divelab/Sys2Bench huggingface dataset:
Question: Of 30 applicants for a job, 10 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
Options:
A)14
B)13
C)9
D)7
E)5
Rationale: C. 9
30 - 3 = 27
27 - 10 - 18 = -9
Then 9 are in the intersection between 4 years experience and degree.
Answer C
Answer: C
Question: A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
Options:
A)104
B)190
C)109
D)278
E)211
Rationale: Explanation:
624/6 = 104 kmph
Answer:C
Answer: C
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)160
B)175
C)180
D)195
E)172
Rationale: Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
Therefore, 160 x 2.40 + x x 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER IS B
Answer: B
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
Options:
A)20
B)18
C)23
D)26
E)24
Rationale: (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
ANSWER E
Answer: E
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present?
Options:
A)61.5
B)60.5
C)63.5
D)62.5
E)64.5
Rationale: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 2x/5
Hence, number of buckets needed = 25x/(2x/5)=(25×5)/2=62.5
Answer is D.
Answer: D
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
Options:
A)1000
B)1250
C)1300
D)1529.41
E)1625
Rationale: 300 gallons of water increases capacity by 30% that means
30% is 300 gallons, so 100% would be = 300*100/30= 1000 gallons
Now 1000 +300 gallons is 85% capacity of tank.
so 100% capacity would be= 1300 *100/85= 1529.41
D is the answer
Answer: D
Question: 8 men can do a piece of work in 12 days. 4 women can do it in 48 days and 10 children can do it in 24 days. In how many days can 10 men, 20 women and 10 children together complete the piece of work?
Options:
A)5 days
B)15 days
C)28 days
D)4 days
E)7 days
Rationale: Explanation:
1 man’s 1 day’s work = 1/8 × 12 = 1/96
10 men’s 1 day’s work = 1 × 10/96 = 5/48
1 woman’s 1 day’s work = 1/192
20 women’s 1 day’s work = 1/192 × 20 = 5/48
1 child’s 1 day’s work = 1/240
10 children’s 1 day’s work = 1/24
Therefore, (10 men + 20 women + 10 children)’s 1 day’s work = 5/48 + 5/48 + 1/24
=1/4
The required No. of days = 4 days
Answer: Option D
Answer: D
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,050 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
Options:
A)25.0
B)30.2
C)35.3
D)40.2
E)41.4
Rationale: Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=1050
r=41.4
Answer:E
Answer: E
Question: On increasing the price of T.V. sets by 30%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
Options:
A)4
B)5
C)56
D)2
E)7
Rationale: Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(130 × 80) = Rs.10400
Increase% = 4001000040010000 × 100 = 4%
Answer: A
Answer: A
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 20%. What is the selling price of the cycle?
Options:
A)s. 1090
B)s. 1120
C)s. 1190
D)s. 1202
E)s. 1204
Rationale: since,c.p=1400
loss%=(c.p-s.p)/c.p*100
20=(1400-s.p)/1400*100
so,after solving answer=1120.
ANSWER:B
Answer: B
Question: A five-digit number is formed by using digits 1, 2, 3, 4 and 5 without repetition. What is the probability that the number is divisible by 4?
Options:
A)1/2
B)4/3
C)8/9
D)4/2
E)1/5
Rationale: In each of these cases, the five digits number can be formed using the remaining 3 digits in 3!=6 ways.
A number divisible by 4 can be formed in 6×4=24 ways.
Total number that can be formed using the digits 1, 2, 3, 4 and 5 without repetition
=5!=120
Required probability,
=24/120
=1/5
E
Answer: E
Question: The average of 20, 40 and 180 is twice the average of 10, 30, and which of the following ?
Options:
A)1)10
B)2)30
C)3)60
D)4)80
E)5)180
Rationale: 20 40 180 = 180+60 = 240/3 = 80.
80/2 = 40
10 30 x = 40+x/3 should be smaller than 40
cross multiply 40*3-40 = 80
D
Answer: D
Question: A person covers a distance in 15 minutes. If runs at a speed of 12 km per hour on an average. Find the speed at which he must run to reduce the time of journey to 5 minutes.
