divelab/Sys2Bench huggingface dataset:
Question: A reading list for a certain course consists of 10 books, of which 5 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
Options:
A)90
B)115
C)130
D)144
E)155
Rationale: Ans: B
Solution: Selection requires at most 2 novels, means=
0N4P + 1N3P + 2N2P
5c0*5c4+ 5c1*5c3 + 5c2*5c2
= 5+ 50 + 100
= 155
Ans: E
Answer: E
Question: A thief steals at a car at 2.30 p.m. and drives it at 40 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Options:
A)6:34 p.m
B)9:34 p.m
C)3:34 p.m
D)2:34 p.m
E)3:41 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
40x = 75(x - 1/2) => x = 15/14hrs.
So, the thief is overtaken at 3:34 p.m.'
Answer: C
Answer: C
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers l did Carl drive each way?
Options:
A) 350
B) 345
C) 320
D) 280
E) 240
Rationale: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try l=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Answer: D
Question: How many different letter arrangements can be made from the letters of the word RECOVER?
Options:
A)1210
B)5040
C)1260
D)1200
E)None of these
Rationale: Possible arrangements are :
7!/2!×2!=1260 [division by 2 times 2! is because of the repetition of E and R]
Answer C
Answer: C
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 48. What is the total number of students in the school?
Options:
A)200
B)300
C)600
D)700
E)100
Rationale: E
100
Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 48 + 2/3 of 48
80/100x = 80
x = 100.
Answer: E
Question: Mr. Jones sold two pipes at $2.50 each. Based on the cost, his profit one was 30% and his loss on the other was 20%. On the sale of the pipes. Find the amount of his profit or loss?
Options:
A)gain 0.25 cents
B)lost 4 cents
C)broke even
D)gained 4 cents
E)gained 10 cents
Rationale: 30 % profit on $ 2.50
= $ 30/100 × 2.50
= $ 0.30× 2.50
= $ 0.75
Similarly, 25 % loss on $ 2.50
= $ 20/100 × 2.50
= $ 0.20× 2.50
= $ 0.50
Therefore, in one pipe his profit is $ 0.75 and in the other pipe his loss is $ 0.50
So profit by amount 0.25 cents
Answer is A.
Answer: A
Question: Parents spend an estimated $200 at the fair every year, and the fair typically wants to reach a goal of bringing profits at $150,000. To achieve that goal, how many parents need to be attending the fair for the 5 days it is open? The amount of parents need to be rounded to whole numbers.
Options:
A)130 people per day
B)145 people per day
C)200 people per day
D)175 people per day
E)150 people per day
Rationale: To find out our answer, we must think about how much the fair could make in the time allotted.
So, we divide 150,000 by 5 to get 30,000
We then divide 30,000 by 200 to get our answer.
This is possible since we are following rules of division for 5 and 200.
Correct Option: E
Answer: E
Question: The average monthly salary of 8 workers and one supervisor in a factory was 430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.@SSWhen@SSthe@SSsupervisor@CC@SSwhose@SSsalary@SSwas@SS430.Whenthesupervisor,whosesalarywas430. When the supervisor, whose salary was 870 per month, retired, a new person was appointed and then the average salary of 9 people was $$420 per month. The salary of the new supervisor is:
Options:
A)233
B)600
C)287
D)780
E)191
Rationale: Explanation:
Total salary of 8 workers and supervisor together = 9 Ã— 430 = 3870
Now total salary of 8 workers = 3870 âˆ’ 870 = 3000
Total salary of 9 workers including the new supervisor = 9 Ã— 420 = 3780
Salary of the new supervisor = 3780 âˆ’ 3000 = 780
Answer: D
Answer: D
Question: In one hour, a boat goes 19 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)2
B)4
C)7
D)12
E)15
Rationale: Sol.
Speed in still water = 1/2 (19+5) kmph = 12 kmph.
