divelab/Sys2Bench huggingface dataset:
Question: From a Group of 8 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina
Options:
A)5/56
B)9/56
C)15/56
D)21/56
E)25/56
Rationale: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members George will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Lina = 6
Number of ways to form a 3 member team that includes George and excludes Lina = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Answer: C
Question: There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from first group.
Options:
A)2/7
B)6/35
C)8/25
D)75/89
E)3/175
Rationale: Please go through my solution and suggest any mistake.
Chances of selecting a white ball from group 1: 5/7----------------------Chances of selecting a white ball from group 2: 1/5
Thus combined probability of section of white ball from group 1:
3/5 x 5/7 = 3/7
Thus combined probability of section of white ball from group 2:
2/5 x 1/5 = 2/25
Out of these chances, chance of occurrence of first case : (3/7) / (3/7 + 2/25) = 75/89
D
Answer: D
Question: In 1995, the Jims spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jims cut back their water usage. By how much must the Jims have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
Options:
A)a)	33 1/3 %
B)b)	40 %
C)c) 50 %
D)d)	66 2/3 %
E)e)	100 %
Rationale: Let x be the water usage and c be the cost water of Jims.
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Answer: A
Question: In 10 years, P will be as old as Q is now. Twenty years ago, Q was twice as old as P was then. How old is P now?
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Q = P+10
Q-20 = 2(P-20)
P-10 = 2P-40
P = 30
The answer is A.
Answer: A
Question: Excluding stoppages, the speed of a bus is 72 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)7 min
B)8 min
C)9 min
D)10 min
E)55.8 min
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 67 km =(67/72)x60 = 55.8 min
answer : E
Answer: E
Question: Bruce and Bhishma are running on a circular track of length 600m. Speed of Bruce is 30 m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same direction. When will they meet again for the first time?
Options:
A)40
B)45
C)50
D)60
E)70
Rationale: Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of Bhishma, they will be together again as a person when completes the total length it starts retracing he same path and thus Arjun and Bhishma can be together again.
Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60 second.
D
Answer: D
Question: A snail, climbing a 20 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
Options:
A)12
B)16
C)17
D)20
E)21
Rationale: total transaction in two days = 4-2 = 2 feet
in 16 days it will climb 16 feet
on the 17th day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =17
ANSWER:C
Answer: C
Question: The total population of dogs in a community is estimated to be 50% male and 50% female.The total number of black dogs is 20% greater than the total number of male black dogs. If the total number of female dogs is eight times more than the number of female black dogs what percentage of male dogs is black?
Options:
A)84.4
B)70.2
C)80.1
D)60.8
E)62.5
Rationale: Since we are dealing in percentage let us pick 100 as the number of black male dogs.
That means that the total number of black dogs is= 120 (20% more),
therefore the number of black female dogs is 20.
The total number of female dogs is 8x the number of black female= 20*8=160 female dogs.
Male dogs are 50% of the dogs, and because there are 160 female dogs, then there must also be 160 male dogs
Therefore percentage of male dogs that are black= 100/160*100=62.5
Correct option is E
Answer: E
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)Rs.500
B)Rs.250
C)Rs.896
D)Rs.789
E)Rs.999
Rationale: Explanation:
a^2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 =Rs. 999
Answer : E
Answer: E
Question: A set of data consists of the following 6 numbers: 0, 2, 4, 6,10 and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
Options:
A)-1 and 9
B)4 and 4
C)3 and 5
D)2 and 6
E)0 and 8
Rationale: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding 0 and 8 , results in a value that would change the SD to the least. Hence E
Answer: E
Question: Of the 300 employees of a certain company, 65 are accountants. Two employees of the company will be selected at random. Which of the following is closest to the probability that neither of the employees selected will be an accountant?
Options:
A)0.3
B)0.4
C)0.5
D)0.6
E)0.7
Rationale: Total = 300
Accountants = 65
Non Accountants = 300 - 65= 235
Two employees of the company will be selected at random so probability that neither of the employees selected will be an accountant is
235 C 2 / 300 C 2 = 235 * 234 / 300 * 299 = 0.611 ~ 0.6
Hence D 0.6 is the correct answer
Answer: D
Question: A number when multiplied by 3 and then subtracted by 2 becomes the reverse of itself. Can you find out which smallest number is that?
