divelab/Sys2Bench huggingface dataset:
Question: Two circles are there one with arc area 60digree equal to 45digree of another circle find the area of circle1:circle2 ratio
Options:
A)3:4
B)1:4
C)1:2
D)2:3
E)1:3
Rationale: area for first circle=(3.14*r^2)/6
area of second circke=(3.14*R^2)/8
therefore, ratio=3:4
ANSWER:A
Answer: A
Question: A $500 investment and a $1,500 investment have a combined yearly return of 22 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?
Options:
A)29%
B)20%
C)27%
D)25%
E)12%
Rationale: The equation we can form the question :
Return on Total Investment = Sum of individual Investments
(500+1500)(22)=(500âˆ—7)+(1500x), where x is the return on investment of 1500.
Solving the equation, we get x = 27% ( Option C )	ANSWER:C
Answer: C
Question: Robert tossed a fair coin 3 times. What is the probability that the coin landed heads up exactly twice?
Options:
A)0.125
B)0.250
C)0.375
D)0.75
E)0.875
Rationale: Total number of outcomes = 2 * 2 * 2 = 8
Out of 3 times we need heads exactly 2 times = 3C2 = 3
Probability = 3/8 = 0.375
The answer is, therefore, (C).
Answer: C
Question: Two unbiased coins are tossed. What is probability of getting at most one tail ?
Options:
A)1/2
B)1/3
C)3/2
D)3/4
E)None of these
Rationale: Explanation:
Total 4 cases = [HH, TT, TH, HT]
Favourable cases = [HH, TH, HT]
Please note we need atmost one tail, not atleast one tail.
So probability = 3/4
Option D
Answer: D
Question: Sara and Alan start a company with Rs.100000 and Rs.50000 respectively. how should they share their profits at the end of one year?
Options:
A)1:2
B)3:4
C)3:8
D)3:1
E)3:2
Rationale: The ratio of the investments made by A and B =
100000: 50000=> 2:1.Answer: A
Answer: A
Question: The radius of a cylindrical water tank is reduced by 50%. However, the speed by which water is filled into the tank is also decreased by 50%. How much more or less time F will it take to fill the tank now?
Options:
A) 50% less time
B) 50% more time
C) 75% less time
D) 75% more time
E) 100% more time
Rationale: (VC)Volume of the cylinderical vessal is directly proportional to R^2.
So if radius is 50% less volume will be 1/4th of the original volume.(VC/4)
Now if with velocity V tank can be filled in T1 time of volume VC
So now Velocity is 50% less i..e V/2
So time taken to fill the capacity VC/4 by V/2 velocity is T2.
VT1 = VC
V/2*T2 = VC/4
So T1/T2 = 1/2
So Tank will be filled in less time. that is F=50 % less.A
Answer: A
Question: Dawson sold an item for Rs.3600/- and incurred a loss of 10%. At what price should he have sold the item to have gained a profit of 10%?
Options:
A)4000
B)4100
C)4200
D)4300
E)4400
Rationale: Explanation:
10% loss means SP = 90% of CP
:. CP = Rs.3600x100/90 = Rs.4000.
The SP for a gain of 10% = 4000+10% of 4000 = 4000+400 =Rs4400.
Answer: Option E
Answer: E
Question: There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability Y that at least one will be orange?
Options:
A)Y=7/10
B)Y=3/5
C)Y=2/5
D)3/10
E)1/10
Rationale: Method 1
Probability that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10
Method 2
Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10
Method 3
Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue
= 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled)
= 1 - 3C2/5C2
= 1-(3/10) = 7/10
Answer :A
Answer: A
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)7m
B)8m
C)4m
D)3m
E)2m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:E
Answer: E
Question: How many numbers between 10 - 99 yield a reminder of 8 when divided by 10 and also yield a remainder of 2 when divided by 8?
Options:
A)One
B)Three
C)Two
D)Five
E)Four
Rationale: Answer = B) Three
Numbers between 10 - 99 giving remainder 8 when divided by 10 = 18, 28, 38, 48, 58, 68, 78, 88, 98
The above Numbers giving remainder 2 when divided by 8 = 18, 58, 98 = 3
Answer: B
Question: In how much time will a train of length 100 m, moving at 54 kmph cross an electric pole?
Options:
A)sec
B)sec
C)sec
D)sec
E)sec
Rationale: Convert kmph to mps. 54 kmph = 54 * 5/18 = 15 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/15= 6.7 sec.
