divelab/Sys2Bench huggingface dataset:
Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
Options:
A)180 min
B)144 min.
C)126 min
D)114 min
E)124 min
Rationale: Explanation:
Let time taken by the faster pipe to fill the tank =x minutes.
Then, time taken by the slower pipe to fill the tank =4x minutes.
Time taken by both pipes together to fill the tank=x x 4x /x+4 x=4 x / 5
4x/5=36
⇒x=45
Time taken by the slower pipe to fill the tank=4x=180 minutes.
Answer: Option A
Answer: A
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
Options:
A)400 km
B)500 km
C)360 km
D)550 km
E)600 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Answer: C
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
Options:
A)1 hr 20 min
B)1 hr 10 min
C)1 hr 11 min
D)1 hr 12 min
E)none
Rationale: Sol.
New speed = 6/7 of usual speed.
New time = 7/6 of usual time
∴ [7/6 of usual time] - (usual time) = 1/5 hr.
⇒ 1/6 of usual time = 1/5 hr ⇒ usual time = 6/5 hr = 1 hr 12 min.
Answer D
Answer: D
Question: How many even three-digit integers greater than 700 are there such that all their digits are different?
Options:
A)40
B)72
C)80
D)112
E)120
Rationale: Case 1: Numbers starting with 7
7 _ _
The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8*5=40
Case 2: Numbers starting with 8
8 _ _
The unit digit can take 4 numbers (0,2,4,6) to be EVEN so 4 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8*4=32
Case 3: Numbers starting with 9
9 _ _
The unit digit can take 5 numbers (0,2,4,6,8) to be EVEN so 5 ways.
The tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways.
Total = 8 *5 = 40
Hence 40+32+40=72, correct answer is D
Answer: D
Question: The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
Options:
A)33 1/3%
B)43 1/3%
C)83 1/3%
D)36 1/3%
E)33 1/7%
Rationale: 100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer:A
Answer: A
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
Options:
A)288
B)200
C)279
D)992
E)208
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer: D
Answer: D
Question: P is three times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
Options:
A)11 days
B)16 days
C)13 days
D)15 days
E)19 days
Rationale: B
16 days
P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 12 days, which means Q can do the work in 48 days.
Hence, P can do the work in 16 days.
Answer: B
Question: If the price of a certain bond on May 1st was 3/4 the price of the bond on June 1st and the price of the bond on July 1st was 25% greater than the price of the bond on May 1st. then the price of the bond on June 1st st was what percent of the average (arithmetic mean) price of the bond on May 1st and July 1st?
Options:
A)50%
B)75%
C)118.5%
D)133 1/3%
E)150%
Rationale: The price on June 1st = 12 (assume);
The price on May 1st = 3/4*12 = 9;
The price on July 1st = 9*1.25 = 11.25.
The average price of the bond on May 1st and July 1st = (9+11.25)/2 = 10.125.
The price of the bond on June 1st (12) is 32/27 times (118.5%) the average price of the bond on May 1st and July 1st.
Answer: C.
Answer: C
Question: What should come in place of the question mark (?) in the following equation?
17 2⁄3 of 180 + 1⁄4 of 480 = ?
Options:
A)3180
B)3420
C)3200
D)3300
E)None of these
Rationale: 17 2⁄3 of 180 + 1⁄4 of 480 = ?
or, ? = 53⁄3 of 180 + 1⁄4 of 480 = = 3180 + 120 = 3300
Answer D
Answer: D
Question: Present ages of Kiran and Shyam are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Shyam's present age in years?
Options:
A)12
B)18
C)24
D)32
E)43
Rationale: Ratio of the present age of Kiran and Syam = 5 : 4
=Let the present age of Kiran = 5x
Present age of Shyam = 4x
After 3 years, ratio of their ages = 11:9
= (5x + 3) : (4x + 3) = 11 : 9
= (5x+3) / (4x+3) = 11/9
= 9(5x + 3) = 11(4x + 3)
= 45x + 27 = 44x + 33
= x = 33-27 =6
Shyam's present age = 4x = 4×6 = 24
answer :C
Answer: C
Question: Four persons can cross a bridge in 3,7,13,17 minutes.Only two can cross at a time.Find the minimum time taken by the four to cross the bridge ?
Options:
A)20 minutes.
B)25 minutes.
C)30 minutes.
D)40 minutes.
