divelab/Sys2Bench huggingface dataset:
Question: Sylvia can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of X by selling Y watches, then in terms of M and X and Y, what is the percent of the markup from her buy price to her sell price?
Options:
A)100*(YM)
B)100X*(YM)
C)100X/(YM)
D)100X-(YM)
E)100X+(YM)
Rationale: Algebraic Solution:If she makes a total profit of X for Y watches, then that must be a profit of X/Y for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (X/Y)/M *100 = 100X/(YM)
Answer : C
Answer: C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 14%?
Options:
A)20%
B)29%
C)13 1/30%
D)12%
E)13%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 86
2/3 SP1 = 86
SP1 = 129
100 --- 29 => 29%
ANSWER:B
Answer: B
Question: Find the smallest four-digit number which is a multiple of 112.
Options:
A)896
B)1008
C)1120
D)1024
E)None of these
Rationale: The smallest four digit number is 1000. If 1000 is divided by 112, the remainder is 104.
112 - 104 = 8, if 8 is added to 1000, it will become the smallest four digit number and a multiple of 112.
ANSWER:B
Answer: B
Question: 25% of 30% of 45% is equal to?
Options:
A)0.03375
B)0.03372
C)0.0337
D)0.03377
E)0.03376
Rationale: (25/100) * (30/100) * (45/100)
1/4 * 3/10 * 9/20
27/800 = 0.03375
Answer:A
Answer: A
Question: A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
Options:
A)28 min past 7pm on wednesday
B)20 min past 7pm on wednesday
C)20 min past 8pm on wednesday
D)29 min past 7pm on wednesday
E)20 min past 5pm on wednesday
Rationale: Explanation:
This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct tine, it has to gain 5 min.
Answer: B) 20 min past 7pm on wednesday
So the correct time will be shown on wednesdy at 7:20 PM
Answer: B
Question: Tom, who has 50 math questions, will get 7 points per question if he chooses a correct answer. If he chooses a wrong answer to a question or skips one, he will lose 2 points per question. Then, which of the following can be the score if he solves all the 50 questions?
Options:
A)192
B)193
C)194
D)195
E)197
Rationale: Let x be the correctly answered questions. y be the wrongly answered/ skipped ones.
We have x + y = 50;
Score = 7x-2y
2x+2y = 100; 7x-2y = Score;
==> 9x = 100+Score;
check for answer choices where 100+Score is divisible by 9
Choice (E) 197 fits the equation !
Answer: E
Question: In how many different number of ways 5 boys and 3 girls can sit on a bench?
Options:
A)700
B)40320
C)720
D)730
E)740
Rationale: npn = n!
8p8 = 8 X 7 X 6 Ã— 5 Ã— 4 Ã— 3 Ã— 2 Ã— 1 = 40320
B
Answer: B
Question: If selling price of an article is Rs. 250, profit percentage is 25%. Find the ratio of the cost price and the selling price
Options:
A)4:5
B)3.:2
C)2:1
D)9:3
E)4:2
Rationale: selling price = 250
Profit=25%
cost price =250*100/125=200
Required ratio =200:250=4:5
Answer: Option A
Answer: A
Question: If n is a natural number, then 6n^ 2 + 6n is always divisible by?
Options:
A)6 only
B)6 and 12
C)12 only
D)18 only
E)20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: B
Question: If the sum of two numbers is 45 and the H.C.F and the sum of the reciprocals of the numbers are 3 and 103/100 respectively, then the LCM of the numbers is equal to:
Options:
A)460
B)300
C)245
D)100
E)200
Rationale: Let the numbers be a and b and LCM be x,
Then, a + b = 45 and ab = 3 * x = 3x
Required sum = 1/a + 1/b = (a + b)/ab = 103/300
103/300=45/3x
x=100
ANSWER:D
Answer: D
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 2/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
Options:
A)(a) 7/16
B)(b) 7/11
C)(c) 10/21
D)(d) 17/35
E)(e) 1/2
Rationale: A simpler way i guess would be to think that in total 5 cups were sold. Out of which 2 are small and 3 are large. Now let the small ones cost $6. so the large ones would cost $7.
So,
2*6=12 and 3*7=21.
Total revenue was 12+21=33
and Large cup sales as found above is 21
Therefore answer is 21/33 i.e 7/11
B
Answer: B
Question: Light glows for every 15 seconds . How many times did it between 1:57:58 and 3:20:47 am
Options:
A)381
B)332
C)383
D)334
E)385
Rationale: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/13 = 331.
so total 332 times light ll glow
ANSWER:B
Answer: B
Question: A 250m long train is travelling at 30km/hr. Another 200m long train travelling at 40km/hr in the same direction overtakes it. How long would it take to pass the first train completely?
Options:
A)2min32secs.
B)1min32secs.
C)3min42secs.
