divelab/Sys2Bench huggingface dataset:
Question: The total of the ages of Mahesh, Suresh, Ramesh is 102 years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
Options:
A)32years
B)42years
C)45years
D)35years
E)30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 102
x = 8
Ramesh present age = 4*8+10 = 42 years
Answer is B
Answer: B
Question: How many digits will be there to the right of the decimal point in the product of 98 and .08216 ?
Options:
A)5
B)6
C)9
D)7
E)8
Rationale: Product of 98 and .08216 is 8.05168.
Therefore number of digits to right of decimal point is 5
Answer is A.
Answer: A
Question: If two numbers are in the ratio 5:6. If 10 is added to both of the numbers then the ratio becomes 6:7 then find the smallest number?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Explanation:
5:6
5x + 10 : 6x + 10 = 6 : 7
7[5x + 10] = 6[6x + 10]
35x + 70 = 36x + 60
36x - 35x = 70 - 60
x = 10
Then smallest number is =5
5x = 50
Answer: Option E
Answer: E
Question: The king of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the king must sit in the center chair, how many different seating arrangements are possible for the 5 people?
Options:
A) 4
B) 5
C) 24
D) 20
E) 120
Rationale: IMO C
Given that one chair is taken, i think the remaining 4 dignitaries can be arranged 4!=24.
Answer: C
Question: X, Y and Z, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $2350, what will be Z's share of the earnings?
Options:
A)$525
B)$550.50
C)$1080.02
D)$522.3
E)$1020.2
Rationale: The dollars earned will be in the same ratio as amount of work done
1 day work of Z is 1/12 (or 2/24)
1 day work of the combined workforce is (1/6 + 1/8 + 1/12) = 9/24
Z's contribution is 2/9 of the combined effort
Translating effort to $ = 2/9 * 2350 = $522.3
hence:D
Answer: D
Question: 3 no. leave remainders of 43, 47 & 49 on division by N. The sum of the three no.'s leaves a remainder 9 on division by N. What are the values N can take?
Options:
A)34
B)35
C)38
D)67
E)More than one value is possible
Rationale: In this question, the sum of the three numbers should leave a remainder 43 + 47 + 49 = 139. Or, it should be of the form N * k + 139, where K is an integer.
However, it leaves a remainder 9, or it is of the form N * m + 9.
N * k + 139 = N * m + 9
N * (m - k) = 130
Or, N should be a factor of 130. Since the remainders left on division by N are 43, 47 and 49, N should be greater than 49.
The only factors of 130 that are greater than 49 are 65 and 130. So, N can take 2 values – 65 or 130
E
Answer: E
Question: In how many ways can a group of 16 friends be seated round 2 tables if one of the tables can seat 10 and the other can seat 6 people?
Options:
A)15C5 * 9! *4!
B)15C3 * 8! *3!
C)15C4 * 9! *3!
D)16C4 * 9! *5!
E)16C5 * 10! *4!
Rationale: 10 people can be selected from 16 people in 16C10 ways.
Remaining 6 people can be selected from 6 people in 6C6 ways.
Now, arranging 10 people on a round table = (10-1) ! = 9!
Arranging 6 people on a round table = (6-1) ! = 5!
Hence, total number of ways = 16C10 * 9! * 6C6 * 5!
= 16C4 * 9! * 5!
D
Answer: D
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=ab+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 Ⅰ& Ⅲ
E)only Ⅱ & Ⅲ
Rationale: If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (X).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (O).
Thus, Ⅰ& Ⅲ are the answers. Therefore, D is the answer.
Answer: D
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $25?
Options:
A)45
B)49
C)53
D)57
E)61
Rationale: $25 = 4 * $6 + $1
The number of doughnuts is 4*12 + 1 = 49
The answer is B.
Answer: B
Question: Square A has an area of 65 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
Options:
A)0.25
B)0.5
C)0.75
D)0.1
E)0.3
Rationale: I guess it's mean that square B is placed within square Aentirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 65-16=48 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=48/64 = 0.75.
Answer: C
Answer: C
Question: 32 = a + 2b
|a| > 2
If ‘a’ and ‘b’ are both integers, then what is the smallest possible values of ‘a’ that can be used to solve the above equation.
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Let us understand the meaning of |a| > 2
Mod is very easy concept if you solve mod question by considering as a distance. when a mod is written as |x-(a)| = b, this means the distance from point 'a' (both side left and right of 'a' on number line) is b. |x-(a)| < b means the distance is between the two extreme distance(left and right side of 'a' on number line, considering the max distance is 'b' from 'a' - as per this scenario.....hence the value of 'a' must be between these two extremes. |x-(a)| > b means the distance is greater than the distance of 'b'..i.e the value of a could be anywhere more than 'b' (i.e. current case).
