divelab/Sys2Bench huggingface dataset:
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 30 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
Options:
A)89
B)90
C)92
D)99
E)96
Rationale: The average score in an examination of 10 students of a class is 60 --> the total score = 10*60 = 600;
The 5 smallest scores have an average of 55 --> the total score of the 5 smallest scores = 275.
From above, the total score of the 5 largest scores = 600 - 275 = 325.
Say the 5 largest scores are a, b, c, d, and e (where a<b<c<d<e, since each of the top five scorers had distinct scores). We want to maximize e. To maximize e, we need to minimize a, b, c, and d. The least value of a, is 55 (The least score of the top 5 , a, should be equal to the highest of the bottom 5 and to minimize the highest of the bottom 5, all scores from the bottom 5 should be equal). In this case the least values of b, c, and d are 56, 57, and 58 respectively:
a + b + c + d + e = 55 + 56 +57 + 58 + e = 325;
e = 99.
Answer: D.
Answer: D
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 86 players took part in that tournament. How many matches were played?
Options:
A)90 matches
B)95 matches
C)99 matches
D)85 matches
E)87 matches
Rationale: D 85 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 85 matches were played.
Answer: D
Question: The speed at which a man can row a boat in still water is 15 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 100 meters?
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: The speed of the boat downstream = 15 + 3 = 18 km/hr
18 km/hr * 5/18 = 5 m/s
The time taken to cover 100 meters = 100/5 = 20 seconds.
The answer is D.
Answer: D
Question: In a sports club with 30 members, 17 play badminton and 18 play tennis and 2 do not play either. How many members play both badminton and tennis?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(18-x)+x+2=30
37-2x+x=30
37-x=30
x=7
So 7 members play both badminton and tennis.
A
Answer: A
Question: The positive value of x that satisfies the equation (1 + 2x)^3 = (1 + 3x)^4 is between
Bunuel, can you please explain this one?
Options:
A)0 and 0.5
B)0.5 and 1
C)1 and 1.5
D)1.5 and 2
E)2 and 2.5
Rationale: Trial and error would probably be the easiest way to solve this problem. When x is large enough positive number, then because of the exponents (5>4), LHS will be more than RHS (as you increase the positive value of x the distance between the values of LHS and RHS will increase).
Try x=1 --> LHS=3^5=81*3=243 and RHS=4^4=64*4=256, so (1 + 2x)^5 < (1 + 3x)^4. As you can see LHS is still slightly less than than RHS. So, the value of x for which (1 + 2x)^5 = (1 + 3x)^4 is slightly more than 1.
Answer: B.
Answer: B
Question: The average of first five multiples of 2 is?
Options:
A)6
B)8
C)9
D)5
E)7
Rationale: Average = 2(1 + 2 + 3 + 4 + 5)/5
= 30/5
= 6.
Answer:A
Answer: A
Question: When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the integer B is ?
Options:
A)11
B)44
C)24
D)25
E)22
Rationale: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44
0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.
Only option A-11 satisfies this
for remainder 11,
A=236 and B=25
Ans - D
Answer: D
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.3600. How much third person will get?
Options:
A)2400
B)1600
C)2980
D)2707
E)2872
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 3600 = 1600
Answer:B
Answer: B
Question: If 10 crates have 98 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
A)5
B)10
C)15
D)20
E)0
Rationale: Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20
Answer: D
Answer: D
Question: A company that ships boxes to a total of 15 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)
Options:
A)8
B)7
C)6
D)5
E)9
Rationale: Back-solving is the best way to solve this problem.
You basically need 12 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - D
Answer: D
Question: What is the difference between the compound interest on Rs.12000 at 20% p.a. for one year when compounded yearly and half yearly?
Options:
A)Rs.140
B)Rs.120
C)Rs.130
D)Rs.110
E)None of these.
