divelab/Sys2Bench huggingface dataset:
Question: 50 litres of diesel is required to travel 600 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 800 km using 1200 cc engine?
Options:
A)80 litres
B)90 litres
C)100 litres
D)170 litres
E)None of these
Rationale: Explanatory Answer
To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 800/600*50 = 66.67 litres.
However, the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity.
i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too.
Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800*66.67 = 100 litres.
Answer C
Answer: C
Question: There are 5 bags three of which each contains 4 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from first group.
Options:
A)2/7
B)6/35
C)8/25
D)5/6
E)3/5
Rationale: Please go through my solution and suggest any mistake.
Chances of selecting a white ball from group 1: 2/3---------------------Chances of selecting a white ball from group 2: 1/5
Thus combined probability of section of white ball from group 1:
3/5 x 2/3 = 2/5
Thus combined probability of section of white ball from group 2:
2/5 x 1/5 = 2/25
Out of these chances, chance of occurrence of first case : (2/5) / (2/5 + 2/25) = 5/6
D
Answer: D
Question: In an office in Singapore there are 60% female employees. 50 % of all the male employees are computer literate. If there are total 62% employees computer literate out of total 1400 employees, then the no. of female employees who are computer literate ?
Options:
A)588
B)674
C)672
D)960
E)None
Rationale: Solution: Total employees,
= 1400
Female employees, 60% of 1400.
= (60 *1400) /100 = 840.
Then male employees,
= 560
50 % of male are computer literate,
= 280 male computer literate.
62 % of total employees are computer literate,
= (62 *1400) /100 = 868 computer literate.
Thus, Female computer literate = 868 - 280
= 588.
Answer: Option A
Answer: A
Question: 9 - 3 ÷ 1/3 + 5 = ?
Options:
A)5
B)3
C)6
D)9
E)12
Rationale: 9 - 3 1/3 + 5
=9-3÷1/3+5
=9-(3X3) +5
=9-9+5
=5
CORRECT ANSWER : A
Answer: A
Question: a product of ages of ankit and nikita is 240. if twice the age of nikita is more than ankit's by 4 years. what is the nikita's age?
Options:
A)12yrs
B)13yrs
C)14yrs
D)15yrs
E)11yrs
Rationale: if ankit age=x
nikita age=240/x
then (2*(240/x))-x=4 so,x=20
ankit age=20yrs
nikita age=(240/20)=12yrs
ANSWER:A
Answer: A
Question: The average weight of 22 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)48.89
B)42.25
C)50
D)51.25
E)52.25
Rationale: Explanation:
Average weight of 22 boys = 50.25
Total weight of 22 boys = 50.25 × 22
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 16)+ (45.15 × 8)
Total boys = 22 + 8 = 30
Average weight of all the boys = ((50.25×22)+(45.15×8))/30
=48.89
Answer: Option A
Answer: A
Question: An seller earns an income of Re 3 on the first day of his business. On every subsequent day, he earns an income which is just thrice of that made on the previous day. On the 15th day of business, he earns an income of:
Options:
A)19
B)22
C)25
D)20
E)36
Rationale: 2nd day he earns = 3(2 – 3)
3rd day he earns = 3(3 – 3)
On 15th day he earns 3(15 -3) = 36 rupees
ANSWER:E
Answer: E
Question: It rained as much as on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was 3 cms, How much did it rain on Wednesday?
Options:
A)10.9
B)10.5
C)10.2
D)10.1
E)10.6
Rationale: Explanation:
Let the rainfall on wednesday = 6x.
∴ Rainfall on the remaining days = 6x
Given,
(6x + 6x )/7 = 3
⇒12x = 21
⇒6x = 10.5
Answer: B
Answer: B
Question: Find the value of x from the below equation? : 3x^2+5x+2 = 0
Options:
A)-1
B)1
C)2
D)3
E)4
Rationale: a = 3, b = 5, c = 2
x1,2 = (-5 ± √(52 - 4×3×2)) / (2×3) = (-5 ± √(25-24)) / 6 = (-5 ± 1) / 6
x1 = (-5 + 1)/6 = -4/6 = -2/3
x2 = (-5 - 1)/6 = -6/6 = -1
A
Answer: A
Question: Of the science books in a certain supply room, 50 are on botany, 55 are on zoology, 90 are on physics, 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same area science?