Options:
A)18 m/s
B)4 m/s
C)15 m/s
D)10 m/s
E)5 m/s
Rationale: Explanation:
T = 15 m
Spees = 12 kmph
= 12 x 5/18 = 10/3 m/s
Let new speed be "x"
15 x (10/3) = 5x
x = 10 m/s
Answer: Option D
Answer: D
Question: How many diagonals does a 61-sided convex polygon have?
Options:
A)1182
B)1769
C)2456
D)3538
E)4209
Rationale: A 61-sided convex polygon has 61 vertices.
If we examine a single vertex, we can see that we can connect it with 58 other vertices to create a diagonal. Note that we can't connect the vertex to itself and we can't connect it to its adjacent vertices, since this would not create a diagonal.
If each of the 61 vertices can be connected with 58 vertices to create a diagonal then the total number of diagonals would be (61)(58) = 3538
However, we must recognize that we have counted every diagonal twice.
To account for counting each diagonal twice, we must divide 3538 by 2 to get 1769.
The answer is B.
Answer: B
Question: if you toss a coin two times what is the probability that it will land either heads both times or tails both times?
Options:
A)A)1/8
B)B)1/6
C)C)1/4
D)D)1/2
E)E)1
Rationale: Prob to get 2 heads = 1/2*1/2 = 1/4
Prob to get 2 tails = 1/2*1/2 = 1/4
So, Prob to get eithe r 2 heads or 2 tails = 1/4+1/4 = 1/2
Answer will be D.
Answer: D
Question: A cricket bat is sold for $850, making a profit of $245. The profit percentage would be
Options:
A)24%
B)25%
C)30%
D)36%
E)40%
Rationale: 245/(850 - 245) = 245/605 = 49/121 = 40%.
Answer: E.
Answer: E
Question: Rs378 is divided among the three children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of Esha.how much the Rupee anusha get?
Options:
A)74
B)84
C)94
D)104
E)114
Rationale: If money with Anusha=a, Babu=b & Esha=e, then
a+b+e=378 ---(i) &
12a=8b=6e, so b=3a/2 & e=2a
Substituting these values of b & e in (i), a+(3a/2)+2a=378 , On solving, a=84
So, b=126, e=168
ANSWER:B
Answer: B
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 390 m long platform?
Options:
A)19
B)27
C)51
D)47
E)28
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +390)/ 36 * 5/18
= 51 min.
Answer:C
Answer: C
Question: A walks with a speed of 6 km/hr and after 5 hr of his start, B starts running towards A at a speed of 8 km/hr. At what distance from start will B catch A.
Options:
A)100 Km
B)110 Km
C)120 Km
D)140 Km
E)NONE
Rationale: Explanation :
In 5hrs, A will cover 30 km. Now, at some distance ‘x’. So A will cover X distance and B will cover 30 + X.
x/6 = (30+x)/8
x = 90. So distance from start after which B will catch A = 90+30 =120km
Answer – C
Answer: C
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 4 less, he would have made a profit of 10%. The C.P. of the article was
Options:
A)344
B)600
C)200
D)800
E)700
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 4
=> x = 800
Answer: D) Rs 800
Answer: D
Question: P = {105, 106, 107, 108, 109, x}
Set P above consists of 6 integers. For what value of x are the mode, the median and the average equal?
Options:
A)105
B)106
C)107
D)108
E)109
Rationale: Mode of a set is the number with max frequency.
Median for an even numbered set is the average of middle terms.
Average or mean is the sum of the set/No. of elements in the set.
Going from the answer choices, if we use 107 as the missing number.
The set becomes {105, 106, 107, 107, 108, 109}
Now the mode, median and mean are all same, 107
ANS (Option C)
Answer: C
Question: The sum of x, y coordinate values is 2490. if 6.5% of one coordinate is equal to 8.5% of the other, then the coordinate values are :
Options:
A)989,1501
B)1011,1479
C)1401,1089
D)1411,1079
E)None of these
Rationale: Explanation :
Solution: Let the coordinates be x and y. then, 6.5% of x = 8.5% of y
=> x = 85/65
y = 17/13 y
Now, x+y =249017y/13+y = 2490
=> 30y/13 = 2490
=> y = 2490*13/30 = 1079.
