divelab/Sys2Bench huggingface dataset:
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 30 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
Options:
A)18/79
B)1/6
C)1/25
D)1/150
E)1/900
Rationale: So there are 900 cars that they have to search.. Each takes 30mins, total of 27000 mins.. Have to find in 180 mins.. Prob180/27000 = 1/150 (ANSWER D)
Answer: D
Question: Given that there are 11 cricket players per team, how many ways can you select 10 cricket players from 2 teams if no more than 5 players can be selected from each team?
Options:
A)245631
B)457845
C)145256
D)356586
E)213444
Rationale: Now from each group we have to select 5 persons only: 11C5 * 11C5= 462 * 462 = 213444
Total ways=313444 ways.
Answer E
Answer: E
Question: A man sitting in a train which is traveling at 45 kmph observes that a goods train, traveling in opposite direction, takes 8 seconds to pass him. If the goods train is 340 m long, find its speed
Options:
A)102 kmph
B)106 kmph
C)108 kmph
D)62 kmph
E)72 kmph
Rationale: Explanation:
Relative speed = 340/8 m / sec = ((340/8)×(18/5)) kmph = 153 kmph.
Speed of goods train = (153 - 45) kmph = 108 kmph
Answer: Option C
Answer: C
Question: A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
Options:
A)240
B)245
C)250
D)255
E)260
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 260)/9 = 500/9 => x = 240.
Answer: Option A
Answer: A
Question: In a certain growth fund, 3/5 of the investment capital is invested in stocks, and of that portion, 1/3 is invested in preferred stocks. If the mutual fund has $846,000 invested in preferred stocks, what is the total amount of money invested in the fund?
Options:
A)$1,974,000
B)$2,538,000
C)$3,264,000
D)$3,826,000
E)$4,230,000
Rationale: Total invested in preferred stocks is =(3)/(5)∗(1)/(3) = (1)/(5) * Investment Capital
= 846,000
Total amount of money invested in the fund= 846,000 * 5 = 4,230,000
Answer is E
Answer: E
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
Options:
A)11
B)17
C)18
D)101
E)1322
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: B
Answer: B
Question: The area of square ABCD above is 32. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
Options:
A)18−9/4∗π
B)18−9/2∗π
C)9+9/4∗π
D)32-8∗π
E)9/2−9/4∗π
Rationale: =Square - Quarter circle
=32- pi*32/4
=32- pi*8
ANSWER:D
Answer: D
Question: The average of 10 numbers was calculated as 19. It is discovered later on that while calculating the average, one number, namely 76, was incorrectly read as 26. What is the correct average?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: 10*19 - 26 + 76 = 240
240 / 10 = 24
The answer is D.
Answer: D
Question: The positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y , which of the following represents the least common multiple of p and r?
Options:
A)12xy
B)6xy
C)xy
D)12
E)6
Rationale: P and R have exactly 3 factors i.e. 2 , 2 and 3 which comes out to be 12 ;
so p and r will have 12 for sure as a factor ; ok .
now considering that both p -> x as a prime factor and r-> y as prime factor and x is not equal to y ;
LCM will be 12 * x * y
eg: -
let p and r be 12 and 12 each ; then 7 added to p and 11 added to r we get Least LCM as
12 *7* 11 ; ANSWER:A
Answer: A
Question: In power plant, If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it ?
Options:
A)40 hours
B)50 hours
C)60 hours
D)70 hours
E)None of these
Rationale: Explanation :
Let the required number of hours be x. Then,
Less men, More hours (Indirect Proportion)
15 : 36 : : 25 : x => (15 * x) = (36 * 25)
x=(36 x 25)/15 = 60
Hence, 15 men can do it in 60 hours.
Answer : C
Answer: C
Question: In a group of hats consisting of only blue hats, green hats, and purple hats, the ratio of blue hats to green hats to purple hats is 7:4:12. If there are a total of 138 hats in this group, how many of these hats are not blue?
Options:
A)28
B)42
C)48
D)96
E)76
Rationale: Since the hats Blue, Green and Purple are in ratio of 7:4:12...The total no. of balls will be
7x+4x+12x=138 or 23x=138...here 7x,4x and 12x represent hats of each type
23x=138 so x=6...Blue hats =7*6=42...Not blue will be 138-42=96.
Ans D
Answer: D
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
The sum of the first 52 positive even integers is 2550. What is the sum of the even integers from 98 to 200 inclusive?
Options:
A)5,100
B)7,748
C)10,100
D)15,500
E)20,100
Rationale: even numbers from 98 to 200=102/2+1=52
Sum= (200+98)x52/2=7748
So B is the ans.
