divelab/Sys2Bench huggingface dataset:
Question: There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
Options:
A)22
B)28
C)269
D)26
E)82
Rationale: The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 hours, completely full after 26 hours.
Answer:D
Answer: D
Question: Find the sum of first 30 natural numbers
Options:
A)470
B)468
C)465
D)463
E)487
Rationale: Explanation:
Sum of n natural numbers
=n(n+1) / 2
=30(30+1) / 2=30(31) / 2=465
Option C
Answer: C
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
Options:
A)298
B)608
C)279
D)280
E)269
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer:D
Answer: D
Question: If K is the sum of reciprocals of the consecutive integers from 53 to 58, inclusive, then K is closest in value to which of the following?
Options:
A)1/12
B)1/10
C)1/8
D)1/6
E)1/10
Rationale: 1/53 , 1/54 , 1/55 , 1/56 , 1/57 , 1/58
Hypothetically , assume all 6 Numbers to be 1/53
Hence sum of it would result in = 6/53 ( almost equals 1/7 , or slightly less than 1/7 - )
If all 6 nos were to be 1/58 ... Sum of which would result in 6/58 = 1/10 .
Hence answer should lie between 1/7 and 1/10
E i.e 1/10
Answer: E
Question: John takes a trip and drives 9 hours from Town X to Town Z at a rate of 60 miles per hour. On his way back, John drives 85 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y?
Options:
A)1.75
B)1.25
C)1.45
D)4.15
E)3.14
Rationale: distance from X to Z =9 hr* 60 mph= 540 miles
hence distance from Y to Z= 1/2*540=270
time=270/85=4.15 hrs
IMO: D
Answer: D
Question: A company has 100 employees, 40% of whom are employed part time. If it hires 25 new employees, 40% of whom are employed part time, what will be the percent increase in part time employees?
Options:
A)1 2/3 %
B)2 2/3 %
C)4 %
D)25 %
E)9 %
Rationale: Total employee = 100
Part time Empl = 40
New part time empl = 25 * (40/100)
= 10
Total new part time Emp = 10+40= 50
Old part time Emp = 40
% increase = (new - old)*100/old
=10*100/40
= 25%
Ans-D
Answer: D
Question: In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?
Options:
A)22
B)32
C)30
D)28
E)11
Rationale: Let the number of boys and girls participating in sports be 3x and 2x respectively.
Then, 3x = 15 or x = 5.
So, number of girls participating in sports = 2x = 10.
Number of students not participating in sports = 60 - (15 + 10) = 35.
Let number of boys not participating in sports be y.
Then, number of girls not participating in sports = (35 -y).
Therefore (35 - y) = y + 5 2y 30 y = 15.
So, number of girls not participating in sports = (35 - 15) = 20.
Hence, total number of girls in the class = (10 + 20) = 30.
Answer:C
Answer: C
Question: To furnish a room in a model home an interior decorator is to select 4 chairs and 4 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 75 different combinations are possible, how many tables are there in the warehouse?
Options:
A)A)6
B)B)8
C)C)10
D)D)15
E)E)30
Rationale: Total number of ways to choose 4 chairs from 5= 5C4=5
Total number of combination=75
That means we need get 15 combinations from the selection of tables....
Screening through the answers.... 6C4=15..... 15*5=75
Answer is 6... A
Answer: A
Question: A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Options:
A)66 km/hr
B)72 km/hr
C)78 km/hr
D)81 km/hr
E)85 km/hr
Rationale: Explanation:
4.5 km/hr =(4.5 x	5/18)m/sec =	5/4m/sec = 1.25 m/sec, and
5.4 km/hr =(5.4 x5/18)m/sec =3/2m/sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
=> 8.4x - 10.5 = 8.5x - 12.75
=> 0.1x = 2.25
=> x = 22.5
Speed of the train =(22.5 x	18/5)km/hr = 81 km/hr.
ANSWER IS D
Answer: D
Question: 160 is what percent of 50 ?
Options:
A) 5%
B) 20%
C) 320%
D) 200%
E) 500%
Rationale: 50*x=160 --> x=3.2 --> 3.2 expressed as percent is 320%.
Answer: C.
