divelab/Sys2Bench huggingface dataset:
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
Options:
A)60.0
B)50.0
C)40.0
D)30.0
E)20.0
Rationale: Let us first find the distance d jogged
distance = rate × time = (12 km / hr) × 30 minutes
= (12 km/hr) × 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 × 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer is E)20.000
Answer: E
Question: Insert the missing number.
3, 5, 6,10 , 9, 15, 12, 20, 15, (....)
Options:
A)25
B)20
C)10
D)30
E)15
Rationale: Explanation:
There are two series, beginning respectively with 3 and 5. In one 3 is added and in another 5 is added.
The next number is 20 + 5 = 25.
Answer: A) 25
Answer: A
Question: If a fair 6-sided die is rolled three times, what is the probability that exactly one 2 is rolled?
Options:
A)25/216
B)50/216
C)25/72
D)25/36
E)5/6
Rationale: Total ways in which a 6-sided die can be rolled three times = 6*6*6 = 216
To get exactly one 2, there are three ways:
A 2 on the first roll and non 2 on other two rolls. This can be done in 1*5*5 = 25 ways.
The 2 could be on the second or third roll too. So total favorable cases = 25*3 = 75
Required Probability = 75/216 = 25/72
Answer (C)
Answer: C
Question: An equal number of desks and bookcases are to be placed along a library wall that is 15 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookcases are to be placed along the wall, then the space along the wall that is left over will be how many G meters long?
Options:
A)0.5
B)1
C)1.5
D)2
E)3
Rationale: Let x be the number of desks and bookcases that are placed along the library wall.
2x + 1.5x < 15
3.5x < 15
Since x is a non negative integer, the largest number x can be is 4.
When x is 4, the desks and bookcases take up 3.5 * 4 = 14m, leaving 1m of empty space.
Thus, I believe the answer is B) 1
Answer: B
Question: Find the least which when divided y 16,18,20, and 25 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Options:
A)17004
B)18000
C)18002
D)18004
E)18005
Rationale: Solution
L.C.M. of 16,18,20,25 = 3600. required number is of the form 3600 k + 4.
Least value of k for which (3600 k + 4 ) is divisible by 7 is k = 5.
So, Required number = (3600 × 5 + 4) = 18004. Answer D
Answer: D
Question: 53, 60, 56, 8, 54, 3, 8
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
Options:
A)18
B)29
C)46
D)53
E)55
Rationale: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 3, 8, 8, 53, 54, 56, 60
Median is very easy to tell - its 53. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 53? DE are already out.
Now, we have 18, 29 and 46 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 46. (Notice, if 18 is more than mean then 46 is also. If 28 is more than mean, 46 is also. )
Hence C it is!
Answer: C
Question: Double of Quarter of 4 percent written as a decimal is :
Options:
A)0.003
B)0.0005
C)0.25
D)0.02
E)None of these
Rationale: Explanation :
Solution: (2)*(1/4)*4% = 2*(1/4 * 1/100)= 0.02.
Answer : D
Answer: D
Question: There are 10 points on a circle. A hexagon can be formed by linking 5 of the 10 points. How many such hexagons are possible?
Options:
A)60
B)120
C)200
D)252
E)600
Rationale: 5 points can be selected out of 10 points in 10C5 ways
=10 !/5!*5!=252
Ans D
Answer: D
Question: 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability L that one more throw to this series will increase the mean score?
Options:
A)1/6
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability L is 1/2.C
Answer: C
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29 1/5
B)37 1/4
C)42
D)54
E)48
Rationale: After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 125 : 150 :: 35 : x <=> 125 x x = 150 x 35
=> x =150 x 35/125
=> x = 42.
Correct answer is C
Answer: C
Question: If it is true that x< 8 and 2x> -4, which of the following must be true?
Options:
A) -8 < x< 4
B) x> 2
C) x> -8
D) x< 4
E) None of the above
Rationale: Two points:
1) x< 8
2) 2x> -4 or x> -2
From 1 and 2: -2 < x< 8
(A) is not true because x could be > 4.
(B) is not true because x could be < 2.
(C) is true because x value is always > -8.
(D) is not true because x could be >4.
(E) is not true because C is true.