Answer: B
Question: A juice drink contains 6% of the recommended daily amount of vitamin A. If the juice drink contains 3 units of vitamin A, how many units of vitamin A are recommended daily?
Options:
A)70
B)50
C)60
D)56
E)66
Rationale: 6% of the recommended amount of vitamin A is 3 units.
If the total number of units recommended is X then
6/100 = 3/X
100/6 * 3 = X
300/6 = X
50 = X
B)
Answer: B
Question: A parallelogram has a height that is the square root of the size of it's base. The total area of this parallelogram is Sq ft. What is the height of the parallelogram?
Options:
A)7
B)10
C)15
D)9
E)3
Rationale: x^2 * x = 343 => x
= 7
Answer: A
Answer: A
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
Options:
A)Rs. 4000
B)Rs. 4500
C)Rs. 5500
D)Rs. 6000
E)Rs. 6500
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12/120 * x + 15/125 * (12000- x) = 1360
x/10 + 3/25(12000-x) = 1360
5x + 72000 - 6x = 1360 x 50
x = 4000.
Answer = A
Answer: A
Question: Kyle has a custom bicycle shop, from each bicycle he sells for $150, he invest $65.50 in tools, paint and accessories. He also pays a $25 commission to his friend Lucas for each bike he helps him sell. If Lucas helped Kyle sell 6 bikes in one week, how much profit did Kyle made from those sells?
Options:
A)$200
B)$357
C)$157
D)$355.50
E)$230
Rationale: Answer is (B). Kyle sells each bicycle for $150, from that subtract $65.50 in expenses and the $25 commission for each bicycle Lucas helped him sell. That's $59.50 profit from each bicycle sold multiplied by the number of bicycles sold that week (6), (59.5 x 6) would net him a total of $357 net profit.
Answer: B
Question: Total number of 4 digit number do not having the digit 3 or 6.
Options:
A)22
B)28
C)27
D)19
E)11
Rationale: Answer:D
Answer: D
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, 19
B)7, 9, 15
C)7, 9, 17
D)7, 9, 11
E)7, 9, 12
Rationale: 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: A teacher gets paid $20 a day for in school classes. For extra classes outside of school, she charges $5 per hour for every child. If she teaches 25 students inside of school, and 12% of these students take extra classes for 4 hours. How much money does the teacher make for a week of five days total from teaching?
Options:
A)400
B)100
C)300
D)500
E)200
Rationale: Total in school classes pays $20* 5 days= $100
Total students for external tutoring is 0.12*25= 3
Total external classes pays ($5*4 hours)*3 students= $60, which is $60*5= $300 for the week.
Total pay for week is $100+$300= $400.
Answer is A.
Answer: A
Question: In a suite there are men and cats. In all, there are 15 heads and 40 feet. How many men and how many cats are in the suite?
Options:
A)8 men and 7 cats.
B)7 men and 8 cats.
C)6 men and 9 cats.
D)10 men and 5 cats.
E)11 men and 4 cats.
Rationale: 10 men and 5 cats.
Let M = men and C = cats. We can come up with 2 equations.
M + C = 15
2M + 4C= 40
Solving the 2 equations will give 10 men and 5 cats.
Answer D
Answer: D
Question: If you roll one fair six-sided die, what is the probability that the number is even or less than 4?
Options:
A)1/6
B)1/3
C)2/ 3
D)3/4
E)5/6
Rationale: Total favourable outcomes: 1,2,3 (less than 4), 4,6(even) = 5
Total possible outcome= 6
Probability=5/6.
Answer: Option E
Answer: E
Question: If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S
Options:
A)25:16
B)24:25
C)5:6
D)4:5
E)4:9
Rationale: Rectangle is R; say; l=6, w=4
Perimeter of R= 2(l+w)=2(6+4)=2*10=20 (not 24)
Area of R = 6*4=24
Perimeter of S = Perimeter of R (Given)
Perimeter of S = 4 * side_of_S
Perimeter of R = 20
4*side_of_S = 20
side_of_S, say s = 20/4=5
Area of S = s^2 = 5^2=25
Ratio; Area of R/Area of S = 24/25
Ans:B
Answer: B
Question: If 5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days then how many artists r required to make 25 paintings using 25 canvases in 25 days?
Options:
A)3/2
B)5/2
C)7/2
D)11/2
E)1/2
Rationale: 5/2 artists make 5/2 paintings using 5/2 canvases in 5/2 days. So, 1 artist make 1 painting using 1 canvas in 5/2 days. So, 1/10 artist make 1 painting using 1 canvas in 25 days.