Now come to the question. First its given |a| > 2 ==> a > 2 i.e. a can have any value bigger than 2 (i.e. 3, 4, 5…).
Now, lets move to equation a + 2b = 32 ==> b = (32 – a)/2 ==> b = 16 – (a/2). According to question, b is an integer, hence to make ‘b’ integer a must be divisible by 2. Minimum possible value of ‘a’ that is divisible by 2 is 4 (a is greater than 2 so the next number that is divisible by 2 is 4). So the answer is C (value 4).
Answer: C
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)4
B)5
C)34
D)7
E)9
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer:D
Answer: D
Question: What is the dividend. divisor 20, the quotient is 8 and the remainder is 6
Options:
A)A)145
B)B)148
C)C)150
D)D)153
E)E)166
Rationale: D = d * Q + R
D = 20 * 8 + 6
D = 160 + 6
D = 166
Answer : E
Answer: E
Question: What is the greatest positive integer x such that 3^x is a factor of 9^9?
Options:
A)5
B)9
C)10
D)18
E)30
Rationale: What is the greatest positive integer x such that 3^x is a factor of 9^9?
9^9 = (3^2)^9 = 3^18
D. 18
Answer: D
Question: each man in a gang of 100 investors has investments ineither equities or securities or both. Exactly 2525 of the investors in equities haveinvestments in securities, exactly 4040 of the investorsin securities have investments inequities. How many have investmentsin equities?
Options:
A)70
B)80
C)90
D)100
E)120
Rationale: The investors can be categorized into three groups:
(1) Those who have investments in equities only.
(2) Those who have investments in securities only.
(3) Those who have investments in both equities and securities.
Let xx, yy, and zz denote the number of people in the respective categories. Since the total number of investors is 110, we have
x+y+z=110x+y+z=110 ------------- (1)
Also,
The number of people with investments in equities is x+zx+z and
The number of people with investments in securities is y+zy+z.
Since exactly 25%25% of the investors in equities have investments in securities, we have the equation
25100×(x+z)=z25100×(x+z)=z
25100×x=25100×z25100×x=25100×z
x=3zx=3z ------------------- (2)
Since exactly 40%40% of the investors in securities have investments in equities, we have the equation
40100×(y+z)=z40100×(y+z)=z
(y+z)=5z2(y+z)=5z2
y=3z2y=3z2
Substituting equations (2) and (3) into equation (1) yields
3z+3z2+z=1103z+3z2+z=110
11z2=11011z2=110
z=110×211=20z=110×211=20
Hence, the number of people with investments in equities is:
x+z=3z+z=3×20+20=60+20x+z=3z+z=3×20+20=60+20= 80
B
Answer: B
Question: An alloy is to contain copper and zinc in the ratio 5:3. The zinc required to be melted with 40kg of copper is?
Options:
A)15kg
B)20kg
C)8kg
D)24kg
E)32kg
Rationale: Let the required quantity of copper be x kg
5:3::40:x
5x = 40*3
x = 24kg
Answer is D
Answer: D
Question: Pipe A can fill a tank in 9 hours, pipe B in 18 hours and pipe C in 54 hours. If all the pipes are open,in how many hours will the tank be filled ?
Options:
A)5.1
B)5.4
C)5
D)5.2
E)5.5
Rationale: 1/9+1/18+1/54=10/54=1/5.4. so 5.4 hrs
ANSWER:B
Answer: B
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)87
B)37
C)80
D)36
E)13
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer: C
Answer: C
Question: 12 welders work at a constant rate they complete an order in 3 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
Options:
A)5
B)2
C)8
D)4
E)6
Rationale: 1. We need to find out the time taken by 3 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 12*3 = 36 days
4. But on day 1 twelve workers had already worked finishing 1/3 of the job. So 3 workers have to finish only 2/3 of the job.
5. Total time taken by 3 workers can be got from formula used at (2). i.e., 3* total time taken = 36. Total time taken by 3 workers to finish the complete job is 36/ 3 = 12 days.
6. Time taken by 6 workers to finish 2/3 of the job is 2/3 * 12 =8 days.
The answer is choice C
Answer: C
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Options:
A)175.5
B)170
C)169.5
D)180
E)190
Rationale: Since first and second varieties are mixed in equal proportions.
average price = 126+135/2 = 130.50
o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x - 153 = 22.50
x = 175.50
ANSWER A
Answer: A
Question: What approximate value should come in place of the question mark (?) in the following equation ?
5⁄7 of 1596 + 3015 = ? – 2150
Options:
A)7200
B)48000
C)5300
D)58000
E)6300
Rationale: ? ≈ 5 × 230 + 3000 + 2150
= 1150 + 3000 + 2150 = 6300
Answer E
Answer: E
Question: A 12% stock yielding 8% is quoted at?