Answer D
Answer: D
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 40 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
Options:
A)79
B)89
C)95
D)72.72
E)97.2
Rationale: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 40*5 = 200
Student's average = (600+200)/11 = 72.72
Answer D
Answer: D
Question: The bankerâ€™s discount on Rs. 1600 at 12% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
Options:
A)2 months
B)4 months
C)5 months
D)7 months
E)None
Rationale: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 12%.
âˆ´ Time = [100 * 80 / 1600 * 12] year = 3/7 year = 5 months.
Answer C
Answer: C
Question: Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 110000 and 1100000 ?
Options:
A) 10
B) 11
C) 101
D) 1011
E) 10001
Rationale: Binary Divison can provide a quick answer if you are comfortable with it.
as option E is the biggest binary number we try with it first :
100010000/ 11 =10000
1000100000/ 11 =100000
so answer is option is B
Answer: B
Question: Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 30 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 12 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
Options:
A)52
B)67
C)71
D)73
E)64
Rationale: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)
n(E or F or I) = 26 + 26 + 30 - 0 - 12 - 6 + 0
Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.
n(E or F or I) = 64
Answer (E)
Answer: E
Question: Each term of a certain sequence is 3 less than the previous term. The first term of this sequence is 23. If the sum of the first n terms of the sequence is n, what is the value of positive integer n?
Options:
A)1
B)13
C)15
D)19
E)47
Rationale: We know that it is a decreasing sequence i.e. the terms keep decreasing till 0 and then negative terms start.
What does this imply?If the sum of the first n terms of the sequence is n
Since number of terms will definitely be positive, we are looking for a positive sum.
19 + 16 + 13 + 10 + 7 + 4 + 1 -2 -5 -7 -10 .... and so on
Note that the first 7 terms are positive and all others negative. Every negative term has greater absolute value than the corresponding positive terms i.e. -2 absolute value is greater than 1 absolute value, -5 absolute value is greater than 4 absolute value, and so on...
Since we have 7 positive terms, we must have less than 7 negative terms to get the sum as positive. If we have 6 negative terms, we will have a total of 13 terms. Of the given options, only 13 is possible and hence it must be the answer.
Answer (C)
Answer: C
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)5
B)4
C)7
D)3
E)1
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: B
Question: If a company allocates 15 percent of its budget to advertising, 10 percent to capital improvements, and 60 percent to salaries, what fraction of its budget remains for other allocations?
Options:
A)4/5
B)3/5
C)3/20
D)1/5
E)1/10
Rationale: 15 + 10 + 60 = 85% 100 - 85 = 15% to all others
C
Answer: C
Question: If a and d are both integers, a>d, and -3c>19, then the largest value of d would be?
Options:
A)-5
B)-6
C)-7
D)-8
E)-10
Rationale: No, your thinking is incorrect. When we know that a>d and a<-6.33, the largest value of a can be -7 while if a=-7, then largest value of d < -7 will be -8.For negative numbers, -7 > -8 and -8> -10.
You are right in saying that d can take any value less than -7 ---> d could be -8, -9, -10 .... and out of all these values, -8 is the greatest.
Look at the numbers on the number line. For any 2 numbers, the ones on the right are greater than the ones on the left:
.......-11 -10 -9 -8 -7 -6 -5 ..... 0 1 2 3 4 5 6 ... (-11< -10, -10< -8, 4< 5 etc).
So, as per the question if d<a and a = -7 , then d's largest 'possible' value has to be -8.
-10 is smaller than -8=D
Answer: D
Question: A retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles. What is the percentage of profit made by the retailer?
Options:
A)66.67%
B)33.33%
C)40%
D)25%
E)20%
Rationale: Let Cost Price = x
Profit = y
Selling Price = x+y
50y = 20(x+y)
30y = 20x
Percentage Profit =y/x∗100=20/30∗100=66.667
Answer = A
Answer: A
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 4000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
Options:
A)100000
B)100500
C)84000
D)Data inadequate
E)None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 4000) From the question,
(x - 4000) × 126⁄100 = 6⁄5x ⇒ x = 84000
Answer C
Answer: C
Question: The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the Mother insists of standing by her younger Child, as the song says?
Options:
A)12
B)24
C)30
D)48
E)120
Rationale: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that M and C2 are always together.
