RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If a and b are distinct positive integers. The units digit of a^2 is equal to the units digit of a, and the units digit of b^2 is equal to the units digit of b. If the units digit of a·b is equal to neither the units digit of a nor the units digit of b, then what is the units digit of a·b?
A.0
B.1
C.4
D.5
Answer: A.0
Explanation: There are four digits which when squared give the same units digits: 0, 1, 5, 6
0^2 = 0
1^2 = 1
5^2 = 25
6^2 = 36
So a and b must take 2 of these values. They are positive integers so 0 is not possible.
If one of the digits is 1, when the other is multiplied by 1, you will get the same digit. 1*5 = 5
So 1 is out of the picture.
Then you have only two digits left 5 and 6. So out of a and b, one must be 5 and the other 6.
5*6 = 30 so units digit of their product = 0
Answer (A)
Question: The total age of A and B is 16 years more than the total age of B and C. C is how many years younger than A ?
A.12
B.16
C.21
D.18
Answer: B.16
Explanation: (A+B) - (B+C) = 16
A - C = 16.
C is younger than A by 16 years.
Answer: B
Question: In a recent election, Ms. Robbins received 7,200 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 60 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
A.0.06N + 3,200
B.0.1N + 7,200
C.0.04N + 7,200
D.0.1N + 8,000
Answer: C.0.04N + 7,200
Explanation: I will go with option C
According to question 60 percent of total votes (N) cas were cast by independent voters. This implies 40 percent of N are voters that belong to political party. And she received 7200 votes from independent voters and 10 percent from registered voters (i.e 0.1 * 0.4 * N = 0.04N). Hence total votes = 7200 + 0.04N ....option C
Question: The variables m and n are positive integers. When m is divided by 18, there is a remainder of 12, and when n is divided by 24, there is a remainder of 14. Which of the following are possible values of m + n?
I. 26
II. 70
III. 90
A.I only
B.III only
C.I and II
D.I​ and III
Answer: A.I only
Explanation: m = 18k + 12 --> Values are 12, 30, 48, 66, 84
n = 24k + 14 --> Values are 14, 38, 62, 86
I. 26 --> 12 + 14 --> Possible
II. 70 --> Not possible
III. 90 --> Not possible
Answer: A
Question: Two letters from the word NOTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
Two letters from the word NOTHING are selected at random. What is the probability that at least one of the selected letters is a consonant?
A.A)1/500
B.B)1/28
C.C)27/28
D.D)124/125
Answer: C.C)27/28
Explanation: There are 5 consonants and 2 vowels in NOTHING .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/7C2 = 1/21
So, Answer is 1 - 1/21 = 20/21 ------> C.
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
A.59028
B.59010
C.59190
D.59000
Answer: D.59000
Explanation: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer:D
Question: If a large pizza has a radius that is 40% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
A.40%
B.80%
C.96%
D.112%
Answer: C.96%
Explanation: Let the radius of medium pizza be r. Then the radius of large pizza is 1.4r.
The area of the medium pizza is pi*r^2
The area of the large pizza is pi*(1.4*r)^2 = 1.96*pi*r^2, an increase of 96%.
The answer is C.
Question: In case O is the only individual sewing on committee B, which among the following shouldserve on committee A?
A.V and U
B.V and T
C.U and S
D.P and Q
Answer: D.P and Q
Explanation: P and Q should serve on A
ANSWER:D
Question: How many ONE letter words are formed using the letters of the word WALK?
A.1
B.16
C.7
D.4
Answer: D.4
Explanation: The number of letters in the given word is 4.
The number of ONE letter words that can be formed using these four letters is 4P1=4*1=4
Answer:D
Question: A can do a piece of work in 20 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
A.10days
B.6days
C.7.5days
D.8.5days
Answer: A.10days
Explanation: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =20∗1/2=10days
Option A
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
A.4/5
B.1/3
C.3/2
D.4/3
Answer: B.1/3
Explanation: . Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: B
Question: A car covers a distance of 624 km in 3 1/5 hours. Find its speed?
A.104 kmph
B.195 kmph
C.109 kmph
D.174 kmph
Answer: B.195 kmph
Explanation: 624/3 1/5
=195 kmph
Answer:B
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
A.72
B.55
C.66
D.11
Answer: A.72
Explanation: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72.Answer: A
Question: Mangala completes a piece of work in 12 days, Raju completes the same work in 34 days. If both of them work together, then the number of days required to complete the work is?
A.8 3/4 days
B.10 1/4 days
C.11 1/4 days
D.12 2/3 days
Answer: A.8 3/4 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 12× 34/46= 8 3/4 days
A)
Question: Ella can fill K cans of water in 4 minutes. If there are T cans of water in one gallon, how many gallons can Ella fill in 36 minutes?