Options:
A)28
B)11
C)10
D)35
E)47
Rationale: A
28 is the required number.
28 * 3 - 2 = 82.
Answer: A
Question: In country Z, 10% of the people do not have a university diploma but have the job of their choice, and 30% of the people who do not have the job of their choice have a university diploma. If 40% of the people have the job of their choice, what percent of the people have a university diploma?
Options:
A)35%
B)48%
C)55%
D)65%
E)75%
Rationale: Setting up a matrix is how I solve this one.
Diploma No Diploma Totals
Job of Choice w/Diploma
Job of Choice w/o Diploma = 10%
Job of Choice Total = 40%
Not Job of Choice with Diploma =.3X
Not Job of Choice w/o Diploma= .7X
Total Not Job of Choice = X
Total with Diploma
Total without Diploma
Total citizen = 100
If 40% of people have their job of choice, then 60% of people do NOT have their job of choice. 30% of 60% = 18%. We can also see that 30% of the people have their job of choice and a diploma (40%-10%=30%). 30% + 18% = 48%. Therefore 48% of the people in Country Z have a diploma.
Ans B
Answer: B
Question: A salesmanâ€™s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 100 more than that by the previous schema, his sales were worth?
Options:
A)s. 14,000
B)s. 12,000
C)s. 32,000
D)s. 40,000
E)s. 50,000
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 100
X = 32000
ANSWER:C
Answer: C
Question: In one alloy there is 10% chromium while in another alloy it is 6%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
Options:
A)7.2%
B)9%
C)9.2%
D)8.6%
E)8.4%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.10*15+0.06*35=3.6 kg, so the percentage is 3.6/50*100=7.2%.
Answer: A.
Answer: A
Question: A pharmaceutical company received $2 million in royalties on the first $12; million in sales of generic equivalent of one of its products and then $4 million in royalties on the next $48 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $12 million in sales to the next $48 million in sales?
Options:
A)20%
B)25%
C)30%
D)50%
E)55%
Rationale: change in ratio of royalties to sales = 2/12 -4/48 = 1/12
% decrease = (1/12)/(2/12) *100 = 50% (approx)
Answer: D)
Answer: D
Question: A do 2/5 part of work in 12 days and B do 3/4 part of work in 15 days.so,both together in how many days can finish the work?
Options:
A)15
B)8
C)10
D)12
E)14
Rationale: work of A in 12 days=2/5,work of A in 1 days=1/30
work of B in 15 days =3/4,work of B in 1 days=1/20
(A+B) work in 1 days=[1/30+1/20]=1/12
so,both together finish the work in 12 days
answer D
Answer: D
Question: Two pipes A and B can fill a cistern in 37 1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after
Options:
A)5 min
B)9 min
C)10 min
D)15 min
E)16 min
Rationale: Explanation:
Solution 1
Pipe A alone can fill the cistern in 37 1/2 = 75/2 minutes. Since it was open for 30 minutes, part of the cistern filled by pipe A =2/75 X 30 =4/5
So the remaining 1/5 part is filled by pipe B.
Pipe B can fill the cistern in 45 minutes. So, time required to fill 1/5 part
=45/5 =9 minutes.
i.e., pipe B is turned off after 9 minutes.
ANSWER IS B
Answer: B
Question: Which of the following best approximates the value of q if 5^29+5^11=5^q ?
Options:
A)40
B)30
C)29
D)27
E)17
Rationale: We have: 5^29+5^11=5^q
==> because 5^11 > 0 --> 5^q MUST be equal or greater than 5^29 ==>q MUST be equal or greater than 29
==> Option D and E are out immediately.
Divide both sides by 5^q and q >= 29
We have:
5^(29-q) + 5^11/5^q = 1
Because q >= 29 ==>5^11/5^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 5^(29-q) must be approximately 1
==> 29-q = 0 ==> q is approximately 29
C is the answer.