Answer: C
Question: If $ 5,000 is invested in an account that earns 10% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
Options:
A)$ 4
B)$ 8
C)$ 12
D)$ 16
E)$ 10
Rationale: Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.10/2)^2= 5410
Amount (SI) = P+PTR/100 = 5000+(5000*1*10/100)=5400
Difference = 5410-5400=10 $
E
Answer: E
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)10.39
B)10.37
C)10.3
D)10.31
E)10.32
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.Answer:C
Answer: C
Question: John found that the average of 15 numbers is 40. If 14 is added to each number then the mean of number is?
Options:
A)54
B)45
C)65
D)78
E)64
Rationale: (x+x1+...x14)/15 = 40
54
Option A
Answer: A
Question: Given a spinner with four sections of equal size labeled R, B, C, and D, what is the probability of NOT getting an R after spinning the spinner two times?
Options:
A)15/16
B)9/16
C)1/2
D)1/4
E)1/8
Rationale: The probability of NOT getting an R after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Answer: B
Question: On a 26 question test, five points were deducted for each wrong answer and eight points were added for each correct answer. If all the questions were answered, how many were correct, if the score was zero ?
Options:
A)10
B)12
C)11
D)13
E)16
Rationale: Explanation :
Let the correct answer be : x
Therefore wrong answers = (26 - x)
Total socre = 8x - 5(26-x) = 0
or, 13x = 130
Therefore x = 10
Answer : A
Answer: A
Question: Ramu bought an old car for Rs. 36000. He spent Rs. 15000 on repairs and sold it for Rs. 62900. What is his profit percent?
Options:
A)16%
B)17%
C)18%
D)58%
E)23%
Rationale: Total CP = Rs. 36000 + Rs. 15000
= Rs. 51000 and SP = Rs. 62900
Profit(%)
= (62900 - 51000)/51000 * 100
= 23%
Answer: E
Answer: E
Question: A thief is noticed by a policeman from a distance of 450 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Options:
A)150 m
B)200 m
C)170 m
D)100 m
E)350 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 450 - 100 = 350 m
E
Answer: E
Question: Dan’s car gets 32 miles per gallon. If gas costs $4/gallon, then how many miles can Dan’s car go on $46 of gas?
Options:
A)124
B)256
C)368
D)424
E)512
Rationale: 46/4 = 11.5 gallons
11.5*32 = 368 miles
The answer is C.
Answer: C
Question: R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Options:
A) None
B) Two
C) Four
D) Five
E) Seven
Rationale: R is the set of positive even integers less than 101, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=2,4,6,8,10,12...
S=4,16,36,64...
Numbers: 4, 16, 36, 64, and 100 are even integers (less than 101) that are in both sets.
Solution: Five
Answer: D
Answer: D
Question: If Z is a positive integer greater than 1, what is the sum of the multiples of Z from Z to Z^2, inclusive?
Options:
A) Z(Z + 1)(Z-1)
B) Z^2(Z + 1)/2
C) Z^2(Z-1)
D) (x^3 + 2x)/2
E) x(x-1)^2
Rationale: Ans :- B=Z^2(Z + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
Answer: B
Question: Out of eight crew members three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.
Options:
A)864
B)863
C)865
D)1728
E)None
Rationale: Solution:
Required number of ways, = 3C2 *4! *4! = 1728.
Answer: Option D
Answer: D
Question: A 14% stock yields 8%.The market value of the stock is :
Options:
A)Rs. 175
B)Rs. 92
C)Rs. 112.50
D)Rs. 116.50
E)None of these
Rationale: solution
To obtain Rs. 8, investment = Rs. 100.
To obtain Rs. 14, investment = Rs.(100/8X14)= Rs. 175
∴ Market value of Rs. 100 stock = Rs.175
Answer A
Answer: A
Question: If the digits 27 in the decimal 0.00027 repeat indefinitely, what is the value of (10^5-10^3)(0.00027)?
Options:
A)0.27
B)0.027
C)27
D)0.0027
E)2.7e-06
Rationale: 99*0.27=26.73 approx. 27
Answer : C
Answer: C
Question: What is the remainder when 7^74 - 5^74 is divided by 2?
