RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If x is an integer, then x(x - 1)(x - k) must be evenly divisible by three when k is any of the following values except
A.-4
B.-6
C.-1
D.2
Answer: B.-6
Explanation: if we put k=-1 we get:
X(x-1)(X+1) rearrange:(x-1)X(X+1)
so it looks like a sequenc,
if we assume that X =2 and put number from the answer then we get:
(x – 1)x(x – k)
k=5 =1.2.-3
k=2 =1.2.0
k=-1 =1.2.3
k=-4 =1.2.6
but when we put
k=-6 =1.2.8 not satisfied
so,answer is B
Question: There are 24 distinct numbers in set M, there are 28 distinct numbers in set N, and there are 12 distinct numbers that are in both sets M and N. Set H is the set containing the elements that are in at least one of sets M and N. How many elements are in set H?
A.39
B.40
C.51
D.58
Answer: B.40
Explanation: {Total} = {M} + {N} - {Both}
{Total} = 24 + 28 - 12 = 40.
Answer: B.
Question: Five carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if four of the carpenters work together at their respective rates ?
A.11/15
B.3/5
C.11/30
D.47/75
Answer: D.47/75
Explanation: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(4/5) = ?
47/75 or (D)
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
A.4/5 km
B.9/5 km
C.4/8 km
D.4/9 km
Answer: A.4/5 km
Explanation: Explanation:
x/3 – x/4 = 4/60
x = 4/5 km
Answer: Option A
Question: What is x if x + 2y = 100 and y = 25?
A.25
B.50
C.75
D.100
Answer: B.50
Explanation: Substitute y by 25 in x + 2y = 100
x + 2(25) = 100
x + 50 = 100
If we substitute x by 50 in x + 50 = 100, we have 50 + 50 = 100. Hence
x = 50 correct answer B
Question: Determine a man’s present age if his present age is 125% of his age 10 years ago and 83.333% of his age 10 years from now.
A.76
B.97
C.50
D.99
Answer: C.50
Explanation: Explanation:
According to the question current age of the man is:
1.	125% of his age 10 years ago
2.	83.333% of his age 10 years from now
Let the current age of the man be x.
Therefore, equating the two equations generated:
125/100(x-10) = 250/3(x+10)
x = 50
ANSWER: C
Question: Two numbers are respectively 20% and 50% more than a third number. The percentage that is first of the second is?
A.45%
B.80%
C.78%
D.94%
Answer: B.80%
Explanation: I II III
120 150 100
150----------120
100-----------? => 80%
Answer:B
Question: Thirty men can do a work in 24 days. In how many days can 20 men can do the work, given that the time spent per day is increased by one-third of the previous time?
A.25 days
B.26 days
C.20 days
D.27 days
Answer: D.27 days
Explanation: D
27 days
Let the number of hours working per day initially be x. we have M1 D1 H1= M2 D2 H2
30 * 24 * x = 20 * d2 * (4x)/3 => d2 = (30 * 24 * 3)/(24 * 4) = 27 days.
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 11 more than the first integer. Find the three integers?
A.7, 9, 29
B.5,7,9
C.7, 9, 10
D.7, 9, 11
Answer: B.5,7,9
Explanation: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 11 => x = 5
Hence three consecutive odd integers are 5, 7 and9.
Answer:B
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?
A.31
B.46
C.88
D.13
Answer: A.31
Explanation: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 130.
Total score of the batsman in the 30 matches = 930.
Average score of the batsman = 930/30 = 31.
Answer:A
Question: When sold at a 50% discount, a sweater nets the merchant a 40% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?
A.20%
B.64.29%
C.70%
D.80%
Answer: B.64.29%
Explanation: we should be careful about what are we measuring % on/what is the base..
let the Marked up price =100..
Selling price= 100-50%of 100=50..
profit= 40%..
therefore the wholesale purchase cost= x.... 1.4x=50
or x=35.71...
marked price was 100 so ...
so answer is 64.29%..
B
Question: If x is divisible by 2, 14, and 70, which of the following must be the least multiple of x?
A.70
B.140
C.210
D.350
Answer: A.70
Explanation: We are looking for the LCM (which is not 0) of 2, 70 = 2*7*5, 14 = 2*7:
2 * 5 * 7 = 70
The answer is A.