Rationale: When compounded annually, interest
= 12000[1 + 20/100]1 - 12000 = Rs.2400
When compounded semi-annually, interest
= 12000[1 + 10/100]2 - 12000 = Rs.2520
Required difference = 2520 - 2400 = Rs.120
ANSWER:B
Answer: B
Question: If the probability E of rain on any given day in city x is 50% what is the probability it with rain on exactly 3 days in a five day period?
Options:
A)8/125
B)2/25
C)5/16
D)8/25
E)3/4
Rationale: 5C3 (1/2)^3(1/2)^2
= (5 * 4 * 3!)/2!3! * 1/32
E= 5/16
Answer - C
Answer: C
Question: If a young child was 16 months old one year ago, how old was the child, in months, x months ago?
Options:
A)x − 28
B)x − 12
C)16 − x
D)24 − x
E)28 − x
Rationale: The child's age today is 16 months + 12 months = 28 months
x months ago, the child's age was (28 - x) months old.
The answer is E.
Answer: E
Question: The sector of a circle has radius of 28 cm and central angle 90o. Find its perimeter?
Options:
A)100 cm
B)85 cm
C)75 cm
D)95 cm
E)110 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (90/360 * 2 * 22/7 * 21) + 2(28)
= 44 + 56 = 100 cm
Answer: A
Answer: A
Question: how many internal diagonals does a nonagon (nine sided polygon) have?
Options:
A)25
B)27
C)40
D)56
E)80
Rationale: Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 9
No. of diagonals = 9(9 - 3)/2
= 27
Ans B
Answer: B
Question: Students in Class I, II and III of a school are in the ratio of 3 : 5 : 8. Had 15 more students admitted to each class, the ratio would have become 6 : 8 : 11. How many total students were there in the beginning?
Options:
A)112
B)64
C)96
D)80
E)None
Rationale: Explanation:
Increase in ratio for 3 classes is 6 - 3 = 8 - 5 = 11 - 8 = 3.
Given, 15 more students are admitted to each class.
Therefore, 3 :: 15 ⇒ 1 :: 5
Therefore, 3 + 5 + 8 = 16 :: 16 x 5 = 80.
Hence, total students in the beginning were 80.
Correct Option: D
Answer: D
Question: A voltmeter is used:
Options:
A)22
B)266
C)27
D)26
E)81
Rationale: Explanation:
Answer: Option C
Answer: C
Question: Of the three-digit integers greater than 900, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A) 90
B) 82
C) 80
D) 45
E) 36
Rationale: Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)
[example numbers: 774,779,882,993 etc]
Case II.[ X=Z ]Y is not equal to XZ:XYXorZYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Z can be chosen in 1 way
After XZ are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)
[example numbers: 747,797,828,939 etc]
Case III.[ Y =Z ]X is not equal to YZ :XYYorXZZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 9 ways
After Y is chosen, Z can have 1 way
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)
[example numbers: 744,799,822,933 etc]
Therefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80
One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 900.
Answer:(A)
Answer: A
Question: 0, 6, 18, 36, 60, 90, ?What number should replace the question mark?
Options:
A)126
B)120
C)119
D)126
E)147
Rationale: A 126add 6, 12,18,24,.....
Answer: A
Question: In how many ways can 7 boys be seated in a circular order?
Options:
A)120
B)360
C)420
D)720
E)480
Rationale: Number of arrangements possible = (7-1)!
= 6!
= 6*5*4*3*2*1
=720
Ans -D
Answer: D
Question: A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?
Options:
A)4991
B)4992
C)2777
D)2977
E)2781
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer: A
Answer: A
Question: A and B started a business investing Rs. 10,000 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)1:2
E)18:4
Rationale: A: B = 10000 : 20000 = 1 : 2
ANSWER:D
Answer: D
Question: There is a circular table. It has 60 chairs. Drakula came and sit on a chair beside another person. What is the minimum no. of person will be so, that wherever he sits he always gets to sit beside a person
Options:
A)30
B)20
C)15
D)10
E)5
Rationale: if total seats N = 5 in a circular arrangement ( _ _ M _ _ M ) where first ( _ ) is connected with last Man(M), then min no of persons required= 2.
similarly If N = 9, Man required = 3 i.e,( _ _ M _ _ M _ _ M )
If N= 12, Man required = 4 i.e, ( _ _ M _ _ M _ _ M _ _ M)
have u got any relation??
the no of man required is = Total no of seats in circle / 3
So, A/Q total seat = 60. Man required = 60/3=20
ANSWER:B
Answer: B
Question: An employer pays Rs.20 for each day a worker works and for felts Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal?