Answer: C
Question: What will come in place of the x in the following Number series? 46080, 3840, ?, 48, 8, 2, 1
Options:
A)1
B)384
C)5
D)7
E)9
Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
48 /6 = 8
8/4 = 2
2 /2 = 1
B
Answer: B
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
Options:
A)10%
B)20%
C)25%
D)30%
E)45%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: C
Question: Find the average of first 20 natural numbers?
Options:
A)5.5
B)7.2
C)10.5
D)12.3
E)15.5
Rationale: Sum of first n natural numbers = n(n+1)/2
sum of first 20 natural numbers = 20*21/2 =210
average = 210/20 = 10.5
Answer is C
Answer: C
Question: The inverse ratio of 4: 2: 1 is?
Options:
A)2:4:8
B)2:3:9
C)2:3:2
D)2:3:6
E)2:3:1
Rationale: 1/4: 1/2: 1/1 = 2:4:8
Answer:A
Answer: A
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)3
B)8
C)9
D)6
E)4
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: A password of a computer used two digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
Options:
A)1/32
B)1/16
C)1/8
D)2/5
E)1/4
Rationale: We have two digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10=1/4(E)
Answer: E
Question: Three times the first of three consecutive odd integers is 8 more than twice the third. The third integer is:
Options:
A)9
B)11
C)13
D)15
E)20
Rationale: Let the three integers be x, x + 2 and x+ 4.
Then,
3x = 2(x + 4) + 8
x = 16
Third integer = x + 4 = 20.
ANSWER:E
Answer: E
Question: NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day?
Options:
A)22
B)60
C)28
D)11
E)218
Rationale: Here 2km is immaterial. The given problem can be written in a tabular form like below.
We can apply chain rule now.
Total men required to complete the remaining work = 100×2525×810×2313100×2525×810×2313 = 160
So additional men required = 160 - 100 = 60
Answer:B
Answer: B
Question: Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 60 km and the other at the rate of 90 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)4.85
B)7.85
C)6.85
D)5.85
E)6.62
Rationale: T = (111 + 165)/ (60 + 90) * 18/5
T = 6.62
ANSWER:E
Answer: E
Question: A train 500 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)277 m
B)700 m
C)800 m
D)187 m
E)1678 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (500 + x)/60 = 65/3
x = 800 m.
Answer:C
Answer: C
Question: The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?
Options:
A)80%
B)75%
C)65%
D)50%
E)45%
Rationale: consider base price - $100
25% increase = 1.25*100 = $125
another 40% increase on new price = 1.4* 125 = $175
so final price of radio - $175
therefore a 75% increase
correct option - B
Answer: B
Question: Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is :
Options:
A)500 km
B)630 km
C)900 km
D)660 km
E)None
Rationale: Sol.
At the time of meeting, let the distane travelled byb the second train be x km. Then,
distance covered by the first train is (x + 100) km
∴ x/40 = (x+100)/50 ⇔ 50x = 40x 4000 ⇔ x = 400.
So, distance between P and Q = (x+x+100) km = 900 km.
Answer C
Answer: C
Question: What is the investment made if one invests in 15% stock at 50 and earns Rs.2000?
Options:
A)5000
B)2767
C)2697
D)126967
E)19771
Rationale: Explanation:
To earn Rs.15, investment = Rs.50.
Hence, to earn Rs.1500, investment = (1500*50)/15
= Rs.5000
ANSWER: A
Answer: A
Question: The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 25 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?
Options:
A)1/6
B)1/3
C)2/3
D)5/6
E)17/18
Rationale: priyalr
6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane.
the view of the window of 25 rows is blocked. two wings, therefore 50 window seats are blocked.
Total window seats = 60
Total blocked window seats = 50
Total unblocked seats = 10
We know that a window seat was given, therefore probability for not window seat is 10/60 =1/6
ANS A
Answer: A
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan.
Options:
A)Rs.7000
B)Rs.5000
C)Rs.6000
D)Rs.Rs.4000
E)Rs.6500
Rationale: 3:1
2:1
------
6:1
7 ----- Rs.28000
1 ----- ? => Rs.28,000/7=Rs. 4000
Answer: D
Answer: D
Question: A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?
Options:
A) 1.50
B) 1.75
C) 2.00
D) 2.50
E) 3.00
Rationale: Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6= 109.50 --> x=2.5.
Answer: D.
Answer: D
Question: Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Z of time will elapse before they chime together again?
Options:
A)2 hr. and 24 min.