D)2min42secs,
E)4min12secs.
Rationale: Relative speed =x-y x,y are their speeds. Distance =(250+200)m =450m Relative speed = (40-30)km/hr =450m =25/9 m/s Time taken to cover 450m = 450*9/25 secs. =162 secs. =2min.42sec. Answer : D
Answer: D
Question: A boy is traveling from his house to school at 3km/hr and reached school 9minutes late. Next day he traveled 4km/hr and reached 6minutes early. Then find the distance between house and school?
Options:
A)3km
B)4.5km
C)5km
D)2.5km
E)6km
Rationale: Let distance be x
S1 = 3km/hr
S2 = 4km/hr
T1 = x/3hr
T2 = x/4hr
Difference in time = 9+6 = 15m = 1/4hr
(x/3)-(x/4) = 1/4
x = 3km
Answer is A
Answer: A
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
Options:
A)37
B)23
C)25
D)29
E)17
Rationale: Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 5B = 125 B = 25.
Answer: C
Answer: C
Question: There are r red ball, b blue ball and w white ball in a bag. What is the ratio of the number of blue ball to the total no. of ball in terms of r, b and w.?
Options:
A)(r + b + w)
B)r / (r + b + w)
C)r * (r + b + w)
D)r / (r + b )
E)r / (r + w)
Rationale: The total number of marbles is
r + b + w
The total ratio of blue marbles to the total number of marbles is
r / (r + b + w)
B
Answer: B
Question: What is the total number of X integers between 100 and 200 that are divisible by 3?
Options:
A) 33
B) 32
C) 31
D) 30
E) 29
Rationale: yes there is a different way of arriving at that answer ....
u can also use airthmetic progression to get the answer
since the first term to be divisble by 3 is 102 ..take that as A .. the starting no
and since 198 is the last digit to be divisible by 3 take that as N ...
since the difference is 3 take that as D
no u have to find what term is 198 take that as nth term
the formula for that is N = A + (n-1) * d
198 = 102 +(n-1) * 3
from this u get n =33
Answer: A
Question: Half of the workers in Palabras bookstore have read the latest book by J. Saramago, and 1/6 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 42 workers in the Palabras bookstore, how many of them have read both books?
Options:
A)3
B)12
C)9
D)8
E)7
Rationale: There are total 42 workers.
Half of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 21 have read Saramago.
1/6 of the workers have read the latest book by H. Kureishi.
So (1/6) * 42 = 7 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 20 - B have read Saramago but not Kureishi.
So, (21 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
42 = 21 + 7 - B + (21 - B - 1)
B = 3
Answer (A)
Answer: A
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
A)33
B)63
C)22
D)29
E)177
Rationale: Explanation:
Required number of ways = \inline {\color{Black}(7C_{5}\times 3C_{2})=(7C_{2}\times 3C_{1})=63}
Answer: B) 63
Answer: B
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:
Options:
A)4cm
B)6cm
C)8cm
D)10cm
E)9cm
Rationale: Explanation:
Curved surface area of sphere =4/πr2Surface area of cylinder =2πrh
=>4/πr2=2πrh
=>r2=6∗12/2
=>r2=36
=>r=6
Note: Diameter of cylinder is 12 so radius is taken as 6.
Option B
Answer: B
Question: If cost of sugar increases by 52%. How much percent consumption of sugar should be decreased in order to keep expenditure fixed?
Options:
A)34.21
B)35.15
C)36.32
D)28.21
E)26.54
Rationale: 100
152
-----
152 ----- 52
100 ------ ? => 34.21%
Answer:A
Answer: A
Question: Three numbers are in the ratio 1:4:8 and their H.C.F is 3. The numbers are?
Options:
A)3, 15, 24
B)3, 12, 27
C)3, 12, 22
D)3, 12, 24
E)3, 12, 21
Rationale: Let the required numbers be x, 4x and 8x. Then, their H.C.F = x. So, x = 3.
The numbers are 3, 12, 24.
Answer: D
Answer: D
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
Options:
A)80% p.a
B)10% p.a
C)20% p.a
D)28% p.a
E)30% p.a
Rationale: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer:C
Answer: C
Question: In a class of 40 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
Options:
A)6
B)8
C)10
D)11
E)14
Rationale: 26 + 20 - 17 = 29
40 - 29 = 11 play neither
Answer is D
Answer: D
Question: Express 20 mps in kmph?
Options:
A)23
B)88
C)90
D)72
E)21
Rationale: 20 * 18/5 = 72 kmph
Answer:D
Answer: D
Question: Edward is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 6 miles per hour and returns along the same route at an average speed of 9 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
Options:
A) 5.5
B) 5.8
C) 6.0
D) 6.3
E) 7.2
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here Edward's uphill speed = 6 mph
Edward's downhill speed = 9 mph
2*6*9/(6+9) = 108/15 = 7.2
Correct answer - E
Answer: E
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs. 1400 per sq. metre.