So, 25/10 (=5/2) artists make 25 paintings using 25 canvases in 25 days.
ANSWER:B
Answer: B
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 55 kms. what was the total distance travelled in 12 hours?
Options:
A)252 kms
B)152 kms
C)552 kms
D)792 kms
E)152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(55+57+59+.....upto 12 terms)
This is an A.P with first term, a=55, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 55+{12-1) x 2]
=6(132)
= 792 kms.
Answer: D
Answer: D
Question: Ken bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
Options:
A)50RW/Q.
B)50QR/W.
C)25RQ/W.
D)25RW/Q.
E)RW/(4Q).
Rationale: Ken bought 2Q steaks for W dollars, so 1 steak = W/2Q
Jerome buys R steaks for a 50% discount: r* (W/4Q)
in cents the answer will be : r* (100 W/4Q)= 25 RW/ Q=D
Answer: D
Question: A bookseller has two display windows. She plans to display 2 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
Options:
A)24
B)72
C)12
D)336
E)420
Rationale: The left window will have permutations of the 2 fiction books, so the number of possibilities for that window is
permutations = 2! = (2)(1) = 2
The right window will have permutations of the 3 non-fiction books, so the number of possibilities for that window is
permutations = 3! = (3)(2)(1) = 6
Any of the 24 displays of the left window could be combined with any of the 6 displays of the right window, so the total number of configurations is 2*6 = 12
Answer: C.
Answer: C
Question: In an election, candidate A got 70% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
Options:
A)355600
B)355800
C)356500
D)356800
E)333200
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 70 %
Therefore, the number of valid votes polled in favour of candidate A = 70 % of 476000
= 70/100 × 476000
= 33320000/100
= 333200
E)
Answer: E
Question: John makes $60 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)17%
D)17.61%
E)17.56%
Rationale: Increase = (10/60)*100 = (1/6)*100 = 16.66%.
B
Answer: B
Question: Primrose wants to buy hot cocoa for her 9 friends who she volunteers with at the Ohio No-Kill Animal Shelter. Hot cocoa costs $2.00 per cup. Primrose has $15.00 in her pocket. How much money will Primrose have to get from her purse to pay for the drinks?
Options:
A)$1
B)$2
C)$3
D)$4
E)$5
Rationale: Answer= C
The 9 cups of cocoa will cost a total of $18.00. Primrose has $15.00 in her pocket.
$18 - $15 = $3
Primrose needs to get an extra $3.00 from her purse to have the $18.00
Answer: C
Question: A certain telescope increases the visual range at a particular location from 60 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
Options:
A) 30%
B) 33 1/2%
C) 40%
D) 60%
E) 150%
Rationale: Original visual range = 60 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-60)/60 * 100%
= 3/2 * 100%
= 150 %
Answer E
Answer: E
Question: 40 is subtracted from 70% of a number, the result is 30. Find the number?
Options:
A)150
B)997
C)266
D)288
E)100
Rationale: (70/100) * X – 40 = 30
7X = 700
X = 100
Answer:E
Answer: E
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 17. The larger of the two numbers is:
Options:
A)276
B)299
C)391
D)345
E)355
Rationale: Clearly, the numbers are (23 x 13) and (23 x 17).
Larger number = (23 x 17) = 391. Answer: Option C
Answer: C
Question: In digging a pond 20 m * 15 m * 5 m the volumes of the soil extracted will be?
Options:
A)3387
B)1000
C)2866
D)1500
E)1121
Rationale: 20 * 15 * 5 = 1500
Answer: D
Answer: D
Question: Find the resultant profit if A sells a cupboard at a profit of 6% to B and B sells the same to C at a profit of 9%.
Options:
A)15.59%
B)15.24%
C)15.54%
D)55.24%
E)15.44%
Rationale: Explanation:
The resultant profit = 1.06 * 1.09 = 1.1554 = 15.54%
Alternatively, the resultant profit = [x + y + xy/100]
= 6 + 9 + (6*9)/100
= 15 + 0.54
= 15.54%
ANSWER: C
Answer: C
Question: An inspector rejects 0.07% of the meters as defective. How many will he examine to reject 2?
Options:
A)A)1500
B)B)2000
C)C)2857
D)D)3000
E)E)3100
Rationale: Let the number of meters to be examined be x
Then, 0.07% of x = 2
(7/100)*((1/100)*x = 2
x = 2857
Answer is C
Answer: C
Question: A container holds 4 quarts of diesel and 4 quarts of petrol. How many quarts of water must be added to the container to create a mixture that is 3 parts dieselto 5 parts water by petrol?
