divelab/Sys2Bench huggingface dataset:
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 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)5
C)8
D)13
E)15
Rationale: Total # of students = 40
Avg # of books per student = 2
Total # of books = 40*2 = 80
# of student borrowed at least 3 books = 40-2-12-10 = 16
# of books borrowed by above 16 students = 80-(12*1)-(10*2) = 48
Considering that 15 out of above 16 students borrowed only 3 books, # of books borrowed = 15*3 = 45
So maximum # of books borrowed by any single student = 48-45 = 3
option A
Answer: A
Question: The some of present ages of father and son is 60.If 6 years ago fathers age was five times the sons age,then what will be sons age after six years??
Options:
A)15
B)18
C)20
D)22
E)24
Rationale: Let f nd s be the present ages of father nd son
f + s = 60
f = 60 - s
(f-6) = 5(s-6)
f-6 = 5s - 30
f = 5s - 24
Equate "f"
60 - s = 5s - 24
6s = 84
s = 14
f = 60 - 14
f = 46
Present age of son is 14
Age of son after 6 years = 14+6 = 20
ANSWER:C
Answer: C
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. Find out the age of the youngest child?
Options:
A)9
B)8
C)7
D)6
E)4
Rationale: Let the age of the youngest child =x
Then, the ages of 5 children can be written as x,(x+3),(x+6),(x+9) and (x+12)
x+(x+3)+(x+6)+(x+9) +(x+12)=50
⇒5x+30=50⇒5x=20⇒x=205=4
Answer is E.
Answer: E
Question: A number when divided by a divisor leaves a remainder of 30. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Options:
A)12
B)13
C)35
D)43
E)59
Rationale: Let the number is N, the divisor = D,
I will make the two equations-
N = xD+30
2N = yD+11
where x and y are integers
Solving them: D(y-2x) = 43
as D is also integer and 43 is a prime number, the D should be 43 to satisfy the above equation.
Hence answer is 'D'
Answer: D
Question: Two employees X and Y are paid a total of Rs. 600 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)s.200.72
B)s.250.72
C)s.272.72
D)s.300.72
E)s.310.72
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 600
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 600
⇒ y[12/10 + 1] = 600
⇒ 22y/10 = 600
⇒ 22y = 6000
⇒ y = 6000/22 = Rs.272.72
C
Answer: C
Question: If x and y are positive real numbers such that x + y = 1, which of the following could be the value of 100x + 300y?
I. 80
II. 150
III. 299
Options:
A)II only
B)III only
C)I and II
D)I and III
E)II and III
Rationale: We know that x and y are both between 0 and 1.
The minimum limit of 100x + 300y is 100, when x is close to 1 and y is close to 0.
The maximum limit of 100x + 300y is 300, when x is close to 0 and y is close to 1.
The expression can take on any value between 100 and 300.
The answer is E.
Answer: E
Question: A train covers a distance of 18 km in 3 min. If it takes 4 sec to pass a telegraph post, then the length of the train is?
Options:
A)370
B)380
C)390
D)400
E)410
Rationale: Speed = (18/3 * 60) km/hr = (360 * 5/18) m/sec = 100 m/sec.
Length of the train = 100 * 4 = 400 m.
Answer: Option D
Answer: D
Question: The average runs scored by a batsman in 15 matches is 30. In the next 20 matches the batsman scored an average of 15 runs. Find his average in all the 30 matches?
Options:
A)31.56
B)25.65
C)21.43
D)28.36
E)27.96
Rationale: Total score of the batsman in 15 matches = 450.Total score of the batsman in the next 20 matches = 300.Total score of the batsman in the 35 matches = 750.Average score of the batsman = 750/35 = 21.43.Answer: C
Answer: C
Question: 16 boys or 24 girls can construct the wall in 6 days. the number of days that 8 boys and 6 girls Will take to construct?
Options:
A)7 days
B)14 days
C)6 days
D)8 days
E)9 days
Rationale: Explanation:
16 boys =24 girls, 1 boy = 24/16 girls
1 boy = 6/4 girls
8 boys +6 girls = 8 Ã— 6/4 + 12 = 12 + 6 = 18 girls
8 days to complete the work
Answer: Option D
Answer: D
Question: In how many ways can a leap year have 53 Sundays?
Options:
A)365C7
B)7
C)4
D)5
E)6
Rationale: Explanation :
In a leap year there are 366 days i.e. 52 weeks + 2 extra days.
So, to have 53 Sundays one of these two days must be a Sunday.
This can occur in only 2 ways.
i.e. (Saturday and Sunday) or (Sunday and Monday).
Thus, the required number of ways is 2.
