divelab/Sys2Bench huggingface dataset:
Question: 6 points are marked on a straight line and another 5 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
Options:
A)21
B)91
C)168
D)196
E)135
Rationale: Solution: select 2 from 5 and one from 6 + select 2 from 6 and 1 from 5
5C2*6C1 + 6C2*5C1
= 135
Answer : E
Answer: E
Question: 4,7,11,18,29,47,...?..,123,199
Options:
A)84
B)102
C)76
D)70
E)none of the above
Rationale: the addition of difference between each no. is equal to latter no.
so, difference between 47 and 76 is 29 which is previous no. of 47
answer C
Answer: C
Question: Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.60 a kg to produce a mixture worth Rs. 6.30 a kg
Options:
A)2:0
B)2:3
C)2:1
D)2:2
E)7:9
Rationale: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 70 : 90 = 7 : 9
Answer: E
Answer: E
Question: We invested a total of $1,000. We invested one part of the money at 5% and the rest of the money at 6%. The total investment with interest at the end of the year was $1,054.50. How much money did we invest at 5%?
Options:
A)$400
B)$450
C)$500
D)$550
E)$600
Rationale: Let x be the money invested at 5%.
1.05x+1.06(1000-x)=1054.50.
0.01x=1060-1054.50.
0.01x=5.50.
x=550.
The answer is D.
Answer: D
Question: James 5 days earnings are {500, 650, 750, 800, 850 }, how much less is the mean of the earnings of James than the median of the earnings of James?
Options:
A)50
B)55
C)60
D)40
E)85
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (500+ 650+ 750+ 800+ 850 )/5 = 710
Median = 750
Difference = 40
Option D
Answer: D
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 4000 possible combinations,and she can try 100 different possibilities,what is the probability that she does not pick the one correct combination.
Options:
A)1
B)159/160
C)0.975
D)0.775
E)0
Rationale: If Denise does not pick the correct combination in first 100 try, then the correct combination is one of remaining 3900. So Probability = 3900/4000 = 0.975.
answer is C.
Answer: C
Question: A metallic sheet is of rectangular shape with dimensions 50 m x 30 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 5 m, the volume of the box (in m cube) is:
Options:
A)4120 m cube
B)4140 m cube
C)5140 m cube
D)5120 m cube
E)None of these
Rationale: Explanation:
l = (50 - 10)m =40 m, [because 5+5 = 10]
b = (30 -10)m = 20 m,
h = 5 m.
Volume of the box = (40 x 20 x 5) m cube
= 4000 m cube.
Option E
Answer: E
Question: How many multiples of 6 are less than 3600, and also multiples of 36?
Options:
A)94
B)100
C)625
D)832
E)833
Rationale: The LCM of 6 and 36 is 36. Divide 3600/36 = 100.xxx. So B is your answer.
Answer: B
Question: A can finish a work in 12days and B can do the same work in half the time taken by A. Then, working together what part of the same work they can finish in a day?
Options:
A)1/2
B)1/3
C)2/5
D)1/4
E)3/7
Rationale: 1days work of A+B = (12+6)/12*6 = 1/4
Answer is D
Answer: D
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 40% are drinking beer, 30% are drinking mixed drinks, and 30% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
Options:
A)2/5
B)4/7
C)12/17
D)7/24
E)7/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
40% drink beer = 16
30% mixed = 12
30% both = 12
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 16+18 =34 and both = 20
thus 24/34 = 12/17
Hence C
Answer: C
Question: V and B are integers. The expression (V+1)(B+1) is even. What can be said about V and B?
Options:
A)They are both even numbers.
B)At least one of them is even.
C)At least one of them is odd.
D)They are both odd.
E)Nothing can be said surly on V and B
Rationale: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (V+1) or (B+1) needs to be Even
So either V or B needs to be odd
Or At least one of them is odd.
At least one of them is odd=C
Answer: C
Question: A certain company charges $10 per package to ship packages weighing less than 2 pounds each. For a package weighing 2 pounds or more, the company charges an initial fee of $10 plus $3 per pound. If the company charged $31 to ship a certain package, which of the following was the weight of the package, in pounds?
Options:
A)8
B)5
C)7
D)4
E)6
Rationale: Let the weight of the package be X. Then the cost is 3*X + 10= 31 ---> 3X=21 ---> X=7
Answer : C
Answer: C
Question: A mother said to her daughter, “I was as old as you are at now at the date of your birth.” If the mother’s age is 38 years now, the daughter’s age 5 years back was?
Options:
A)16 years
B)19 years
C)24 years
D)14 years
E)21 years
Rationale: D
14 years
Daughter’s current age = A years
Then, (38 – A) = A
2A = 38
A = 19 years
Daughter’s age Five years back = (19 – 5) years
= 14 years
Answer: D
Question: In the class of 100 students, 50 speak Hindi and 70 speak English. What is the lowest possible number of students who
speak both the languages?