Question: The maximum number of student amoung them 1204 pens and 840 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
A.91
B.28
C.56
D.89
Answer: B.28
Explanation: Solution
Required number of student = H.C.F of 1204 and 840 = 28. Answer B
Question: The price of a stock has decreased by 75% since the year 2000. How many percent should the stock price increase in order to gain the same value as in the year 2000?
A.300%
B.30%
C.75%
D.150%
Answer: A.300%
Explanation: Let P be the price of the stock in the year 2000.
Now the stock price is 0.25P
The price needs to increase 0.75P
0.75P/0.25P = 300%
The answer is A.
Question: If Re.1 amounts to Rs.9 over a period of 20 years. What is the rate of simple interest?
A.90%
B.30%
C.80%
D.40%
Answer: D.40%
Explanation: 8 = (1*20*R)/100
R = 40%
Answer:D
Question: An archer is shooting arrows from various distances. She shoots at a target from 30 yards, 40 yards, and 50 yards. The probability that she hits within the bullseye from 30 yards is 5/6, the probability that she hits within the bullseye from 40 yards is 4/5, and the probability that she hits within the bullseye from 50 yards is 3/4. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
A.104/105
B.119/120
C.139/140
D.9/10
Answer: B.119/120
Explanation: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses all shots = (prob that she misses from 30 yards)*(prob that she misses from 40 yards)*(prob that she misses from 50 yards)
Prob that she misses from 30 yards = 1 - 5/6 = 1/6; Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4
Thus the probability that she misses all shots = (1/6)*(1/5)*(1/4) = 1/120
Thus the probability that she makes at least one shot = 1 - (1/120) = 119/120
B
Question: 12 times a number gives 156. The number is
A.11
B.12
C.13
D.None
Answer: C.13
Explanation: Explanation:
Let the number be 'N'
12×N=156⇒N=13
Correct Option: C
Question: A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
A.wednesday at 7:20 PM
B.wednesday at 7:21 PM
C.wednesday at 7:22 PM
D.wednesday at 7:23 PM
Answer: A.wednesday at 7:20 PM
Explanation: This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct time, it has to gain 5 min.
54/5 min-> 180 hours
5 min -> ?
5/54/5x 180
83 1/3 hrs = 72 hrs+11 1/3 hrs =3 days+11 hrs + 20 min
So the correct time will be shown on wednesday at 7:20 PM
Answer A
Question: A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
A.71.11 km/hr
B.66.11 km/hr
C.78.11 km/hr
D.81.11 km/hr
Answer: A.71.11 km/hr
Explanation: A
71.11 km/hr
Total time taken = (160/64 + 160/8) = 9/2 hrs.
Average speed = 320 * 2/9 = 71.11 km/hr.
Question: one person Tharak speed with the current is 10 km/hr and the speed of the current is 2 km/hr. Tharak's speed against the current is:
A.6 km/hr
B.1 km/hr
C.2 km/hr
D.3 km/hr
Answer: A.6 km/hr
Explanation: Man's speed with the current = 10 km/hr
=> speed of the man + speed of the current = 10 km/hr
speed of the current is 2 km/hr
Hence, speed of the man = 10-2 = 8 km/hr
man's speed against the current = speed of the man - speed of the current
= 8-2 = 6 km/hr
ANSWER:A
Question: A tap can fil up an empty tank in 5 hours wheras it can be emptied by a pipe in 6 hours. How long will it take to fill the empty tank if both the taps and pipe are opened together?
A.40 hrs.
B.30 hrs.
C.50 hrs.
D.60 hrs.
Answer: B.30 hrs.
Explanation: Explanation:
In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as
Part filled by rap in 1 hr= 1/5
Part emptied by pipe in 1 hr= 1/6
work done by (tap+pipe) in 1 hr= 1/5 - 1/6
= 1/30
So both tap and pipe opened the tank will fill in 30 hrs.
Option B
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 5 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
A.77
B.35
C.75
D.80
Answer: A.77
Explanation: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 5 = 73
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 73 + 4 = 77
A
Question: Thomas worked in the factory @ 4550/- per week.
Owner told him to give the amount after one month. Then how much amount will be paid to Thomas ?