Answer : D
Answer: D
Question: If the tens digit of positive integers h, y are 6, how many values of the tens digit of 2(h+y) can be there?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: If the tens digit of positive integers h, y are 6, how many values of the tens digit of 2(h+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If h=y=60, 2(h+y)=240 is derived. If h=y=69, 2(h+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Answer: C
Question: By investing Rs. 1620 in 8% stock, Michael earns Rs. 135. The stock is then quoted at:
Options:
A)96
B)70
C)75
D)80
E)100
Rationale: To earn Rs. 135, investment = Rs. 1620.
To earn rs 8 investment = (1620/135*8) = 96
Market value of rs 100 stock = rs 96
ANSWER A
Answer: A
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 1500 widgets?
Options:
A)2 hour and 20 minutes
B)2 hour and 24 minutes
C)2 hour and 30 minutes
D)2 hour and 36 minutes
E)2 hour and 40 minutes
Rationale: (350+250)t=1500
600t=1500
t=5/2
t=2 hour and 30 minutes
Answer: C
Answer: C
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 8 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Answer:	Part filled by A + B + C in 1 hour = 1/4 + 1/8 + 1/8= 1/2
All the three pipes together will fill the tank in 2 hours.
Answer: A
Answer: A
Question: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?
Options:
A)20
B)15
C)18
D)40
E)25
Rationale: No of ways = 10+ 15 = 25
ANSWER E
Answer: E
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)7:3
B)4:9
C)4:3
D)2:3
E)4:9
Rationale: 12:9
= 4:3
Answer:C
Answer: C
Question: A man pointing to a photo says "The lady in the photograph is my nephew’s maternal grandmother". How is the lady in the photograph related to the man’s sister who has no other sister ?
Options:
A)Cousin
B)Sister-in-law
C)Mother
D)Mother-in-law
E)None of these
Rationale: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister.
ANSWER:C
Answer: C
Question: Which of the following is a multiple of 4!+6?
Options:
A)2!+3
B)4!+12
C)5!+6
D)5!+30
E)8!+12
Rationale: considering prime factors:
4! + 6 = 4 * 3 * 2 + 6 = 6(4 + 1) = 6 * 5 = 2 * 3 * 5
So the correct answer is the one which is a multiple of 2, of 3 and of 5.
ANSWER:D
Answer: D
Question: Aden and Brad can do a piece of work in 18 days. Brad can Cody can do it in 24 days and Cody and Aden can do it in 36 days. If Aden, Brad, Cody work together, in how many days will they finish the work?
Options:
A)10 days
B)12 days
C)14 days
D)16 days
E)17 days
Rationale: (Aden + Brad)’s 1 day’s work = 1/18
(Brad + Cody)’s 1 day’s work = 1/24
(Cody + Aden)’s 1 day’s work = 1/36
Therefore, 2 (Aden + Brad + Cody)’s 1 day’s work = 1/18 + 1/24 + 1/36
= (4 + 3 + 2)/72
= 9/72
= 1/8
(Aden + Brad + Cody)’s 1 day’s work = 1/2 × 8 = 1/16
Therefore, Aden, Brad, Cody together will complete this work in 16 days. ANSWER : D
Answer: D
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)9
B)8
C)6
D)4
E)2
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: B
Question: The average age of 37 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
Options:
A)35 years
B)45 years
C)51 years
D)52 years
E)None of these
Rationale: Explanation:
Age of the teacher = (38 * 15 - 37 * 14) years = 52 years. Answer: D
Answer: D
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)257 m
B)632 m
C)245 m
D)737 m
E)243 m
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C
Answer: C
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 5000. He sold both the items together for Rs. 25000. What percentage of profit did he make?
Options:
A)1.00%
B)15.21%
C)41.10%
D)19.04%
E)10.00%
Rationale: The total CP = Rs. 16000 + Rs. 5000
= Rs. 21000 and SP = Rs. 25000
Profit(%) = (25000 - 21000)/21000* 100
= 19.04%
Answer: D
Answer: D
Question: A father is now three times as old as his son. Seven years back, he was four times as old as his son. The age of the son (in years) is
Options:
A)12
B)15
C)18
D)20
E)21
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-7 = 4*(S-7)
3S-7 =4S-28
S=21
F=63 years
ANSWER:E
Answer: E
Question: If 'a' and 'b' are non-zero numbers such that their sum is five times the product, what is the value of 1/a + 1/b?
Options:
A)4
B)5
C)6
D)10
E)15
Rationale: a+b = 5ab
1/a + 1/b = (b + a)/(ab) = 5.
The answer is B.