Answer:D
Answer: D
Question: There are 10 books on a shelf, of which 4 are paperbacks and 6 are hardbacks. How many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback?
Options:
A)75
B)120
C)210
D)246
E)252
Rationale: Paperbacks - 4, hardbacks - 6
5 books in total and at least 1 from each.
Total combinations for 5 books = (1pb, 4 hb) + (4pb, 1hb) + (3pb, 2hb) + (2pb, 3hb)
1pb, 4hb = 4c1*6c4 = 60
4pb,1hb = 4c4*6c1 = 6
3pb,2hb = 4c3*6c2 = 60
2pb,3hb = 4c2*6c3 = 120
Total combinations of 5 books = 60+6+60+120 = >246
Ans D.
Answer: D
Question: If an integer n is to be chosen at random from the integers 1 to 84, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
Options:
A)9/14
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 84, there are 42 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (42 + 12)/84
= 54/84
= 9/14
Ans is A
Answer: A
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
Options:
A)90
B)95
C)100
D)105
E)110
Rationale: 10 and 190 inclusive would mean there are 19 terms.
No need to add up all the terms and further divide by 19 since the terms are evenly spaced in ascending order from 10, 20, 30........190
The middle term is the average which is the tenth term = 100
C is the answer.
Answer: C
Question: 82*83*84*..89 what is the digit in units place?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: In the product
82*83*84 *85*86......*89
last( unit) digit will be zero as 82 * 85 will give zero as last (unit ) digit and further multiplication with any number will also give zero at unit place.
ANSWER:A
Answer: A
Question: A certain company’s profit in 1996 was 25 percent greater than its profit in 1995, and its profit in 1997 was 30 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?
Options:
A)5%
B)62.5%
C)33%
D)35%
E)38%
Rationale: Profit in 1995 - 100
Profit in 1996 - 125
%increae Profit in 1997 in comparison to 1995 = 25 + 125*30%= 62.5
Correct Option : B
Answer: B
Question: Average age of students of an adult school is 40 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
Options:
A)1200
B)120
C)360
D)240
E)None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 40x + 120*32 = (x + 120)36 ⇒ x = 120
So, Required no. of students after joining the new students
= x + 120 = 240.
Answer : D
Answer: D
Question: A sum of money is sufficient to pay A's wages for 20 days and B's wages for 30 days. The same money is sufficient to pay the wages of both for?
Options:
A)12days
B)15days
C)20days
D)18days
E)22days
Rationale: Let the total money be $x
A's 1day work = $ x/20
B's 1day work = $ x/30
A+B 1day work = $ x/12
Money is sufficient to pay the wages of both for 12days
Answer is A
Answer: A
Question: On a sum of money, the simple interest for 2 years is Rs. 326, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
Options:
A)15%
B)14.25%
C)8.58%
D)10.5%
E)11.5%
Rationale: Explanation:
The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum
= (R Ã— SI)/(2 Ã— 100)
Difference between the compound interest and simple interest = 340 - 326 = 14
(R Ã— SI)/(2 Ã— 100) = 14
(R Ã— 326)/(2 Ã— 100) = 14
R = 8.58%
Answer: Option C
Answer: C
Question: If 2x + 3y = 15; 2y + z = 19 and x + 2z = 29, what is the value of x + y + z ?
Options:
A)19
B)32
C)26
D)22
E)None of these
Rationale: On solving equation we get
x = 3, y = 3, z = 13
Answer A
Answer: A
Question: There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
Options:
A)71 ways
B)83 ways
C)85 ways
D)91 ways
E)98 ways
Rationale: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.
case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.
Thus, total number of ways is 7+84= 91 ways.
D
Answer: D
Question: An amount of Rs.3120 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
Options:
A)720
B)360
C)250
D)280
E)290
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 3120 = Rs. 720
Answer: A
Answer: A
Question: The length of the bridge, which a train 170 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)239
B)277
C)205
D)88
E)232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (170 + X)/30
= 25/2 ==> 2(170 + X) = 750 ==> X = 205 m.
Answer: C
Answer: C
Question: A man swims downstream 28 km and upstream 12 km taking 2 hours each time, what is the speed of the man in still water?
Options:
A)10
B)8
C)5
D)2
E)4
Rationale: 28 --- 2 DS = 14
? ---- 1
12 ---- 2 US = 6
? ---- 1 M = ?
