divelab/Sys2Bench huggingface dataset:
Question: The Weirdo Holiday Resort follows a particular system of holidays for its employees. People are given holidays on the days where the first letter of the day of the week is the same as the first letter of their names. All employees work at the same rate.
Starting on February 25, 1996, if Raja had finished his job on April 2, 1996, when would T and S together likely to have completed the job, had they started on the same day as Raja?
Options:
A)March 15, 1996
B)March 14, 1996
C)March 22, 1996
D)Data Insufficient
E)None
Rationale: Explanation :
Raja doesn't have his name's first letter common to any of the day.so he won't rest. He works for 38 days to complete the job. So, he does 1/38 work in a day. Now, S will take break on saturday, sunday and T on tuesday, thursday. So on monday, wednesday and friday, they both will work simultaneously.
Now, we'll apply Zeller's rule to determine what day was it on feb,1996. It'll come out to be a sunday.
Now, if we start a week from sunday they'll do 10/38 amount of work in aweek. So, in 3 weeks they'll complete 30/38 amount of work and within next friday to complete the rest, total 21 + 6 = 27 days is required.
Answer : C
Answer: C
Question: A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
Options:
A)1909
B)1900
C)1908
D)1905
E)1901
Rationale: 65 * 6 : 84 * 5 : 100 * 3
26:28:20
C share = 74000 * 95/100 = 7030 * 20/74 => 1900
Answer: B
Answer: B
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 2, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
Options:
A)600
B)1200
C)1500
D)3600
E)6000
Rationale: Sugar:Flour = 5:2 = 25:10;
Flour:Soda = 10:1 = 10:1;
Thus we have that Sugar:Flour:Soda = 25x:10x:1x.
Also given that 10x/(1x+60) = 8/1 --> x=240 --> Sugar = 25x = 6000
Answer: E.
Answer: E
Question: Calculate the HCF of 30, 108, 660
Options:
A)6
B)5
C)4
D)3
E)2
Rationale: Explanation:
Lets solve this question by factorization method.
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 660 are: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
Then the greatest common factor is 6.
Answer: Option A
Answer: A
Question: Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers.
Options:
A)26,37
B)25,38
C)27,36
D)28,35
E)29,34
Rationale: Sum of the terms of the ratio = 3 + 4 = 7
Sum of numbers = 63
Therefore, first number = 3/7 × 63 = 27
Second number = 4/7 × 63 = 36
Therefore, the two numbers are 27 and 36.
Answer:C
Answer: C
Question: The 19th of September 1987 was a Saturday. If 1988 was a leap-year, what day of the week was the 26th of September 1990?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Thursday
E)Friday
Rationale: 19th September
1987: Saturday
1988: Monday (due to leap year)
1989: Tuesday
1990: Wednesday
Hence 26th September was a Wednesday.
The answer is C.
Answer: C
Question: A train 330 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)18
B)6
C)5
D)54
E)1
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 330 * 3/55 = 18 sec.
Answer: A
Answer: A
Question: What is the area inscribed by the lines y =4, x = 2, y = 6-2x on an xy-coordinate plane?
Options:
A)a) 1
B)b) 2
C)c) 4
D)d) 6
E)e) 8
Rationale: First, let's graph the lines y = 4 and x = 2
At this point, we need to find the points where the line y = 6-2x INTERSECTS the other two lines.
For the vertical line, we know that x = 2, so we'll PLUG x = 2 into the equation y = 6-2x to get y = 6-2(2) = 2
Perfect, when x = 2, y = 2, so one point of intersection is (2,2)
For the horizontal line, we know that y = 4, so we'll PLUG y = 4 into the equation y = 6-2x to get 4 = 6-2x. Solve to get: x = 1
So, when y = 4, x = 1, so one point of intersection is (1,4)
Now add these points to our graph and sketch the line y = 6-2x
At this point, we can see that we have the following triangle.
The base has length 1 and the height is 2
Area = (1/2)(base)(height)
= (1/2)(1)(2)
= 1
Answer:
A
Answer: A
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)2500 m^2
B)2510 m^2
C)2520 m^2
D)2600 m^2
E)2670 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: Kiran started a business investing Rs. 20,000. After 4 months, Sanket joined with a capital of Rs. 12000. At the end of the year, they earn a profit of Rs. 14,000. Find what will be the share of Sanket in the profit?
Options:
A)Rs. 4000
B)Rs. 4007
C)Rs. 4001
D)Rs. 4002
E)Rs. 4047
Rationale: Explanation:
Kiran : Sanket = (20000 * 12) : (12000 * 8) = 5 : 2
Sanket's share = Rs. 14,000 * (2/7) = Rs. 4000
ANSWER: A
Answer: A
Question: Rajan and Rakesh started a business and invested Rs.20000 and Rs.25000 respectively. After 4 months Rakesh left and Mukesh joined by investing Rs.15000. At the end of the year there was a profit of Rs.4600. What is the share of Mukesh?