.'. One coordinate is = y= 1079, other coordinate = 17y/13 =1411
Answer : D
Answer: D
Question: a fruit vender buys 4 varieties of apple costing rs. 140,rs.150,rs.160 and rs.170 per kg in the ratio 2:3:4:1 and mixes all the four varieties and sells at 50% profit. What is the selling price per kg of apple?
Options:
A)225
B)228
C)230
D)231
E)235
Rationale: CP = 140*2+150*3+160*4+170*1=1540
SP = 1.5*1540=2310
Total no.of kgs=2+3+4+1=10
SP per kg=2310/10=231
ANSWER:D
Answer: D
Question: Which of the following is the lowest positive integer that is divisible by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12?
Options:
A)15,450
B)18,760
C)21,520
D)24,360
E)27,720
Rationale: The number needs to be divisible by 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, and 2^2*3.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 * 11 = 27,720
The answer is E.
Answer: E
Question: The remainder when 1!+2!+3!...+50! divided by 5! will be
Options:
A)21
B)33
C)77
D)927
E)19
Rationale: The remainder when the terms greater than 5! are divided by 5! becomes 0 so we need to consider the terms upto 4!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.
So remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120)
So remainder is 33.
Answer:B
Answer: B
Question: Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/5, 1/3, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?
Options:
A)1/30n
B)(n-1)/15n
C)1/5n
D)(n+2)/3n
E)(3n-2)/5n
Rationale: 1/5 * 1/3 * (1-1/n)
= 1/15 * (n-1)/n
= (n-1)/15n
Answer - B
Answer: B
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 5 years older than B the present age of B is
Options:
A)37
B)38
C)39
D)35
E)41
Rationale: let present age of A be a and B be b
a+10 = 2*(b-10)
=> 2b-a = 30 ......(i)
a = b+5
=>2b-b-5 = 30
b=35
so the present age of b is 35 years
ANSWER:D
Answer: D
Question: Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.
Options:
A)12 sec
B)24 sec
C)48 sec
D)60 sec
E)50 sec
Rationale: Relative speed =(45 + 30) km/hr
=(75 x(5/18)) m/sec
=(125/6)	m/sec.
We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.
So, distance covered = Length of the slower train.
Therefore, Distance covered = 500 m.
Therefore Required time =	(500 x6/125)= 24 sec.
Answer :B
Answer: B
Question: 99,994^2 - 6^2 =
Options:
A)10^10 - 2
B)(10^5 – 2)^2
C)10^4(10^5 – 2)
D)10^5(10^4 – 2)
E)10^5(10^5 – 12)
Rationale: (99,994)^2 - (6)^2 = (100,000 -6)^2 - (6)^2 = (100,000)^2 - 2*6*100,000 + 6^2-6^2=(10^5)^2 - 12*(10^5) = 10^10 - 12*(10^5)=10^5(10^5 - 12) Answer E
Answer: E
Question: Of the three numbers, second number is two times bigger than the first number and is also three times bigger than the third number. If the average of the three numbers is 44, the largest number is
Options:
A)24
B)36
C)72
D)108
E)210
Rationale: Explanation :
Let 3rd number is x. Then, second number = 3x.
First number = 3x / 2
(x + 3x + 3x/2)/3 = 44 or (x+3x+3x/2)=44*3 or 11x/2 = 44*3 or x=24.
Answer : A
Answer: A
Question: Andy has 20 pairs of matched gloves. If he loses 12 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
Options:
A)9
B)11
C)13
D)14
E)15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair
Once you understand the question, You have to choose an answer choice in seconds. Answer will be either it is minimum (A - 9) or maximum (E - 15). Eliminate B,C and D. Since 12 gloves are gone, we can ignore A and straight away choose the maximum [Here its 15 i.e E]
Since there cant be any ambigous answer it should be minimum or maximum in the listed answer choice.