M = (14 + 6)/2 = 10
Answer:A
Answer: A
Question: Combine terms: 12a + 26b -4b – 16a.
Options:
A)4a + 22b
B)-28a + 30b.
C)-4a + 22b
D)28a + 30b.
E)-30b+28a
Rationale: 12a + 26b -4b – 16a.
= 12a – 16a + 26b – 4b.
= -4a + 22b
correct answer C
Answer: C
Question: Kanul spent $35000 in buying raw materials, $40000 in buying machinery and 20% of the total amount he had as cash with him. What was the total amount?
Options:
A)$87952
B)$93750
C)$89542
D)$95820
E)$84256
Rationale: Let the total amount be x
then, (100-20)% of x = 35000+40000
80% of x = 75000
80x/100 = 75000
x = $93750
Answer is B
Answer: B
Question: In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
Options:
A)24
B)48
C)96
D)64
E)none
Rationale: Solution:
5 questions can be selected in the following ways,
2 question from first group and 3 question from second group Or 3 question from first group and 2 question from second group.
(4C2 * 4C3) +(3C4 *2C4),
= 24 +24 = 48
Answer: Option B
Answer: B
Question: A worker's daily wage is increased by 40% and the new wage is $35 per day. What was the worker's daily wage before the increase?
Options:
A)$20
B)$21
C)$24
D)$25
E)$28
Rationale: Let x be the daily wage before the increase.
1.4x = $35
x = $25
The answer is D.
Answer: D
Question: A division of a company consists of six men and six women. If two of these twelve employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
Options:
A)5/22
B)7/22
C)5/33
D)7/33
E)5/66
Rationale: The total number of ways to choose two representatives is 12C2=66.
The number of ways to choose two females is 6C2=15.
P(choosing two female representatives)=15/66=5/22
The answer is A.
Answer: A
Question: There are 12 towns grouped in four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that each every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required ?
Options:
A)72
B)90
C)96
D)144
E)128
Rationale: Explanation :
There are 3 towns.
Each town connects with the other town in 3 lines.
Hence total number of lines is 3 x 3 = 9.
Hence 1 zone has 9 direct links within it.
So 4 zones have 9 x 4 = 36 direct links within it.
Now, between zones/ interzone:
Consider a town in Zone 1. There are 9 towns outside this zone.
Hence 9 lines are required to connect between this town and the other 9 towns.
Similarly, there are 12 towns, each with 9 towns outside its own zone.
So, totally, there will be 9 x 12 / 2 = 9 x 6 = 54 lines inter zone (Divided by 2 comes here because, after half, it is repeated).
So, the total number of lines will be 36 (within zone) + 54 ( inter zone) = 90.
Answer : B
Answer: B
Question: In an examination, 25% of total students failed in Hindi, 48% failed in English and 27% in both. The percentage of these who passed in both the subjects is :
Options:
A)23
B)54
C)28
D)40
E)81
Rationale: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 25 + 48 â€“ 27 = 46
Therefore students who passed = 100 â€“ 46 = 54.
Answer: B
Answer: B
Question: A bag contains a total of 93 coins in the form of one rupee and 50 paise coins. If the total value of coins in the bag is Rs.56, find the number of 50 paise coins in the bag?
Options:
A)60
B)56
C)64
D)74
E)72
Rationale: Let the number of one rupee coins in the bag be x.
Number of 50 paise coins in the bag is 93 - x.
Total value of coins
[100x + 50(93 - x)]paise = 5600 paise
=> x = 74
ANSWER:D
Answer: D
Question: A train is moving at 6/7 of its usual speed. The train is 10 minutes too late. What is the usual time (in hours) for the train to complete the journey?
Options:
A)0.5
B)1
C)1.5
D)2
E)2.5
Rationale: new time = d / (6v/7) = 7/6 * usual time
10 minutes represents 1/6 of the usual time.
The usual time is 1 hour.
The answer is B.
Answer: B
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is
Options:
A)5
B)2
C)6
D)9
E)22
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
Answer: E
Answer: E
Question: A, B and C invested Rs.2400, Rs.7200 and Rs.9600 respectively, in a partnership business. Find the share of A in profit of Rs.9000 after a year?