Options:
A)81
B)159
C)166
D)285
E)314
Rationale: The worst case scenario is to remove all the books on botany, zoology, and geology.
Also we can remove 79 books each from physics and chemistry.
The total is 50 + 55 + 50 + 79 + 79 = 313.
The next book removed must either be physics or chemistry, ensuring 80 books in that subject.
The answer is E.
Answer: E
Question: The average weight of 8 girlsincreases by 2.5 kg when a new gitl comes in place of one of them weighing 65 kg. What might be the weight of the new girl?
Options:
A)65 kg
B)75 kg
C)85 kg
D)90 kg
E)92 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg
C
Answer: C
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 7000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?
Options:
A)$28000
B)$15000
C)$12000
D)$10000
E)$9000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($7,000*2)*2=$28,000 (after 9 years investment will become $7,000*2=$14,000 and in another 9 years it'll become $14,000*2=$28,000).
Answer: A.
Answer: A
Question: From a Group of 9 People, Including George and Nina, 4 people are to be selected at random to work on a certain project. What is the probability that 4 people selected will include George but not Nina
Options:
A)5/56
B)9/56
C)15/56
D)35/120
E)25/56
Rationale: Number of ways of selecting 4 people out of 9 people = 9C4
In the three members George will always be there in the team. At this step we have vacancy for 3 more members and 8 members are available. Nina cannot be there in the team. So 3 members have to be selected and the number of available members = 8 - Nina = 7
Number of ways to form a 4 member team that includes George and excludes Nina = 7C3
Probability = 7C3/9C4 = 35/120
Answer: D
Answer: D
Question: A train crosses a platform in 25 sec, same train crosses another platform of length 400 m in 30 sec. If the length of the train is 200m , find the length of the platform?
Options:
A)280m
B)180m
C)350m
D)300m
E)267m
Rationale: Length of the platform be ‘X’
(X + 200)/25 = (200 + 400)/30
6X + 1200 = 3000
X = 300m
Answer: D
Answer: D
Question: In a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Options:
A)12.9
B)12.1
C)12.3`
D)12.6
E)12.5
Rationale: Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years
Answer: D
Answer: D
Question: A number x is 6 times another number y. The percentage that y is less than x is
Options:
A)12.5%
B)83.3%
C)80%
D)11%
E)1%
Rationale: Say y=1 and x=6.
Then y=1 is less than x=6 by (6-1)/6*100=5/6*100=83.3%.
Answer: B.
Answer: B
Question: A football player scores 4 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be
Options:
A)4
B)6
C)8
D)10
E)16
Rationale: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.
Here, I'll start with Answer E = 16 goals
If....
Total goals = 16 goals
5th game = 4 goals
1st 4 games = 12 goals
Avg. for 1st 4 games = 12/4 = 3 goal/game
Avg. for all 5 games = 6/5 = 3.2 goals/game
This is an EXACT MATCH for what we're told in the prompt, so Answer E MUST be the answer.
Answer: E
Question: Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R ?
Options:
A)377
B)500
C)287
D)179
E)112
Rationale: Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 - (p + q) => r = Rs.500.
Answer: B
Answer: B
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $170. What is the share of Rahul?
Options:
A)$68
B)$40
C)$60
D)$100
E)$90
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 170*2/5 = $68
Answer is A
Answer: A
Question: The function F(n) is defined as the product of all the consecutive positive integers between 2 and n^2, inclusive, whereas the function G(n) is defined as the product of the squares of all the consecutive positive integers between 1 and n, inclusive. The exponent on 2 in the prime factorization of F(3)/G(3) is
Options:
A)	1
B)	2
C)	3
D)	4
E)	5
Rationale: F(3)/G(3)
=product(1 to 3 ^2) / 1.2^2.3^2
=1.2.3.4.5.6.7.8.9/1.4.9
=1.2.3.(2^2).5.(2.3).7.(2^3).9/1.(2^2).9
=1.(2^7).3.5.7.9/1.(2^2).9
Loof for 2^7/2^2=2^5 ----Exponent 3
Answer: C
Answer: C
Question: S is a set of 85 consecutive multiples of 5. If the smallest number in S is 90, then the greatest number in S is
Options:
A)158
B)597
C)599
D)402
E)510
Rationale: last term =first term +(total no. of terms-1)consecutive difference
S is a set of 85 consecutive multiples of 5. If the smallest number in S is 90, then the greatest number in S is
first term = 90 ; total terms =85 ; difference = 5
90+(84)5 = 510
Ans E
Answer: E
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 9. What is the value of x?