Answer: B
Question: The G.C.D of 1.08, 0.36 and 0.9 is
Options:
A)0.13
B)0.17
C)0.18
D)0.12
E)0.11
Rationale: Given numbers are 1.08, 0.36 and 0.90.
H.C.F of 108, 36 and 90 is 18.
H.C.F of a given numbers = 0.18
Answer:C
Answer: C
Question: A shipment of 250 smartphones contains 76 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
Options:
A)1/250
B)1/84
C)1/11
D)1/9
E)1/3
Rationale: Probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = (76/250)
Probability of chosing one defective phone from a lot of 249(we already picked one) which ontains 75(we already picked one) defective phones is = (75/249)
Combined probability of series of events = product of the probabilities = (76/250)*(75/249)
76/250 is close to (7/23) and (75/249)= (25/83)
so answer is (7/23)*(25/83) = (1/11)
So, answer will be C
Answer: C
Question: Of the following values of n, the value of (-1/3 )^(-n) will be greatest for n =
Options:
A)3
B)-3
C)0
D)-2
E)2
Rationale: imo -2
(-1/3)^-2=
1/(1/9)=9
oops i meant 2
E
Answer: E
Question: The sum of four consecutive even numbers is 140. What would be the smallest number?
Options:
A)32
B)88
C)70
D)123
E)12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 =140 => x = 18
Smallest number is: 2(x - 2) = 32
Answer: A
Answer: A
Question: Carol budgeted 18 dollars for gifts for each of the 15 people on her Christmas list. After a disagreement with some of her neighbors, she reduces her Christmas list to 10 people. How much can she spend on each?
Options:
A)20
B)27
C)18
D)23
E)30
Rationale: A1*P1=A2*P2
18*15=A2*10 => A2=27
Answer:B
Answer: B
Question: In how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: number of ways = 2*2!*2! = 8
Answer is B
Answer: B
Question: A goods train runs at the speed of 72 km/hr and crosses a 260 m long platform in 26 sec. What is the length of the goods train?
Options:
A)278
B)166
C)151
D)260
E)109
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 260)/26 = 20
x = 260 m.
Answer:D
Answer: D
Question: If '+' means ' ÷ ', '-' means '×', '' means '-'' means '+', then (280 + 1020) - 86 is -------.
Options:
A)70
B)112
C)-392
D)58
E)None
Rationale: (280/1020)*86
14/51 * 86
1204/51
Getting a fraction...
So none...
ANSWER:E
Answer: E
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1200 per sq.metre.
Options:
A)Rs. 15,000
B)Rs. 24,750
C)Rs. 15,600
D)Rs. 16,500
E)None
Rationale: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (1200 x 20.625)
= Rs.24,750.
Answer B
Answer: B
Question: When two different numbers are divided by a certain divisor the remainders are 147 and 192. When the sum of the two numbers is divided by the same divisor the remainder is 38: Find the divisor.
Options:
A)300
B)301
C)302
D)303
E)304
Rationale: Let divisior be x.so 1st no.=a+147
2nd no=b+192.
After adding:(a+147+b+192)/x=>a+b+339/x
Remainder of above expression is 38(given).so rem[a+b+(301+38)]/x=>38 therefore x would be 301.
ANSWER:B
Answer: B
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?
Options:
A)0.6976
B)0.783
C)0.986
D)1.243
E)1.3445
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: A
Question: A carpenter worked alone for 1 day on a job that would take him 4 more days to finish. He and another carpenter completed the job in 2 more days. How many days would it have taken the second carpenter to do the complete job working alone?
Options:
A)5
B)7
C)9
D)14
E)24
Rationale: A carpenter worked only 1 day on something that takes him 4 MORE days.
Means;
Carpenter finishes his work in 5 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/5 AND 1/x
To complete 1 work:
First guy worked for 3 days @ rate=1/5 per day.
Second one worked for 2 days @ rate=1/x per day
Expression:
Days*Rate=Work
3*1/5+2*1/x=1
3x+10=5x
2x=10
x=5 days.
Ans:A
Answer: A
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.16
B)7.19
C)7.13
D)7.15
E)7.11
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
Answer: D
Question: Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
Options:
A)30
B)90
C)120
D)168
E)188
Rationale: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232
So, in the image we know that the number of students in the zone with the black boundary = 232
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 400, we can write:
232 +b+w= 400
Or,b+w= 400 - 232 = 168
That is,b= 168 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 168
D
Answer: D
Question: If points A and B are (6-1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Answer: A
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 50% of that number?
Options:
A)A)148
B)B)210
C)C)105
D)D)248
E)E)258
Rationale: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 50/100 = 210/2 = 105
ANSWER:C
Answer: C
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/4 and |b| = 1/2, which of the following CANNOT be the result of a + b?