A.9500
B.17500
C.18200
D.19500
Answer: D.19500
Explanation: Total salary paid to Thomas in one week : 4550/-
Salary for one day : 4550 /7= 650/-
Total for one month = 650/- * 30days = 19500/-
Answer is Option (D)
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/4.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
A.9
B.11
C.10
D.12
Answer: A.9
Explanation: answer of 1st
just add the given probabilities p(blue)+p(red)+p(green) i.e
1/4+1/5+1/10=11/20
now we know p(blue)+p(red)+p(green)+p(yellow)=1
11/20+p(yellow)=1
p(yellow)=9/20
i.e why yellow balls are 9.
A
Question: What is the total cost of 2 sandwiches at $1.49 each and 4 sodas at $0.87 each?
A.$3.36
B.$6.46
C.$8.46
D.$10.08
Answer: B.$6.46
Explanation: Answer = B
2 * 1.49 + 4 * 0.87
= 2 (1.50 - 0.01) + 4 (1.00 - 0.13)
= 3 + 4 - 0.02 - 0.52
= 7 - 0.54
= 6.46
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was:
A.19 years
B.14 years
C.33 years
D.38 years
Answer: B.14 years
Explanation: Let the son's present age be x years.
Then, (38 - x) = x
2x = 38 => x = 19
Son's age 5 years back = (19 - 5) = 14 years.
ANSWER:B
Question: If a, b, and c are consecutive integers such that a > b > c and the sum of a, b, and c is a multiple of 10, which of the following could be the value of a?
A.0
B.1
C.9
D.10
Answer: B.1
Explanation: We're given a very specific set of restrictions in this prompt:
1) A, B and C are CONSECUTIVE INTEGERS
2) A > B > C
3) A+B+C = a multiple of 10
We're asked which of the 5 answer COULD be the value of A given these restrictions. Rather than staring at the screen or doing layered math, we canbrute forcethe answers until we find one that fits these restrictions..
Answer A: A = 0
In this case, the numbers would be 0, -1, and -2. The sum = -3 which is NOT a multiple of 10. Eliminate A.
Answer B: A = 1
In this case, the numbers would be 1, 0, and -1. The sum = 0 which IS a multiple of 10. B IS the answer.
Final Answer:
B
Question: Find the odd man out.
331, 482, 551, 263, 383, 362, 284
A.348
B.383
C.377
D.399
Answer: B.383
Explanation: Explanation:
In each number except 383, the product of first and third digits is the middle one.
Answer: B) 383
Question: Which one of the following is the least number of four digits divisible by 71?
A.1006
B.1065
C.1094
D.1056
Answer: B.1065
Explanation: 1000/71 = 14 6/71
1000 + 71 – 6 = 1065
ANSWER:B
Question: Salad dressing A is made up of 30% vinegar and 70% oil, and salad dressing B contains 10% vinegar and 90% oil. If the 2 dressing are combined to produce a salad dressing that is 15% vinegar, dressing A comprises what % of the new dressing?
A.15%
B.20%
C.25%
D.40%
Answer: C.25%
Explanation: The total combination must be 100%. Let X% of dressing 1 is used.
30 * x + 10 * (100-x) = 15*100
solving, x= 25%
C is the answer.
Question: A and B started a business with their capitals Rs. 12,000 and 36,000 respectively. Annual profit will be distributed between them in the ratio
A.2:3
B.1:3
C.1:4
D.2:5
Answer: B.1:3
Explanation: 12,000:36,000
Ans. 1:3
ANSWER:B
Question: How many positive integers less than 60 have a reminder 01 when divided by 4?
A.13
B.14
C.15
D.16
Answer: C.15
Explanation: 1 also gives the remainder of 1 when divided by 4. So, there are total of 15 numbers.
Answer: C.
Question: On a test, students receive 6 points for each correct answer and are penalized by losing 3 points for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?
A.-2
B.-1
C.0
D.1
Answer: C.0
Explanation: For the minimum possible score, let us take the worst case scenario
Suppose, he gets all of the last 3 qs wrong whose correct answer options are B and one of the first 3 qs wrong whose correct option is C
In that case, he will get only 2 out of the first 3 qs right.
Therefore, minimum possible score=(6*2)-(4*3)=0
Answer C
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 34 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
A.4830
B.5120
C.4608
D.7500
Answer: C.4608
Explanation: l = (48 - 16)m = 32 m,
b = (34 -16)m = 18 m,
h = 8 m.
