divelab/Sys2Bench huggingface dataset:
Question: If a certain sample of data has a mean of 22.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)14.0
C)17.0
D)23.5
E)26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5*SD=7.5. So the value must be either less than 22-7.5=14.5or more than 22+7.5=29.5.
Answer:B.
Answer: B
Question: There are three prizes to be distributed among six students. If no students gets more than one prize, then this can be done in?
Options:
A)10
B)45
C)5
D)20
E)None of these
Rationale: Explanation :
3 prize among 6 students can be distributed in 6C3 ways = 20 ways.
Answer : D
Answer: D
Question: The positive two-digit integers k and m have the same digits, but in reverse order. Which of the following must be a factor of k + m?
Options:
A)6
B)9
C)77
D)12
E)14
Rationale: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9
and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187
77 is multiple of 11
Answer : C
Answer: C
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)3944
B)3828
C)4176
D)5020
E)5000
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
ANSWER A
Answer: A
Question: If a*b denotes the greatest common divisor of a and b, then ((12*16)*(30*24)) = ?
Options:
A) 24
B) 12
C) 6
D) 4
E) 2
Rationale: The greatest common divisor of 12 and 16 is 4. Hence 12*16 = 4 (note that * here denotes the function not multiplication).
The greatest common divisor of 30 and 24 is 6. Hence 30*24 = 6.
Hence ((12*16)*(30*24)) = 4*6.
The greatest common divisor of 4 and 6 is 2.
Answer; E.
Answer: E
Question: If the cost price is 95% of selling price then what is the profit percentage.
Options:
A)5.26
B)5.16
C)5.61
D)5.52
E)5
Rationale: selling price=Rs100 : then cost price=Rs 95:profit =Rs 5.
Profit={(5/95)*100}%=5.26%
Answer is A.
Answer: A
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
Options:
A)3.5
B)4.0
C)4.2
D)4.9
E)4.6
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E
Answer: E
Question: A and B are two circles. The radius of A is thrice as large as the radius of B. What is the ratio between the areas of the circles?
Options:
A)1:8.
B)1:2.
C)1:4.
D)1:9
E)1:6.
Rationale: Given : The radius of A is thrice as large as the radius of B. => R(a) = 3*R(b). The radius are in ratio of 1:3 thus the area will be in the ratio of square of radius. 1:9. Hence D.
Answer: D
Question: Two goods trains each 680 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)228
B)65.28
C)48.32
D)27
E)21.1
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 680 + 680 = 1360 m.
Required time = 1360 * 6/125 = 65.28 sec.
Answer:B
Answer: B
Question: Look at this series: 5.3, 4.8, 4.3, 3.8, ... What number should come next?
Options:
A)3.7
B)3.5
C)3.6
D)3.4
E)3.3
Rationale: E
3.3
In this simple subtraction series, each number decreases by 0.5.
Answer: E
Question: How many positive integers less than 100 are neither multiples of 4 or 5.
Options:
A)a)30
B)b)60
C)c)32
D)d)33
E)e)34
Rationale: To answer this Q we require to know
1) multiples of 4 till 100 = 100/4 = 25
2) Multiples of 5 till 100 = 100/5 = 20
add the two 25+20=45 ; subtract common terms that are multiple of both 4 and 5..
LCM of 4 and 5 = 20
Multiples of 20 till 100 = 100/20 = 5 =
so total multiples of 4 and 5 = 45-5 = 40
ans = 100-40 = 60
B
Answer: B
Question: A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 8:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
Options:
A)26
B)30
C)36
D)38
E)40
Rationale: at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 8 strikes, there would be 7 intervals.
According to the question, the time spent in the strike and the interval is same.
At 6'o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs.