Options:
A)10
B)40
C)30
D)20
E)50
Rationale: Suppose a worker remained ideal for x days then he worked for 60-x days
20*(60-x)-3x=280
1200-23x=280
23x=920
x=40
Answer is B.
Answer: B
Question: If a and b are the two values of t that satisfy
the equation t2 – 6t + 8 = 0, with a > b, what is the value of a – b?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Factor the left side of the equation:
t2 – 6t + 8 = 0
(t – 2)(t – 4) = 0
Split this equation into two equations and solve:
t – 2 = 0 t – 4 = 0
t = 2 t = 4
Thus, a = 4 and b = 2. So a – b = 4 – 2 = 2.
correct answer A)2
Answer: A
Question: A and B can do a piece of work in 11 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
Options:
A)15.5 days
B)19.5 days
C)17.5 days
D)9.2 days
E)18.5 days
Rationale: C = 1/5 – 1/11 = 6/55 => 9.2 days
ANSWER:D
Answer: D
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Rs. 15
B)Rs. 12.10
C)Rs. 19.70
D)Rs. 16.80
E)None of these
Rationale: Explanation :
Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25 − (30/100) − x)(6/100) = 30/100
⇒ 6(25 − 0.3 − x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
Answer : Option C
Answer: C
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 500. Find the average mark scored by all the three boys?
Options:
A)384
B)826
C)240
D)269
E)208
Rationale: Average mark scored by all the three boys =
[64/100 (500) + 36/100 (500) + 44/100 (500)] / 3
= 240
Answer: C
Answer: C
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 22 miles, how many miles was Mike's ride?
Options:
A)30
B)36
C)42
D)48
E)54
Rationale: The cost of Annie's ride was 2.5+5+(0.25*22) = $13
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 13
0.25*x = 10.5
x = 42 miles
The answer is C.
Answer: C
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 64, the dividend is:
Options:
A)10301
B)10302
C)10303
D)10304
E)10305
Rationale: Divisor = (5 * 64) = 320
= 10 * Quotient = Divisor
=> Quotient = 320/10 = 32
Dividend = (Divisor * Quotient) + Remainder
Dividend = (320 * 32) + 64 = 10305.
E
Answer: E
Question: A dinner has to be hosted with 5 managers.Find the number of ways in which the managers may be selected from among 9 managers,if 2 managers will not attend the meeting together.
Options:
A)1.35
B)2.None of these
C)3.12
D)4.126
E)5.15
Rationale: 9 managers, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two managers in it. That would mean selecting 5, from the remaining 7 which is 7C5 = 21
2. Meeting with one of the two managers. select 1 manager from two, and then select 4 from the remaining 7, which is 2C1 X 7C4 = 70.
So, answer is 21 + 70 = 91.
Answer : B
Answer: B
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 6 times his original investment. What is the value of n?
Options:
A)50 years
B)25 years
C)62 years 6 months
D)37 years 6 months
E)40 years
Rationale: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $600.
Therefore, the Simple Interest earned = 600 - 100 = $500.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 500 = (100 * n * 8) / 100
Or 8n = 500
Or n = 62.5 years.
correct choice is (C)
Answer: C
Question: The cost price of a cow and a horse is 3 lakhs. The cow is sold at 20% profit and horse at 10% loss.Overall gain is Rs.4200. What is the cost price of the cow?