Answer: C
Question: Which is the smallest no which divides 2880 and gives a perfect square?
Options:
A)4
B)9
C)3
D)5
E)6
Rationale: Breaking 2880 into multiples:
2880 = 5*9*64 = 5 * 3^2 * 8^2 = 5* 24^2
5 being a prime number with only one multiple will divide 2880 & result in 9*64 which is a perfect square (9*64= 24^2 = 576)
ANSWER:D
Answer: D
Question: One morning is starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?
Options:
A)2:22:55am
B)5:22:55am
C)1:22:55am
D)6:22:55am
E)7:22:55am
Rationale: Let the depth of snow at time t to be t units. The speed of the plow at time t will be 1/t. Define t=0 as the time it started snowing and t=x the time the plow started.
The distance covered in the first hour is the integral from x to x+1 of 1/t dt. The antiderivative of 1/t is ln(t) so the total distance covered in the first hour is ln((x+1)/x).
By the same reasoning the distance covered in the second hour in ln((x+2)/(x+1)).
Using the fact that it the plow traveled twice as far in the first hour as the second: ln((x+1)/x) = ln((x+2)/(x+1))2
Exp both sides and you have (x+1)/x = ((x+2)/(x+1))2.
Solving for x you get x=(51/2-1)/2, which is the number of hours that elapsed between the time it started snowing and the snow plow left.
It started snowing at (51/2-1)/2 hours before 6:00am, or 5:22:55am.
correct answer B
Answer: B
Question: If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 9), what is the value of x?
Options:
A)9
B)11
C)13
D)15
E)17
Rationale: (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 9)
2^x - 2^(x-2) = 3. 2^9
Hence x = 11.
Answer is B
Answer: B
Question: Joe went on a diet 4 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 180 pounds?
Options:
A) 3
B) 3.5
C) 3
D) 4.5
E) 5
Rationale: 222 - 198 = 24 pounds lost in 4 months
24/4 = 6, so Joe is losing weight at a rate of 6 pounds per month.
...in approximately how many months will he weigh 180 pounds?
A simple approach is to just list the weights.
Now: 198 lbs
In 1 month: 192 lbs
In 2 months: 186 lbs
In 3 months: 180 lbs
Answer: C
Answer: C
Question: Three consecutive odd integers are in increasing order such that the sum of the last two integers is 13 more than the first integer. Find the three integers?
Options:
A)7, 9, 29
B)7, 2, 10
C)7, 9, 10
D)7, 9, 11
E)7, 9, 29
Rationale: Explanation:
Let the three consecutive odd integers be x, x + 2 and x + 4 respectively.
x + 4 + x + 2 = x + 13 => x = 7
Hence three consecutive odd integers are 7, 9 and 11.
Answer:D
Answer: D
Question: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 2400 different outfits, then for how many garments does Dave have exactly five choices?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 2400 = 24*100 = 24*5^2*2^2
Dave has exactly 5 choices for two garments.
The answer is C.
Answer: C
Question: What is the sum of the different positive prime factors of 1040?
Options:
A)10
B)14
C)15
D)18
E)20
Rationale: I think answer is E: 20
1040 = 2*2*2*2*5*13
Sum of theDIFFERENTpositive prime factors = 2 + 5 + 13 = 20
Answer: E
Question: In Arun's company 60% of the employees earn less than $50,000 a year, 60% of the employees earn more than $40,000 a year, 11% of the employees earn $43,000 a year and 5% of the employees earn $49,000 a year. What is the median salary for the company?
Options:
A)43.0
B)45.5
C)46.0
D)49.0
E)50.0
Rationale: In Arun's company 60% of the employees earn less than $50,000 a year, 50 and 51 employee will be each 43K. hence median = (43K+43k)/2
Answer: A
Question: Look at this series: V, VIII, XI, XIV, XVII, __, ... What number should fill the blank?
Options:
A)IX
B)XXIII
C)XV
D)XX
E)None
Rationale: Explanation: This is a simple addition series; each number is 3 more than the previous number.