Options:
A)5
B)1
C)2
D)3
E)None of these
Rationale: easiest way for me: 7^74 - 5^74 = (49)^37-25^37 = (24*2+1)^37 - (24+1)^37 -> remainder is 1^37 - 1^37 = 0
Ans :E
Answer: E
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options:
A)145 m
B)176 m
C)268 m
D)129 m
E)218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
Answer:A
Answer: A
Question: If a 4-member subcommittee is to be formed from a certain 6-member committee, how many different such subcommittee are possible?
Options:
A)6
B)15
C)20
D)60
E)216
Rationale: Another way:
1st member can be selected in 6 ways
2nd can be selected in 5 ways
3rd can be selected in 4 ways
4th can be selected in 3 ways
So total ways : 360
But to avoid the similar scenarios 360/4!=15
B
Answer: B
Question: In a function they are distributing noble prize. In how many ways can 4 prizes be distributed among 5 boys when a boy gets any no. of prizes?
Options:
A)48
B)50
C)625
D)602
E)525
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the four prizes can be given in 5 ways, i.e. (5*5*5*5) ways = 54 ways = 625 ways Or nr ways = 54 ways = 625 ways
Answer: C
Question: If an object travels 90 feet in 3 seconds, what is the object’s approximate speed in miles per hour? (Note: 1 mile = 5280 feet)
Options:
A)17.36
B)20.45
C)23.87
D)26.92
E)29.56
Rationale: 90 feet/3 seconds = 30 feet/second
(30 feet/second)*(3600 seconds/hour)*(1 mile/5280 feet) = 20.45 miles/hour (approximately)
The answer is B.
Answer: B
Question: Rs.8000 become Rs.8652.8 in a certain interval of time at the rate of 4% per annum of C.I. Find the time?
Options:
A)6 years
B)8 years
C)9 years
D)3 years
E)2 years
Rationale: 8652.8 = 8000(26/25)N
(26/25)^2 = (26/25)N => N = 2
At the end of two years what will be the comp.Answer: E
Answer: E
Question: The mean of 50 observations was 36. It was found later that an observation 34 was wrongly taken as 23. The corrected new mean is :
Options:
A)36.0
B)36.5
C)36.24
D)36.12
E)36.22
Rationale: Explanation:
Correct Sum = (36 * 50 + 434 - 23) = 1825.
Correct mean = = 1811/50 = 36.5
Answer: E) 36.22
Answer: E
Question: On a ranch, a rancher can place a loop of rope, called a lasso, once in every 3 throws around a cow’s neck. What is the probability that the rancher will be able to place a lasso around a cow’s neck at least once in 3 attempts?
Options:
A)1/3
B)5/9
C)7/9
D)19/27
E)23/27
Rationale: P(missing all 3)=(2/3)^3=8/27
P(success on at least one attempt)=1-8/27=19/27
The answer is D.
Answer: D
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 10 cm?
Options:
A)827 cm2
B)216 cm2
C)285 cm2
D)178 cm2
E)190 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (10)
= 190cm2
Answer:E
Answer: E
Question: A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction Q of the selected films are in color?
Options:
A)1/130
B)1/5
C)3/13
D)10/13
E)30/31
Rationale: It's y/xpercentnot y/x.
If x=20 and y=10. Then:
20x=400 black-and-white films;
6y=60 color films.
y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose Q=60/62=30/31 of the selected films.
Answer: E.
Answer: E
Question: If the price has fallen by 14% what percent of its consumption be: increased so that the expenditure may be the same as before?
Options:
A)11 1/8%
B)11 1/5%
C)16 12/43%
D)17 7/9%
E)21 1/9%
Rationale: 100 â€“ 14 = 86
86------14
100------? => 16 12/43%
Answer: C
Answer: C
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?
Options:
A)Equal to 3
B)Less than 3
C)More than 10
D)Less than 10
E)none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10
ANSWER:C
Answer: C
Question: A train 345 m long passed a pole in 15 sec. How long will it take to pass a platform 760 m long?
Options:
A)76 sec
B)43 sec
C)45 sec
D)15 sec
E)16 sec
Rationale: Speed = 345/15 = 23 m/sec.
Required time = (345 + 760)/23
= 48 sec.
Answer:B
Answer: B
Question: In a series of four football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 4 draws in the series?
Options:
A)24/576
B)125/864
C)1/25
D)1/256
E)1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 4 draws in 4 matches is (1/4)^4=1/256.
