divelab/Sys2Bench huggingface dataset:
Question: Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 17 boys and 43 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
Options:
A)5
B)4
C)6
D)8
E)10
Rationale: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.
Table method is shown above; here is how you will use logic:
There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.
We have 6 happy boys and 6 sad boys. Total we have 17 boys. So 17 - 6 - 6 = 5 boys must be neither happy nor sad.
Answer (A)
Answer: A
Question: In a weight-lifting competition, the total weight of Joe's two lifts was 900 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?
Options:
A)225
B)275
C)325
D)350
E)400
Rationale: This problem is a general word translation. We first define variables and then set up equations.
We can define the following variables:
F = the weight of the first lift
S = the weight of the second lift
We are given that the total weight of Joe's two lifts was 900 pounds. We sum the two variables to obtain:
F + S = 900
We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:
2F = 300 + S
2F – 300 = S
We can now plug in (2F – 300) for S into the first equation, so we have:
F + 2F – 300 = 900
3F = 1,200
F = 400
Answer is E.
Answer: E
Question: Find the invalid no.from the following series 3, 8, 15, 31, 63, 127, 255
Options:
A)11
B)8
C)27
D)63
E)127
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 8 is wrong.
B
Answer: B
Question: 7/10 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
Options:
A)28%
B)41%
C)60%
D)72%
E)78%
Rationale: Total population = 100 (assume).
7/10*100=70 people from Montague.
3/10*100=30 people from Capulet.
0.2*70=14 people from Montague support Juliet.
0.7*30=21people from Capulet support Juliet.
The probability that a Juliet supporter chosen at random resides in Capulet is 21/(14+21)=~60.
Answer: C
Answer: C
Question: In an election between two candidates, the winner has a margin of 10% of the votes polled. If 2000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?
Options:
A)20000
B)25000
C)24000
D)23000
E)22000
Rationale: Winner - Looser
55% - 45%
If 2000 people change their mind and vote for the loser:
Winner - Looser
45% - 55%
Thus 2,000 people compose 10% of all voters, which means that the total number of votes is 20,000.
Answer: A.
Answer: A
Question: John has Rs 360 for his expenses. If he exceeds his days by 4 days he must cut down daily expenses by Rs 3. The number of days of John 's tour program is
Options:
A)10
B)15
C)20
D)24
E)27
Rationale: Let John under takes a tour of x
days.
Then, expenses for each day = 360x
360x+4=360x−3
x=20
and −24
Hence, x
= 20 days.
C
Answer: C
Question: A sock drawer contains eight socks, each one a different solid color. The colors of the socks are red, orange, white,yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?
Options:
A)12
B)15
C)21
D)36
E)28
Rationale: Since here order of socks is not important then we'll have 8C2 i.e. 28 combinations.
Answer : E
Answer: E
Question: What will be the fraction of 75%
Options:
A)3/4
B)1/5
C)1/10
D)1/11
E)None of above
Rationale: Explanation:
It will 75*1/100 = 3/4
Option A
Answer: A
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?
Options:
A)3/10
B)1/2
C)2/5
D)3/7
E)1/6
Rationale: Here, S = {1,2,3,......,19,20}
E= event getting a multiple of 3 = {3,6,9,12,15,18}
probability = 6/20 = 3/10
correct option is A
Answer: A
Question: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
Options:
A)1/4
B)1/10
C)7/15
D)8/15
E)2/13
Rationale: A's 1 day's work =1/15;
B's 1 day's work =1/20;
(A + B)'s 1 day's work =(1/15)+(1/20)=7/60
(A + B)'s 4 day's work =(7/60)*4=7/15
Therefore, Remaining work =(1-(7/15))=8/15
Option D
Answer: D
Question: If y is the smallest positive integer such that 4410 multiplied by y is the square of an integer, then y must be
Options:
A)2
B)5
C)6
D)7
E)10
Rationale: 4410 = 2*3^2*5*7^2
To be perfect square, we need to multiply by at least 2*5 = 10.
The answer is E.
Answer: E
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 150 m is?