Now mathematical approach for understanding:
Case1: If 12 gloves are gone the maximum probability of losing maximum gloves is 12 pairs of gloves out of 20. This means i m having 8 pairs of gloves. [Minimum number of gloves i can have is 8 pairs]
Case2: If 12 gloves are gone the maximum probability of losing minimum gloves is 12/2 = 6 means i can lose 6 glove. in this scenario i will be having 14 gloves.
Hence10 < Available Glove Pair < 15
any given time I cant possess 15 glove pair for the above mentioned scenario. And thats the answer. E.
Answer: E
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
Options:
A)83.43%
B)83.73%
C)83.23%
D)83.93%
E)83.33%
Rationale: Percentage of milk in the mixture formed
= [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%
= 5/6 * 100% = 83.33%.
Answer:E
Answer: E
Question: When positive integer N is divided by positive integer J, the remainder is 5. If N/J = 105.20, what is value of J?
Options:
A)10
B)50
C)30
D)15
E)25
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 105.20
Here 105 is the quotient.
Given that Remainder = 5
So, 105.20 = 105 + 5/J
So, J = 25
Answer: E
Answer: E
Question: Two trains 161 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)6.18
B)7.12
C)7.1
D)8.09
E)8.11
Rationale: T = (161 + 165)/ (80 + 65) * 18/5
T = 8.09
Answer:D
Answer: D
Question: Twenty four meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
Options:
A)2√2
B)2√5
C)6
D)4√2
E)none of these
Rationale: Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 24
=> x/360*2*pi*r +2r= 24
=> 2A/r+2r=24
=> A= r12-r^2
= r12-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 12-2r=0
r=6
C
Answer: C
Question: In how many a committee of 5 members can be selected from 6men
5 ladies consisting of 3 men and 2 ladies
Options:
A)30
B)150
C)50
D)250
E)200
Rationale: (3 men out of 6) and (2 ladies out of 5) are to be chosen
Required number of ways
=(6C3 * 5C2)
= 200
ANSWER E 200
Answer: E
Question: A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
A)6 days
B)2 days
C)4 4/5 days
D)3 days
E)9 days
Rationale: Work done by A in 2 days = 2/10 = 1/5
Remaining work = 4/5
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days.
Answer: C
Answer: C
Question: Salesperson A's compensation for any week is $350 plus 6 percent of the portion of A's total sales above $1,000 for that week. Salesperson B's compensation for any week is 8 percent of A's total sales for that week. For what amount of total weekly sales would both salepeople earn the same compensation?
Options:
A)$21,000
B)$18,000
C)$15,000
D)$ 14,500
E)$4,000
Rationale: sometime, setting up an equation is an easy way to go with:
350 + 0.06 (x - 1000) = 0.08 x
x = 14,500
Ans : D
Answer: D
Question: You are renting an apartment and you need √900 for each side, how many feet are you looking to measure?
Options:
A)21
B)22
C)23
D)25
E)30
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 900.
Answer E
Answer: E
Question: After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
Options:
A)22 days
B)77 days
C)20 days
D)17 days
E)18 days
Rationale: 1/3 ---- 6
1 -------? A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30
2/3 ----? => 20 days
Answer:C
Answer: C
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of :
Options:
A)Rs. 3100
B)Rs. 6240
C)Rs. 6500
D)Rs. 9600
E)Rs. 9800
Rationale: Solution
To obtain Rs. 10, investment = Rs. 96.
To obtain Rs. 650, investment = Rs.(96/10x650) = Rs. 6240.
Answer B
Answer: B
Question: Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability E, that a book selected at random is either a hard cover book or a chemistry book?
Options:
A)1/10
B)3/20
C)1/5
D)1/4
E)9/20
Rationale: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, E=9 provide the desired outcome, making the answer E.
Answer: E
Question: Carmen made a sculpture from small pieces of wood. The sculpture is 2 feet 10 inches tall.Carmen places her sculpture on a base that is 8 inches tall. How tall are the sculpture andbase together?