Volume of the box = (32 x 18 x 8) m3 = 4608 m3.
Answer: Option C
Question: How many of the positive factors of 14 are not factors of 21?
A.4
B.3
C.1
D.2
Answer: C.1
Explanation: Factors of 14 - 1, 2, 7, 14,
factors of 21- 1, 3, 7, 21,
Comparing both, we have three factors of 14 which are not factors of 21- 2,14
The answer is C
Question: A manufacturer of a certain product can expect that between 0.3 percent and 0.5 percent of the units manufactured will be defective. If the retail price is $2,500 per unit and the manufacturer offers a full refund for defective units, how much money can the manufacturer expect to need to cover the refunds on 20,000 units?
A.Between $15,000 and $25,000
B.Between $30,000 and $50,000
C.Between $60,000 and $100,000
D.Between $150,000 and $250,000
Answer: D.Between $150,000 and $250,000
Explanation: Number of defective units is between = .3 % of 20000 and .5% of 20000
= 60 and 100
Retail Price per unit = 2500 $
Expected price of refund is between = 2500 x 60 and 2500 x 100
=1,50,000 and 2,50,000 dollars
Answer D
Question: In Mike's opinion, his weight is greater than 65kg but leas than 72 kg. His brother does not agree with Mike and he thinks that Mike's weight is greater than 60kg but less than 70kg. His mother's 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 Mike?
A.60 kg
B.61.5 kg
C.62 kg
D.66.5 kg
Answer: D.66.5 kg
Explanation: Let Mike's weight be X kg.
According to Mike, 65 < X < 72.
According to Mike's brother, 60 < X < 70.
According to Mike's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
D
Question: The number of timeshare condos available at Sunset Beach is 2/5 the number of timeshare condos available at Playa del Mar. If the total number of timeshare condos available at the two beaches combined is 280, what is the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar?
A.60
B.90
C.120
D.150
Answer: C.120
Explanation: Let x be the number of timeshare condos available at Playa del Mar.
Then number of timeshare condos available at Sunset Beach = 3/5x
We know, x + 2/5 x = 280
Hence, x = 200. So, number of timeshare condos available at Playa del Mar = 200
the difference between the number of condos available at Sunset Beach and the number of condos available at Playa del Mar = x - 2/5x = 2/5x = 3/5(200) = 120
The correct answer is C
Question: A boat can travel with a speed of 15 km/hr in still water. If the speed of the stream is 6 km/hr, find the time taken by the boat to go 86 km downstream.
A.4.1 hr
B.5.25 hr
C.8.25 hr
D.2.25 hr
Answer: A.4.1 hr
Explanation: speed of boat in still water = 15 km/hr
speed of the stream = 6 km/hr
Speed downstream = (15+6) = 21 km/hr
Time taken to travel 86 km downstream = 86â„16 = 17â„4 = 4.1 hours
Answer is A
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.
A.Rs.420.20
B.Rs.319.06
C.Rs.306.04
D.Rs.294.75
Answer: C.Rs.306.04
Explanation: Explanation:
A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer IS C
Question: If we have 10 people in a meeting, in how many ways they can sit around a table?
A.10*9!
B.9*8!
C.8*7!
D.7*6!
Answer: B.9*8!
Explanation: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=10
(n-1)!=9!=9*8!
Ans:B
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference W between the greatest and least of the five integers?
A.4K
B.4k^2 -4k
C.4-4k
D.4
Answer: D.4
Explanation: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference W= 10k - 3 - (10k - 7)
= 4
Answer - D
Question: Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
A.1
B.3
C.5
D.6
Answer: A.1
Explanation: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
A
Question: In how many ways can you distribute 6 prizes among 5 children if every child must get atleast one?
A.125 Ways
B.135 Ways
C.120 Ways
D.115 Ways
Answer: A.125 Ways
Explanation: 5 Prizes can distribute to 5 children by 5! ways
6 prize (last prize) can be given to any one of child. So there are 5 ways to distribute the sixth gift among 5 children.