E)60 minutes.
Rationale: Explanation:
First send 17 and 7. After 7 minutes, 7 is at finish and 17 needs 10 more minutes to complete his travel. now send 13. After 10 minutes 17 reaches finish and 13 needs 3 more minutes to complete. now send 3. both 3 and 13 reach destination at the same time after 3 minutes. hence the time taken is 7+10+3=20 minutes.
Answer A
Answer: A
Question: 16.02 Ã— 0.01 = ?
Options:
A)0.1602
B)0.001602
C)1.6021
D)0.01602
E)None of these
Rationale: 16.02 Ã— 0.01 = 0.1602
The answer is A.
Answer: A
Question: A man can row his boat with the stream at 25 km/h and against the stream in 13 km/h. The man's rate is?
Options:
A)1 kmph
B)2 kmph
C)6 kmph
D)8 kmph
E)3 kmph
Rationale: DS = 25
US = 13
S = ?
S = (25 - 13)/2 = 6 kmph
Answer:C
Answer: C
Question: The average of a batsman for 40 innings is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, his average drops by 2 runs. Find his highest score.
Options:
A)172
B)173
C)174
D)175
E)None of the above
Rationale: Total runs = 40 × 50 = 2000
Let his highest score be = x
Then his lowest score = x – 172
Now 200−x−(x−172)/38=48
⇒ 2x = 2172 – 1824
⇒ x = 174
Answer C
Answer: C
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 8 km each. Then they turned left and ran for another 6 km.
What is the distance (in kilometers) between the the two twins when they stop?
Options:
A)18
B)20
C)22
D)24
E)26
Rationale: The distance between them is the hypotenuse of a right angle triangle with sides 12 km and 16 km. The hypotenuse = sqrt(12^2 + 16^2) = 20
The answer is B.
Answer: B
Question: A bag marked at Rs. 80 is sold for Rs. 68. The rate of discount is
Options:
A)10%
B)15%
C)20%
D)22%
E)None
Rationale: Solution
Rate of discount	= (12 / 80 x 100)%
= 15%.
Answer B
Answer: B
Question: A woman introduces a man as the son of the brother of her mother. How is the man, related to the woman ?
Options:
A)Nephew
B)Son
C)Cousin
D)Uncle to Grandson
E)Uncle
Rationale: Explanation:
Brother of mother — Uncle: Uncle's son — Cousin
Answer: C) Cousin
Answer: C
Question: 3 candidates in an election and received 6136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election?
Options:
A)46%
B)49%
C)57%
D)59%
E)61%
Rationale: Total number of votes polled = (6136 + 7636 + 11628) = 25400
So, Required percentage = 11628/25400 * 100 = 46%
A
Answer: A
Question: An empty fuel tank with a capacity of 204 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
Options:
A)160
B)150
C)100
D)66
E)50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 204-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 204-A gallons of fuel B is 0.16(204-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(204-A)=30 --> A=66.
Answer: D.
Answer: D
Question: X can do 1/4 of a work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of work in 13 days. Who will complete the work first?
Options:
A)X
B)Y
C)Z
D)N
E)V
Rationale: Whole work will be done by X in 10*4 = 40 days.
Whole work will be done by Y in (40*100/40) = 100 days.
Whole work will be done by Z in (13*3) = 39 days
Therefore, Z will complete the work first.
Answer : C.
Answer: C
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Options:
A)8
B)7
C)6
D)5
E)4
Rationale: [15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 96
15000[(1 + R/100)2 - 1 - 2R/100] = 96
15000[(100 + R)2 - 10000 - 200R]/10000 = 96
R2 = (96 * 2)/3 = 64 => R = 8
Rate = 8%.Answer: A
Answer: A
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?
Options:
A)1100
B)1134
C)1349
D)1430
E)1490
Rationale: 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
Answer: C
Question: In a particular 100 meter race, 8 athletes are participating that are numbered 1-8. In how many ways can athlete #4 finish ahead of #2 provided there's no tie among the athletes?
Options:
A)14,540
B)16,580
C)18,920
D)20,160
E)24,320
Rationale: The total number of ways for the athletes to finish is 8! = 40,320.
#4 will be ahead of #2 in exactly half of these possibilities.
40,320/2 = 20,160
The answer is D.
Answer: D
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
A.
B.
C.
D.
E.