Options:
A)2238
B)2378
C)1200
D)2877
E)1812
Rationale: Explanation:
Rajan is in the business for 12 months, Rakesh is for 4, and Mukesh is for 8.
Profits will be divided in ratio of (20 × 12) : (25 × 4) : (15 × 8) = 24 : 10 : 12
Share of Mukesh = 1246×4600=1200
Answer: C
Answer: C
Question: The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 hours, then the speed of the first train is:
Options:
A)47.4 km/hr
B)57.19 km/hr
C)68.13 km/hr
D)96.25 km/hr
E)86.25 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = (440/4) = 110
x = (110/8) = 13.75
Hence, speed of first train = (7 x 13.75) km/hr = 96.25 km/hr.
Answer : D.
Answer: D
Question: A circular well with a diameter of 2 metres , is dug to a depth of 14 metres. What is the volume of the earth dug out?
Options:
A)32 m3
B)36 m3
C)40 m3
D)44 m3
E)None
Rationale: Solution
Volume	= πr2h
‹=› (22 /7 ×1×1×14)m3
‹=›44 m3.
Answer D
Answer: D
Question: A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 4 hours. Working alone, the outlet pipe can empty out the tank in 4 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?
Options:
A)02:30 pm
B)03:30 pm
C)01:30 pm
D)04:30 pm
E)05:30 pm
Rationale: In 6 hours the inlet pipe will pump in water equal to 6*1/4 = 6/4 of the pool. So, 2/4 more than necessary, which should be compensated by the outlet pipe. To pump out 2/4 of the water the outlet pipe needs 8/4 = 2 hours.
Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 2 hours = 01:30 pm.
Answer: C
Answer: C
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)20/9
B)20/2
C)20/7
D)40/2
E)20/1
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer: C
Answer: C
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
A)6 days
B)2 days
C)8 days
D)3 days
E)9 days
Rationale: Work done by A in 2 days = 2/5
Remaining work = 3/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 3/5 * 10/3 = 2 days.
Answer: B
Answer: B
Question: A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
Options:
A)290
B)304
C)285
D)270
E)275
Rationale: In a month of 30 days beginning with a Sunday, there will be 4 complete weeks and another two days which will be Sunday and Monday.
Hence there will be 5 Sundays and 25 other days in a month of 30 days beginning with a Sunday
Average visitors on Sundays = 510
Total visitors of 5 Sundays = 510 × 5
Average visitors on other days = 240
Total visitors of other 25 days = 240 × 25
Total visitors = (510 × 5) + (240 × 25)
Total days = 30
Average number of visitors per day
=((510×5)+(240×25))/30
=((51×5)+(24×25))/3
=(17×5)+(8×25)=85+200=285
Answer is C.
Answer: C
Question: A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle?
Options:
A)13π
B)26π
C)262√π
D)52π
E)4π
Rationale: The distance between the two points is sqrt(8)
radius = sqrt(8)/2
Area= pi*(sqrt(8)/2)^2
E.4π
Answer: E
Question: IT COSTS RE 1.TO PHOTOGRAPHY A SHEET OF PAPER. HOWEVER, 2% DISCOUNT IS ALLOWED ON ALL PHOTOCOPIES DONE AFTER FIRST 100 SHEETS.HOW MUCH WILL IT COST TO COPY 5000 SHEETS OF PAPER?
Options:
A)RS.3920
B)RS.3980
C)RS.4900
D)RS.4920
E)NONE OF THESE
Rationale: TOTAL COST =RS.(1*100+(100-2)% OF 1*4000)
=RS.(10000+0.98*4000)=RS.(1000+3920)RS.4920
CORRECT OPTIONS: D
Answer: D
Question: If Janice was 23 years old z years ago and Lisa will be 21 years old in p years, what was the average (arithmetic mean) of their ages 7 years ago?
Options:
A)(z + p)/2
B)(z - p + 30)/4
C)(z - p + 20)/4
D)(z + p + 40)/2
E)(z - p + 30)/2
Rationale: Today, J = z+23 and L = 21-p
7 years ago, J = z+16 and L = 14-p
The average of their ages was (z-p+30) / 2
The answer is E.
Answer: E
Question: Jackson has $313,196 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
Options:
A)$1
B)$2
C)$3
D)$4
E)$5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,196 = 23 and 18 is divisible by 9.