At 8'o clock, the 8 strikes and 7 intervals will take 2*(8+7) = 30 secs
B
Answer: B
Question: A cicketer Has a certain average for 10 innings, In the eleventh inning, he scorod 88 runs, thereby increasing his average by 6 runs. His new average is
Options:
A)18 runs
B)28 runs
C)48 runs
D)42 runs
E)46 runs
Rationale: Explanation:
Let average for 10 innings be x. Then,
(10x + 88)/11 = x + 6 => 11x + 66 = 10x + 88 => x = 22.
New average = (x + 6) = 28 runs.
Answer: B
Answer: B
Question: 252 can be expressed as a product of primes as:
Options:
A)2 x 2 x 3 x 3 x 7
B)2 x 2 x 2 x 3 x 7
C)3 x 3 x 3 x 3 x 7
D)2 x 3 x 3 x 3 x 7
E)7 x 3 x 3 x 3 x 7
Rationale: 252 = 2 x 2 x 3 x 3 x 7.
answer :A
Answer: A
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability that this product will be a multiple of 45?
Options:
A)1/32
B)1/28
C)1/24
D)1/16
E)1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability = 1/24. Answer C.
Answer: C
Question: How many minutes does it take John to type y words if he types at the rate of t words per minute?
Options:
A)x/y
B)y/t
C)xy
D)60x/y
E)y/(60x)
Rationale: time*rate=job --> time*t=y --> time=y/t.
Answer: B.
Answer: B
Question: The greatest number of four digits which is divisible by 10, 20, 40 and 60 is:
Options:
A)9200
B)9300
C)9400
D)9600
E)9700
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 10, 20, 40 and 60 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
ANSWER :D
Answer: D
Question: The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 9 years more than twice the age of the son.Find the present age of the father.
Options:
A)88
B)77
C)30
D)44
E)55
Rationale: Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+9 x=9 Hence father's present age = 3x+3 =[ (3 x 9) + 3] = 30 years.
Answer: C
Answer: C
Question: What is the remainder when 43^88 is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
88 has the form 4k so the units digit of 43^88 is 1.
The remainder when dividing by 5 is 1.
The answer is B.
Answer: B
Question: In order to obtain an income of Rs. 900 from 20% stock at Rs. 102, one must make an investment of
Options:
A)Rs.6000
B)Rs.4590
C)Rs.4560
D)Rs.4500
E)Rs.4570
Rationale: Explanation :
Market Value = Rs. 102.
Required Income = Rs. 900.
Here face value is not given. Take face value as Rs.100 if it is not given in the question
To obtain Rs.20(ie,20% of the face value 100), investment = Rs.102
To obtain Rs.900, investment = 102/20Ã—900=Rs.4590
Answer : Option B
Answer: B
Question: How much water should be added to 10 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
Options:
A)25 liters
B)27 liters
C)30 liters
D)32 liters
E)35 liters
Rationale: Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=10+x)))
2=5%*(10+x)-------->x=30
ANSWER:C
Answer: C
Question: Seller selling an apple for Rs.15, a Seller loses 1/6th of what it costs him. The CP of the apple is?
Options:
A)10
B)12
C)16
D)18
E)20
Rationale: SP=15Loss=CP16Loss=CP−SP=CP−15⇒CP16=CP−15⇒15 CP16=15⇒CP16=1⇒CP=16
C
Answer: C
Question: Car Dealership X, the total profit from sales increased by 9 percent over the previous years, while the number of cars sold decreased by 9 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
Options:
A)18%
B)19.78%
C)22%
D)23%
E)25%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.09x / 0.91 y = 109/91 (x/y)
Increase in profit per car = ((18/91) (x/y)) / (x/y) * 100 = 19.78%
Answer = B
Answer: B
Question: You are given with two ropes with variable width. However if we start burning both the ropes, they will burn at exactly same time i.e. an hour. The ropes are non-homogeneous in nature. You are asked to measure 45 minutes by using these two ropes.
How can you do it? Please note that you can’t break the rope in half as it is being clearly stated that the ropes are non-homogeneous in nature.