Options:
A)20
B)60
C)100
D)120
E)150
Rationale: y = 0.5*0.5*x = x/4
y%*x = 9
(y/100)*x = 9
(x/400)*x = 9
x^2 = 9*400
x = 60
The answer is B.
Answer: B
Question: One day a car rental agency rented 3/4 of its cars, including 2/3 of its cars with CD players. If 3/5 of its cars have CD players, what percent of the cars that were not rented had CD players?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/6
Rationale: The cars with CD players which were not rented is (1/3)(3/5) = 1/5 of all the cars.
The cars which were not rented is 1/4 of all the cars.
The percent of non-rented cars which had CD players is (1/5) / (1/4) = 4/5
The answer is D.
Answer: D
Question: To produce an annual income of Rs. 1200 from a 12 % stock at 90,the amount of stock needed is :
Options:
A)Rs. 10,000
B)Rs. 10,800
C)Rs. 14,400
D)Rs. 16,000
E)Rs. 46,000
Rationale: Solution
For an income of Rs. 12, stock needed = Rs. 100.
For an income of Rs. 1200, stock needed = Rs. 10/12x12000=10,000
Answer A
Answer: A
Question: .007/?= .01
Options:
A).7
B).07
C).007
D).0007
E)None of them
Rationale: Let .007/x = .01;
Then x = .007/.01
= .7/1
= .7
Answer is A
Answer: A
Question: A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs. 1800 and Rs. 1600 respectively, find the monthly income of B
Options:
A)Rs. 3400
B)Rs. 2700
C)Rs. 1720
D)Rs. 7200
E)Rs. 8200
Rationale: Explanation:
Incomes of A and B=5x and 6x and expenses of A and B = 3y and 4y
Then, savings of A = 5x-3y = 1800—?(1)
Savings of B = 6x-4y = 1600—?(2)
By solving equations (1) and (2)
y = 1400
Monthly income of B = Expenses of B + savings of B
= 4y+1600 = 4(1400) + 1600 = Rs. 7200
Answer: D
Answer: D
Question: John has 10 pairs of matched socks. If he loses 9 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 4 pairs(8 socks) out of 10 pairs 1 sock from the 5th pair.
Thus the no of matching socks pair remaining = 10 -5 = 5
Answer C
Answer: C
Question: Jim takes a seconds to swim d meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?
Options:
A)c(b-a)/ a+b
B)d(a-b)/a+b
C)c(a+b)/a-b
D)ab(a-b)/a+b
E)ab(b-a)/a+b
Rationale: Both JimRoger are travelling at constant speedin opposite direction:
So, speed of Jim = d/a speed of Roger = d/b
Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (c-x) from point Q
[x would be less than (c-x) as Jim is travelling slow]
From above, time taken by Jim to travel x = xa/d....................... (1)
Also, time taken by Roger to travel (c-x) = (d-x)b/d.....................(2)
Time taken by both JimRoger is same, so (1) = (2)
xa/d = (d-x)b/d,
Solving further, x = bd/(a+b).................... (3)
We require to find how many fewer meters will Jim have swum i.e
additional distance travelled by Roger = (d - x) - x
= d-2x
Substituting value of x from (3)solving the equation further, we get Answer = d(a-b)/a+b
Answer = (B)
Answer: B
Question: In the first 10 overs of a cricket game, the run rate was only 3.4. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)4.25
B)5
C)6.2
D)7
E)7.5
Rationale: Required run rate = 282 - (3.4 x 10) =	248
248/40 = 6.2
C)
Answer: C
Question: Which of the following equations describes a line that is perpendicular to y=x-7?
Options:
A)y = x + 7
B)y = −5 − x
C)y = 7x
D)y = 7x+1
E)y = 1/x - 7
Rationale: Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x-7 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
Answer: B
Question: A taxi company with a fleet of 50 taxis, plans to replace all their taxis with electric cars. Every year it retires 10 of their old taxis and buys 12 electric cars to replace them. How many years will it take to reduce their old taxi fleet to below 50% of their entire fleet if they started in 2003.