Hence we need to subtract 5 to this number for it to be divisible by 9
Correct Option: E
Answer: E
Question: During a trip, joe 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?
Options:
A)(180-x)/2
B)(x+60)/4
C)(300-x)/5
D)600/(115-x)
E)12000/x+300
Rationale: 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
E
Answer: E
Question: An bus covers a certain distance at a speed of 200 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
Options:
A)920 km/hr
B)970 km/hr
C)996 km/hr
D)1021 km/hr
E)1000 km/hr
Rationale: Distance = (200 x 5) = 1000 km.
Required speed = 1000 km/hr
E
Answer: E
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 9.5km apart, if they walk in the same direction?
Options:
A)15 hours
B)16 hours
C)17 hours
D)18 hours
E)19 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 9.5 km
Time = Distance/Speed
Time= 9.5km / 0.5 kmph = 19 hrs
answer :E
Answer: E
Question: There are 13 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 13 points that contain the point A?
Options:
A)66
B)105
C)182
D)210
E)455
Rationale: Any 2 points out 12 points will create triangle with third point A, so the answer is 12C2=66.
Answer: A.
Answer: A
Question: Find out the C.I on Rs.1000 at 4% p.a. compound half-yearly for 1 1/2 years.
Options:
A)A)Rs.41.20
B)B)Rs.51.20
C)C)Rs.61.20
D)D)Rs.71.20
E)E)Rs.81.20
Rationale: A = 1000(51/50)3
= 1061.20
1000
-----------
61.20
ANSWER:C
Answer: C
Question: A car takes 6 hours to cover a distance of 324 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)50 Kmph
B)60 Kmph
C)65 Kmph
D)36 Kmph
E)None
Rationale: Time = 6
Distence = 324
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 324/9 = 36 Kmph
D)
Answer: D
Question: A baseball card decreased in value 10% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
Options:
A)19%
B)30%
C)32%
D)36%
E)72%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.9 = 90
After second year price = 90 *0.9 = 81
final decrease = [(100 - 81)/100] * 100 = 19%
correct answer - A
Answer: A
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 46 years. What will be the age of the B ten years hence?
Options:
A)39
B)92
C)28
D)96
E)26
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 46 => b + c = 92 --- (2)
Answer: B
Answer: B
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
Options:
A)If x>y
B)X>=Y
C)If x < y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Answer: B
Question: Sarah is driving to the airport. After driving at 25 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 50 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
Options:
A)100
B)175
C)210
D)245
E)280
Rationale: After driving at 25 miles per hourfor one hour, this distance left to cover is d-25. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 25 miles per hour and 50 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/25 - x/50 = 3/2 --> 2x/50 - x/50 = 3/2 --> x/50 = 3/2 --> x = 75.
Total distance = x + 25 = 100 miles.
Answer:A
Answer: A
Question: 12 men take 36 days to do a work while 12 women complete 3/4th of the same work in 36 days. In how many days 10 men and 8 women together will complete the same work?
Options:
A)6 days
B)12 days
C)27 days
D)28 days
E)None of these
Rationale: Explanation:
1 man’s 1 day’s work = 1/ 36 × 12 = 1/432
10 men’s 1 day’s work = 10/432
12 women can finish the whole work in 4 × 36/3 = 48 days
1 woman’s 1 days work = 1/ 48 × 12 = 1/576
8 women’s 1 day’s work = 8/572 = 1/72
(10 men + 8 women)’s 1 day’s work = 10/432 + 1/72 = 10 + 6/432 = 16/432
= 1/27
Therefore, the required No. of days = 27 days.
Answer: Option C
Answer: C
Question: The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250.The sum of the numbers is :
Options:
A)30
B)50
C)60
D)90
E)40
Rationale: Solution
Let the numbers be 3x,4x and 5x.Then,
9x2+6x2+25x2 = 1250=50x2= 1250=x2 = 25=x = 5.
∴ Sum of numbers = (3x+4x+5x) = 12 x =(12x5) = 60.
Answer C
Answer: C
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
Options:
A)229
B)787
C)144
D)128
E)121
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
Answer: C
Answer: C
Question: x^2 + sx + 72 = 0 has two distinct integer roots; how many values are possible for s?
Options:
A)3
B)6
C)8
D)12
E)24
Rationale: For a quadratic equation ax^2+sx+c=0, we know that -s/a is sum of roots and c/a is product of roots.
The quadratic equation here is x^2 + sx + 72 = 0, where product of roots is 72.
If we find all the factors of 72, we have the answer.
By prime factorization, we get 72= 2^3*3^2.
We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D
Answer: D
Question: Look at this series: 8, 43, 11, 41, __, 39, 17, ... What number should fill in the blank?