Options:
A)113000
B)114000
C)115000
D)116000
E)124000
Rationale: let costs of cow and horse are x,y so x+y=300000------(1)
(x*120/100)+(y*90/100)=304200
120x+90y=30420000------(2).
solve equations (1) and (2)
x=114000
ANSWER:B
Answer: B
Question: If u, v and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^(uv)?
I. u+v
II. v^u
III. u^2 * v^2
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: given that p and q are factors of r.
so we can picture it this way r=u*v*n (n-some another factor of r)
so, r^uv= (u*v*n)^uv
I. u+v .since the question is MUST BE TRUE, we eleminate this option
II. (u*v*n)^uv / v^u= integer YES!
III.(u*v*n)^uv/ u^2 * v^2 YEs, since we are said that integer u>1 and integer v>1
Answer: E
Question: A committee of 3 has to be formed randomly from a group of 6 people. If Tom and Mary are in this group of 6, what is the probability that Tom will be selected into the committee but Mary will not?
Options:
A)1/10
B)1/5
C)3/10
D)2/5
E)1/2
Rationale: We have three units - Tom (T), Mary (M) & the Rest (R).
Total ways of making a community of 3 from 6 people = 6 x 5 x 4 = 120
Now ways the community can be formed with Tom in it and Mary NOT in it:
TRR
RTR
RRT
TRR posb = 1 (way of picking Tom) x 4 (4 people left excluding Tom and Mary) x 3 (3 people left after excluding Tom, Mary and the person selected before) = 12
RTR and RRT have the possibility as TRR. Therefore possibilities the community can be formed with Tom in it and Mary NOT in it = 12 + 12 + 12 = 36
Hence probability =36/120=3/10
Option C
Answer: C
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)28
C)26
D)27
E)21
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A
Answer: A
Question: If 5% more is gained by selling an article for Rs. 360 than by selling it for Rs. 340, the cost of the article is?
Options:
A)127
B)688
C)400
D)121
E)123
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 360 - 340 = 20
x/20 = 20 => x = 400
Answer: C
Answer: C
Question: Difference between the length &breadth of a rectangle is 15m. If its perimeter is 206 m, then its area is?
Options:
A)1400 m^2
B)2500 m^2
C)2520 m^2
D)1800 m^2
E)2580 m^2
Rationale: Solving the two equations, we get: l = 45 and b = 40.
Area = (l x b) = (45 x 40) m2 = 1800 m^2
D
Answer: D
Question: By selling 8 pens for a rupee a woman loses 25%. How many for a rupee should he sell in order to gain 25%?
Options:
A)2
B)14
C)3
D)5
E)6
Rationale: D
75% --- 8
125% --- ?
75/125 * 8 = 5
Answer: D
Question: If the wheel is 10 cm then the number of revolutions to cover a distance of 1056 cm is?
Options:
A)16.8
B)26
C)14
D)12
E)91
Rationale: 2 * 22/7 * 10 * x = 1056 => x
= 16.8
Answer: A
Answer: A
Question: If the price of rice rises from Rs. 6 per kg to Rs. 8 per kg, to have no increase in his expenditure on rice, a person will have to reduce his consumption of sugar by
Options:
A)25
B)62
C)27
D)19
E)71
Rationale: Explanation:
Let original consumption = 100 kg and consumption = y kg.
So, 100 x 6 = y x 8
y = 75 kg
Reduction in consumption = 25 %.
ANSWER: A
Answer: A
Question: If the area of circle is 616 sq cm then its circumference?
Options:
A)22
B)88
C)99
D)66
E)41
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88.Answer:B
Answer: B
Question: If x+y=25 and x^2y^3 + y^2x^3=25, what is the value of xy?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: x^2*y^3 + y^2*x^3=25
=> x^2*y^2*(y+x)=25
=> x^2*y^2*25=25 [given, x+y=25]
=> (xy)^2 = 1
=> xy = 1
ANSWER:B
Answer: B
Question: The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.4.50, Rs.5.50, Rs.8.00 and Rs.10.00 each. As Rahul wanted 40 cards, he took five each of two kinds and fifteen each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?