Options:
A)15/64
B)30/64
C)1/2
D)1/4
E)52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days = 15/64
Ans A
Answer: A
Question: The profit earned by selling an article for 892 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
Options:
A)960
B)1005
C)1,200
D)920
E)None of these
Rationale: Let the profit or loss be x
and 892 – x = 448 + x or, x = 444⁄2 = 222
\ Cost price of the article = 892 – x = 448 + x = 670
\ SP of the article = 670 × 150⁄100 = 1005
Answer B
Answer: B
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers E are there between 6* + 2 and 6* + 6, inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes E in this range.
Answer: A.
Answer: A
Question: Seven people enter a race. There are 4 types of medals. Winner - platinum, runner up - gold, next two racers - silver and the last 3 - bronze. Ways to do it?
Options:
A)7!/3!
B)7!/2!3!
C)1*1*2!*3!
D)7*6*2!*3!
E)7*6*5*4
Rationale: let me take the approach adopted by you..
platinum-7 different people..
gold- remaining 6 different people..
silver- 2 out of remaining 5=5C2= 5!/2!3!...
bronze - 1 as all the three remaining are getting it..
total ways= 7*6*5!/2!3!=7!/2!3!.
ANS:B
Answer: B
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 60% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
Options:
A)7:15
B)7:10
C)7:8
D)7:4
E)7:2
Rationale: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.
This $36 should be a 60% increase over cost. Here, we need to think about percentage increases as multipliers.
Using multipliers
(cost)*1.60 = $36
cost = 36/1.6 = $22.5
If he wants a 60% increase over cost on the sale of one liter of his milk-water, the cost has to be $22.5
Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 22.5/33 = 15/22 of a liter. If milk is 15/22 of the liter, then water is 7/22 of the liter, and the ratio of water to milk is 7:15. Answer choice(A)
Answer: A
Question: The ratio between the number of sheep and the number of horses at the Stewart farm is 2 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
Options:
A)18
B)16
C)32
D)56
E)60
Rationale: Let the number of sheeps and horses be 4x and 7x.
Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8
Sheeps = 2x = 2*8 = 16. Hence B
Answer: B
Question: In a group of 90 people, 55 have visited Iceland and 33 have visited Norway. If 51 people have visited both Iceland and Norway, how many people have visited neither country?
Options:
A)50
B)51
C)52
D)53
E)54
Rationale: This is an example of a standard Overlapping Sets question. It has no 'twists' to it, so you'll likely find using the Overlapping Sets Formula to be a fairly easy approach. If you're not familiar with it, then here is the Formula:
90= 55 + 33 - 51 + (# in Neither Group)
=53
The prompt gives you all of the numbers you need to get to the correct answer. Just plug in and solve.
D
Answer: D
Question: What is the smallest positive integer x such that 280-x is the cube of a positive integer
Options:
A)5
B)64
C)62
D)60
E)12
Rationale: Given 280-x is a perfect cube
so we will take 216= 6*6*6
280-x = 216
x =280-216 = 64
correct option is B
Answer: B
Question: If a farmer sells 15 of his chickens, his stock of feed will last for 4 more days than planned, but if he buys 10 more chickens, he will run out of feed 6 days earlier than planned. If no chickens are sold or bought, the farmer will be exactly on schedule. How many chickens does the farmer have?
Options:
A)20
B)50
C)40
D)30
E)60
Rationale: Let x = total feed required for the planned period
n= number of chicken
t = total time of the planned feed
x = nt
1) x = (n-15) * (t+4)
2) x = (n+10) * (t-6)
equating 1&2
(n-15) * (t+4) = (n+10) * (t-6) or nt+4n-15t-60 =nt-6n+10t-60
10n = 25t
n =5/2 *t or t = 2n/5
x= n *2n/5
substituting this value in 1
n * 2n/5 = (n-15) * (2n/5+4)
2n = 60
n =30
D
Answer: D
Question: If p + | p | = 0, which of the following must be true?
Options:
A)p > 0
B)p≥0
C)p < 0
D)p≤0
E)p = 0
Rationale: Manipulate the equations:
p + | p | = 0
|p| = -p
-p > 0 OR -p = 0
This means p could be 0 or p is less than 0.