Options:
A)Rs. 15000
B)Rs. 15550
C)Rs. 15600
D)Rs. 28875
E)None of these
Rationale: Solution
Area of the floor = (5.5 × 3.75) m2 = 20.625 m2
∴ Cost of paving = Rs. (1400 × 20.625) = 28875. Answer D
Answer: D
Question: At the time of marriage, a man was 8 years elder to his wife. 15 years after their marriage, his age is 5/4 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
Options:
A)15 years
B)30 years
C)18 years
D)17 years
E)26 years
Rationale: let wifes age= x
husband age = x+8
now after 15 years of mrg x+15 wifes age
x+8+15 husbands age
5/4(x+15)=x+8+15
after solving x=17
ANSWER:D
Answer: D
Question: It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?
Options:
A)2^16
B)7 * 2^23
C)7 * 2^33
D)5 * 2^32
E)2^96 + 1
Rationale: Assume 2^32 = x
Therefore , (2^32 + 1) = (x + 1) --------eq. 1
2^96 + 1 = (2^32)^3 + 1
= x^3 + 1 = x^3 + 1^3
= (x + 1) (x^2 - x +1)---------eq. 2
From eq. 1 and 2
Option E is correct.
Answer: E
Question: List L: ABC, BCA, CAB
In list L above, there are 3 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
Options:
A)47
B)114
C)152
D)161
E)488
Rationale: Sum = (100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B) = 111*(A + B + C).
So, we have that the sum will be a multiple of 111=3*37.
As for A + B + C: if A=1, B=2 and C=4, then A + B + C = 7, so the sum will also be divisible by 7 BUT if A=1, B=2 and C=8, then A + B + C = 11, so the sum will also be divisible by 11. This implies that A + B + C will not produce the same factors for all possible values of A, B and C.
Therefore, we can say that 111*(A + B + C) MUST be divisible only by 111 --> so, by 1, 3, 37, and 111 --> 1 + 3 + 37 + 111 = 152.
Answer: C.
Answer: C
Question: If the cost price of 50 articles is equal to the selling price of 46 articles, then the gain or loss percent is?
Options:
A)22
B)65
C)78
D)33
E)8.69
Rationale: Given that, cost price of 50 article is equal to selling price of 46 articles.
Let cost price of one article = Rs. 1
Selling price of 46 articles = Rs. 50
But Cost price of 46 articles = Rs. 46
Therefore, the trader made profit.\Percentage of profit = 4/46 * 100 = 8.69%
Answer:E
Answer: E
Question: The ratio between the present age of P and Q is 6 : 7. if Q is 4 years old then P, what will be the ratio of the ages of P and Q after 4 year ?
Options:
A)3 : 4
B)3 : 5
C)7 : 8
D)4 : 3
E)None of these
Rationale: Solution
Let P's age and Q's age be 6x years and 7x years respectively.
Then, 7x - 6x = 4 ⇔ x = 4.
∴ Required ratio = (6 x + 4) : (7 x + 4) = 28 : 32 = 7 : 8 .Answer C
Answer: C
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
Options:
A)2/5
B)3/5
C)3/7
D)3/11
E)None
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5.
A)
Answer: A
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)333 Sec
B)190 Sec
C)176 Sec
D)2687 Sec
E)1876 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: B
Question: A, B can Complete a work in 15 days &10 days respectively. They started doing thework together after 2 days B had to leave and A alone completed the remaining work.The whole work wascompleted in how many days?
Options:
A)8 days
B)10 days
C)12 days
D)14 days
E)16 days
Rationale: A and B can complete whole work in
30/(2+3)=6 days
Part of work completed together in
3 days =2/6=1/3 part
Now 2/3 part will be completed by A in
2/3*15=10 days
Hence, whole work will be completed in
2+10=12 days
C
Answer: C
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability E that the World Series will consist of fewer than 7 games?
Options:
A) 12.5%
B) 25%
C) 31.25%
D) 68.75%
E) 75%
Rationale: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability E that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Answer: D
Question: Find the sum of first 30 natural numbers
Options:
A)470
B)468
C)465
D)463
E)485
Rationale: Explanation:
Sum of n natural numbers
=n(n+1)2
=30(30+1)2=30(31)2=465
Answer: Option C
Answer: C
Question: What should come in place of the question mark(?) in the following equation?
4 1⁄2 × 4 1⁄3 - 8 1⁄3 ÷ 5 2⁄3 = ?
Options:
A)8
B)18 1⁄34
C)13 3⁄34
D)7⁄17
E)None of these
Rationale: ? = 9⁄2 × 13⁄3 - 25⁄3 × 3⁄17
= 39⁄2 - 25⁄17 = 663−50/34=613/34=18 1/34
Answer B
Answer: B
Question: Tina’s cat weighs 3.2 kilograms. Her dog weighs 5 times as much as her cat. How much does her dog weigh in kilograms?
