RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: If n is a positive integer and n^2 is divisible by 36, then the largest positive integer that must divide n is
A.6
B.12
C.24
D.36
Answer: A.6
Explanation: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=6, is n divisible by 48? No. So, n is not always divisible by 48.
A
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold a bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2a
II. y > a
III. y > 3
A.I only
B.II only
C.I and II
D.II and III
Answer: D.II and III
Explanation: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(a-12) where x is the total number of bikes sold (when a>12).
A = cycles sold last week
AS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2AS
lets test all statements with A=0;
AS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with A=1;
AS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with A=6;
AS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Question: Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat?
A.3!
B.8!
C.11!
D.12!
Answer: A.3!
Explanation: Ans.(A)
Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 2 ounces of corn syrup, how many ounces of water does it contain?
A.15
B.30
C.45
D.60
Answer: B.30
Explanation: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 2.
So, x = 32.5 ounces.
Water = (60 / 65) * (65/2) = = 30 ounces.
Ans B
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
A.150,222
B.150,209
C.150,200
D.150,202
Answer: C.150,200
Explanation: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer: C
Question: In a card game, a combination of three aces beats all others. If Jose is the first to draw from a standard deck of 52 cards, what is the probability that he wins the game with the best possible combination?
A.1/5000
B.1/5520
C.1/5525
D.1/5545
Answer: C.1/5525
Explanation: he best possible combination is the case when he wins in his first two draws
There are 52 cards in a deck of cards with 4 aces in it.
Probability of first card to be ace = 4/52
Probability of Second card to be ace = 3/51
Probability of third card to be ace = 2/50
Probability of Best possible case = (4/52)*(3/51)*(2/50) = 1/5525
C
Question: At a certain health club, 30 percent of the members use both the pool and sauna, but 50 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?
A.33 1/3%
B.46 2/3%
C.50%
D.62 1/2%
Answer: B.46 2/3%
Explanation: P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
50% of (70-x) = x => 35 - 0.5x = x => x = 23 1/3% so only P = 70 -23 1/3 = 46 2/3%
Answer B
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 1: 00 p.m., at what time were there 32 million bacteria in the dish?
A.7: 00 p.m.
B.8: 00 p.m.
C.6: 00 a.m.
D.8: 00 a.m.
Answer: A.7: 00 p.m.
Explanation: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 1 PM, we get 7 AM as the answer.
Option A
Question: Ram's salary is 25% more than Raja's. How much percent is Raja's salary less than Ram's?
A.10%
B.15%
C.20%
D.25%
Answer: C.20%
Explanation: Raja's salary less than Ram's by 25/(100+25) * 100% = 20%
Answer is C
Question: A box contains 7 pairs of shoes (14 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?
A.1/190
B.1/20
C.1/19
D.1/13
Answer: D.1/13
Explanation: The problem with your solution is that we don't choose 1 shoe from 14, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/13(as after taking one at random there are 13 shoes left and only one is the pair of the first one)=1/13
Answer: D.
Question: In a certain game, you perform three tasks. You flip a coin, and success would be heads. You roll a single die, and success would be a two. You pick a card from a full playing-card deck, and success would be picking a spades card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
A.11/16
B.15/32
C.14/36
D.23/48
Answer: D.23/48
Explanation: The answer is D
Probability of just one enent will be happining
So, Probability heads=1/2
Probability number 2 =1/6
Probability picking a spades card =1/4
so, Probability win by getting tails= 1/2*5/6*3/4 = 15/48
Probability win by getting number 6 = 1/2*1/6*3/4 = 3/48
Probability win by picking a spades card =1/2*5/6*1/4=5/48
Probability wining= 15/48+3/48+5/48 =23/48
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.2.7 sec
C.3.5 sec
D.2.9 sec
Answer: A.2.5 sec
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 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: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 100
Total = 100 + 100 = 200
Answer (D)
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
A.18
B.99
C.77
D.55
Answer: A.18
Explanation: Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
Answer: A
Question: If A,B,C,D,E,F,G,H,I,J are in an decreasing Arithmetic Progression as such. Then Which of the following operations will result in only median being modified not the mean.