Consider F and M to be one unit, then we would have total of four units: {F}, {C1}, {MC2}, {D}. The number of arrangements of these four units is 4!, but M and C2 within their unit can be arranged in 2 ways: {C2M} or {MC2}, so total number of arrangements is 4!*2=48.
Answer: D.
Answer: D
Question: if 8 people take an hour to complete a piece of work, then how long should 16 people will take to complete the same piece of work?
Options:
A)15 min
B)30 min
C)26 min
D)28 min
E)18 min
Rationale: if 8 people take an hour to complete a piece of work, then
16 people will take 8*60/16 = 30 mins to complete the same piece of work.
ANSWER:B
Answer: B
Question: .04 × ? = .000016.
Options:
A)0.0004
B)0.04
C)4
D)0.4
E)None of these
Rationale: Solution
Let .04 × x = .000016. Then, x = .000016/.04 = .0016/4 = .0004. Answer A
Answer: A
Question: A's speed is 20/13 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that B beats A by 25% of the length of the race?
Options:
A)44%
B)48%
C)52%
D)42%
E)61%
Rationale: First calculate the distance, B has covered with his speed in the time, in which A reached 60% of the race.
Then Add the remaining distance as head start for B to win the race.
Its best to apply Ratios concept here.
Since A's speed is 20/13 of B, therefore, B's speed is 13/20 of A
Distance covered by B = speed x time = (13/20) x (0.6) = 0.39%
(Which means B would have covered 0.39 of the race length during the time in which A has covered 0.6 of the race length.
Therefore to win, B needs a headstart of (1 - 0.39 = ) 0.61 of the race length.
So the answer is E
Answer: E
Question: The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
Options:
A)Rs. 60
B)Rs. 108
C)Rs. 110
D)Rs. 112
E)Rs. 122
Rationale: P.W. = Rs. (540 - 90) = Rs. 450.
S.I. on Rs. 450 = Rs. 90.
S.I. on Rs. 540 = Rs. (90/450)X540	= Rs. 108.
B.D. = Rs. 108.
ANSWER :B
Answer: B
Question: What will be the percentage increase in the area of the cube's surface if each of the cube's edges grows by 40%?
Options:
A)95%
B)90%
C)85%
D)96%
E)25%
Rationale: The question is very easy. My logic is the following:
A surface = 6*a^2
After 40% increase A surface = 6* ((1.4a)^2) = 6*1.96*a^2
The increase in the surface area = (6*1.96*a^2 - 6*a^2)/6*a^2 = (6*a^2(1.96-1))/(6*a^2) = 1.96-1=0.96 = 96%
Answer :D
Answer: D
Question: A, B and C can do a piece of work in 4 days, 8 days and 20 days respectively. How long will they taken, if all the three work together?
Options:
A)2
B)4
C)5
D)67
E)2 6/17
Rationale: 1/4 + 1/8 + 1/20 = 17/40 => 40/17 => 2 6/17 days
Answer: E
Answer: E
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 20 as remainder. Find the no. is?
Options:
A)122456
B)220020
C)220022
D)235467
E)220026
Rationale: (555 + 445) * 2 * 110 + 20 = 220000 + 20 = 220020
B
Answer: B
Question: The total age of A and B is 14 years more than the total age of B and C. C is how many years younger than A ?
Options:
A)14
B)27
C)21
D)18
E)11
Rationale: (A+B) - (B+C) = 14
A - C = 14.
C is younger than A by 14 years.
Answer: A
Answer: A
Question: When the integer n is divided by 17, the quotient is x and the remainder is 2. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?
Options:
A) 23x + 17y =19
B) 17x –23y = 12
C) 17x +23y =19
D) 14x + 5y = 6
E) 5x – 14y = -6
Rationale: From the problem it follows:
n=17x+2
n=23y+14
So, 17x+2=23y+14
17x-23y=12
The answer is B
Answer: B
Question: If 625^(-x) +5^(-2x) + 5^(-4x) = 15, what is the value of x?