Options:
A)3
B)4
C)1
D)2
E)10
Rationale: Total fleet--50
End of year 2003 -- (retires 10 and buys 12) total fleet--52(40 old 12 new).
End of year 2004 -- (retires 10 and buys 12) total fleet--54(30 old 24 new).
End of year 2005 -- (retires 10 and buys 12) total fleet--56(20 old 36 new).
Answer is A--after 3 years the company has a total of 56 taxis (20 old 36 new), the old taxis are already less than 50% of its fleet.
Answer: A
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
Options:
A)628 ways
B)600 ways
C)767 ways
D)762 ways
E)672 ways
Rationale: Two men, three women and one child can be selected in 4C2 * 6C3 * 5C1 ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5
= 600 ways.
Answer:B
Answer: B
Question: If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
Options:
A)10 km
B)8 km
C)6km
D)4km
E)7 km
Rationale: Sol. Let the required distance be x km
Difference in the time taken at two speeds=1 min =1/2 hr
Hence x/5-x/6=1/5<=>6x-5x=6
x=6
Hence, the required distance is 6 km
Option C
Answer: C
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
Options:
A)5 to 4
B)3 to 2
C)2 to 1
D)5 to 1
E)6 to 1
Rationale: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6
# of 4 letter code words:
nPr = 10! / (10 – 4)! = 10*9*8*7
# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8*7) = 6 = 6/1
Answer is E.
Answer: E
Question: A husband and wife can complete a certain task in 1 and 3 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
Options:
A)a)15:46
B)b)3:10
C)c)12:23
D)d)5:16
E)e)10:3
Rationale: couples one hour work=1/1+1/3=4/3
so total time=3/4.
now, kids one hour work=1/4+1/6=5/12
so total time=12/5..
ratio=3/4:12/5=5:16
ans D
Answer: D
Question: How many different committees each composed of 2 Republicans and 3 Democrats can be formed from a group of 4 Republicans and 5 Democrats?
Options:
A)12
B)24
C)60
D)72
E)120
Rationale: Let's take the Republicans. How many combinations of 2 can be created.
There are four total so: 4!/2!2! = 6
Democrats: 5!/3!2! = 10
6 x 10 = 60
ANSWER:C
Answer: C
Question: 10^25 - 260 is divisible by all of the following except:
Options:
A)A.10
B)B.8
C)C.5
D)D.4
E)E.2
Rationale: The last three digits ( 1000 - 260 ) 740
740 is divisible by 10,4,2,5
740 is not evenly divisible by 8 so the answer is B) 8
Answer: B
Question: M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 2, 3}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
Options:
A)0
B)1/3
C)2/5
D)1/2
E)3/5
Rationale: Answer C.
Total # of outcomes: 5*5= 25
# of outcomes where Product is -ve : (-6,1) ,(-6,2), (-6,3)... Hence, total: 10
Probability: 10/25 = 2/5
Answer: C
Question: A train 600 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is:
Options:
A)45 km/hr
B)149 km/hr
C)54 km/hr
D)55 km/hr
E)56 km/hr
Rationale: Speed of the train relative to man = (600/15) m/sec = 40 m/sec. [40 * (18/5)] km/hr = 144 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 144 ==> x = 149 km/hr.
ANSWER: B
Answer: B
Question: 3/4th of a number exceeds its 2/3rd by 8. What is the number?
Options:
A)96
B)36
C)72
D)144
E)146
Rationale: Explanation:
Let the number be x.
3/4x = 2/3x + 8
Multiply by 12
9x = 8x + 96
x = 96
ANSWER :A
Answer: A
Question: If p/q =4/5, then the value of 18/7 + {(2q - p) / (2q + p)} is ?
Options:
A)3 / 7
B)34
C)1
D)2
E)3
Rationale: Answer
Given Exp. = 18 / 7 + {(2q - p) / (2q + p)}
Dividing numerator as well as denominator by q,
Exp = 18/7 + {2-p/q) / (2 + p/q)}
= 18/7 + {(2 - 4/5) / (2 + 4/5)}
= 18/7 + 6/14
= 18/7 + 3/7
=21/7
=3
Correct Option: E
Answer: E
Question: The total age of A and B is 13 years more than the total age of B and C. C is how many years younger than A?
