 on its four sides. Four colors pink, purple,brown and yellow are used to paint the four sides of the square. If the adjacent sides are painted with the different colors, in how many ways can the sides be painted?
A.4
B.12
C.9
D.27
Answer: A.4
Explanation: If the base of the square is pink, then in order the adjacent faces to be painted with the different colors, the top must also be pink. 4 side faces can be painted in Brown-Purple-yellow Brown-Purple-Yellow OR Purple-yellow- Brown-Purple-yellow- Brown (2 options).
But we can have the base painted in either of the four colors, thus the total number of ways to paint the square is 2*2=4.
Answer: A.
Question: If a company gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265
A.800
B.700
C.750
D.850
Answer: A.800
Explanation: cost P = 125/100 * 115/100 * 110/100 = 1265
253/160p=1265==> p =800
ANSWER A
Question: The ages of Raju and Biju are in the ratio 3:1. Fifteen years hence, the ratio will be 2:1. Their present
ages are:
A.30yrs, 10yrs
B.45 yrs, 15yrs
C.21 yrs, 7 yrs
D.60yrs, 20yrs
Answer: B.45 yrs, 15yrs
Explanation: Expl : Let the ages of raju and Biju is 3x and x years respectively.
Then, (3x +15)/ (x+15) = 2/1; -> 2x + 30 = 3x + 15 -> x = 15
So Raju’s age = 3*15 = 45 and Biju’s age = 15 years
Answer:B
Question: If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B ?
A.108
B.120
C.132
D.144
Answer: C.132
Explanation: Two two-digit positive integers have the same digits but in reverse order
So they must be in the form 10x+y and 10y+x
Adding both of them will give us 11x+11y -----------> 11(x+y) -----------> that means 11 is the factor of sum
Among the answer choices only 132(choice C) has 11 as its factor and it is the possible sum of two integers A and B
ANSWER:C
Question: A cab driver 5 days income was $600, $250, $450, $400 , $800. Then his average income is?
A.$460
B.$480
C.$500
D.$520
Answer: C.$500
Explanation: avg = sum of observations/number of observations
avg income=(600+250+450+400+800)/5 = 500
Answer is C
Question: A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 9 minutes?
A.486
B.54
C.108
D.216
Answer: A.486
Explanation: ONE Veggiematik machine can chop 36 carrots in 4 minutes
So, ONE Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes
In other words, ONE Veggiematik machine can chop 54 carrots in4minutes
So,SIXVeggiematik machines can chop (9)(54) carrots in9minutes
In other words, SIX Veggiematik machines can chop 486 carrots in9minutes
Answer A
Question: A box contains 5 red, 4 blue, and 3 white balls. In how many ways can we select 4 balls such that at least 2 are red?
A.235
B.270
C.280
D.285
Answer: D.285
Explanation: Explanation:
You decline to mention whether balls of the same color are identical. If they are, then you have only 99 ways to do so. Why? Two positions are dedicated to red. For the remaining two, you can have red, blue or white (all are sufficiently numerous to allow that) and so that's 3×3=93×3=9 ways.
If, on the other hand balls of the same color are non-identical, then you can select four balls of any color is (5+4+3/4)=495(5+4+34)=495 ways. No red ball is selected in (4+3/4)=35 ways. Exactly one red ball is selected in 5×(4+3/3)175 ways. Thus, you select at least two red balls in 495−(35+175)=285 ways
Answer is D
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.35000?
A.11585
B.11879
C.12779
D.12672
Answer: A.11585
Explanation: A = 35000(11/10)^3
= 46585
= 35000
----------
11585
Answer: A
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
A.7
B.8!
C.7
D.5
Answer: B.8!
Explanation: Total number of letters
= 8
Using these letters the number of 8 letters words formed is ⁸P₈
= 8!.
Answer: B
Question: 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
A.18
B.15
C.16
D.12
Answer: A.18
Explanation: Sol.
Capacity of each bucket = 9 litres.
Number of buckets needed = (162/9) = 18.
Answer A
Question: If log1087.5 = 4.9421, then the number of digits in (875)10 is?
A.60
B.28
C.27
D.26
Answer: A.60
Explanation: X = (875)10 = (87.5 x 10)10
Therefore, log10X = 10(log4087.5 + 1)
= 10(4.9421 + 1)
= 10(5.9421) = 59.421
X = antilog(59.421)
Therefore, number of digits in X = 60.