A) A is removed
B) A and J are removed
C) B and I are removed
D) A,B,C,H,I,J are removed
E) A and E are removed
A.1) A and B
B.2) A and E
C.3) A,C,E
D.4) None of them
Answer: D.4) None of them
Explanation: There are 10 equidistant numbers on the number line.
Mean and median will be the average of middle two numbers.
If you remove two numbers which is equidistant from either extreme (e.g. B and I), the total deviation on either side of the mean stays the same so mean stays the same. Also, the median is still the average of middle two numbers. But there is no change possible where median will change and mean will not change.
Answer: D
Question: A tank is filled in SIXTEEN hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
A.56 hours
B.28 hours
C.55 hours
D.66 hours
Answer: A.56 hours
Explanation: 1/A + 1/B + 1/C = 1/16 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/16
=> (1 + 2 + 4)/2B = 1/16
=> 2B/7 = 16
=> B = 56 hours.
Answer: A
Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?
A.21
B.24
C.27
D.36
Answer: C.27
Explanation: Let the numbers be 3x, 3x + 3, 3x + 6
Then, 3x + 3x + 3 + 3x + 6 = 72 ===> 9x = 63 ==> x = 7.
so the largest number is 3x + 6 = 27.
hence the correct answer is option C) 27.
Question: Sum of 36 odd numbers is?
A.1294
B.1295
C.1296
D.1297
Answer: C.1296
Explanation: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 36 odd numbers = 36^2 = 1296
ANSWER:C
Question: Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?
A.3.2 hr
B.3.4 hr
C.3.6 hr
D.3.8 hr
Answer: A.3.2 hr
Explanation: let see d/t =v then x/20 + (400-x)/70 =8
x= 64 kmh
t = 64/20 = 3.2 hr
ANSWER:A
Question: A train passes a station platform in 31 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.228
B.240
C.165
D.166
Answer: C.165
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/31 = 15 => x = 165 m.
Answer: C
Question: Company M produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were deluxe. If it takes 1.5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
A.7/15
B.14/31
C.3/7
D.17/35
Answer: C.3/7
Explanation: The easiest way for me is to plug in numbers.
Let the number of basic stereos produced be 40, and number of delux stereos produced be 20. Total of 60 stereos.
If it takes an hour to produce a basic stereo then it will take 1.5 hours to produce a deluxe stereo.
40 basic stereos = 40 hours.
20 delux stereos = 30 hours.
Total hours = 70.
Then the fraction would be 30/70 = 3/7 Therefore answer
C.
Question: In a six-sided polygon WQRSTV ∠W measures 48° less than the average (arithmetic mean) of the remaining five angles. What does ∠W equal to, in degrees?
A. 72
B. 80
C. 88
D. 96
Answer: B. 80
Explanation: The sum of interior angle in a polygon is (n-2)*180
so for a six sided figure, (6-2)*180 = 720
let the A.M of the other 5 angles be 'm'
--> m*5 + W = 720, we know ∠W=m-48
--> m*5 + m - 48 = 720, solving we get m=128
hence ∠W= 128-48 = 80
Ans B.
Question: Calculate the value of r: 6r^2-17r+6 = 254
A.8
B.10
C.5
D.9
Answer: A.8
Explanation: Using the elimination method substitute options for x and find the correct option.
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.2888
B.288
C.178
D.150
Answer: D.150
Explanation: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer: D
Question: A person crosses a 600600 metre long street in 55 minutes. What is his speed in km per hour?
A.8.2
B.4.2
C.6.1
D.7.2
Answer: D.7.2
Explanation: Explanation:
Solution 1Distance =600=600 metre =0.6=0.6 km
Time =5=5 minutes =112=112 hour
Speed=distancetime=0.6(112)Speed=distancetime=0.6(112) =7.2 km/hr
Answer is D
Question: If M/N = 6/5,then 3M+2N = ?