Options:
A)25 minutes
B)35 minutes
C)45 minutes
D)55 minutes
E)65 minutes
Rationale: Solution:
45 minutes
Explanation :
All you have to do is burn the first rope from both the ends and the second rope from one end only simultaneously. The first rope will burn in 30 minutes (half of an hour since we burned from both sides) while the other rope would have burnt half. At this moment, light the second rope from the other end as well. Where, the second rope would have taken half an hour more to burn completely, it will take just 15 minutes as we have lit it from the other end too.
Thus you have successfully calculated 30+15 = 45 minutes with the help of the two given ropes.
Answer C
Answer: C
Question: An even positive integer 'x' has 'y' positive integral factors including '1' and the number itself. How many positive integral factors W does the number 4x have?
Options:
A)4y
B)3y
C)16y
D)5y
E)Cannot be determined
Rationale: I tried for x=2,4 and 6. The integral factors W for x and 4x did not have any specific relation.
My answer is E.
Answer: E
Question: A trader bought a car at 30% discount on its original price. He sold it at a 50% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)7%
B)62%
C)12%
D)19%
E)5%
Rationale: Original price = 100
CP = 70
S = 70*(150/100) = 105
100 - 105= 5%
Answer: E
Answer: E
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L?
.
Options:
A)1/3.
B)1/2.
C)2.
D)3.
E)6
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 15 and L be 5, 15 - 5 = (15 + 5 )/2
Answer is D : 3
Answer: D
Question: If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?
Options:
A)-22.5
B)16
C)-10.5
D)-17.5
E)Cannot be determined
Rationale: Explanatory Answer
We know that the product of the roots of a quadratic equation ax2 + bx + c = 0 is c/a
In the given equation, x2 + mx + 24 = 0, the product of the roots = 24/1 = 24.
The question states that one of the roots of this equation = 1.5
If x1 and x2 are the roots of the given quadratic equation and let x1 = 1.5
Therefore, x2 = 24/1.5= 16.
In the given equation, m is the co-efficient of the x term.
We know that the sum of the roots of the quadratic equation ax2 + bx + c = 0 is-b/a = -m/a = -m
Sum of the roots = 16 + 1.5 = 17 = -17.5.
Therefore, the value of m = -17.5
correct choice is (D)
Answer: D
Question: Raviraj invested an amount of 10000000 at compound interest rate of 10 pcpa for a period of three years. How much amount will Raviraj get after three years?
Options:
A)12,310
B)13,21000
C)13,320
D)13,120000
E)13310000
Rationale: Amount = 10000000(1 + 10⁄100)3
= 10000000 × 11⁄10 × 11⁄10 × 11⁄10
= 13310000
Answer E
Answer: E
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 6 years the amount to be paid is?
Options:
A)8118
B)8127
C)8618
D)9490
E)8128
Rationale: A = 7500(26/25)6
= 9490
Answer: D
Answer: D
Question: A coin is tossed live times. What is the probability that there is at the least one tail?
Options:
A)31/32
B)15/46
C)12/87
D)45/96
E)3/2
Rationale: Explanation:
Let P(T) be the probability of getting least one tail when the coin is tossed five times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/32 ; P(T) = 1 - 1/32 = 31/32
Answer:A
Answer: A
Question: The average age of applicants for a new job is 35, with a standard deviation of 30. The hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age. Assuming that all applicants' ages are integers and that the endpoints of the range are included, what is the maximum number of different ages of the applicants?
Options:
A)8
B)16
C)31
D)18
E)34
Rationale: Minimum age = Average - 1 Standard deviation = 35 - 30 = 5
Maximum age = average + 1 Standard deviation = 35+ 30 = 35
Maximum number of different ages of the applicants = 35- 5 + 1 = 31
Answer C
Answer: C
Question: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
Options:
A)12,28
B)14,30
C)16,32
D)18,34
E)None of these
Rationale: Explanation:
Let the age of younger person is x,
Then elder person age is (x+16)
=> 3(x-6) = (x+16-6) [6 years before]
=> 3x-18 = x+10
=> x = 14.