Options:
A)4/3
B)5/3
C)7/3
D)8/3
E)10/3
Rationale: An alternate to the alligation method is the more direct/algebraic method:
Let x be the amount of petrol to be added.
New total amount of water = 4+x
Total amount of diesel= 4
New total = 4+4+x=8+x
Final ratio required (for petrol) = 5/(5+3)=5/8
Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.
D is thus the correct answer.
Answer: D
Question: Together, Andrea and Brian weigh p pounds; Brian weighs 20 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds?
Options:
A) p/2 - 10
B) 3p/4 - 10
C) 3p/2 - 5
D) 5p/4 - 10
E) 5p - 5
Rationale: Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 20 --> A + (A + 20) = p --> A = (p - 20)/2 = p/2 - 10.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 10) + p/4 = 3p/4 -10.
Answer: B.
Answer: B
Question: Present ages of X and Y are in the ratio 4:5 respectively. Five years hence this ratio will become 5:6 respectively. What is X's present age in years?
Options:
A)35
B)36
C)37
D)20
E)40
Rationale: Let the present ages of X and Y be 4x and 5x years respectively.
Then, (4x + 5)/(5x + 5) = 5/6
6(4x + 5) = 5(5x + 5) => 24x+30= 25x+25 => x =5
X's present age = 4x = 4*5 = 20
ANSWER:D
Answer: D
Question: If the sum of a list of consecutive odd integers is 10, which of the following could be true?
I. The average (arithmetic mean) of the list is equal to 10.
II. The median of the list is equal to 10.
III. The range of the list is equal to 10.
Options:
A)I
B)II
C)III
D)I and II
E)III &I
Rationale: Let the numbers be x-4, x-2, x , x+2, x+ 4 and given sum of all 5 number is 10, which is 5x =10 and meaning x is 2
So the list is -2, -0, 2, 4, 6.
ans I
A
Answer: A
Question: If six persons sit around a round table the probability that some specified three of them are always together is
Options:
A)1/5
B)1/20
C)3/10
D)4/10
E)5/20
Rationale: six persons and three grouped => 3! 3! ways
P = (3!3!)5! == 3/10
ANSWER C
Answer: C
Question: Two trains 140m and 160m long run at the speed of 60kmph and 48kmph in opposite directions in parallel tracks. The time which they take to cross each other is?
Options:
A)5.6sec
B)8.9sec
C)10 sec
D)12.6sec
E)15sec
Rationale: Relative speed = 60+48 = 108 kmph * 5/18 = 30 m/s
Distance covered in crossing each other = 140+160 = 300m
Required time = 300*1/30 = 10 sec
Answer is C
Answer: C
Question: Cindy has her eye on a sundress but thinks it is too expensive. It goes on sale for 15% less than the original price. Before Cindy can buy the dress, however, the store raises the new price by 25%. If the dress cost $51 after it went on sale for 15% off, what is the difference between the original price and the final price?
Options:
A)$0.00
B)$1.00
C)$3.75
D)$5.00
E)$6.80
Rationale: 0.85*{Original Price} = $51 --> {Original Price} = $60.
{Final Price} = $51*1.25 = $63.75.
The difference = $63.75 - 60$ = $3.75.
Answer: C.
Answer: C
Question: Michelle deposited a certain sum of money in a savings account on July 1st, 2007. She earns an 6% interest compounded semiannually. The sum of money in the account on December 31st, 2009 is approximately what percent of the initial deposit?
Options:
A)117%
B)120%
C)121%
D)135%
E)140%
Rationale: Since Michelle earns 6% interest compounded semiannually, then she earns 3% interest every 6 months.
Now, the simple interest earned in 5 periods (30 months = 5*6 months) would be 3%*5=15%. But, since the interest iscompoundedevery 6 months, then there would be interest earned on interest (very small amount) thus the actual interest earned would be a little bit more than 15%, only answer choice A fits.
Answer: A
Answer: A
Question: A room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles. What will be the least number of square tiles required to cover the floor?
Options:
A)176
B)124
C)224
D)186
E)190
Rationale: LENGTH = 5 M 44 CM = 544 CM
BREADTH = 3 M 74 CM = 374 CM
AREA = 544 * 374
HCF = 34
AREA OF SQUARE = 34 * 34 CM2
NO OF TILES REQ = 544* 374/34*34 = 16 * 11 =176
ANSWER A
Answer: A
Question: 600 men have provisions for 20 days. If 200 more men join them, for how many days will the provisions last now?