A.4T/K
B.4KT
C.9T/K
D.9K/T
Answer: D.9K/T
Explanation: Ella can fill this number of cans in 36 minutes: (36/4)K = 9K.
One can is 1/T gallons.
Ella can fill 9K*(1/T) = 9K/T gallons of water in 36 minutes.
The answer is D.
Question: A 240 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
A.228
B.144
C.1266
D.188
Answer: B.144
Explanation: S = 240/6 * 18/5 = 144 kmph
Answer: B
Question: An auction house charges a commission of 15% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
A.$115,000
B.$160,000
C.$215,000
D.$240,000
Answer: C.$215,000
Explanation: Say the price of the house was $x, then 0.15*50,000+0.1*(x-50,000)=24,000 --> x=$215,000 (15% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: C
Question: Felix earned 50% more per month than Oscar. If Felix’s salary is decreased 10% and Oscar’s salary is increased by 10%, then Felix would be earning what percent more than Oscar?
A.25%
B.9.09%
C.14%
D.22.73%
Answer: D.22.73%
Explanation: This Q is all about taking the correct BASE for taking %s..
the very first step requires taking some numbers for each..
ONE should be 100...
it is easy to take 50 and 100 here..
but the BASE is 100 here, so the salary can be 100 and 150..
100 increases 10% =110..
150 decreases 10%=135..
so the increase is 25..
again the BASE is 110, so answer 25/110 * 100= 22.73% D
without calculations,
answer cannot be equal to or greater than 25, as 25 is on 110..
so D is the only one left
Question: A box is in the shape of a semicircle with a radius of 12. What is the approximate perimeter of the semicircle?
A.54
B.62
C.25
D.34
Answer: B.62
Explanation: perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*12 + 2*12 = 61.68 approximately 62
answer B
Question: a and b are positive integers less than or equal to 7. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab?
A.3
B.4
C.2
D.6
Answer: A.3
Explanation: 686868 when divided by 2 gives the result 343434
CONCEPT: Rule of Divisibility of 2 isIf sum of the digits of the Number is divisible by 2 then the number will be divisible by 2
SUm of the digits of No. which is divisible by 2 hence the Number 686868 will be divisible by 2
Question: There are 50 students in a class. If 2 % are absent on a particular day, find the number of students present in the class.
A.43
B.36
C.28
D.49
Answer: D.49
Explanation: Number of students absent on a particular day = 1 % of 50
i.e., 2/100 × 50 = 1
Therefore, the number of students present = 50 - 1 = 49 students.
Answer:D
Question: A boat can move upstream at 22 kmph and downstream at 42 kmph, then the speed of the current is?
A.15
B.16
C.18
D.10
Answer: D.10
Explanation: US = 22
DS = 42
M = (42 - 22)/2 = 10 Answer:D
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
A.10
B.20
C.24
D.26
Answer: B.20
Explanation: 2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios
a * d ~ b * c = 2 * 4 ~ 3 * 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 * 3 = 30 and 10 * 4 = 40,
Then 30 ~ 40 = 10
===> 1 -----> 10
===> 2 -----> 20
B
Question: Mr. Yutaro’s class contains 11 boys and 5 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?
A.11/24
B.9/20
C.11/28
D.27/48
Answer: A.11/24
Explanation: Probability of a girl being chosen first, then a girl:
5/16 * 11/15
Probability of a boy being chosen first, then a boy:
11/16 * 5/15
Probability of a boy and a girl being chosen:
(5*11+5*11) / (15*16)
=11+11/3*16
=22/48
=11/24,
Answer:A
Question: On his drive to work, Leo listens to one of three radio stations A, B or X. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to X. If X is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
A.0.027
B.0.09
C.0.417
D.0.657
Answer: D.0.657
Explanation: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to X and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Question: The fourth proportional to 10, 15 and 18 is?
A.21
B.27
C.55
D.88
Answer: B.27
Explanation: (15*18)/10
= 27
Answer:B
Question: Which is a better offer out of (i) a cash payment now of Rs.8100 or (ii) a credit of Rs.8250 after 6 months(6.5% S.I)
A.(i)
B.(ii)
C.both (i) and (ii)
D.only (i)
Answer: A.(i)
Explanation: Explanation:
PW=100*Amount / 100+(R+T)
ANSWER IS A
Question: The number 0.5 is how much greater than 1/6 ?