Options:
A)25
B)20
C)24
D)32
E)30
Rationale: Explanation :
Let the four cards be a, b ,c and d. 'x' be the number of notes.
Then, according to the question,
=> 5a + 5b + 15c + 15d = 10*x.
=> a + b + 3(c+d) = 2 * x . -----------------------------(i)
Since, a + b = 4.5+5.5 =10.
And,
=> c + d = 8+10=18
Putting these values in (i), we get :-
=> 10+ 3 * 18 = 2 * x.
=> x =32 .
Answer : D
Answer: D
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
Options:
A)38 5/7 years
B)31 5/7 years
C)81 5/7 years
D)31 9/7 years
E)41 5/7 years
Rationale: Required Average
= [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7 = 31 5/7 years.
Answer:B
Answer: B
Question: A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance V that he will have a matched pair?
Options:
A)V=2/5
B)V=3/5
C)1/5
D)1/2
E)7/5
Rationale: P(both doves) + P(both rabbits) = p(matched pair)
(3/5)*(2/4) + (2/5)*(1/4) = 2/5
Hi How did you get the probability 2/4 and 1/4???
You have 3 doves and 2 rabbits i.e. a total of 5 animals.
The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)
The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)
Similarly,
The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)
The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. Also only 4 animals are left to choose from)
Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: A
Question: Charlene's annual bonus is calculated in the following manner: Charlene receives 20 percent of her first $11,000 in sales and 32 percent of her sales in excess of $11,000. If Charlene received a bonus of $7,300, what were her annual sales?
Options:
A)$ 18,687
B)$ 22,000
C)$ 24,000
D)$ 26,000
E)$ 28,000
Rationale: Let x be the total sales in $.
For the 1st 11,000 you get 20% ---> 0.2*11000 = 2200$
For the remaining (x-11000) $, you get 32% ---> 0.32*(x-11000)
Thus, 0.32*(x-11000) + 2200 = 7300 ----> x= 18,687 $
A is thus the correct answer.
Answer: A
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 200 m is?
Options:
A)299 m
B)777 m
C)200 m
D)100 m
E)128 m
Rationale: 2(l + 200) = 600 => l
= 100 m
Answer:D
Answer: D
Question: A 140 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
Options:
A)41.1 sec
B)20.2 sec
C)31.8 sec
D)43.2 sec
E)none of the above
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 140 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 660 m
Time = Distance / Speed
= 660 x 18 / (5 x 55)
= 43.2 sec
Ans is :D
Answer: D
Question: If S is the sum of the reciprocals of the consecutive integers from 71 to 80, inclusive, which of the following is less than S?
I. 1/7
II. 1/8
III. 1/9
IV. 1/7>S >1/8
Options:
A)I
B)IV
C)II
D)III
E)I&II
Rationale: Since we summarize the reciprocals from 80 to 71, we can say also that we add ten numbers who are all (with one exception 1/80) greater than 1/80, so that the sum must be greater than 1/8.
On the other side we can say that we add the reciprocals from 71 to 80, so that the sum has to be less than the sum of ten times 1/81.
sum has to be greater than 1/8 and less than 1/7
B
Answer: B
Question: A ship sails 4 degrees north, then 13 S. then 17 N. then 19 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
Options:
A)STARTED WITH EQUATOR
B)STARTER WITH NORTH POLE
C)STARTER WITH SOUTH POLE
D)STARTER WITH 80 DEGREE NORTH POLE
E)STARTER WITH NORTH OF SOUTH POLE
Rationale: Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 19 = -11
And x = 0.
Answer: A
Question: A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 6% special additives while oil B consists of 8% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
Options:
A)a.	A – 260
B)b.	B – 280
C)c. C – 290
D)d.	D – 300
E)e.	E – 420
Rationale: 6%*x + 8% *(480-x)=30
8.4 = 2 %*x
x=420
E
Answer: E