Options:
A)150 m
B)778 m
C)200 m
D)276 m
E)971 m
Rationale: 2(l + 150)
= 600 => l
= 150 m
Answer:A
Answer: A
Question: A 6% stock yields 8%. The market value of the stock is:
Options:
A)Rs. 48
B)Rs. 75
C)Rs. 96
D)Rs. 133.33
E)Rs. 122
Rationale: Explanation:
For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.100/8*6= Rs. 75.
Market value of Rs. 100 stock = Rs. 75.
ANSWER IS B
Answer: B
Question: Find the average of all numbers between 1 and 76 which are divisible by 5
Options:
A)40
B)20
C)25
D)30
E)35
Rationale: Explanation:
Average=(5+10+15+20+25+30+35+40+45+50+55+60+65+70+75)/15=600/15=40
Answer: Option A
Answer: A
Question: For all positive integers m, [m]=3m when m is odd and [m]=(1/2)*m when m is even. What is [5]*[8] equivalent to?
Options:
A)[40]
B)[60]
C)[80]
D)[120]
E)[150]
Rationale: [5]*[8] = 15*4 = 60 = (1/2)(120) = [120]
The answer is D.
Answer: D
Question: If a > 1, which of the following is equal to (2a - 2)/(a^2 + 2a - 3)?
Options:
A)a
B)a + 3
C)2/(a - 1)
D)2/(a + 3)
E)(a - 1)/2
Rationale: Here's the algebraic approach:
(2A - 2)/(A^2 + 2A - 3) can be rewritten as...
2(A - 1)/(A+3)(A-1)
We can simplify the fraction, which leaves us with...
2/(A+3)
Ans : D
Answer: D
Question: Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: x : the total number of toys
x/10 : the number of toys for first child
x/10 + 12 : the number of toys for second child
x/10 + 1 : the number of toys for the third child
2(x/10 + 1) : the number of toys for the fourth child
x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x
x = 30 toys : solve for x
Answer: C
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
Options:
A)15 hours
B)16 hours
C)17 hours
D)18 hours
E)19 hours
Rationale: Explanation:
In this type of questions we need to get the relative speed between them,
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time = Distance/Speed
Time= 8.5km / 0.5 kmph = 17 hrs
Option C
Answer: C
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 24 kmph, find the speed of the stream?
Options:
A)18 kmph
B)6 kmph
C)8 kmph
D)10 kmph
E)12 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 24/3 = 8 kmph.
Answer: C
Answer: C
Question: What range of values of 'x' will satisfy the inequality 15x - 2/x > 1?
Options:
A)x > 0.4
B)x < 1/3
C)-1/3 < x < 0.4, x > 15/2
D)-1/3 < x < 0, x > 2/5
E)x < --1/3 or x > 2/5
Rationale: This will hold true for the following values of 'x': -1313 < x < 2/5 and x < 0.
Combining, we get -1/3 < x < 0.
Therefore, the range of values of x for which the above inequality will hold true is:
-1/3 < x < 0 âˆª x > 2/5.
ANSWERT : D
Answer: D
Question: A train of length 330 meters crosses a platform of length 550 meters in 44 seconds. What is the speed of the train?
Options:
A)11
B)76
C)5
D)4
E)3
Rationale: Answer:E
Answer: E
Question: In a jar there are 28 white balls, 32 green balls and 41 blue balls. How many balls must be taken out in order to make sure we have 30 balls of the same color?
Options:
A)a)	23
B)b)	46
C)c)	57
D)d)	66
E)e)	67
Rationale: Here, we need to find minimum number of marbles to be taken out to get 30 marbles of same color.
For a instance, if we take 2 white marbles 1st and followed by 22 Green and then 22 Blue.
Total will be 21 + 22+ 22= 65 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 30.
So Minimum we need to take 65+1 = 66 Times to get 30 marbles of same color(either Green or Blue).
Answer : D.
Answer: D
Question: When 23 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: This means that 20 must be a multiple of k.
The factors of 20 are 1, 2, 4, 5, 10, and 20.
Out of these, k can be 4, 5, 10, and 20.
The answer is D.
Answer: D
Question: Tough and Tricky questions: Ratios
3/5 of a certain class left on a field trip. 2/3 of the students who stayed behind did not want to go on the field trip (all the others did want to go). When another vehicle was located, 1/2 of the students who did want to go on the field trip but had been left behind were able to join. What fraction of the class ended up going on the field trip?