Answer: D.
Answer: D
Question: A flight takes off at 2.00 a.m. from a place at 18N 10E and landed 10 hours later at a place with co-ordinates 36N 70W. What is the local time when the plane landed?
Options:
A)6.00 a.m.
B)6.40 a.m.
C)7.00 a.m.
D)7.40 a.m.
E)8.00 a.m.
Rationale: Time difference between places will be 4*(70+10) minutes = 320 min =
5 hrs 20 min
as change of 1 degree in longitude cause change of 4 minutes in time.
and that change is 80 degrees here.
so when plane land. time will be = 2.00 + 10.00 -5.20 = 6.40 a.m.
ANSWER:B
Answer: B
Question: If log 27 = 1.401, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.998
Rationale: log 27 = 1.401
log (3cube ) = 1.401
3 log 3 = 1.401
log 3 = 0.467
log 9 = log(3square ) = 2 log 3 = (2 x 0.467) = 0.934.
Answer: Option A
Answer: A
Question: 95 80 85 65 50 85 35 ? ?
Options:
A)25 15
B)25 85
C)20 85
D)85 35
E)25 75
Rationale: 95-15=80
again 85
80-15=65
65-15=50
again 85
50-15=35
35-15=20
again 85
then answer is 20 ,85
ANSWER:C
Answer: C
Question: A, B, C subscribe Rs. 50,000 for a business. If A subscribes Rs. 4000 more than B and B Rs. 5000 more than C, out of a total profit of Rs. 35,000, what will be the amount A receives?
Options:
A)14700
B)15700
C)16700
D)18700
E)24700
Rationale: Total amount invested = 50000
Assume that investment of C = x.
Then investment of B = 5000 + x ,
Investment of A = 4000+5000+x = 9000+x
x + 5000+x + 9000+x = 50000
=> 3x + 14000 = 50000
=> 3x = 50000 – 14000 = 36000
=> x = 36000/3 = 12000
=> Investment of C = x = 12000 ,
Investment of B = 5000 + x = 17000,
Investment of A = 9000+x = 21000
Ratio of the investment of A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12
Share of A = Total Profit * 21/50 = 35000 * 21/50 = 700*21 = 14700
Answer is A
Answer: A
Question: Suppose f(x) is an odd function for which f(x + 2) = f(x) for all x, and
f(x) = x2nd for xε2 (0,1). Compute f(-3/2) + f(1).
Options:
A)-1
B)-1/2
C)-1/4
D)1/4
E)1/2
Rationale: Because f is periodic, we know that f(-3/2) = f(1/2) = (1/2)2 = 1/4. Because f
is odd, we know that f(1) = -f(-1), but because f is periodic, f(1) = f(-1). Therefore,
f(1) = 0 and the answer is 1/4.
correct answer D
Answer: D
Question: Six men and six women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?
Options:
A)5!*6!
B)6!*6!
C)5!*7!
D)6!*7!
E)7!*7!
Rationale: The number of arrangements of n distinct objects in a row is given by n!.
The number of arrangements of n distinct objects in a circle is given by (n-1)!.
The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!
Now, 6 men in a circle can be arranged in (6-1)! ways and if we place 6 women in empty slots between them then no two women will be together. The # of arrangement of these 6 women will be 6! and not 5! because if we shift them by one position we'll get different arrangement because of the neighboring men.
So the answer is indeed 5!*6!.
A
Answer: A
Question: A man saves Rs 250 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
Options:
A)Rs 827.53
B)Rs 862.01
C)Rs 822.02
D)Rs 862.03
E)None of these
Rationale: Explanation:
=[250(21/20Ã—21/20Ã—21/20)+250(21/20Ã—21/20)+250(21/20)]=827.53
Option A
Answer: A
Question: A certain candy manufacturer reduced the weight of Candy Bar M by 40 percent buy left the price unchanged. What was the resulting percent increase in the price per ounce of Candy Bar M?