Options:
A)1125
B)2400
C)7200
D)2500
E)2511
Rationale: Explanation:
2400:7200:9600
1:3:4
1/8 * 9000 = 1125
Answer: A
Answer: A
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
Options:
A)4
B)16
C)8
D)1
E)0
Rationale: Explanation :
Let the required number of mats be x
More mat-weavers, more mats (direct proportion)
More days, more mats (direct proportion)
⇒ 4 × 4 × x = 8 × 8 × 4
⇒ x = 2 × 2 × 4 = 16. Answer : Option B
Answer: B
Question: Sandy bought 65 books for $1180 from one shop and 55 books for $860 from another shop. What is the average price that Sandy paid per book?
Options:
A)$13
B)$15
C)$17
D)$19
E)$21
Rationale: average price per book = (1180 + 860) / (65 + 55) = 2040 / 120 = $17
The answer is C.
Answer: C
Question: A rectangular lawn 70 m × 30 m has two roads each 5 metres wide, running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling the road at the rate of 4 per square metre.
Options:
A)2,000
B)1,800
C)1,900
D)1,700
E)None of these
Rationale: Total area of road
= Area of road which parallel to length + Area of road which parallel to breadth – overlapped road
= 70 × 5 + 30 × 5 – 5 × 5
= 350 + 150 – 25
= 500 – 25 = 475 m2
∴ Cost of gravelling the road
= 475 × 4 = 1900
Answer C
Answer: C
Question: Cream costs twice as much as skim milk. A certain brand of milk is 4/5 cream and 1/5 skim milk. What fraction of the cost of this brand is due to the cream?
Options:
A)3/4
B)4/5
C)5/6
D)7/8
E)8/9
Rationale: Let x be the cost of the skim milk in the mixture.
The cost of the cream is 4x*2 = 8x.
The total cost is x+8x = 9x and the fraction due to the cream is 8x / 9x = 8/9
The answer is E.
Answer: E
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 91000, then the share of B is?
Options:
A)A)44500
B)B)42000
C)C)44098
D)D)43007
E)E)44098
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 91000
Share of B = 6/13 (91000)
= Rs. 42000
Answer:B
Answer: B
Question: Find the average (arithmetic mean) of x and y if the average of x, y, and 50 is 20 more than the average of x, y, 50, and 70.
Options:
A)100
B)120
C)140
D)180
E)200
Rationale: consider "60 is 20 more than 40": 60 = 40 + 20
similarly
(x+y+50)/3 = (x+y+50+70)/4 + 20
(x+y+50)/3 = (x+y+120)/4 + 80/4
(x+y+50)/3 = (x+y+120+80)/4
(x+y+50)/3 = (x+y+200)/4
cross multiply
4(x+y+50) = 3(x+y+200)
4x+4y+200 = 3x+3y+600
4x-3x +4y-3y = 600 - 200
x + y = 400
so
(x+y)/2 = 400/2
(x+y)/2 = 200
thus the average of x and y is 200
E
Answer: E
Question: A spirit and water solution is sold in a market. The cost per liter of the solution is directly proportional to the part (fraction) of spirit (by volume) the solution has. A solution of 1 liter of spirit and 1 liter of water costs 30 cents. How many cents does a solution of 1 liter of spirit and 2 liters of water cost?
Options:
A)13
B)30
C)50
D)51
E)52
Rationale: Yes, ensure that you understand the relation thoroughly!
Cost per liter = K * Fraction of Spirit
30 cents is the cost of 2 liters of solution (1 part water, 1 part spirit). So cost per liter is 15 cents. Fraction of spirit is 1/2.
15 = K * (1/2)
K = 30
Cost per liter = 30 * (1/3) (1 part spirit, 2 parts water)
Cost for 3 liters = 30 * (1/3) * 3 = 50 cents
B. 30 cents
Answer: B
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)64/8kmph
B)64/3kmph
C)64/9kmph
D)64/6kmph
E)64/4kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24
= x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph
= 21 (1/3)kmph.
Answer: B
Answer: B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 60 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)30
B)35
C)18
D)12
E)38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (60 + 60)/12 => x = 5
Speed of each train = 10 m/sec.
= 5 * 18/5 = 18 km/hr.
Answer: Option C
Answer: C
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 15 minutes less than they can row it in still water. How long would they take to row down with the stream
Options:
A)45 or 23 minutes
B)63 or 12 minutes
C)69 minutes
D)19 minutes
E)25 minutes
Rationale: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-15))
giving t = 69
C
Answer: C
Question: The ratio between the length and the breadth of a rectangular park is 1 : 3. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 4 min, then the area of the park (in sq. m) is?