Options:
A)13
B)24
C)C is elder than A
D)Data inadequate
E)None
Rationale: Solution
[(A+B) - (B+C)]	= 13
â€¹=â€ºA - C
= 13.
Answer A
Answer: A
Question: A group consists of 7 men, 7 women and 6 children. In how many ways can 2 men , 1 woman and 2 child selected from the given group?
Options:
A)2210
B)2205
C)2215
D)2230
E)2245
Rationale: Two men, one woman and two child can be selected in 7C2 * 7C1 * 6C2 ways
7*6/2*1*7*6*5/2*1
=2205 ways
Answer : B
Answer: B
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 45%?
Options:
A)600
B)887
C)256
D)654
E)725
Rationale: Cost price = Rs.500
profit = 45% of 500 = Rs.225
Selling price = Cost price + Profit
= 500 + 225 = 725
Answer: E
Answer: E
Question: Suresh started a business, investing Rs.18000. After 3 months and 4 months respectively, Rohan and Sudhir joined him with capitals of 12000 and 9000. At the end of the year the total profit was Rs.3795. What is the difference between Rohan’s and Sudhir’s share in the profit?
Options:
A)s.345
B)s.350
C)s.352
D)s.362
E)s.368
Rationale: Suresh : Rohan : Sudhir
Ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8
= 6 : 3: 2
The difference between Rohan’s and Sudhir’s share = 1 share
:.i.e. = Rs. 3795 × 1/11 = Rs.345.
A
Answer: A
Question: The average weight of a group of 30 friends increases by 3 kg when the weight of their 3 football coaches was added. If average weight of the group after including the weight of the 3 football coach is 33 kg, what is the average weight of their football coaches ?
Options:
A)31 kg
B)63 kg
C)61 kg
D)62 kg
E)91 kg
Rationale: let c=coach's avg. weight
original total weight=(30 friends)(30 kg avge)=900kg
(900+3c)/(30+3)=33 kg avg.
c=63 kg
Answer B
Answer: B
Question: Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?
Options:
A)20 years
B)22 years
C)25 years
D)27 years
E)29 years
Rationale: let varuns age =x
x+1=2(x-12)
der4 x=25..
ANSWER:C
Answer: C
Question: Two members of a club are to be selected to represent the club at a national meeting. if there are 120 different possible selections of the 2 members, how many members does the club have?
Options:
A)20
B)27
C)16
D)57
E)95
Rationale: I have done this problem by substituting numbers
We have n!/2!(n-2)! = 120
or n(n-1)/2 = 120 or n^2-n =240 or (n-16)(n+15)
n=16 satisfies the equation
C
Answer: C
Question: In covering a distance of 15 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A's speed is:
Options:
A)5 km/h
B)8 km/h
C)10 km/h
D)15 km/h
E)2.5 km/h
Rationale: Let A's speed be X km/hr.
Then, 15/x - 15/2x = 3
7.5/x = 3
x = 2.5 km/hr.
Answer : E
Answer: E
Question: If x = 8 and y = −2, what is the value of (x − 2y)^y?
Options:
A)−100
B)0.007
C)0.25
D)4
E)8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
by inversing and squaring 0.007
Answer: B
Answer: B
Question: When 12 + 10 = 1205, 11 + 8 = 885, then 16 + 15 = ?
Options:
A)2405
B)3205
C)2463
D)2631
E)3425
Rationale: A
2405
12 + 10 => 12 × 10 = 120 => 120 × 10 + 5 = 1205
11 + 8 => 11 × 8 = 88 => 88 × 10 + 5 = 885
16 + 15 => 16 × 15 = 240 => 240 × 10 + 5 = 2405
Answer: A
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different Y ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
Options:
A)5
B)6
C)9
D)12
E)18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible Y is 2*6=12.
Answer: D.
Answer: D
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long Q would it have taken for him to walk both ways.
Options:
A)8 h 45 min
B)7 h 45 min
C)6 h 45 min
D)5 h 30 min
E)None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back Q=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: A
Question: I. a2 + 11a + 30 = 0,
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
Options:
A)If a < b
B)If a ≤ b
C)If the relationship between a and b cannot be established
D)If a > b
E)If a ≥ b
Rationale: I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b
ANSWER:B
Answer: B