So other person age is x + 16 = 30
Option B
Answer: B
Question: D and E are two points respectively on sides AB and AC of triangle ABC such that DE is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium DECB is 25:144 and BC=13 cm, then find the length of DE.
Options:
A)12
B)5
C)14
D)11
E)15
Rationale: ABC and ADE are similar triangles.
So (side of ABC/side of ADE)^2=169/25
side of ABC/side of ADE = 13/5
So the length of DE = 5
Answer - B
Answer: B
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer: B
Answer: B
Question: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 660-mile journey? Assume that the train makes no intermediate stops.
Options:
A)8
B)8.5
C)11
D)9.5
E)10
Rationale: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 660-mile journey? Assume that the train makes no intermediate stops.
I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)
Hour miles/hour Total miles
1 10 10
2 20 30
3 30 60
4 40 100
5 50 150
6 60 210
7 70 280
8 80 360
9 90 450
10 100 550
11 110 660
It takes a total of nine hours to cover the 660 mile distance.
ANSWER: C. 11
Answer: C
Question: Find the odd man out. 2, 3, 5, 9, 12, 17, 23
Options:
A)12
B)9
C)23
D)2
E)1
Rationale: Explanation :
2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 4 = 12
12 + 5 = 17
17 + 6 = 23
ie, 8 should have come in place of 9. Answer : Option B
Answer: B
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 30 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
Options:
A)50%
B)53%
C)54%
D)55%
E)57%
Rationale: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.75=45 Democrats are expected to vote for Candidate A;
40*0.30=12 Republicans are expected to vote for Candidate A.
Thus total of 45+12=57 registered voters are expected to vote for Candidate A, which is 57% of the total number of registered voters.
Answer: E.
Answer: E
Question: What annual installment will discharge a debt of $100 due in 3 years at 10% simple interest?
Options:
A)25.6
B)50.2
C)30.3
D)45
E)56
Rationale: Let each installment be x
[x + (x*10*1/100)] + [x + (x*10*2/100)] + x = 100
11x/10 + 12x/10 + x = 100
x = 30.3
Answer is C
Answer: C
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
Options:
A)17/26
B)17/25
C)17/21
D)17/20
E)14/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer:D
Answer: D
Question: Rs.8000 become Rs.9159.20 in a certain interval of time at the rate of 7% 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: 9159.20 = 8000(61/57)N
(61/57)^2 = (61/57)N => N = 2
At the end of three years what will be the comp.Answer: E
Answer: E
Question: A Glee club of 20 members is performing two songs for the school talent show. 50% of its members are part of the first one, and 60% are performing in the second one. How many Glee club members are performing in both songs at the talent show?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The total number of Glee club members is n=20.
The number of members performing the first song is 50% of it, thus
n (A)=50/100×20=10.
The number of members performing in the second one is 60%, thus
n (B)=60/100×20=12.
In order to calculate the number of Glee club members performing in both songs we can use the following equation:
n (AnB)=n (A)+n (B) -n =10+12-20=22-20=2.
ANSWER: C
Answer: C
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.
Options:
A)338
B)267
C)877
D)300
E)911
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11 => x/60 + x/50 = 11 => (5x + 6x)/300 = 11 => x
= 300 km
Answer:D
Answer: D
Question: Two trains 50 m and 120 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9 sec
B)14.8 sec
C)6.12 sec
D)10.8 sec
E)20.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 50 + 120 = 170 m.
Required time = 170 * 9/250 = 6.12
= 6.12 sec.
Answer: C
Answer: C
Question: A supplier undertakes to supply 2000 pieces of a particular item at Rs. 25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out. 50% of the items were rejected. what is the loss to the supplier?