A.1/3
B.2/10
C.1/50
D.1/500
Answer: A.1/3
Explanation: let x be the difference
then
.5-1/3=x
5/10-1/3=x
x=1/3
ans A
Question: M is 30% of Q. Q is 20% of P. N is 50% of P. Find M:N ratio
A.3:25
B.3:24
C.3:23
D.3:22
Answer: A.3:25
Explanation: Let p be 100
N = 50% of 100 (P=100) = 50
Q= 20% of 100 (P=100) = 20
M = 30% of 20 (Q=20) = 6
M:N = 6:50
M:N = 3:25
ANSWER:A
Question: A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
A.2 hr 30 min
B.2 hr
C.4 hr
D.1 hr 15 min
Answer: A.2 hr 30 min
Explanation: Explanation:
Speed upstream =2/2=1km/hr
Speed downstream =1/(20/60)=3km/hr
Speed in still water =1/2(3+1)=2km/hr
Time taken to travel 5 km in still water
=5/2=2(1/2)hours=2 hour 30mins
ANSWER IS A
Question: 10% of a 50% alcohol solution is replaced with water. From the resulting solution, again 10% is replaced with water. This step is repeated once more. What is the concentration of alcohol in the final solution obtained?
A.3%
B.20%
C.25%
D.36%
Answer: D.36%
Explanation: Since the numbers in the answers are pretty far apart. I just simplified and rounded.
Alcohol = 50%
Total - 10% * 3 = 70%
.5 * .7 = .35 (so that means 70% of 50% of the total is 35%)
Answer: D) 36
Question: Two boats start from opposite banks of river perpendicular to the shore. One is faster then the other. They meet at 720 yards from one of the ends. After reaching opposite ends they rest for 10mins each. After that they start back. This time on the return journey they meet at 400yards from the other end of the river. Calculate the width of the river.
A.1660 yard
B.1760 yard
C.1860 yard
D.1560 yard
Answer: B.1760 yard
Explanation: Let us assume that width of river d yards and speed of boats - x and y yards/min respectively.Hence the two equations are :1) (d-720)/x = 720/y2) (d/y+10+400/y) = (d/x + 10 + (d-400)/x)Solving the two equationsWe get d=1760 yard
ANSWER:B
Question: A train 360 m long is running at a speed of 48 km/hr. In what time will it pass a bridge 140 m long?
A.40 sec
B.11 sec
C.37.5 sec
D.19 sec
Answer: C.37.5 sec
Explanation: Speed = 48 * 5/18 = 40/3 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 3/40 = 37.5 sec
Answer: C
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 600 shares of the company's stock?
A.$92
B.$312
C.$104
D.$120
Answer: B.$312
Explanation: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*600 --> $312
answer is B
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
A.1/216
B.1/212
C.1/272
D.1/220
Answer: A.1/216
Explanation: Explanation:
The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=
n(S) =
Let X be the event that all dice show the same face.
X = { (1,1,1,1,), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)}
n(X) = 6
Hence required probability
Answer: A) 1/216
Question: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?
A.60 liters
B.70 liters
C.80 liters
D.90 liters
Answer: C.80 liters
Explanation: Let x be the quantity of the 20% alcohol solution to be added to the 40 liters of a 50% alcohol. Let y be the quantity of the final 30% solution. Hence
x + 40 = y
We shall now express mathematically that the quantity of alcohol in x liters plus the quantity of alcohol in the 40 liters is equal to the quantity of alcohol in y liters. But remember the alcohol is measured in percentage term.
20% x + 50% * 40 = 30% y
Substitute y by x + 40 in the last equation to obtain.
20% x + 50% * 40 = 30% (x + 40)
Change percentages into fractions.
20 x / 100 + 50 * 40 / 100= 30 x / 100 + 30 * 40 / 100
Multiply all terms by 100 to simplify.
20 x + 50 * 40 = 30 x + 30 * 40
Solve for x.
x = 80 liters
80 liters of 20% alcohol is be added to 40 liters of a 50% alcohol solution to make a 30% solution
Answer C
Question: Peter walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:30. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 30 meters. What is Peter's speed in meters per minute?
A.100
B.180
C.198
D.216
Answer: A.100
Explanation: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×30(per block dist)
Speed = 3000mts/30min =100m/min
A is the answer
Question: A clock gains 15 minutes per day. It is set right at 12 noon. What time will it show at 4.00 am, the next day?
A.4 : 10 am
B.4 : 45 am
C.4 : 20 am
D.5 : 00 am
Answer: A.4 : 10 am
Explanation: The clock gains 15 min in 24 hours.
Therefore, in 16 hours, it will gain 10 minutes.
Hence, the time shown by the clock will be 4.10 am.