D. p≤0
E. p=0
Answer: D
Answer: D
Question: A positive whole number has factors of 5 and 10. The number MUST be divisible by:
I. 10
II. 30
III. 60
Options:
A)I
B)II
C)I & II
D)III
E)I & III
Rationale: 10 , 30 is not divisible by 60.But 60 is divisible by 5,10,30,60.
So answer is III
Answer : D
Answer: D
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,25,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)80000
B)60000
C)50000
D)75000
E)90000
Rationale: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (125000 - x) respectively. Then,
=1/3 x = 1/2 (125000 - x)
=x/3 + x/2 = 62500
=5x/6 = 62500
=x = 62500 x 6 /5	= 75000
Savings in Public Provident Fund = Rs. (125000 - 75000) = Rs. 50000
Answer is C.
Answer: C
Question: Of 70 players on a football team, 31 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)57
B)59
C)63
D)71
E)92
Rationale: Total = 70
Thrower = 31
Rest = 70 - 31 = 39
Left Handed = 39/3 = 13
Right handed = 26
If all Thrower are right handed then total right handed is 31 + 26 = 57
so A. 57 is the right answer
Answer: A
Question: There are 2 vessels A & B containing 25 liters each of pure milk and pure water respectively. 5 liters of milk from A is taken and poured into B , then 6 liters of mixture from B is taken and poured in A. What is ratio of water A and B respectively.
Options:
A)1:3
B)1:4
C)1:5
D)1:6
E)1:7
Rationale: At first
A cotain Milk = 25 Water = 0
B cotain Milk = 00 Water = 25
5 litres of milk taken from A and poured in B then
A cotain Milk = 20 Water = 0
B cotain Milk = 5 Water = 25
6 litres(1 lit Milk & 5 lit Water) of mixture from B and poured in A.
So, Finally
A cotain Milk = 21 Water = 5
B cotain Milk = 4 Water = 20
Ratio of water in A & B is 5:20 = 1:4
ANSWER:B
Answer: B
Question: A certain number of men can finish a piece of work in 10 days. However, if there were 10 less men it will take 10 days more for the work to be finished. How many men were there originally?
Options:
A)10 men
B)30 men
C)40 men
D)20 men
E)none of these
Rationale: Let x be the number of men originally
Thus, 10x=(10+10)(x-10)
10x=20(x-10)
x=2(x-10)
x = 20
ANSWER:D
Answer: D
Question: A letter lock consists of two rings each marked with four different letters. The number of distinct unsuccessful attempts to open the lock is at the most ?
Options:
A)17
B)19
C)15
D)168
E)167
Rationale: Since each ring consists of four different letters, the total number of attempts possible with the two rings is
= 4*4 = 16. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 16 - 1
= 15.
Answer: C
Answer: C
Question: how many prime no. are there from 0 to 50?
Options:
A)14
B)15
C)16
D)17
E)19
Rationale: we calculate it manually.we know the definition of prime no.prime no. should only have two distinctâ€‹ natural no. divisor 1 and itself.
note:1 is not a prime no.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
total no.=15
answer B
Answer: B
Question: Boston is 4 hr ahead of Frankfurt and 2 hr behind India. X leaves Frankfurt at 6 p.m. on Friday and reaches Boston the next day. After waiting there for 2 hr, he leaves exactly at noon and reaches India at 1 a.m. On his return journey, he takes the same route as before, but halts at Boston for 1hr less than his previous halt there. He then proceeds to Frankfurt.
What is X's average speed for the entire journey (to and fro)?
Options:
A)176 mph
B)180 mph
C)165 mph
D)Data insufficient
E)None of these
Rationale: Explanation :
X reaches Boston at 10 AM. At the same moment, time in Frankfurt is 6 AM. Hence, the journey time was 12 hours.
X reaches India at 1 AM. At the same moment, time in Boston is 11 PM. Hence, the journey time was 11 hours.
Waiting time = 2 hours.
So, total time = 12 + 2 + 11 = 25 hours.
Avg speed = 180 mph .
Answer : B
Answer: B
Question: The height of a triangle is decreased by 5% and its base increased by 50%. Its area will
Options:
A)decrease by 12.5%
B)increase by 12.5%
C)decrease by 25%
D)Increase by 25%
E)Increase by 42.5%
Rationale: Explanation :
Let the initial height be 100 and the base be 200 units.