B)4 hr. and 48 min.
C)1 hr. and 36 min.
D)5 hr.
E)2 hr.
Rationale: It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother.
So the LCM of the three time intervals (18, 24,32) would be the answer.
LCM (18, 24, 32) Z= 288 => 4 hours 48 mins.B
Answer: B
Question: A man can row downstream at 25 kmph and upstream at 15 kmph. Find the time to reach a destination point at a distance of 50km along the downstream.
Options:
A)4 hrs.
B)1 hrs.
C)3 hrs.
D)2 hrs.
E)2 1/2 hrs.
Rationale: Let the speed of the man in downstream=25 kmph. distance to be covered along the stream=50kmph
=>time taken =D/S =50/25 =2 Hrs.
Answer:D
Answer: D
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: C19, E21, __, I25, K27, ... What number should fill the blank?
Options:
A)D20
B)E21
C)F22
D)G23
E)H24
Rationale: B
G23
In this series, the letters progress by 2, and the numbers increase by 2.
Answer: B
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)276m
B)180m
C)286m
D)288m
E)277m
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: B
Question: The ratio of three numbers is 2:3:5 and their sum is 150. The second number of the three numbers is?
Options:
A)24
B)26
C)27
D)29
E)45
Rationale: 2:3:5
Total parts = 10
10 parts --> 150
1 part ---->15
The second number of the three numbers is = 3*15= 45
Answer : E
Answer: E
Question: For any real number x, the operatoris defined as:
(x) = x(2 − x)
If p + 2 =(p + 2), then p =
Options:
A)1
B)0
C)1
D)-2
E)3
Rationale: (x) = x(2 − x)
(p + 2) = (p + 2)(2 - p - 2) = -p(p+1)
We are given that p + 2 =(p + 2)
Therefore -p(p+2) = (p + 2)
Or (p + 2) + p(p+2) = 0
(p + 2)(p+1) = 0
p = -1,p=-2
Option D
Answer: D
Question: Calculate the circumference of a circular field whose radius is 5 centimeters.
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Circumference C is given by
C = 2πr = 2π*5 = 10 π cm
correct answer E
Answer: E
Question: The average age of five persons is 40 years while the average age of some other 10 persons is 25 years. The average age of all the 15 persons is:
Options:
A)27 Years
B)32 Years
C)37 Years
D)30 Years
E)35 Years
Rationale: x/5==40
x==200
after 10 person
x/10==25
x==250
so avg btwn 15 person is,,
(250+200) / 15==30 ans
ANSWER:D
Answer: D
Question: A slot machine in a Las Vegas casino has an average profit of $600 for each 8-hour shift for the five days Sunday through Thursday, inclusive. If the average per-shift profit on Friday and Saturday is 25% greater than on the other days of the week and the slot machine is in operation every hour of every day, what is the total weekly profit that the casino makes from the slot machine?
Options:
A)a - 4500
B)b - 9000
C)c - 13,500
D)d - 15,500
E)e - 27,000
Rationale: Correct answer is C - 13500.
Total profit per weekday = $600 X 3 (shifts)= $1800
Total profit per week (apart from SaturdaySunday) = $1800 X 5 = $9000
Total profit per shift on weekends = $600 X 125/100 = $750
Total profit on weekends = $750 X 3 (shifts) X 2 (Saturday, Sunday) = $4500.
Hence the answer is - $4500 + $9000 = $13,500. (C)
Answer: C
Question: What is the greatest prime factor of 2^10 - 1?
Options:
A)17
B)19
C)23
D)29
E)31
Rationale: 2^10-1 = (2^5-1)(2^5+1) = 31*33
The answer is E.
Answer: E
Question: A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Options:
A)81 km/hr
B)88 km/hr
C)62 km/hr
D)46 km/hr
E)34 km/hr
Rationale: Explanation:
Let x is the length of the train in meter and y is its speed in kmph
x/8.4 = (y-4.5)(10/36) ---(1)
x/8.5 = (y-5.4)(10/36) ---(2)
Dividing 1 by 2
8.5/8.4 = (y-4.5)/ (y-5.4)
=> 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4
.1y = 8.5×5.4 - 8.4×4.5
=> .1y = 45.9-37.8 = 8.1
=> y = 81 km/hr
Answer: Option A
Answer: A
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
Options:
A)three times as much
B)twice as much
C)the same
D)half as much
E)a third as much
Rationale: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
correct answer B
Answer: B
Question: There are 32 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
Options:
A)1800
B)1820
C)1150
D)1122
E)1900
Rationale: The total number of stations= 34
From 34 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 34P2 ways.