Options:
A)A)10.4kg
B)B)38kg
C)C)22kg
D)D)48kg
E)E)16kg
Rationale: 3.2*5=16kg.Answer is E.
Answer: E
Question: A certain telephone company company charges 3.10 cents for the first 1/5 of a minute plus 0.40 cents for each additional 1/5 of a minute. What would this company charge for a talk time of 8 minutes long?
Options:
A)15.60
B)16.0
C)17.8
D)18.7
E)19.1
Rationale: first 1/5 minute charge = 3.10 cents
rest of the minute = 8 - (1/5) = 39/5
charge for the rest of the minute = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7 cents
Answer is D.
Answer: D
Question: How many numbers with 3 different digits can be formed using only the even-numbered digit?
Options:
A)10
B)24
C)40
D)60
E)120
Rationale: Odd digits are 2, 4, 6, 8.
We want 3 different digits.
First digit can be chosen in 4 ways.
Second digit can be chosen in 3 ways.
Third digit can be chosen in 2 ways.
Total ways = 4*3*2
= 24
Hence option (B).
Answer: B
Question: A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x?
Options:
A)16
B)18
C)20
D)22
E)24
Rationale: The median is (6+8)/2 = 7
The mean is (4+5+6+8+15+x)/6 = (38+x)/6
(38+x) /6 * 3/4 = 7
x = 56-38 = 18
The answer is B.
Answer: B
Question: If a boat goes upstream at 5 km/hr and downstream at 7 km/hr what is the speed of the stream?
Options:
A)1.5 kmph
B)1.2 kmph
C)1.1 kmph
D)1.3 kmph
E)1 kmph
Rationale: Sol.
Speed of stream = 1/2(7 -5) kmph = 1 kmph.
Answer E
Answer: E
Question: 4 friends went for a cinema, and everyone decided to contribute equally to the total bill of $60. If one of the friends had a coupon for 8% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
Options:
A)13
B)13.1
C)13.2
D)13.8
E)14
Rationale: At the non-discounted price, each friend would pay $15, as $60 divided by 4 friends is $15 per friend. But if the bill is 8% off, then each friend would pay 8% less. 8% of $15 is $1.2, so each friend saves $1.2 and pays the remaining 13.8
CORRECT OPTION:OPTION D
Answer: D
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)Rs.3990
B)Rs.3967
C)Rs.3927
D)Rs.3900
E)Rs.3282
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer: D
Answer: D
Question: Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?
Options:
A)67.8
B)67.4
C)67.2
D)67.6
E)67.0
Rationale: If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,
average speed of the whole journey = (2xy)/x+y kmph.
By using the same formula, we can find out the average speed quickly.
Average speed
=(2×84×56)/(84+56)
=(2×84×56)/140
=(2×21×56)/35
=(2×3×56)/5
=3365=67.2
Answer is C.
Answer: C
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40. What is the reduced price/dozen?
Options:
A)3
B)4
C)5
D)6
E)9
Rationale: Sol. lie purchases 6a bananas mere for 4096 of Rs 40 or, Rs 16. Reduced price per do 3
A
Answer: A
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
Options:
A)20
B)25
C)30
D)40
E)50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 40
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, D is the answer
Answer: D
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
Options:
A)1/2
B)1
C)2/3
D)3/5
E)3/8
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: A
Question: A, B, C subscribe Rs. 50,000 for a business, A Subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, C receives :
Options:
A)8400
B)14703
C)37798
D)13777
E)14778
Rationale: Explanation:
Let C = x. Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000 <=> 3x = 36000 <=>
x = 12000.
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
C's share = Rs. (35000 * 12/50 ) = Rs. 8,400.
Answer: A)
Answer: A
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability R of generating an odd prime digit is between
Options:
A)0 and 1/6
B)1/6 and 1/3
C)1/3 and 1/2
D)1/2 and 2/3
E)2/3 and 5/6
Rationale: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability R= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Answer: B
Question: P and Q invested in a business. The profit earned was divided in the ratio 2 : 3. If P invested Rs 40000, the amount invested by Q is
Options:
A)30000
B)50000
C)40000
D)20000
E)60000
Rationale: Let the amount invested by Q = q
40000:q=2:3
⇒40000×3=2q
⇒q=(40000×3)/2=60000
Answer is E.
Answer: E
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)5 kmph
B)13 kmph
C)65 kmph
D)55 kmph
E)14 kmph
Rationale: Speed of the boat in still water
= (70+80)/2
= 75 kmph. Speed of the stream
= (80-70)/2
= 5 kmph.
Answer: A
Answer: A