Answer: D
Answer: D
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Options:
A)2775
B)2888
C)1888
D)4200
E)2589
Rationale: 15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer:D
Answer: D
Question: Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)12 min. 40 sec.
B)13 min. 40 sec.
C)14 min. 30 sec.
D)14 min. 20 sec.
E)14 min. 40 sec.
Rationale: Part filled in 4 minutes = 4	(1/15+1/20)=7/15.
Remaining part =1 -	7/15	=8/15
Part filled by B in 1 minute = 1/20
1/20	:8/15:: 1 : x
x =(8/15 x 1 x 20)= 10 2/3 min = 10 min. 40 sec.
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.
Answer is E
Answer: E
Question: If 16^5*15^4*14^3*13^2 = x, what is the units digit of x ?
Options:
A)2
B)3
C)6
D)5
E)0
Rationale: 16^5*15^4*14^3*13^2 = x
Units digit of x will be
6^5 * 5^4 * 4^3 * 3^2
=6 * 5 * 4 * 9
= 1080
Therefore , units digit of x = 0
Answer E
Answer: E
Question: Find the value of a from (15)^2 x 8^3 Ã· 256 = a.
Options:
A)250
B)420
C)440
D)650
E)450
Rationale: Given Exp. =(15)^2 x 8^3 Ã· 256 = a
= 225 x 512 Ã· 256 =
450
E
Answer: E
Question: The cost of Type 1 material is Rs. 15 per kg and Type 2 material is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then what is the price per kg of the mixed variety of material?
Options:
A)Rs. 19
B)Rs. 16
C)Rs. 18
D)Rs. 17
E)Rs. 21
Rationale: Explanation:
Solution 1
Cost Price(CP) of Type 1 material is Rs. 15 per kg
Cost Price(CP) of Type 2 material is Rs. 20 per kg
Type 1 and Type 2 are mixed in the ratio of 2 : 3.
Hence Cost Price(CP) of the resultant mixture
=(30+60)/5=90/5=18
=> Price per kg of the mixed variety of material =Rs.18
Answer IS C
Answer: C
Question: Sabrina is contemplating a job switch. She is thinking of leaving her job paying $85,000 per year to accept a sales job paying $40,000 per year plus 15 percent commission for each sale made. If each of her sales is for $1,500, what is the least number of sales she must make per year if she is not to lose money because of the job change?
Options:
A)200
B)177
C)178
D)377
E)378
Rationale: Lets say she sales x items so her commission will be : x * 1500*15/100 = 225x
Salary difference is: 85000 - 40000 = 45000
So commission must at least be equal to salary difference i.e. x = 45000/225 = 200 (Approx).
Hence answer is A
Answer: A
Question: The perimeter of a semi circle is 144 cm then the radius is?
Options:
A)87
B)28
C)26
D)27
E)25
Rationale: 36/7
r = 144
=> r = 28
Answer: B
Answer: B
Question: In a store the product A costs twice as much as the product B minus the cost of product C, If 4 products B plus 2 products C bought the price is $ 8, if 2 products you buy A plus 2 products B the price is $ 6, which is the price of the product C?
Options:
A)1.2
B)2
C)1.5
D)1.8
E)2.4
Rationale: We propose equations products
A = 2B-C
4B + 2C = 8 $
2A + 2B = 6 $
substituting
C = 1.2 $
Answer: A
Answer: A
Question: How long will a boy take to run round a square field of side 40 meters, if he runs at the rate of 12km/hr?
Options:
A)52sec
B)48sec
C)60sec
D)25sec
E)39sec
Rationale: Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 40*4 = 160m
Time taken = 160*3/10 = 48sec
Answer is B
Answer: B
Question: Seven people went to a restaurant for dinner. Six of them spent $11 each on their meals and the seventh person spent $6 more than the average expenditure of all seven people. What was the total amount of money that the seven people spent?
Options:
A)$80
B)$81
C)$82
D)$83
E)$84
Rationale: Let T be the total amount of money spent.