Options:
A)1/2
B)2/3
C)11/15
D)23/30
E)4/5
Rationale: let total no. of students be 30
students left on a field trip = 3/5(30) =18
thus 12 students left behind
2/3(12)=8 students did not want to go. thus 4 students want to go on the trip
1/2(4)=2 were able to join the other students on the field trip.
thus total number of students that went on a field trip =18+2 =20
thus required fraction = 20/30 =2/3
B
Answer: B
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 7 hours of the journey.
Options:
A)342 km
B)352 km
C)252 km
D)742 km
E)382 km
Rationale: The total distance covered by the car in the first 7 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 = sum of 7 terms in AP whose first term is 30 and last term is 42 = 7/2 [30 + 42] = 252 km.
ANSWER:C
Answer: C
Question: John has 10 pairs of matched socks. If he loses 11 individual socks, what is the greatest number of pairs of matched socks he can have left?
Options:
A) 7
B) 6
C) 5
D) 4
E) 3
Rationale: Because we have to maximize the pair of matched socks, we will remove 5 pairs(10 socks) out of 10 pairs 1 sock from the 6th pair.
Thus the no of matching socks pair remaining = 10 -6 = 4
Answer D
Answer: D
Question: How many 3-letter words can be formed out of the letters of the word ‘CORPORATION’, if repetition of letters is not allowed?
Options:
A)336
B)297
C)266
D)259
E)297
Rationale: Explanation:
There are in all 11 letters in the word ‘CORPORATION’. Since repetition is not allowed, there are 8 different letters that can be used to form 3-letter word.
Therefore, total number of words that can be formed = 8P3 = (8*7*6)
= 336
ANSWER: A
Answer: A
Question: The price of the jewel, passing through three hands, rises on the whole by 62%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
Options:
A)20
B)8
C)5
D)2
E)30
Rationale: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =162% Of P ((100+X)/100*125/100*120/100*P)=(162/100*P)
==> (100+X)=(162*100*100)/(125*120)=108=>X=8%
Answer B)
Answer: B
Question: What is the value of 8 1/3% of 600+ 37 ½ of 400
Options:
A)100
B)300
C)150
D)200
E)250
Rationale: 25*600/300 + 75*400/200 =50+150
= 200
ANSWER:D
Answer: D
Question: If one-third of one-fourth of a number is 15, then three-tenth of that number is:
Options:
A)48
B)40
C)50
D)54
E)64
Rationale: Let the number be x.
Then 1/3 of 1/4 of x =15
X=15x12 = 180
Required Number = (3/10)x180 =54
Answer : D
Answer: D
Question: Sam purchased 20 dozens of toys at t he rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)3.5
B)4.5
C)5.6 percent
D)6.5
E)None
Rationale: Solution
C.P of 1 toy	= Rs.(375/12)
= Rs.31.25
S.P of 1 toy	= Rs.33.
Therefore,Profit	= (1.75/31.25×100)%
=(28/5)%
=5.6%.
Answer C
Answer: C
Question: A pump can fill a tank with water in 5 hours. Because of a leak, it took 7 hours to fill the tank. The leak can drain all the water in ?
Options:
A)15hr 10min
B)16hr 20min
C)17hr 30min
D)15hr
E)14hr 25min
Rationale: Work done by the leak in 1 hour = 1/5 - 1/7 = 2/35
Leak will empty the tank in 35/2 hrs = 17hr 30min
Answer is C
Answer: C
Question: what is the least number. which should be added to 221 to make it a perfect square?
Options:
A)5
B)8
C)4
D)6
E)7
Rationale: 221+4=225
15^2
ANSWER:C
Answer: C
Question: How many numbers from 10 to 100 are exactly divisible by 9?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 10/9 = 1 and 100/9 = 11 ==> 11 - 1 = 10. Therefore 10 digits.
A)
Answer: A
Question: A person incurs 5% loss by selling a watch for $1140 . At
what price should the watch be sold to earn 5% profit?