If p/q = 5/4 , then 2p+q= ?
If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST
A.18/5
B.28/5
C.27/5
D.26/5
Answer: B.28/5
Explanation: 3M+2N (divide by N)
3M/N+2
3*(6/5)+2
28/5 ANSWER:B
Question: If a and b are positive integers and (3^a)^b = 3^3, what is the value of 3^a*3^b?
A.3
B.9
C.81
D.27
Answer: C.81
Explanation: 3^ab =3^3 therefore ab=3 either a=1or3 or b=3 or 1
therefore 3^a* 3^b = 3^(a+b)= 3^4 =81
C
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
A.1/9
B.1/7
C.1/2
D.1/1
Answer: B.1/7
Explanation: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability
= 1/7
Answer:B
Question: A man can row upstream at 55 kmph and downstream at 65 kmph, and then find the speed of the man in still water?
A.27
B.70
C.60
D.80
Answer: C.60
Explanation: US = 55
DS = 65
M = (55 + 65)/2
= 60
Answer:C
Question: In a room with 10 people, 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
A.5/21
B.3/7
C.4/5
D.5/7
Answer: C.4/5
Explanation: (6/10)(7/9) + (5/10)(6/9) if you choose one of the 6 with one other friend, then you have a 7/9 chance of not picking their friend 2nd. If you choose one of the 5 with 2 friends, you have a 6/9 chance of not picking one of their friends second. Add them up.
42/90 + 30/90
72/90 = 4/5
C. 4/5
Question: If an integer x is to be selected at random from 1 to 100, inclusive, what is probability x(x+1) will be divisible by 2?
A.3
B.1
C.2
D.4
Answer: B.1
Explanation: because x(x+1) is always an even product of even*odd or odd*even factors,
there is a probability of 1 that that it will be divisible by 2,
1*1=1
Answer : B
Question: The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)
A.77.14 cm
B.25.14 cm
C.84.92 cm
D.94.94 cm
Answer: B.25.14 cm
Explanation: Let the side of the square be a cm.
Parameter of the rectangle = 2(18 + 14) = 64 cm Parameter of the square = 64 cm
i.e. 4a = 64
A = 16
Diameter of the semicircle = 16 cm
Circimference of the semicircle
= 1/2(∏)(16)
= 1/2(22/7)(16) = 352/14 = 25.14 cm to two decimal places
ANSWER:B
Question: A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time will be able to cover 8 km upstream?
A.6 hr
B.2 hr
C.4 hr
D.1 hr
Answer: B.2 hr
Explanation: Explanation :
Speed downstream = 96⁄8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12-4 = 8 kmph
Speed upstream = 8-4 = 4 kmph
Time taken to cover 8 km upstream = 8⁄4 = 2 hours. Answer : Option B
Question: Two tests had the same maximum mark. The pass percentages in the first and the second test were 40% and 45% respectively. A candidate scored 216 marks in the second test and failed by 75 marks in that test. Find the pass mark in the first test?
A.768
B.243
C.246
D.288
Answer: D.288
Explanation: Let the maximum mark in each test be M.
The candidate failed by 75 marks in the second test.
pass mark in the second test = 249 + 75 = 324
45/100 M = 324
Pass mark in the first test = 40/100 M = 40/45 * 324 = 288.
Answer:D
Question: Three pieces of timber 36 m, 42 m and 54 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
A.7 m
B.1 m
C.2 m
D.6 m
Answer: D.6 m
Explanation: Answer
Greatest possible length of each plank = H.C.F of 36, 42, 54 = 6 m
Correct Option: D
Question: A polygon has 54 diagonals. How many sides does it have?
Self made
A. 12
B. 13
C. 14
D. 15
Answer: A. 12
Explanation: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 54
n*(n - 3) = 108
Substitute n from the answer choices. n = 12
Answer: A
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 30%?