Options:
A)165
B)170
C)175
D)150
E)185
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.12, money invested = 100×12/8 = Rs.150
ie, market value of the stock = Rs.150
Answer is D.
Answer: D
Question: 3x + 2y = 19 , and x + 3y = 1. Find the value of 4x + 5y
Options:
A)10
B)18
C)11
D)20
E)5
Rationale: Add these two equations
4x + 5y = 20
Divide by 2 ( to Get 4x + 5y)
Answer will be D. 20
Answer: D
Question: In the coordinate plane, the points F (-1,1), G (1,4), and H (4,1) lie on a circle with center P. What are the coordinates of point P ?
Options:
A)(0,0)
B)(1,1)
C)(1.5,1.5)
D)(1,-2)
E)(2.5, -2.5)
Rationale: I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-1)
But the the center of the circle will lie on (1.5,1.5)
D
Answer: D
Question: George's drawer has 10 loose black socks, 13 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that he had at least two matching pairs of socks in two different colors?
Options:
A)7
B)9
C)11
D)16
E)20
Rationale: The worst case scenario is choosing 13 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.
The answer is D.
Answer: D
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 8 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
Options:
A)1/9
B)29/180
C)9/80
D)1/5
E)39/121
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 8*2 = 16 hours;
In 1 hour 15 journeymen can finish 1/16 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/16=9/80 of the job.
Answer: C
Answer: C
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 6 Gallons of water and 12 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
Options:
A)37.5
B)75
C)100
D)150
E)90
Rationale: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 12 gallons salt is added and 6 gallons of water is added.
So salt now becomes -> (0.2x + 12) and water --> (0.6x+6)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+12) = (0.6x+6)/2 => 0.4x+24=0.6x+6 ->0.2x=18
Solving, x = 90
Answer : E
Answer: E
Question: A group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 10 speak English well, while 40 of them do not speak English. If 75% of students do not speak French, how many students were surveyed?
Options:
A)210
B)225
C)200
D)250
E)300
Rationale: Number of students who speak French are 40 + 10 = 50
Of total students, the percentage of students who do not speak French was 75% --> percentage of who do is 25%
50-------25%
x ------- 100%
x = 50*100/25 = 200 = number of all students
Answer is C
Answer: C
Question: Townville has 100 residents, and 40 of them are females. If half of Townville’s male residents are smokers, and 1/4 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
Options:
A)54
B)58
C)62
D)60
E)64
Rationale: Number of people =100
Females = 40
men = 100-40=60
Half of the men are smoker60/2=30, that means the remaining men 60-30=30 are non smokers.
1/4 females are smoker. i.e 1/4*40 = 10.
40-10=30 females are non smokers
So, total number of non smokers in the town are 30+30 =60
Answer : D
Answer: D
Question: A cricket player whose bowling average was 21.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match?
Options:
A)64
B)72
C)111
D)721
E)108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 21.5w + 52
Total wickets after last match = w + 5
(21.5w + 52) / (w + 5) = 21.5 - 0.5 = 21
w = 106
so total wickets aftr last match = w+5 = 111
ANSWER:C
Answer: C
Question: Three pieces of timber 54 m, 63 m and 81 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
Options:
A)9 m
B)4 m
C)4 m
D)6 m
E)None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 54, 63, 81 = 9 m
Correct Option: A
Answer: A
Question: Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow?
Options:
A)4 mins
B)6 mins
C)5 mins
D)3 mins
E)7 mins
Rationale: Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by A = 3 liters.
Capacity of tank filled in 1 minute by B = 15 liters.
Therefore, capacity of the tank filled by both A and B in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.
ANSWER:C
Answer: C
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $60 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
Options:
A)191
B)213
C)221
D)223
E)226
Rationale: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 10% of the cost:
Sell Price = Cost + $60
Sell Price = $600 + $60
Thus, the Sell Price is $660 for each item. Selling all 100 items gives the retailer...
100($60) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(660) = $33 discount
$627 = $600 + $27
Now, the retailer makes a profit of just $27 per item sold.
To earn $2,000 in profit, the retailer must sell....
$27(X) = $2,000
X = 2,000/27
X = 222.222222 items
You'll notice that this is not among the answer choices.... 221 and 223 are.
Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.
Final Answer:
D
Answer: D
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y?
Options:
A)1
B)S=Cannot be determined
C)S=2
D)5
E)6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: B
Question: 0.0023*0.13/0.236=my age
0.022*0.12/0.220=my wife age
then what is difference b/w ages?