So the total no.of ways are 5!+5 = 120+5 = 125 Ways
ANSWER:A
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
A.12000/x+300
B.(x+60)/4
C.(300-x)/5
D.600/(115-x)
Answer: A.12000/x+300
Explanation: total distance =100 ;total time = T
t1 = x/30 t2 = 100-x /40
T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200
= (10x+3000)/1200
= x+300/120
av speed = 100*120/x+300 = 12000/x+300
A
Question: The cost of 3 kg of sugar is $7.50. What will the cost of 8 kg of sugar be?
A.20
B.40
C.80
D.160
Answer: A.20
Explanation: 3 kg costs $7.50
1 kg costs $2.50
8 kg costs $20
The answer is A.
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 4-cent stamps, what is the least number of 1-cent stamps she could have bought?
A.65
B.70
C.75
D.80
Answer: A.65
Explanation: Let:
# of 5 and 25 cents stamps = n
# of 10 cent stamps = 2n
# of 1 cent stamps = m
Therefore:
5n + 25n + 10(2n) + m = 265 cents
50n + m = 265
Forleastnumber of 1 cents stamps, maximize 50n. Hence,
50*4 + m = 265
m = 65 i.e. 65 stamps 1 cents each
Answer: A
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 8 units?
A.140 sq.units
B.170 sq.units
C.190 sq.units
D.112 sq.units
Answer: D.112 sq.units
Explanation: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 8 = 112 sq.units
Answer: Option D
Question: 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
A.388
B.266
C.350
D.112
Answer: C.350
Explanation: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x
= 350m.
Answer:C
Question: The distance from the x-axis to point P is half the distance from the y-axis to point P. If the coordinates of P are (x,-8), how many units is P from the y-axis?
A.20
B.16
C.8
D.4
Answer: B.16
Explanation: The x-axis is 8 units from the point P.
Thus the y-axis is 16 units from the point P.
The answer is B.
Question: In a group of 650 readers who read science fiction or literacy works or both, 250 read science fiction and 550 read literacy works. How many read both science fiction and literacy works?
A.650
B.250
C.150
D.100
Answer: C.150
Explanation: Consider total number of reader n(S U L) = 650
People who read science fiction n(S) = 250
People who read literacy works n(L) = 550
both science fiction and literacy n(S âˆ© L) = ?
n(S U L) = n(S)+ n(L) - n(S âˆ© L)
650 = 250 + 550 - n(S âˆ© L)
n(S âˆ© L) = 800 - 650
n(S âˆ© L) = 150
SO People read both science fiction and literacy works are 150
ANSWER:C
Question: 9, 16, 22, 25, 36,49
A.9
B.16
C.22
D.25
Answer: C.22
Explanation: Each of the numbers except 22, is perfect square.
Answer: Option C
Question: What percent of 60 is 120?
A.200
B.75
C.60
D.33 1⁄3
Answer: A.200
Explanation: % of 60 is 120?
= 120/60 = 21 = 200%
Thus A is the correct answer.
Question: A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 9 members, then what is the exact number of researchers required?
A.25
B.24
C.23
D.22
Answer: A.25
Explanation: alternatively, we have
9*3-2( because james is included in all the three teams)
=25
A
Question: The banker's gain on a bill due due 1 year hence at 12% per annum is Rs.7.2. The true discount is
A.Rs.72
B.Rs.36
C.Rs.54
D.Rs.60
Answer: D.Rs.60
Explanation: Solution
T.D	= [B.G x 100 / R x T]
= Rs.(7.2 x 100 / 12 x 1)
= Rs.60.
Answer D
Question: In the next Cricket World Cup T-20, Team A has decided to score 200 runs only through 4s and 6s. In how many ways can the Team A score these 200 runs?
A.13
B.15
C.16
D.17
Answer: D.17
Explanation: Team A can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Question: A photo-mat shop charges $0.60 for the first photo inside a film, and 40% cents less for each additional photo. How many photos can we develop with $42 if each film contains 36 photos?
A.3 films and 6 photos
B.5 films and 6 photos
C.5 films and 14 photos
D.6 films and 4 photos
Answer: A.3 films and 6 photos
Explanation: 1st photo = 0.60
Subsequent = 0.6*0.6=0.36
Price of 1 full film=0.6+0.36*35=13.2
Price of 3 full film = 13.2*3=39.6
42-39.6=2.4
2.4=0.6+0.36x
x=5
42--->3 full films and 1+5=6 photos
Answer: A