Options:
A)66.66
B)62.5
C)58
D)60
E)62
Rationale: assume 1oz candy cost $1 before.
now price remain same $1 but weight of candy reduces to 0.6 oz
new price of candy = 1/0.6 =1.6666
price increase 66.66 %
A
Answer: A
Question: What are the maximum value and minimum values of f(x) = |2sin(2x - pi/3) - 5| + 3
Options:
A)max10-min6
B)max11-min7
C)max12-min8
D)max13-min9
E)max14-min10
Rationale: -1 <= sin(2x - pi/3) <= 1 : range of a sine function
-2 <= 2sin(2x - pi/3) <= 2 : mulitply all terms of the double inequality by 2
-2 - 5 <= 2sin(2x - pi/3) - 5 <= 2 - 5 : add -5 to all terms of the inequality.
-7 <= 2sin(2x - pi/3) - 5 <= -3
3 <= |2sin(2x - pi/3) - 5| <= 7 : change the above using absolute value.
3 + 3 <= |2sin(2x - pi/3) - 5| + 3 <= 7 + 3 : add 3 to all terms of the double inequality.
The maximum value of f(x) is equal to 10 and the minimum value of f(x) is equal to 6.
correct answer is A)max10-min6
Answer: A
Question: A train 125 m long passes a man, running at 8 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)53
B)50
C)99
D)288
E)12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 8) km/hr. x - 8 = 45 ==> x = 53 km/hr.Answer: A
Answer: A
Question: Of the 5 numbers, whose average is 100, the first is one-fourth of the sum of the last 4. The first number is?
Options:
A)83.3
B)80
C)78.63
D)56.98
E)67.85
Rationale: Let the first number be x
sum of the 5 numbers = x+5x = 6x
6x/5 = 100
x = 100*5/6 = 83.3
Answer is A
Answer: A
Question: In how many different number of ways 4 men and 3 women can sit on a bench such that girls always sit together.
Options:
A)720
B)740
C)750
D)770
E)780
Rationale: 720
A)
Answer: A
Question: A division of a company consists of four men and six women. If two of these ten employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
Options:
A)1/6
B)1/5
C)1/4
D)1/3
E)1/2
Rationale: The total number of ways to choose two representatives is 10C2=45.
The number of ways to choose two females is 6C2=15.
P(choosing two female representatives)=15/45=1/3
The answer is D.
Answer: D
Question: If an item that originally sold for A dollars was marked up by x percent and then discounted by L percent, which of the following expressions represents the final price of the item?
Options:
A)(10,000z + 100z(x – y) – xyz)/10,000
B)(10,000z + 100z(y – x) – xyz)/10,000
C)(100z(x – y) – xyz)/10000
D)(100z(y – x) – xyz)/10000
E)10000 /(x – y)
Rationale: value of item =A ..marked up by x% = Ax/100
total value = A +ax/100 .discounted by L% on Total L/100 * ( A+Ax/100)
Final price =(A+ Ax/100) - L/100 ( A +Ax/100)
C
Answer: C
Question: The sum of the non-prime numbers between 40 and 50, non-inclusive, is
Options:
A)131
B)176
C)274
D)405
E)495
Rationale: The sum of the non-prime numbers between 40 and 50, non-inclusive, are {42, 44, 45, 46, 48, 49}.
6 times 40 something is approx north of 240
Hence the answer is (C) 274
Answer: C
Question: If 75 percent of a class answered the first question on a certain test correctly, 35 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
Options:
A)10%
B)(8) 20%
C)30%
D)50%
E)65%
Rationale: I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
20% appeared in the exam; however did not answer Question AQuestion B correctly
So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.
Now,
100 - [(75 - x) + x + (35 - x)] = 20 .......... values are in percent
x = 20 - 100 + 110
x = 30
Ans: C
Answer: C
Question: A bag contains 3 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
Options:
A)1/7
B)2/9
C)3/11
D)4/17
E)3/10
Rationale: Total number of balls = 3+2 = 5
n(S) = 5C3 = 5*4*3 / 3*2 = 10
n(E) = 2C2* 3C1 = 3
Probability = 3/10
Answer is E
Answer: E
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?
Options:
A)4
B)6
C)12
D)16
E)24
Rationale: The four digits available are 1,2,3 and 6
as the extensions can only be even numbers, the last digit has to be either 2 or 6
If it is 2...it leaves 1,3 and 6 for the first three digits...these can be arranged in 3! ways
If the last digit is 6...it leaves 1,2 and 3 for the first three digits...these can be arranged in 3! ways
Thus answer is 2*3! = 12 C
Answer: C