Options:
A)-4
B)-1/4
C)0
D)1/4
E)4
Rationale: We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.
Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....
With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eliminate A.
With Answer E, we'd have 625^(-4), which would create a TINY fraction (and we'd add some other fractions to it, so the total would be MUCH TOO SMALL). Eliminate E.
With Answer D, we'd have 625^(-1/4), which will also be a fraction (just not as tiny as the one in answer E), but the total would still be TOO SMALL. Eliminate D.
With Answer C, anything to the '0 power' is 1, so we'd have 1+1+1 = 3. This is not 15. Eliminate C.
A
Answer: A
Question: The average number of shirts with Salman, Ambani and Dalmiya is 60, if all of them reached a shopping mall in Delhi and purchased 3 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)63
C)62
D)64
E)61
Rationale: Required average
= Old average + New average
= 60 + 3 = 63
answer :B
Answer: B
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
Options:
A)42, 33
B)41, 33
C)42, 35
D)41, 35
E)41, 37
Rationale: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
A)
Answer: A
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference D between the greatest and least of the five integers?
Options:
A)4K
B)4k^2 -4k
C)4-4k
D)4
E)4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference D= 10k - 3 - (10k - 7)
= 4
Answer - D
Answer: D
Question: 3 no.'s A, B & C are in the ratio of 12:15:25. If sum of these no.'s is 312, find the ratio between the difference of B & A & the difference of C & B.
Options:
A)2 : 5
B)3 : 10
C)4 : 5
D)4 : 7
E)5 : 11
Rationale: We have, a = 12, b = 15, c = 25 and x = 312.
ax_ 12 X 312
a+b+c 12+15+25
— 72,
bx _ 15 X 312 B — — 90 a +b+c 12 + 15+ 25 cx 25 X 312 And, C =
a+b+c 12 + 15+ 25
...B-A=18 andC-B=60
- 150
Thus, their ratio = 18 : 60 or 3 : 10
B
Answer: B
Question: A man sells 45 lemons for Rs 40 and loses 20%. At how much price should he sell 24 lemons to the next customer to make a 20% profit?
Options:
A)32
B)20
C)24
D)16
E)14
Rationale: Explanation:
Let cost price of lemons be x.
Selling price of lemons becomes CP - loss.
=>SP=x-(20/100)x
=>40=x(80/100)
=>50
So 45 lemons cost Rs 50
Cost of 1 lemon = 50/45 Rs
Cost of 24 lemons = (50/45)*24 =80/3 Rs
Selling Price of 24 lemons =(80/3)+(20/100)(80/3)=Rs 32
ANSWER A
Answer: A
Question: three men invested sum. and their ratio is 5:7:6. profit is 1800.then b's share
Options:
A)2000
B)2100
C)700
D)2300
E)2400
Rationale: b's share =7/18*1800=700
ANSWER:C
Answer: C
Question: A group of people participate in some curriculum, 30 of them practice Yoga, 20 study cooking, 15 study weaving, 5 of them study cooking only, 8 of them study both the cooking and yoga, 5 of them participate all curriculums. How many people study both cooking and weaving?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Both cooking and weaving = 20 - (5+8+5) = 2
So, the correct answer is B.
Answer: B
Question: Three candidates contested an election and received 3834 votes, 7606 votes, and 14560 votes respectively. What percentage of the total votes did the winning candidate receive?
Options:
A)55%
B)56%
C)57%
D)58%
E)59%
Rationale: The total number of votes polled = (3834 + 7606 + 14560) = 26000
The winner's percentage = 14560/26000 * 100 = 56%
The answer is B.
Answer: B
Question: (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2] = ?
Options:
A)1.45
B)2.75
C)26.5
D)265
E)None
Rationale: Answer
Given expression = (69 - 14 x 3 + 2) / [ 9 x 5 - (5)2]
= (69 - 42 + 2) / (45 - 25)
= 29 / 20
= 1.45
Correct Option: A
Answer: A
Question: What is the lowest positive integer that is divisible by each of the integers 1 through 7, inclusive?