ANSWER:A
Question: Last year, Company X paid out a total of $1,050,000 in salaries to its 21 employees. If no employee earned a salary that is more than 25% greater than any other employee, what is the lowest possible salary that any one employee earned?
A. $40,384.61
B. $41,667
C. $42,000
D. $50,000
Answer: A. $40,384.61
Explanation: Employee 1 earned $x(say)
Employee 2 will not earn more than $1.25x
Therfore, to minimize the salary of any one employee, we need to maximize the salaries of the other 20 employees
(1.25x*20)+x=1,050,000
Solving for x=$40,384.61
Answer A
Question: A man buys 56 pens at marked price of 46 pens from a whole seller. If he sells these pens giving a discount of 1% , what is the profit percent?
A.7.6 %
B.7.7 %
C.20.52 %
D.23.62 %
Answer: C.20.52 %
Explanation: Explanation:
Let Marked price be Re. 1 each
C.P. of 56 pens = Rs. 46
S.P. of 56 pens = 99% of Rs. 56 = Rs. 55.44
Profit % = (Profit /C.P.) x 100
Profit% = (9.44) x 100 = 20.52 %
ANSWER: C
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.400 in 2 Years?
A.5%
B.6%
C.2%
D.25%
Answer: D.25%
Explanation: Interest for 2yrs = 400
Interest for 1yr = 200
Interest rate = 200/800 x 100 = 25%
Answer : D
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A.9
B.10
C.11
D.12
Answer: B.10
Explanation: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =	9/54	x 60	min	= 10 min.
answer :B
Question: The cost C of manufacturing a product can be estimated by the formula C= 0.03 rs t^2, where r ans s are amounts, in pounds, of two major ingredients and t is production time in hours. if r is increased by 50%, s increased by 20% and t decreased by 30%, by approximately what % will the estimated cost of manufacturing the product change.
A.40% increase
B.12% increase
C.4% increase
D.12% decrease
Answer: D.12% decrease
Explanation: Let r=s=t=100
C = 0.03*r*s(t^2)
=0.03*100*100*(100^2)
=3,000,000
r1 = 50% more than r = 150
s1 = 20% more than s =120
t1 = 30% less than t = 70
C1= 0.03 * 150 *120 * 70 * 70
=0.03 * 1800 * 4900
= 54*4900
=264600
Decrease = C-C1 = 3,000,000-264600=35400
%Decrease = 35400/300000 * 100 = 354/30 = 11.8 ~ 12% Decrease
ANSWER:D
Question: What is 2 2/3 - 1 1/4 divided by 1/2 - 1/3 ?
A.17/36
B.36/17
C.17/6
D.17/2
Answer: D.17/2
Explanation: 2 2/3 - 1 1/4 = 8/3 - 5/4 = (32 - 15 )/12 = 17/12
1/3 - 1/6 = (2-1)/6 = 1/6
So 17/12/1/6 = 17/12 * 6 = 17/2
Answer - D
Question: Robet traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
A.z=3x
B.x=3z
C.y=2x
D.x=2y
Answer: D.x=2y
Explanation: Robet Travelled for x,y and for z min.
Total Time : x + y + z
Which is equal to : 3y
Equating both sides we get
x+y+z = 3y
=> x+z =2y ........ Eqn 1
Looking out at options
D Says x =2y
Using it in Eqn 1
2y + z = 2y
=> Z = 0 mins, Which I guess is not possible.
The Ans isD
Question: Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?
A.1/13
B.2/15
C.4/13
D.3/17
Answer: C.4/13
Explanation: Here, n(S) = 52
There are 13 cards that are diamond (including one king) and there are 3 more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13 + 3) = 16
P (E) = 16 / 52 = 4/13
C
Question: What will be the difference between simple and compound interest @ 10% per annum on the sum of Rs 1000 after 4 years
A.Rs 62.10
B.Rs 63.10
C.Rs 64.10
D.Rs 65.10
Answer: C.Rs 64.10
Explanation: Explanation:
S.I.=1000∗10∗4 /100=400
C.I.=[1000(1+10 /100)4−1000]=464.10
So difference between simple interest and compound interest will be 464.10 - 400 = 64.10
Option C
Question: A father purchased dress for his 3 daughters. The dresses are of same color but diff size and they are kept in dark room. what is probability that all the 3 will not choose their own dress?
A.22
B.87
C.29
D.26
Answer: B.87
Explanation: Answer:B
Question: A pizza shop made pizzas with many flavours. There are 9 different flavours, in that 2 flavours are taken to make pizza. In how many ways they can arrange?