Options:
A)1160
B)1150
C)1260
D)1260
E)1360
Rationale: Let the new S.P be $ x then,
(100-loss%):(1st S.P)=(100+gain%):(2nd S.P)
(100-5)/1140=(100+5)/x
x=(105*1140)/95=$1260
ANSWER C 1260
Answer: C
Question: 12,21,48,87,__
Options:
A)176
B)186
C)184
D)174
E)164
Rationale: 21=12*2-3
48=21*2+6
87=48*2-9
so next number is 87*2+12=186
ANSWER:B
Answer: B
Question: In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 9,000 have been vaccinated against both, how many have been vaccinated only against rubella?
Options:
A)18,000
B)7,500
C)10,000
D)15,000
E)17,500
Rationale: Use a single variable as far as possible.
Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 9000 (so x = 4500)
Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*4500 = 18,000
Answer (A)
Answer: A
Question: A farm has only chickens and pigs. When the manager of the farm counted the heads of the animals on the farm, the number totaled up to 95. When the number of legs was counted, the number totaled up to 274. How many more chickens than pigs are there on the farm? Note: Each pig has 4 legs and each chicken had 2 legs.
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let x be the number of chickens.
Then 95-x is the number of pigs.
2x+4(95-x)=274
2x=106
x=53 (chickens)
95-x=42 (pigs)
There are 53-42=11 more chickens on the farm.
The answer is E.
Answer: E
Question: g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(a) is divisible by 4^11, what is the smallest possible value for a?
Options:
A) 22
B) 24
C) 28
D) 32
E) 44
Rationale: g(a)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Answer: B
Question: In the Excel Manufacturing Company, 46 percent of the employees are men. If 60 percent of the employees are unionized and 70 percent of these are men, what percent of the non-union employees are women?
Options:
A)90%
B)87.5%
C)66.7%
D)50%
E)36%
Rationale: Lets say there are total 100 employees
Then men = 46 & women = 54
Unionized Emp = 60 & non unionized emp = 40
Men Unionized = .7 * 60 = 42
Women Unionized = 18
Women non-unionized = 54-18 = 36
Percentage of Women non unionized = 36/40 * 100 = 90%
The answer is Option A
Answer: A
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -
Options:
A)1/35
B)1/36
C)1/37
D)1/31
E)1/30
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B
Answer: B
Question: If an article is sold at 12% profit instead of 16% profit, then the profit would be Rs. 105 less. What is the cost price?
Options:
A)Rs. 3000
B)Rs.4000
C)Rs. 3500
D)Rs.4500
E)Rs.6000
Rationale: Explanation:
Let the cost price of an article be Rs. x.
(16% of x) - (12% of x) = 105
16x/100 - 12x/100 = 105 => 4x = 160 * 100
=> x = 1500
Cost price = Rs. 4000
Answer:B
Answer: B
Question: The average age of an adult class is 40years. 10 new students with an avg age of 32years join the class. Therefore
decreasing the average by 4year. Find what was the original strength of class?
Options:
A)10
B)12
C)16
D)20
E)22
Rationale: Let original strength = y
Then , 40y + 10 x 32 = ( y + 10) x 36
â‡’ 40y + 320 = 36y + 360
â‡’ 4y = 40
âˆ´ y = 10
A
Answer: A
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 550 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
Options:
A)550 * sqrt 2
B)550 * sqrt (2^7)
C)550 * sqrt (2^12)
D)550 * the twelfth root of (2^7)
E)550 * the seventh root of (2^12)
Rationale: Let the constant be k.
F1 = 550
F2 = 550k
F3 = 550 k * k = 550 * k^2
F13= 550 * k^12
we know F13 = 2 *F1 = 2 * 550 = 1100
1100/550 = k^12
k = twelfth root of 2
for F7...
F7 = 550 * k^6 ( as we wrote for F2 and F3)
F7 = 550 * (twelfth root of 2) ^ 6
F7 = 550 * sqrt (2)
The answer is A.
Answer: A
Question: Two cars are driving towards one another. The first car is traveling at a speed of 120 Km/h, which is 28% faster than the second car. If the distance between the cars is 855 Km, how long will it takes the cars to meet (in hours)?
Options:
A)2.5.
B)3.
C)3.5
D)4.
E)4.5.
Rationale: Let S be the speed of the slower car.