34P2= 34*33= 1122
ANSWER:D
Answer: D
Question: There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?
Options:
A)110
B)100
C)120
D)140
E)150
Rationale: Let the number of persons in building P = p
and the number of persons in building Q = q
If 15 persons are sent from P to Q,
then the number of persons in each building is the same
=> p-15 = q+15
=> p - q = 30 ----(Equation 1)
If 20 persons are sent from Q to P,
then the number of persons in P is double the number of persons in Q
=> 2(q - 20) = (p + 20)
=> 2q - 40 = p + 20
=> 2q - p = 60 ----(Equation 2)
(Equation 1) + (Equation 2)=> q = 90
From Equation 1, p = 30 + q = 30 + 90 = 120
i.e., Building P has 120 persons
Answer is C.
Answer: C
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes W of the competition are possible?
Options:
A)18
B)20
C)54
D)84
E)120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total W=84 outcomes
D
Answer: D
Question: A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary.
Options:
A)$180000
B)$280000
C)$380000
D)$480000
E)None
Rationale: Solution:
The expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity.
In general for independent activities
[1 – (x1/y1 + x2/y2 + x3/y3)] × Total amount = Balance amount
[1 – (1/5 + 1/10 + 3/5)] × Total salary = $18000
[1 – 9/10] × Total salary = $18000
Therefore total salary = $18000 × 10 = $180000
Answer A
Answer: A
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)5
C)6
D)7
E)9
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer:A
Answer: A
Question: Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and twice the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Options:
A)(16/3)b
B)(17/4)b
C)(13/4)b
D)(9/2)b
E)(7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradley’s total
3b = Andrew’s total
(1/2)b = Charlie’s total
Add each total
b + 3b+ (1/2)b = 4b + (1/2)b = (16/4)b + (1/2)b = (9/2)b
Therefore,choose D.
Answer: D
Question: If a - b = 2 and a2 + b2 = 25, find the value of ab.
Options:
A)A)10.5
B)B)12
C)C)15
D)D)18
E)E)20
Rationale: Explanation:
2ab = (a2 + b2) - (a - b)2
= 25 - 4 = 21
ab =10.5
Answer: A
Answer: A
Question: 3, 7, 15, 31, 63, ?
Options:
A)125
B)112
C)153
D)173
E)127
Rationale: E
127
Each number in the series is the preceding number multiplied by 2 and then increased by 1.
Answer: E
Question: If the complement of a certain angle is two times the measure of that certain angle, then what is the measure of that certain angle?
Options:
A)45°
B)30°
C)22.5°
D)18°
E)15°
Rationale: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is 2x, and together, these add up to 90 degrees.
x + 2x = 90
3x = 90
x = 30°
Answer = (B)
Answer: B
Question: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
Options:
A)2 days
B)1 day
C)3 days
D)5 days
E)7 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
B)
Answer: B
Question: If the sum of 1/3 and 22/99 is converted to a decimal, what is the 3000th digit to the right of the decimal place?
Options:
A)2
B)3
C)5
D)8
E)9
Rationale: 1/3 +22/99 = 5/9=0.555555555...
hence, the 3000th digit would also be 5
Ans: C
Answer: C
Question: Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?
Options:
A)1/11
B)2/13
C)4/13
D)3/17
E)3/19
Rationale: Here, n(S) = 52
There are 13 cards of diamond (including one king) and there are 3 more kings.
Let E = event of getting a diamond or a king.
Then, n(E) = (13 + 3) = 16
P (E) = 16 / 52 = 4/13
C
Answer: C
Question: If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?
Options:
A) -16
B) -10
C) 0
D) 14
E) 16
Rationale: (x+1)^2 <= 16
x <= 3
x >= -5
(y-1)^2< 64
y < 9
y > -7
Max possible value of xy is -5 × -6 = 30
minimum possible value of xy is -5 × 8 = -40
-40 + 30 = -10
Answer : B
Answer: B
Question: If points A and B are (10-5) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: I. The area of a square region with side AB --> side=AB=(10-5) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Answer: A