Options:
A)3.1 feet
B)3.2 feet
C)3.3 feet
D)3.4 feet
E)3.5 feet
Rationale: we know 1 feet =12 inch then
2 feet =24 inch
24+10=34 then
34+8=42
42/12=3.5 feet
ANSWER:E
Answer: E
Question: What is the compound interest paid on a sum of Rs.1500 for the period of 2 years at 10% per annum.
Options:
A)230
B)175
C)225
D)315
E)None of these
Rationale: Solution= Interest % for 1st year= 10
Interest % for 2nd year= 10+ 10% of 10= 10+ 10 *10/100=11
Total % of interest= 10 + 11=21
Total interest = 21 % 1500 = 1500 * (21/100)= 315
Answer D
Answer: D
Question: A invested Rs 76000 in a business. After few months, B joined him with Rs 57000. The total profit was divided between them in the ratio 2 : 1 at the end of the year. After how many months did B join?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Explanation:
Suppose B was there in the business for xx months. Then
A: B =76000×12:57000×x
Therefore,
76000×12:57000×x=2:1
76×12:57x=2:1
76×12×1=57x×2
76×4=19x×2
4×4=x×2
x=8
Hence B was there in the business for 8 months, or joined after 12-8 = 4 months
Answer: Option C
Answer: C
Question: The average height of 35 boys in a class was calculated as 184cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).?
Options:
A)178.27 cm
B)182.29 cm
C)978.29 cm
D)178.89 cm
E)176.29 cm
Rationale: Calculated average height of 35 boys = 184 cm.
Wrong total height of 35 boys = 184 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 184 cm - (166 cm - 106 cm)/35
= 184 cm - 60 /35 cm
= 184 cm - 1.71 cm = 182.29 cm.
Answer: B
Answer: B
Question: The distance between 2 cities A and B is 1000km. A train starts from A at 1 p.m. and travels towards B at 100 km/hr. Another starts from B at 2 p.m. and travels towards A at 150 km/hr. At what time do they meet?
Options:
A)11am.
B)6p.m.
C)3pm.
D)2p.m.
E)1p.m.
Rationale: Suppose they meet x hrs after 1 p.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 1000
100x + 150 (x-1) = 1000
x = 4.60 = 5 hrs
They meet at 1+5 = 6 p.m.
Answer is B
Answer: B
Question: in a tennis match the probability for A to win the match is 2/3 and he has to win 3 sets to win the match so what is the probability for A to win the match
Options:
A)182/243
B)172/243
C)162/243
D)192/243
E)292/243
Rationale: The sequence of winning as follows:
Sequence Probability
----------------- -----------
W W L W 8/81
W W L L W 8/243
W W W 8/27
W L L W W 8/243
W L W L W 8/243
W L W W 8/81
L L W W W 8/243
L W L W W 8/243
L W W L W 8/243
L W W W 8/81
Thus, by adding all the above probabilities, we get the probability for A to win the match as : 192/243
ANSWER:D
Answer: D
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10
B)11
C)12
D)10.8
E)13
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
Answer: Option D
Answer: D
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
Options:
A)1000
B)1250
C)1300
D)1600
E)1625
Rationale: Since pumping in additional 300 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.
So, we have that 1,000 + 300 = 0.8*{total} --> {total} = 1,625.
Answer: E.
Answer: E
Question: For all integers a and b, a%b = (a + b)(a - b). If 7%x = 13, then which of the following could be a value of x?
Options:
A)-6
B)-5
C)2
D)3
E)6
Rationale: 7%x = (7+x)(7-x)
49-x^2 = 13
x^2 = 36
x=-6,6
Ans: A
Answer: A
Question: A firm is comprised of partners and associates in a ratio of 2:61. If 75 more associates were hired, the ratio of partners to associates would be 4:137. How many partners are currently in the firm?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: The ratio 2:61 = 4:122 so the ratio changed from 4:122 to 4:137.
137-122 = 15 which is 1/5 of the increase in 75 associates.
The ratio changed from 20:610 to 20:685.
Thus the number of partners is 20.
The answer is E.
Answer: E