âˆ´ Area = 1/2 x 100 x 200 = 10000sq units
Now, height = 95 units and base = 300 units
âˆ´ New area = 1/2 x 95 x 300 = 14250
âˆ´ Area is increased by (14250 - 10000)/10000 x 100
= 42.5%
Answer : Option E
Answer: E
Question: If P's height is 40% less than that of Q, how much percent Q's height is more than that of P?
Options:
A)75.56%
B)66.66%
C)70.05%
D)80%
E)85%
Rationale: Excess of Q's height over P =(40/(100-40))*100
= => 66.66%
ANSWER B
Answer: B
Question: Car A runs at the speed of 35 km/hr & reaches its destination in 10hr. Car B runs at the speed of 25 km/h & reaches its destination in 6h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)7 : 3
B)5 : 7
C)9 : 7
D)3 : 5
E)11 : 6
Rationale: Sol. Distance travelled by Car A = 36 × 10 = 350 km
Distance travelled by Car B = 25 × 6 = 150 km
Ratio = 350/150 = 7 : 3
A
Answer: A
Question: If a certain sample of data has a mean of 10.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
Options:
A)(5.0; 16.5)
B)(8.5; 21.0)
C)(14.0; 26.5)
D)(16.5; 26.0)
E)(21.0; 26.5)
Rationale: 2.5 standard deviation equals to 2.5*2=5;
2.5 standard deviations from the mean, so5 points, from the mean is the range from {mean-5} to {mean+5}, so from 5 to 15:
The correct answer choice must cover all this range: only answer choice A does this.
Answer:A.
Answer: A
Question: A sum of money is distributed among w,x,y,z in the proportion of 4:2:5:3. If y gets $500 more than z, what is the x's share?
Options:
A)$4000
B)$500
C)$2500
D)$2800
E)$1400
Rationale: Let the shares of w,x,y,z are 4a,2a,5a,3a
5a-3a = 500
2a = 500,a=250
x's share = 2a = $500
Answer is B
Answer: B
Question: In a group of 80 children and 30 youngsters, each child got sweets that are 15% of the total number of children and each youngster got sweets that are 25% of the total number of children. How many sweets were there?
Options:
A)1140
B)1160
C)1180
D)1560
E)1210
Rationale: Number of sweets each child got = 15% of 80 = 15/100 * 80 = 12.
Number of sweets 80 children got = 80 * 12 = 960.
Number of sweets each youngster got = 25% of 80 = 25/100 * 80 = 20.
Number of sweets 10 youngsters got = 30 * 20 = 600.
Total number of sweets = 960 + 200 = 1560.
D)
Answer: D
Question: How many diagonals does a 63-sided convex polygon have?
Options:
A)1890
B)1953
C)3780
D)3843
E)3906
Rationale: A 63-sided convex polygon has 63 vertices.
If we examine a single vertex, we can see that we can connect it with 60 other vertices to create a diagonal. NOTE: there are 60 options because we can't connect the vertex to ITSELF, and we can't connect it to its ADJACENT vertices, since this would not create a diagonal.
If each of the 63 vertices can be connected with 60 vertices to create a diagonal then...
...the total number of diagonals = (63)(60) = 3780
HOWEVER, before we select answer choice C, we must recognize that we have counted every diagonal TWICE.
For example, we might connect vertex A with vertex F and count that as 1 diagonal, and at the same time we connect vertex F with vertex A and count that as 1 diagonal. Of course these diagonals are the SAME.
To account for counting each diagonal twice, we must divide 3780 by 2 to get: 1890
ANSWER:A
Answer: A
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=b+ba
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
Options:
A)only Ⅰ
B)only Ⅱ
C)only Ⅲ
D)only ⅠⅢ
E)only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (X).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, ⅠⅢ are the answers. Therefore, A is the answer.
Answer: A
Question: ♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠0.089 - ♠2.135 =
Options:
A)1.05
B)1.04
C)-1.05
D)-2
E)-0.1
Rationale: ♠0.089 - ♠2.135 =
0.1 - 2.1 = -2
Answer : D
Answer: D
Question: The simplified value of 1.2 + (1.2)2 + (1.2)3 is:
Options:
A)4.248
B)4.368
C)3.248
D)3.368
E)4.368
Rationale: The expression is in geometric progression with a common ratio of 1.2. Formula to sum a geometric sequence is a(1-r^n)/1-r where a=r=1.2.Solving it we get the ans as 4.368
ANSWER:B
Answer: B