Options:
A)15
B)11
C)10
D)8
E)7
Rationale: 600*20 = 800*x
x = 15.Answer: A
Answer: A
Question: A and B started a business investing Rs. 90,000 and Rs 20,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Options:
A)3:2
B)9:2
C)18:20
D)1:4
E)18:4
Rationale: A: B = 90000 : 20000 = 90 : 20 = 18 : 4 = 9 : 2
ANSWER:B
Answer: B
Question: An article is bought for Rs.695 and sold for Rs.900, find the gain percent?
Options:
A)33 1/8%
B)33 8/3%
C)39 1/2%
D)35 1/3%
E)32 1/3%
Rationale: 695 ---- 205
100 ---- ? => 39 1/2%
Answer: C
Answer: C
Question: The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares?
Options:
A)76 cm
B)24 cm
C)88 cm
D)55 cm
E)34 cm
Rationale: We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 32/4 = 8 cm
Area of third Square = 10*10 - 8*8
= 36 cm
So side of third square = 6 [because area of square = side*side]
Perimeter = 4*Side = 4*6 = 24 cm
Answer:B
Answer: B
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5 km/hr, how much time will it take to cover the same distance?
Options:
A)48 min 54sec
B)48min 53sec
C)46min 53sec
D)48min
E)47min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is decreased by 5 km/hr then the
speed of the bus = 45 km/hr
Required time = 110/3*60/45 = 48 min 54sec
A
Answer: A
Question: What is the speed of the train?
I.The train crosses a tree in 13 seconds.
II.The train crosses a platform of length 250 metres in 27 seconds.
III.The train crosses another train running in the same direction in 32 seconds.
Options:
A)I and II only
B)II and III only
C)I and III only
D)Any two of the three
E)None of these
Rationale: Explanation:
Let the speed of the train be x metres/sec.
Time taken to cross a tree = Length of the train/Speed of the train
Time taken to cross a platform = (Length of the train + Length of the Platform)/Speed of the train
I gives, 13 = l/x = 13x.
II gives 27 = l + 250/x
=> 13x + 250/x = 27
=> x = 125/7 m/sec.
7
Thus I and II give the speed of the train.
Answer is (A)
Answer: A
Question: m men agree to purchase a gift for rs D. if three men drop out how much more will each have to contribute towards the purchase of gift
Options:
A)3D/(M^2-3M)
B)3D/(M^1-3M)
C)4D/(M^2-3M)
D)2D/(M^2-3M)
E)3D/(M^2-M)
Rationale: Each of M men have to contribute = D/M.
If three men drop then each of remaining men have to pay = D/(M-3).
Therefore after 3 were drop each have to contribute = [D/(M-3)]-[D/M].
i.e., 3D/(M^2-3M).
ANSWER:A
Answer: A
Question: There are 27 pearls in a bag. One among them is less in weight. You have been given 2 pan weight machine. In how many trials, you will be able to find the defected one?
Options:
A)4
B)3
C)11
D)13
E)18
Rationale: First we would take 13 perls in each pan and if we found that both are equal then the remaining perl(which has not taken for weighing) is having less weight or if there is an imbalance in either side of the pan we would consider those perls to find out the less weight perl. In this way there would be 4 stages at max to find out the less weighing perl by repaeting the same process as 1st. so answer is 4
ANSWER:A
Answer: A
Question: In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?
A.
B.
C
D.
E.
Options:
A)180
B)196
C)286
D)288
E)324
Rationale: Should be 288.
We have to find the total number of 3-digit odd numbers not having 5 as a digit.
Units digits will be among 1,3,7,9
Tenth digits will be among 0,1,2,3,4,6,7,8,9
Hundredth digits will be among 1,2,3,4,6,7,8,9
So total numbers = 4*9*8 =288
ANSWER:D
Answer: D
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 17
III. P is a multiple of 19
Options:
A)I only
B)II only
C)III only
D)None of the above
E)All of the above
Rationale: The correct answer is D.
Answer: D
Question: If a > 1, which of the following is equal to (4a + 12)/(a^2 + 2a - 3)?
Options:
A)a
B)a + 3
C)4/(a - 1)
D)2a/(a - 3)
E)(a - 1)/2
Rationale: Here's the algebraic approach:
(4A + 12)/(A^2 + 2A - 3) can be rewritten as...
4(A + 3)/(A+3)(A-1)
We can simplify the fraction, which leaves us with...
4/(A-1)
Ans : C
Answer: C