6*11 + (T/7 + 6) = T
72 = 6T/7
T = (7*72)/6 = 84
The answer is E.
Answer: E
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
Options:
A)165
B)178
C)180
D)198
E)200
Rationale: Explanation:
The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
E)
Answer: E
Question: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 155kg then find the average weight of all the 7 rounds?
Options:
A)98.5 kgs
B)88.5 kgs
C)86.5 kgs
D)67.5 kgs
E)88.2 kgs
Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 155/7 = 88.5 kgs
Answer:B
Answer: B
Question: Tabby is training for a triathlon. She swims at a speed of 1 mile per hour. She runs at a speed of 10 miles per hour. She wants to figure out her average speed for these two events. What is the correct answer for her?
Options:
A)8 mph
B)5.5 mph
C)3.5 mph
D)4 mph
E)0.5 mph
Rationale: (1 mph +10 mph)/2 = 5.5 mph
Correct option is: B
Answer: B
Question: Using all the letters of the word "WEDNESDAY", how many different words can be formed?
Options:
A)A)7
B)B)9!
C)C)8
D)D)7!
E)E)3
Rationale: Explanation:
Total number of letters = 9
Using these letters the number of 9 letters words formed is 8!.
Answer: Option B
Answer: B
Question: If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
Options:
A)Sunday
B)Saturday
C)Tuesday
D)Wednesday
E)None of these
Rationale: Solution
The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004. Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday (1 day before to 6th March, 2005) Answer A
Answer: A
Question: How many three digits number can be formed by using the digits 4,5,6,7,8,9 if the repetition of digits allowed?
Options:
A)106
B)108.
C)109
D)110
E)320
Rationale: For a number to be odd we must have 5,7 or 9 at the unit place. So there 3 ways of filling the unit place. Since the repetion of digits is allowed, each of the tens and hundreds place can filled in 6ways. Hence required number of numbers = 3x6x6=108. Answer : B
Answer: B
Question: If 4<x<6<y<10, then what is the greatest possible positive integer difference of x and y?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 4 < x < 6 < y < 10;
4 < x
y < 10
4 + y < x + 10
y - x <6.
Positive integer difference is 5 (for example y = 9.5 and x = 4.5)
Answer: C.
Answer: C
Question: In a certain school, there are 80 Freshmen, 100 Sophomores, and 220 Upperclassmen, drawn from three cities: A, B, and C. Sixty percent of students are from A, 30% from B, the rest from C, and all these students from C are freshmen. Half the student from B are upperclassman, and the rest are split evenly between the other two grades. How many sophomores are from A?
Options:
A) 60
B) 70
C) 80
D) 90
E) 100
Rationale: Answer = B = 70
Answer: B
Question: A chair is bought for Rs.200/- and sold at Rs.320/- find gain or loss percentage
Options:
A)75% loss
B)20% gain
C)60% gain
D)30% gain
E)35% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (320- 200)/200 = 60% gain
C
Answer: C
Question: If the selling price of 50 articles is equal to the cost price of 45 articles, then the loss or gain percent is:
Options:
A)45%
B)10%
C)20%
D)60%
E)56%
Rationale: C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 45.
Loss % = 5/50 * 100 = 10%
ANSWER B
Answer: B
Question: A rectangular rug with side lengths of 6 feet and 6 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
Options:
A)A.3/16
B)1/4
C)C.1/2
D)7/16
E)7/8
Rationale: Area of the rectangular rug = 6*6 = 36
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (64 - 36)/64
= 7/16=D
Answer: D
Question: A car travels the first 1/2 of certain distance with a speed of 15 km/hr the next 1/4 distance with a speed of 20 km/hr, and the last 1/4 distance with a speed of 60 km/hr. the average speed of the car for the whole journey is?
Options:
A)12km/hr
B)20km/hr
C)89km/hr
D)52km/hr
E)79km/hr
Rationale: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/2)/15+(x/4)/20+(x/4)/60=x/y
x/30+x/80+x/240=x/y
1/20y=1
y=20km/hr
Answer(B)
Answer: B