A.16
B.26
C.36
D.46
Answer: C.36
Explanation: the answer is 36.because 2 is taken from 9 so its arranged in 9p2 ways i.e., 72
But 2 flavours may be same so it is arranged in 2! ways i.e., 9p2/2!=72/2=36
ANSWER:C
Question: Spandy travels from X to Y at a speed od 40 kmph and returns by increasing his speed by 50%. What is his average speed for the whole journey?
A.36 kmph
B.45 kmph
C.48 kmps
D.45 kmps
Answer: C.48 kmps
Explanation: Explanation :
Let the distance between X and Y be x km.
Time taken from X to Y @ 40 km/h=(x/40)hours
Time taken from Y to X @ 60 km/h=(x/60)hours
Average speed=2x/((x/40)+(x/60))= 48 km/h.
Answer : C
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
A.3:8
B.3:1
C.ratio of 3:4
D.3:9
Answer: C.ratio of 3:4
Explanation: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y = 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y = 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y = 80
Ratio of speeds = 60:80 = 3:4
Answer:C
Question: A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 7, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
A.18
B.36
C.72
D.112
Answer: A.18
Explanation: {1}{2}{greater than 7}{divisible by 3}{3x}{x}:
The third digit can take 2 values: 8, or 9.
The fourth digit can take 3 values: 3, 6, or 9.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 2*3*3 = 18.
Answer: A.
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
A.24
B.25
C.39
D.40
Answer: C.39
Explanation: Option 'C'
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many V hours will it take 12 beavers that work at the same pace, to build the same dam?
A.2.
B.V=4.
C.V=5.
D.V=6.
Answer: C.V=5.
Explanation: C. 5 hrs
If there were 10 beavers it qould have taken double V= 6hrs.. so closest to that option is 5.
Question: If 20% of a = b, then b% of 20 is the same as:
A.None of these
B.10% of a
C.4% of a
D.20% of a
Answer: C.4% of a
Explanation: Explanation :
20% of a = b
⇒b=20/100a
b% of 20 = (b/100)20 = (20/100a) /100X20=20×20×a/100×100 = (4a/100) = 4% of a
Answer : Option C
Question: Xavier starts from P towards Q at a speed of 60 kmph and after every 12 mins increases his speed by 10 kmph. If the distance between P and Q is 60km, then how much time does he take to cover the distance?
A.48
B.59
C.60
D.56
Answer: A.48
Explanation: first 12min = 60 *12/60 =12km
2nd 12min = 70*12/60 = 14km
3rd 12 min = 80*12/60 = 16 km
4th 12 min = 90 *12/60 = 18 KM
TOTAL time 12.4 =48 min
A
Question: If 1/(x+4)+1/(x-4)=1/(x-4), what is the value of x?
A.5
B.4
C.1
D.2
Answer: B.4
Explanation: If we solve the question, we get x=4.
Option: B
Question: Three years ago, the average age of M and N was 18 years. With P joining them, the average age becomes 22 years, How old is P now?
A.24 years
B.27 years
C.28 years
D.30 years
Answer: A.24 years
Explanation: Explanation :
Present age of (M + N) = (18 x 2 + 3 x 2) years = 42 years.
Present age of (M + N + P) = (22 x 3) years = 66 years. P's age = (66 - 42) years = 24 years.
Answer : A
Question: In a class of 79 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A.6
B.15
C.25
D.33
Answer: C.25
Explanation: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 79
54 + NOT = 79
NOT = 79 - 54 = 25
So answer is C
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
A.8/41
B.8/43
C.9/42
D.9/47
Answer: C.9/42
Explanation: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
A.6 days
B.8 days
C.5 days
D.3 days
Answer: A.6 days
Explanation: 4/10 + 9/x = 1 => x = 15
1/10 + 1/15
= 1/6
=> 6 days
Answer:A
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector has a central angle of 66°, what fraction of the wheel’s area is represented by the smallest sector?
A.1/24
B.1/20
C.1/15
D.1/12
Answer: C.1/15
Explanation: The largest angle is 66.
Let d be the difference between any two angles in the progression.
The sum of all the angles will be:
66 + (66-d) + (66-2d) + ... + (66-7d) = 528 - 28d
The sum of all the central angles in a circle = 360
528 - 28d = 360
d = 168/28 = 6
The smallest sector is (66-7d) = 66-7*6 = 24
The fraction of the area covered is 24/360 = 1/15.
The answer is C.