A.650
B.882
C.772
D.652
Answer: A.650
Explanation: Cost price = Rs.500
profit = 30% of 500 = Rs.150
Selling price = Cost price + Profit
= 500 + 150 = 650
Answer:A
Question: Nitin’s salary is reduced by 10% and then reduced salary is increased by 10%. Find ,how many percentage his present salary is less as compared to his previous salary?
A.6%
B.8%
C.1%
D.2%
Answer: C.1%
Explanation: 10*10
-------- = 1%
100
Answer: C
Question: Jill, who lives in City C, plans to visit 5 different cities, M, L, S,N,and O. She plans to visit each city exactly once and return to City C after the 5 visits. She can visit the cities in any order. In how many different orders can she visit the 5 cities?
A. 3
B. 120
C. 8
D. 9
Answer: B. 120
Explanation: 5! = 120 =B
Question: A pair of articles was bought for $900 at a discount of 10%. What must be the marked price of each of the article?
A.$300
B.$500
C.$350
D.$400
Answer: B.$500
Explanation: S.P. of each of the article = 900/2 = $450
Let M.P = $x
90% of x = 450
x = 450*100/90 =$500
Answer is B
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
A.17/29
B.17/25
C.17/21
D.17/20
Answer: D.17/20
Explanation: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer:D
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
A.88
B.70
C.62
D.50
Answer: D.50
Explanation: Explanation:
Assume the length of each train = x
Total distance covered for overtaking the slower train = x+x = 2x
Relative speed = 46-36 = 10km/hr = (10×10)/36 = 100/36 m/s
Time = 36 seconds
2x/ (100/36) = 36
=> (2x × 36 )/100 = 36
=> x = 50 meter
Answer: Option D
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
A.1243
B.1345
C.1349
D.1467
Answer: C.1349
Explanation: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
C
Question: A man sells two articles for Rs.3640 each and he gains 25% on the first and loses 25% on the next. Find his total gain or loss?
A.9%loss
B.2%loss
C.6%loss
D.8%loss
Answer: C.6%loss
Explanation: Explanation:
(25*25)/100
= 6%loss
Answer:C
Question: An athlete runs 200 metres race in 40 seconds. What is his speed?
A.23
B.38
C.18
D.30
Answer: C.18
Explanation: Speed=Distance/Time = 200/40 = 5 m/s = 5 * 18/5 = 3618 km/hr
Answer :C
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
A.10 cm
B.16 cm
C.18 cm
D.20 cm
Answer: C.18 cm
Explanation: 2(l + b)	=	5
b	1
2l + 2b = 5b
3b = 2l
b =	2	l
3
Then, Area = 216 cm2
l x b = 216
l x	2	l	= 216
3
l2 = 324
l = 18 cm.
C)
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.300
B.400
C.500
D.600
Answer: C.500
Explanation: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer: Option C
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.22
B.77
C.18
D.10
Answer: D.10
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
Answer:D
Question: Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5145 Nis, how much more money does Nick contribute than Archi?
A.128 Nis
B.212 Nis
C.234 Nis
D.245 Nis
Answer: D.245 Nis
Explanation: Normalising the fraction from 5:3:2.5 to 10:6:5 (Eric: Nick:Archi)
Given Nick contributes one unit more than Archi and one unit of 5145/(10+6+5) = 245
Answer is D: 245 Nis
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.40
B.50
C.60
D.70
Answer: A.40
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: Option A
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent T?
A.20%
B.80%
C.100%
D.180%
Answer: C.100%
Explanation: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
T=[(2 - 1)/1] * 100% = 100%.C
Question: O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(5.3) + E(–6.7) + o(–7.3) + e(6.6) is:
A.-4
B.-2
C.0
D.2
Answer: B.-2
Explanation: O(5.3) + E(–6.7) + o(–7.3) + e(6.6) = 7 + (-6) + (-9) + 6 = -2
The answer is B.