Answer A
Question: How much more would Rs.40000 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.482
B.725
C.964
D.837
Answer: C.964
Explanation: 40000(11/10)4 - 40000(6/5)2 = 964
Answer:C
Question: A boat running up stram takes 6 hours to cover a certain distance, while it takes 8 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
A.2 : 3
B.5 : 6
C.4 : 5
D.7 : 1
Answer: D.7 : 1
Explanation: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
6(x+y) = 8(x-y)
6x+6y = 8x-8y
14y = 2x
7y = x
x/y = 7/1
7 : 1
Answer: Option D
Question: A coin is tossed 4 times. What is the probability a that the number of Heads is equal to the number of Tails?
A.1/8
B.1/4
C.3/8
D.1/2
Answer: C.3/8
Explanation: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
= 6/16
a= 3/8
The answer is therefore (C)
Question: If x + (1/x) = 5, what is the value of W= x^2 + (1/x)^2?
A.W=21
B.W=22
C.W=23
D.W=24
Answer: C.W=23
Explanation: Squaring on both sides,
x^2 + (1/x)^2 + 2(x)(1/x) = 5^2
x^2 + (1 /x)^2 = 23
Answer: C
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds X in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
A.25%
B.35%
C.45%
D.70%
Answer: B.35%
Explanation: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out X: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Question: How many seconds will a train 60 meters long take to cross a bridge 120 meters long if the speed of the train is 30 m/sec?
A.6 sec
B.8 sec
C.15 sec
D.3 sec
Answer: A.6 sec
Explanation: D = 60+120 = 180
S = 30 mps
T = 180/30 = 6 sec
A) 6 sec
Question: The present worth of a sum due sometime hence is Rs. 576 and the banker’s gain is Rs. 16. The true discount is :
A.36
B.52
C.66
D.96
Answer: D.96
Explanation: Sol.
T.D. = √P.W. * B.G. = √576 * 16 = 96.
Answer D
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.400
B.500
C.550
D.600
Answer: A.400
Explanation: C's 1 day's work =	1	- 1	+	1 =	1	-	7	=	1	.
3	6	8	3	24	24
A's wages : B's wages : C's wages =	1	:	1	:	1	= 4 : 3 : 1.
6	8	24
C's share (for 3 days) = Rs. 3 x	1	x 3200 = Rs. 400.
Option A
Question: What is 15% of 2/3 of 0.7?
A.0.07
B.0.9
C.9
D.90
Answer: A.0.07
Explanation: The best way to solve these questions is to convert every term into fraction
(15/100)*(2/3)*(7/10) = 210/3000 = 0.07
Option A
Question: In Arun's opinion, his weight is greater than 62 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 65 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
A.86.5 kg
B.63.5 kg
C.46.5 kg
D.26.5 kg
Answer: B.63.5 kg
Explanation: Let Arun's weight be X kg.
According to Arun, 62 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 65.
The values satisfying all the above conditions are 63 and 64.
Required average = (63 + 64) / 2 = 63.5 kg
Answer: B
Question: A mixture of sand and cement contains, 3 parts of sand and 5 parts of cement. How much of the mixture must be substituted with sand to make the mixture half sand and half cement?
A.1/3
B.1/4
C.1/5
D.1/7
Answer: C.1/5
Explanation: We have total of 8 parts: 3 parts of sand and 5 parts of cement.
In order there to be half sand and half cement (4 parts of sand and 4 parts of cement), we should remove 1 part of cement. With 1 part of cement comes 3/5 parts of sand, so we should remove 1 + 3/5 = 8/5 part of the mixture, which is (8/5)/8 = 1/5 of the mixture.
Answer: C.
Question: Daniel went to a shop and bought things worth Rs. 40, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.A)34.7
B.B)20
C.C)21.3
D.D)21.5
Answer: A.A)34.7
Explanation: Total cost of the items he purchased = Rs.40
Given that out of this Rs.40, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (40−30/100−x)6/100 = 30/100
⇒ 6(40 −0.3 −x) = 30
⇒ (40 − 0.3 − x) = 5
⇒ x = 40 − 0.3 − 5
= 34.7
Ans - A
Question: What is the smallest positive integer x such that 520-x is the cube of a positive integer
A.5
B.7
C.8
D.9
Answer: C.8
Explanation: Given 520-x is a perfect cube
so we will take 512= 8*8*8
520-x = 512
x =520-512 = 8
correct option is C
Question: If k, (k+200), (k+350), and 15*K are all multiples of D, then D could equal which of the following ?
A.20
B.D=25
C.D=75
D.100
Answer: B.D=25
Explanation: {Multiple of D} - {Multiple of D} = {Multiple of D}.
(K+200) - k = 200 = {Multiple of D}.
(K+350) - k = 350 = {Multiple of D}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
A.1278
B.2799
C.1023
D.1782
Answer: C.1023
Explanation: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer: C