Question: If Dale works at full efficiency he needs a break of 1 day after every 2 days of work and he completes a job in a total of 8 days. If he works at reduced efficiency, he can work without break and finish that same job in 8 days. Dale's output at reduced efficiency is what fraction of his output at full efficiency?
A.4/12
B.3/4
C.6/5
D.11/12
Answer: B.3/4
Explanation: We're told that there are 2 ways for Dale to complete a job:
1) Full Efficiency: 2 days of work followed by 1 dayofffor a total of 8 days.
2) Reduced Efficiency: 8 straight days with no days off.
Working at Full Efficiency creates the following pattern:
2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on, 1 day OFF, 2 days on = 2+1+2+1+2= 8 days
Totals: 6 days on, 2 days off
Reduced Efficiency means that Dale will do 6 days of work in 8 days, thus those Reduceddaysare 6/8=3/4 of Full Efficiency.
Answer : B
Question: If we write 1/3 as a decimal, what number holds the 100th digit's place to the right of the decimal?
A.1
B.3
C.4
D.2
Answer: B.3
Explanation: Writing 1/3 as a decimal we get 0.33333....
This is an infinitely repeating decimal. So, 3 must be the number in the 100th digit's place to the right of the decimal.
Answer: B
Question: If Rs.1000 be invested at interest rate of 5% & the interest be added to the principal every 10 yrs, then the no. of yrs in which it will amount to Rs.2000 is:
A.16 years
B.16 1/3 years
C.16 2/3 years
D.17 years
Answer: C.16 2/3 years
Explanation: Total time= (10+6 2/3) = 16 2/3 years
C
Question: The ratio of oranges to apples in a fruit basket is 3 to 4. However, after Mary and Alan eat four apples, the ratio changes to 3 to 2. How many oranges are there in the fruit basket?
A.2
B.3
C.6
D.9
Answer: C.6
Explanation: O / A = 3/4 => O = 3/4(A).
Now O/A-4 = 3/2 . Now sub O value in this...we get 3A / 4A-16 = 3/2 => A = 8 and O = 6.
ANS option C
Question: A total of 40 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
A.15/40
B.7/12
C.2/3
D.7/8
Answer: A.15/40
Explanation: Let' take the Number of geese to be 100.
Male = 40. Female = 60.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *20 = 4 Geese (Males)
And now we know out of the total 20 geese , 4 are male , then 16 have to be female.
Now the ratio part , Male Geese Ratios = 4/40 = 1/10. - A
Female Geese Ratios =16/60=4/15 - B
Cross Multiply Equations A and B and you get =15/40 .
Ans A
Question: If f(x)=x^3 and g(x)=x^2, and x is a natural number, what CANNOT the answer be for f(g(x))?
A.1
B.64
C.729
D.512
Answer: D.512
Explanation: 512 is not a possible answer because 512 is equal to 8 cubed, because x must first be squared by g(x) before it is cubed by f(x), and 8 is not a perfect square, therefor there is no natural number that can be used to make f(g(x))=512. The answer is D.
Question: By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be:
A.Rs. 2,600
B.Rs. 2,700
C.Rs. 2,800
D.Rs. 3000
Answer: B.Rs. 2,700
Explanation: Solution: Let Cost Price was X.
X + 14% of X = 2850
X + 14X/100 = 2850
X + 0.14X = 2850
1.14X = 2850
X = 2500.
So, Cost Price = Rs. 2500.
Now, Selling Price When profit remains at 8%,
= 2500 + 8% of 2500
= Rs. 2700.
Short-Cut
CP of bicycle = 100/114*2850 = Rs. 2500;
SP for a profit of 8% = 108/100*2500 = Rs. 2700.
Answer: Option B
Question: The 7th grade French and Spanish classes each have 12 students in them, and there are two students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
A.19
B.20
C.21
D.22
Answer: B.20
Explanation: French class + Spanish class = 24 students.
Two students are in both classes so they were counted twice.
The number of students taking just one class is 24 - 2(2) = 20.
The answer is B.
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
A.15
B.16
C.17
D.18
Answer: B.16
Explanation: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35 = 16 sec
Answer: Option B
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 36 photos?
A.4 films and 12 photos
B.5 films and 6 photos
C.5 films and 14 photos
D.6 films and 4 photos
Answer: A.4 films and 12 photos
Explanation: 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.58-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->4 full films and 1+11=12 photos
Answer: A
Shortcut:
Price of 1 full film is 12.1 so we cannot have 5 full films as 12.1*5=60.5 and we need 52.58. Only option A seems valid.