Options:
A)-1
B)-1/4
C)3/4
D)-3/4
E)1/4
Rationale: |a| = 1/4
Absolute value of 'a' can have two values = 1/4 and -(1/4)
|b| = 1/2
Absolute value of 'b' can have two values = 1/2 and -(1/2)
Now different combinations of a + b are as follows:
a + b = (1/4) + (1/2) = 3/4
- a - b = -(1/4) - (1/2) = -3/4
a - b = (1/4) - (1/2) = -(1/4)
-a + b = -(1/4) + (1/2) = 1/4
Cross verifying with the given options, left over option is A.
Answer: A
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing?
Options:
A)2
B)4
C)12
D)0
E)13
Rationale: E13This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next.
Answer: E
Question: A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)280 meter
B)240 meter
C)210 meter
D)200 meter
E)None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 34
=> 300+L = 15×34 = 510
=> L = 510-300 = 210 meter
Answer: Option C
Answer: C
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
Options:
A)Rs.2389
B)Rs.2380
C)Rs.2317
D)Rs.2329
E)Rs.2318
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs.2380.
Answer: B
Answer: B
Question: The least umber of five digits which is exactly
divisible by 12,15 and 18 is?
Options:
A)10000
B)10012
C)10015
D)10018
E)10080
Rationale: Least number of five digits is 10000
L.C.Mof 12,15,18 s 180.
On dividing 10000 by 180,the remainder is 100.
Therefore required number=10000+(180-100)
=10080.
Option E
Answer: E
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
Options:
A)52
B)32
C)62
D)25
E)20
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER A
Answer: A
Question: The product X of two prime numbers is between 17 and 60. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =
Options:
A)18
B)29
C)37
D)44
E)57
Rationale: Option BC can be ruled out as they themselves are prime numbers
18 = 2*9 = 3*6 >> Ignore
44 = 2 * 22 = 4 * 11 >> Ignore
57 = 3*19 >> Answer
Answer = E
Answer: E
Question: Which of the following is a pair of Co - Primes ?
Options:
A)14,35
B)18,25
C)31,92
D)32,62
E)18,43
Rationale: Co Primes - two numbers are said to be co prime if their HCF is 1.
18 and 25 are co prime numbers. ANSWER : B
Answer: B
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 3-cent stamps she could have bought ?
Options:
A) 5
B) 10
C) 15
D) 20
E) 25
Rationale: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.03y
=> 2.65 = 0.30x + 0.20x + 0.03y
=> 265 = 50x + 3y
So Max value of 50x < 265 = 250
Hence y = 5
Answer - A
Answer: A
Question: A committee is reviewing a total of 40x black-and-white films and 10y 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 of the selected films are in color?
Options:
A)50/52
B)55/52
C)60/52
D)40/52
E)30/52
Rationale: Say x=y=10. In this case we would have:
40x=400 black-and-white films;
10y=100 color films.
y/x%=10/10%=1% of the black-and-white films, so 4 black-and-white films and all 100 color films, thus total of 104 films were selected.
Color films thus compose 100/104=50/52 of the selected films.
Answer: A
Answer: A
Question: For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(28)?
Options:
A)2
B)7
C)11
D)13
E)17
Rationale: f(28) = 2*4*6*8*10*12*14*16*18*20*22*24*26*28
The greatest prime factor in this list is 13.
The answer is D.
Answer: D
Question: IF 2+3=13 ; 3+5=31 ; 5+7=59, Then 7+9=?
Options:
A)95
B)86
C)67
D)98
E)89
Rationale: 2 X 2 + 3^2 = 4 + 9 = 13
3 X 2 + 5^2= 6 + 25 = 31
5 X 2 + 7^2= 10 + 49 = 59
and
7 X 2 + 9^2= 14 + 81 = 95
ANSWER:A
Answer: A
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 70. Find the average marks of all the students?
Options:
A)52.5
B)52.9
C)52.1
D)58.75
E)42.5
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 70 = 3500
Sum of the marks for the class of 80 students =
1200 + 3500 = 4700
Average marks of all the students = 4700/80
= 58.75
Answer:D
Answer: D
Question: In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water?
Options:
A)11
B)15
C)22
D)18
E)25
Rationale: Let the speed of motor boat instill water be X kmph
Then, speed in downstream = (X + 2) km
and. speed in upstream = (X - 2) kmph
Time taken to row 10km & back = (10/X+2,10/X-2)
10/X+2 + 10/X-2 = 55/60
11X2 - 240X - 44 = 0
(X - 22)(11x + 2) = 0
X = 22 or X = -2/11
Then X = 22 kmph
Answer is C.
Answer: C