Options:
A)420
B)840
C)1,260
D)2,520
E)5,040
Rationale: The integer should be divisible by: 2, 3, 4(=2^2), 5, 6(=2*3), and 7. The least common multiple of these integers is LCM=2^2*3*5*7=420.
Answer: A.
Answer: A
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
Options:
A)49
B)44
C)77
D)25
E)29
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.Answer:B
Answer: B
Question: Let Q represent a set of five distinct prime numbers. If the sum of the numbers in Q is even and x is a member of Q, then what is the least possible value that x can be?
Options:
A)1
B)2
C)3
D)5
E)7
Rationale: Q = p1+p2+p3+p4+p5 = even (and all primes are distinct)
if the least prime is 2 then we have sum of Q = even
Ans. B. 2
Answer: B
Question: A boat crossed a lake from North to South at the speed of 6 km/h, entered a river and covered twice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 5 km/h that day, what was its approximate downstream speed?
Options:
A)12
B)15
C)16
D)17
E)18
Rationale: Another way will be:
Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed
If 5D is the total distance, then distance covered in lake = D, distance covered upstream = 2D and distance covered downstream = 2D
=>5D/5 = D/4 + 2D/3 + 2D/x (where x is the downstream speed)
=> 5/5 = 1/6 + 2/3 +2/x (div. both sides by D)
=> 1.0 = .16+.66 +.16/x => x=11.98 ~12
option A
Answer: A
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 4 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
Options:
A)1/15
B)4/5
C)4/15
D)1/5
E)2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=4(1/5(x/2))=2/5(x)--->non major=x/2-2/5(x)=1/5(x)
hence 1/5
D
Answer: D
Question: If m and n are both odd prime numbers andm < n, then how many different positive integer factors does2mnhave?
Options:
A) 3
B) 8
C) 6
D) 4
E) 12
Rationale: m and n are both odd prime numbers- It means either m or n is not 2
and since prime numbers have only two factors - 1 and the number itself
m and n each will have (1+1)= 2 factors
Hence 2mn will have (1+1)(1+1)(1+1)= 8 factors
B is the answer
Answer: B
Question: Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)46%
B)57%
C)74%
D)63%
E)68%
Rationale: B
57%
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage =(11628x100/20400)% = 57%.
Answer: B
Question: Two trains 190 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)10.6 sec
B)18.8 sec
C)14.6 sec
D)10.8 sec
E)12.6 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 190 + 160 = 350 m.
Required time = 350 * 9/250 = 63/5 = 12.6 sec.
Answer: E
Answer: E
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.3500 and B Rs.1500, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
Options:
A)1978
B)2707
C)7728
D)7008
E)7291
Rationale: 35:15 => 7:3
9600*10/100 = 960
9600 - 960 = 8640
8640*7/10 = 6048 + 960
= 7008
Answer: D
Answer: D
Question: if p/q=3/4
then3p+7q=?
Options:
A)37/4
B)25/2
C)20/4
D)35/4
E)25/3
Rationale: 3p+7q=?
Divided by q,
3(p/q)+7=x
3*(3/4)+7=37/4
ANSWER:A
Answer: A
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)99
B)277
C)48
D)99
E)22
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 0.9 = 2 km = 2000 m.
Required time = 2000 * 3/125 = 48 sec.
Answer:C
Answer: C
Question: If (x^2 + x - 8) ≤ x + 1, then x could be represented by which of the following?
Options:
A)− 4 ≤ x ≤ − 3
B)− 4 ≤ x ≤ 3
C)− 3 ≤ x ≤ 3
D)− 3 ≤ x ≤ 4
E)3 ≤ x ≤ 4
Rationale: IMO C is correct answer
solving through eqautions
x^2 +x-8<= x+1
(x+3)(x-3)<=0
Answer: C
Question: If r and h are two positive integers and r/h = 1.60, then r can equal which one of the following?
Options:
A) 9
B) 24
C) 20
D) 22
E) 23
Rationale: r/h = 1.60 = 160/100 = 8/5
So, r COULD equal 24
Answer: B
Answer: B