Options:
A)22
B)33
C)14
D)16
E)18
Rationale: C
14
This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2.
Answer: C
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)750
B)7500
C)8500
D)1500
E)7503
Rationale: A : B : C = 20000*24 : 15000*24 : 20000*18 = 20*4 : 15*4 : 20*3
= 4*4 : 3*4 : 4*3
= 4:3:3
Answer is B
B's Share = (25000 * 3)/10 = 7500
Answer: B
Question: A word is defined as a sequence of five dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
Options:
A)10
B)16
C)24
D)32
E)40
Rationale: 2^5 = 32
The answer is D.
Answer: D
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
A)8/3
B)2/1
C)8/5
D)5/8
E)5/3
Rationale: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 450/3 = 150 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 150/75 = 2/1
Answer B
Answer: B
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $230, what were her original savings?
Options:
A)$900
B)$800
C)$1000
D)$920
E)$1500
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $230. So 1 / 4 of her savings is $230. So her original savings are 4 times $230 = $920
correct answer D
Answer: D
Question: Find the largest number of four digits which is exactly divisible by 27,18,16,15
Options:
A)8600
B)8610
C)8620
D)8630
E)8640
Rationale: Explanation:
LCM of 27-18-16-15 is 2160.
After dividing 9999 by 2160 we get 1359 remainder.
So answer will be 9999-1359 = 8640
Option E
Answer: E
Question: A train passes a station platform in 33 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)195 m
B)240 m
C)300 m
D)360 m
E)280 m
Rationale: Speed = 54 x	5/18	m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,	(x + 300)/33	= 15
x + 300 = 495
x = 195 m.Answer: Option A
Answer: A
Question: A husband and wife can complete a certain task in 2 and 3 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
Options:
A)a)15:46
B)b)1:2
C)c)12:23
D)d)5:18
E)e)10:3
Rationale: couples one hour work=1/2+1/3=5/6
so total time=6/5..
now, kids one hour work=1/4+1/6=5/12
so total time=12/5..
ratio=6/5:12/5=1/2
ans B
Answer: B
Question: Murphy and Cooper are having the same amount of petrol in the petrol tanks of their respective cars. Murphy can drive for four hours with that amount whole Cooper can drive for five hours.
They both starts together and keep driving for a few hours. After some time, they find that the amount of petrol remaining in one car is four times that of the other car.
Using all these facts, can you find out how long they drove their cars?
Options:
A)2 3/4 hours.
B)3 3/4 hours.
C)4 3/4 hours.
D)5 3/4 hours.
E)6 3/4 hours.
Rationale: Solution:
3 3/4 hours
Explanation:
Suppose that the amount of petrol in each of the cars in the beginning was M.
Now, suppose that they drove for X hours.
In that case, the amount of petrol used by one car in X hours will be = M*X /4
The amount of petrol used by the other car will be = M*X/5
Therefore, the petrol left in one car = M - M*X / 4
Petrol left in the other car = M - M*X / 5
Now, according to the question,
M - M*X / 5 = 4 (M - M*X / 4)
=> X = 15 / 4 = 3 3/4 hours.
Therefore Murphy and Cooper drove for 3 3/4 hours.
Answer B
Answer: B
Question: If e is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
Options:
A)√n + 1
B)n + 1
C)n^2 + 1
D)e + 2√e + 1
E)n^2 + 2n + 1
Rationale: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
e = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(e) = x
Ans - e + 2 root(e) + 1
This should beD
Answer: D
Question: What is the positive difference between the sum of the squares of the first 5 positive integers and the sum of the prime numbers between the first square and fourth square?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +4^2+5^2 = 55
the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.
So the difference between 41 and 55 is 14.
So the answer is (D).
Answer: D
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum X of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
Options:
A) 6x
B) 4x
C) 5x/3
D) 3x/2
E) 3x/5
Rationale: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<X<5x --> only option B fits.
Answer: B.
Answer: B
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
Options:
A)6
B)5
C)7
D)9
E)2
Rationale: C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days
Answer:D
Answer: D
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Options:
A)4 years
B)8 years
C)10 years
D)12 years
E)14 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years. Answer: Option A
Answer: A
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 16 on Wednesday, what would be the value of D calculated on the following Saturday?
Options:
A)2520
B)2940
C)3360
D)3780
E)4150
Rationale: On Saturday, the value would be 7*6*5*16 = 3360
The answer is C.
Answer: C
Question: which of the following could be the greatest common factor of positive integers a and b?
I. 1
II. a
III. a-b
Options:
A)II only
B)I and II only
C)I and III only
D)II and III only
E)I, II and III
Rationale: It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...
It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...
It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...
Answer: E.
Answer: E