Then the speed of the faster is 1.28S
1.28S = 120
S = 120/1.28
Cumulative speed/rate = S + 1.28S = 2.28S
Time taken to meet = 855/2.28S =855/213.75 = 4hrs
ANSWER:D
Answer: D
Question: A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 330 items for $150 each, what will her monthly salary be?
Options:
A)$1,500
B)$1,800
C)$2,100
D)$2,500
E)$4,150
Rationale: Ans : 1000+ 7.5 % * 150 * (330-50) = $ 4150
ANSWER:E
Answer: E
Question: Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 1/3 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
Options:
A)3/19
B)3/12
C)3/11
D)3/10
E)3/14
Rationale: Let Veena paid x,
so Akshitha paid x/3 , and Lasya paid 2x,
So total bill paid is given by
x+(x/3) +2x = 1, we get
i.e. x = 3/10
Answer: D
Answer: D
Question: A man goes downstream at 15 kmph, and upstream8 kmph. The speed of the stream is
Options:
A)0kmph
B)3.5kmph
C)16kmph
D)2.5kmph
E)26kmph
Rationale: Speed of the stream = 1/2(15-8)kmph
=3.5kmph.
correct option :B
Answer: B
Question: Difference between the length &breadth of a rectangle is 15 m. If its perimeter is 302 m, then its area is?? We have: (l - b) = 15 and 2(l + b) = 302 or (l + b) = 151?
Options:
A)5446 m^2
B)5464 m^2
C)5644 m^2
D)5434 m^2
E)5344 m^2
Rationale: Solving the two equations, we get: l = 83 and b = 68.
Area = (l x b) = (83 x 68) m2 = 5644 m^2
C
Answer: C
Question: What is the perimeter of a square with area 9p^2/64 ?
Options:
A)3p/2
B)3p^2/4
C)3p
D)3p^2
E)4p/3
Rationale: Area of square, (side)^2 = (3p/8)^2
Therefore side of the square = 3p/8
Perimeter of square = 4*side = 4* (3p/8) = 3p/2
Answer is A.
Answer: A
Question: Which number is the odd one out?
9654 4832 5945 7642 7963 8216 3649
Options:
A)4549
B)6549
C)3729
D)3649
E)5416
Rationale: D
3649
In all the others multiply the first two digits together to produce the number formed by the last two digits.
Answer: D
Question: A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)180 m
B)200 m
C)240 m
D)300 m
E)None
Rationale: Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 40 = 15 ⇔ x + 300 = 600 ⇔ x = 300 m.
Answer D
Answer: D
Question: How many integers between 3000 and 4000 that have distinct digits and increase from left to right ?
Options:
A)20
B)48
C)60
D)120
E)600
Rationale: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
345_ --> 4
346_ --> 3
347_ --> 2
348_ --> 1
356_ --> 3
357_ --> 2
358_ --> 1
367_ --> 2
368_ --> 1
378_ --> 1
Number of integers =20
So the answer is A.
Answer: A
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 37380
. What percentage of profit did he make?
Options:
A)80%
B)68%
C)40%
D)70%
E)90%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 31150
Profit(%) = (37380 - 22250)/22250 * 100
= 68%
Answer:B
Answer: B
Question: The least number by which 72 must be multiplied in order to produce a multiple of 112, is
Options:
A)6
B)12
C)14
D)18
E)20
Rationale: Solution
Required numbers is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.
Now, 1008 when divided by 72, gives quotient	= 14.
Required number	= 14.
Answer C
Answer: C
Question: On final examination a student's average (arithmetic mean) score on 4 subjects is 90. What must be his score on a 5th subject for his average score on the 5 subjects to be 92?
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: (4*90+x)/5=92
x=(5*92)-(4*90)
x= 460 - 360
total score required 460 - 360=100
Correct answer is E
Answer: E
Question: If n is a natural number, then(6n^2+6n) is always divisible by?
Options:
A)6 only
B)6 and 12 both
C)12 only
D)by 18 only
E)None of these
Rationale: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Correct Option: B
Answer: B
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 5w widgets.
Options:
A)4
B)6
C)8
D)30
E)12
Rationale: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 30 days to doing 5w widgets.
Answer : D
Answer: D