Options:
A)800 m
B)12000 m
C)36000 m
D)80000 m
E)30000 m
Rationale: Perimeter = Distance covered in 4 min. = (12000 x 4)/60 m = 800 m.
Let length = 1x metres and breadth = 3x metres.
Then, 2(1x + 3x) = 800 or x =100.
Length = 100 m and Breadth = 300 m.
Area = (100 x 300) m2 = 30000 m
E
Answer: E
Question: A set of 11 positive integers has an average of 30. Which of the following is the greatest possible value for the median of this set?
Options:
A)25
B)30
C)36
D)54
E)46
Rationale: for the median to be max , we should take all the values below meadian to be the lowest and the remaining values to be the same..
here 1 is the lowest value(positive int) so the lowest 5 int will equal 5..
remaining 6= 30*11-5=325..
therefore each valueof these 6 int =325/6=54
ans D
Answer: D
Question: The present ages of three persons in proportions 3 : 7 : 5. Eight years ago, the sum of their ages was 51. Find their present ages (in years).
Options:
A)8, 20, 28
B)16, 28, 36
C)15,35,25
D)18, 24, 32
E)None of these
Rationale: Explanation:
Let their present ages be 3x, 7x and 5x years respectively.
Then, (3x - 8) + (7x - 8) + (5x - 8) = 51
15x = 75
x = 5
Their present ages are 3x = 15 years, 7x = 35 years and 5x = 25 years respectively.
Answer: C
Answer: C
Question: The diagonal of a square is the height in an equilateral triangle. If the side of the square is x, what is the side of the equilateral triangle in terms of x?
Options:
A)√(2/3) × x
B)2/√3 × x
C)√3x
D)√(8/3) × x
E)2√3 × x
Rationale: The diagonal of the square
x* sqrt(2)
If that's the altitude of the equilateral triangle, the formula for which is side * sqrt(3)/2
Side is 2 sqrt(2)* x/ sqrt(3)
Answer: (Option D)
Answer: D
Question: What approximate value should come in place of the question mark (?) in the following equation’?
3 3⁄5 of 157.85 + 39% of 1847 = ? – 447.30
Options:
A)1200
B)1500
C)1600
D)1800
E)2100
Rationale: ? ≈ 18⁄5 × 160 + 40⁄1000 × 1850 + 450
≈ 576 + 740 + 450 ≈ 1760 ≈ 1800
Answer D
Answer: D
Question: Calculate the positive root of the polynomial (x - 1)(x - 2)(x - 3)(x - 4)- 63.
Options:
A)5+√37/2
B)4+√37/2
C)3+√37/2
D)2+√37/2
E)6+√37/2
Rationale: Note that
(x - 1)(x - 2)(x - 3)(x - 4) - 63 = [(x - 2)(x - 3)][(x -1)(x - 4)] - 63
= (x2-5x + 6)(x2 - 5x + 4) - 63
= [(x2 - 5x + 5 + 1)(x2 - 5x + 5 -1)] - 63
= [(x2 - 5x + 5)2 - 1] - 63
= (x2 -5x + 5)2 - 64
= (x2 - 5x + 5 + 8)(x2 -5x + 5 - 8)
= (x2 - 5x + 13)(x2- 5x - 3):
The polynomial x2 - 5x + 13 has no real roots, while the polynomial x2 -5x - 3 has roots
x=5+-√37/2.
since 5-√37/2<0,
the only positive root is 5+√37/2
correct answer A
Answer: A
Question: If 1/(x+3)+1/(x-3)=1/(x+3), what is the value of x?
Options:
A)2
B)3
C)-1
D)-2
E)-3
Rationale: If we solve the question, we get x=-3.
Option: E
Answer: E
Question: A octagon marked 1, 2, 3, 4, 5,6,7 and 8 on its eight sides. four colors, pink, yellow,green and blue are used to paint the eight sides of the octagon. If the adjacent faces are painted with the different colors, in how many ways can the octagon be painted?
Options:
A)6
B)4
C)27
D)12
E)8
Rationale: If the base of the Octagon is pink, then in order the adjacent faces to be painted with the different colors, the top must also be pink. 6 side faces can be painted in Yellow-Blue-Green Yellow-Blue-Green OR Blue-Green-Yellow Blue-Green-Yellow(2 options).
But we can have the base painted in either of the three colors, thus the total number of ways to paint the Octagon is 4*2=8.
Answer:E.
Answer: E