Options:
A)0.01073
B)0.02073
C)0.03076
D)0.04078
E)0.0578
Rationale: My age = 0.0023*0.13/0.236 = 0.000299/0.236 = 0.001266949
My wife age = 0.022*0.12/0.220 = 0.00264/0.220 = 0.012
difference b/w ages = 0.012 - 0.001266949 = 0.01073
ANSWER:A
Answer: A
Question: The ratio of cats to dogs to birds to fish is 5:6:7:8. There are no other types of animals in the pet store.which of the followingcannotbe the total number of animals in the store?
Options:
A)52
B)78
C)104
D)130
E)223
Rationale: The parts add up to 5 + 6 + 7 + 8 = 26, so we know that any possible number of total answers must be a multiple of 26. All five answer choices are multiples of 26:
(A) 52= 26*2
(B) 78= 26*3
(C) 104= 26*4
(D) 130= 26*5
(E) 223 = not a multiple of 26
Answer: E
Question: Ashok has Rs.1000, He invests a part of it at 3% per annum and remainder at 8% per annum, He earns Rs.100 in 2 years. Find the sum invested at different rates of interest?
Options:
A)Rs.5000, Rs.500
B)Rs.600, Rs.400
C)Rs.700, Rs.300
D)Rs.300, Rs.700
E)Rs.300, Rs.800
Rationale: (600÷100)×3×2=34
(400÷100)×8×2=64
Total=100
ANSWER:B
Answer: B
Question: If q = 35! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 19
III. 31
Options:
A)I​ only
B)III only
C)II and III
D)I and II
E)I​, II, and III
Rationale: The numbers 11, 19, and 31 are all factors of 35!
Therefore they can not be factors of 35! + 1.
The answer is E.
Answer: E
Question: what is the sum of all the 4 digit numbers that can be formed using all of the digits 2,3,5 and 7?
Options:
A)113323
B)113322
C)114322
D)113321
E)112322
Rationale: Actually there is the direct formula for this kind of problems.
1. Sum of all the numbers which can be formed by using the n digits without repetition is: (n-1)!*(sum of the digits)*(111…..n times).
2. Sum of all the numbers which can be formed by using the n digits (repetition being allowed) is: n^{n-1}*(sum of the digits)*(111…..n times).
so as per question:(4-1)!*(2+3+5+7)*1111=113322
ANSWER:B
Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)27 7/8
B)27 7/6
C)27 7/4
D)27 7/9
E)27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: D
Answer: D
Question: If 25% of x is 30 less than 20% of 1000, then x is?
Options:
A)188
B)216
C)156
D)680
E)121
Rationale: 25% of x = x/4 ; 20% of 1000 = 20/100 * 1000 = 200
Given that, x/4 = 200 - 30 => x/4 = 170 => x = 680.
Answer: D
Answer: D
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum?
Options:
A)198
B)279
C)267
D)200
E)269
Rationale: P(11/10)4 - P(6/5)2
= 482
P = 200
Answer: D
Answer: D
Question: Rose and Anna are partners in a business. Rose runs the business and receives 12% of the profit for managing the business, the rest is divided in proportion of their capitals. Rose invested Rs.12000 and Anna invested Rs.20000. the rest is divided in proportion of their capitals. Out of a total profit of Rs.9000, how much did Rose receive?
Options:
A)5872
B)5839
C)5832
D)5838
E)5832
Rationale: ratio of their investments Rs.12000:20000=3:5
12% of the profit for managing the business =12/100*9000=1080
remaining profit=9000-1080=7920
share profit in ratio of investment 7920/5 =1584
Moses's ratio share=3*1584=4752
total money Moses collects=4752+1080=5832
Answer: C
Answer: C
Question: Find the value of x from this equation? 7(x - 1) = 21
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: 1. Divide both sides by 7:
2. Simplify both sides:
x - 1 = 3
3. Add 1 to both sides:
x - 1 + 1 = 3 + 1
4. Simplify both sides:
x = 4
B
Answer: B
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
Options:
A)11
B)7
C)76
D)37
E)9
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Answer: D
Question: Obra drove 150π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
Options:
A)6.67%
B)12.5%
C)18.75%
D)25%
E)31.25%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 150π/480π =31.25%
Hence, answer is E.
Answer: E
Question: There are four different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
Options:
A)72
B)48
C)64
D)24
E)8
Rationale: Since we have 2 continental pairs (EU, SA, NA), these 2 pairs have 2*1 = 2 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2= 4). So we have 2*4 = 8.
Please correct me if im wrong.
Answer E.
Answer: E
Question: If the numerator of a fraction E is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
Options:
A)16 1⁄6%
B)25%
C)33 1⁄3%
D)50%
E)66 2⁄3%
Rationale: This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction E is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D
Answer: D