Options:
A)Rs.12000
B)Rs.13000
C)Rs.14000
D)Rs.15000
E)None of these
Rationale: Explanation :
Solution: Total cost incurred = Rs. [100/125 * 25* (95% of 2000)]
= Rs. (100/125 * 25 *1900) = Rs. 38000.
Loss of the supplier = Rs. [38000-(25*1000)] = Rs. 13,000.
Answer : B
Answer: B
Question: The average of first 15 even numbers is?
Options:
A)10
B)11
C)12
D)16
E)14
Rationale: Sum of 15 even numbers = 15 * 16 = 240
Average = 240/15 = 16
ANSWER:D
Answer: D
Question: An ant walks an average of 600 meters in 10 minutes. A beetle walks 25% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
Options:
A)2.215.
B)2.5.
C)2.6
D)2.7
E)3.5.
Rationale: the ant walks an average of 600 meters in 10 minutes
600 meters in 5/30 hours
the beetle walks 25% less distance = 600-150=450 meters in 10 minutes
0.450 km in 5/30 = 5/30 hours
speed = 0.450*30/5 = 2.7 km/h
I guess option D should be 2.7
Answer: D
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
Options:
A)50
B)54
C)176
D)180
E)100
Rationale: 25x + 46 = 26(x â€“ 5)
x = 176
ANSWER C
Answer: C
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out 3 socks, how many different color combinations are possible in the selected pair of socks?
Options:
A)12
B)15
C)21
D)35
E)42
Rationale: Since here order of socks is not important then we'll have 7C3 i.e. 35 combinations.
Answer : D
Answer: D
Question: If Leon's income is Rs 16000, calculate his savings given that his income and expenditure are in the ratio 8:3.?
Options:
A)Rs.10000
B)Rs.7000
C)Rs.2500
D)Rs.2450
E)Rs.3000
Rationale: Let the income and the expenditure of the person be Rs.8x and Rs.3x respectively.
Income, 8x = 16000 => x = 2000
Savings = Income - expenditure = 8x - 3x = 5x
So, savings = Rs.10000
Answer: A
Answer: A
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 14^a and y = 9^b, which of the following is a possible units digit of xy?
Options:
A)1
B)6
C)5
D)7
E)8
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=14
a=2; X=196
a=3; X=2744........ Units digit repeat in a cycle of 4,6,4,6......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=9
b=2; Y= 81
b=3; Y= 729....... Units digit repeat in cycle of 9,1,9,1....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=4 and Y=9: Units digit of XY = 6
When X=4 and Y=1: Units digit of XY = 4
When X=6 and Y=9: Units digit of XY = 4
When X=6 and Y=1: Units digit of XY = 6
Only two possibilities for Units digit of XY i.e. 4 and 6.
Only 6 is given in answer choices, therefore answer is B
Answer: B
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 7 greater than the preceding term. Which of the following could not be a term in the sequence?
Options:
A)0
B)200
C)455
D)665
E)763
Rationale: Ans : B
Since 200 is not divisible by 7 , all the other options are divisible by 7
Answer: B
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 13 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: The class borrowed a total of 40*2 = 80 books.
The 27 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 13*2 = 38.
To maximize the number of books borrowed by 1 student, let's assume that 12 students borrowed 3 books and 1 student borrowed the rest.
80 - 38 - 3*12 = 6
The maximum number of books borrowed by any student is 6.
The answer is D.
Answer: D
Question: In a garden, there are three blue flowers, three red flowers, three green flowers, and three pink flowers. What is the probability that a florist will choose three flowers of the same color when randomly picking three flowers?
Options:
A)11/10
B)1/55
C)31/10
D)3/55
E)1/16
Rationale: Total number of ways to pick 3 flowers out of 12 = 12c3
12c3=12!/9!∗3!=220
Total number of favorable outcomes = 4
(Only 3 flowers per colour, so there is only one way all three flowers of any particular colour can be chosen. 4 colours mean 4 favorable outcomes)
Probability = 4/220=1/55
Answer: B
Answer: B