Options:
A)A)8
B)B)10
C)C)20
D)D)30
E)E)32
Rationale: let the student who speaks hindi-x
let the student who speaks english-y
as (xuy)-(xny)=total
50+70-(xny)=100
=20
C)
Answer: C
Question: In an electric circuit, two resistors with resistances M and N are connected in parallel. In this case, if P is the combined resistance of these two resistors, then the reciprocal of P is equal to the sum of the reciprocals of M and N. What is P in terms of M and N?
Options:
A)(N-M)
B)MN/(M + N)
C)(NM)
D)(N-M)/(M+N)
E)NONE OF THESE
Rationale: The wording is a bit confusing, though basically we are told that 1/P= 1/M + 1/N, from which it follows that P=MN/(M + N).
Answer: B
Answer: B
Question: A batsman in his 10th innings makes a score of 85, and thereby increases his average by 3. What is his average after the 10th innings? He had never been ’not out’.
Options:
A)47
B)53
C)39
D)43
E)42
Rationale: Average score before 10th innings
= 85 - 3 × 10= 50
Average score after 10th innings
=> 50+ 3 = 53
ANSWER:B
Answer: B
Question: The sum of two numbers is 20 and their difference is 10. Find their product.
Options:
A)104
B)114
C)75
D)325
E)335
Rationale: Let the numbers be x and y.
Then x + y = 20 and x - y = 10
x = 15; y = 5
xy = 15 * 5 = 75
ANSWER: C
Answer: C
Question: Of the 150 people at a party, 70 were women, and 30 women tried the appetizer. If 60 people did not try the appetizer, what is the total number of men who tried the appetizer?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Total people at party=150
Women=70
so Men 150-70=80
No. of pple who tried appetizer=150-60 (given info)=90
No of women who tried appetizer=30
So Remaining ppl(men) who tried the appetizer =90-30=60
Correct Option C
Answer: C
Question: In the city of San Durango, 40 people own cats, dogs, or rabbits. If 20 people owned cats, 30 owned dogs, 10 owned rabbits, and 10 owned exactly two of the three types of pet, how many people owned all three?
Options:
A)5
B)7
C)9
D)11
E)13
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
40 = 20 + 30 + 10 - (10) - 2x
x = 5
So, answer will be A
Answer: A
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many ways can they selected that at least one boy should be there?
Options:
A)123
B)253
C)209
D)124
E)541
Rationale: We may have( 1 black and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4boys)
=(6c1 x 4c3)+(6c2 x 4c2)+(6c3 x 4c1)+6c4
=24+90+80+15
=209
ANS: C
Answer: C
Question: Rounded to three decimal places, 1.006^4 =
Options:
A)1.024
B)1.006
C)1.008
D)1.012
E)1.016
Rationale: As compared to 1, 0.006 is a very small quantity. Thus, we can write (1+0.006)^4 is nearly equal to (1+4*0.006) = 1.024.As the question asks for approximation to three decimal places, the further terms will anyways not come into picture.
A.
Answer: A
Question: The least number which when add 3 to it, completely divided 8, 12 and 18 is?
Options:
A)71
B)70
C)69
D)68
E)67
Rationale: LCM = 72
72 - 3 = 69
ANSWER:C
Answer: C
Question: A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
Options:
A)76 hrs
B)99 hrs
C)55 hrs
D)90 hrs
E)11 hrs
Rationale: 1/9 - 1/x = 1/10
=> 90 hrs
Answer: D
Answer: D
Question: A developer has land that has x feet of lake frontage. The land is to be subdivided into lots, each of which is to have either 80 feet or 100 feet of lake frontage. If 1/9 of the lots are to have 80 feet of frontage each and the remaining 48 lots are to have 100 feet of frontage each, what is the value of x ?
Options:
A)5,280
B)3,200
C)3,700
D)4,400
E)4,760
Rationale: Total number of plots,be T
Plots with 80ft is (1/9)th of total plots.
Plots with 100ft frontage = (8/9) X total number of plots
i.e 8/9 X T = 48 T = 54
Total lake frontage = 48X100 + 6X80 = 5280
Answer : A
Answer: A
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
Options:
A)299
B)277
C)276
D)270
E)281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: D
Answer: D
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 42 as quotient. What is the correct quotient ?
Options:
A)0
B)12
C)13
D)20
E)24
Rationale: 12*42=504
504%21=24
ANSWER:E
Answer: E
Question: The ratio between the speeds of two trains is 3 : 8. If the second train runs 600 kms in 6 hours, then the speed of the first train is
Options:
A)37.5 km/h
B)60.5 km/h
C)42.5 km/h
D)32.5 km/h
E)35.5 km/h
Rationale: A
37.5 km/h
Answer: A
Question: How many prime numbers exist in 67 x 353 x 1110 ?
Options:
A)30 prime number
B)29 prime number
C)27 prime number
D)31 prime number
E)None of these
Rationale: Solution:
=(2 x 3)7 x (5 x 7)3 x 1110
=27 x 37 x 53 x 73 x 1110
Thus, there are (7 + 7 + 3 + 3 + 10) = 30 prime number
ANSWER:A
Answer: A
Question: A car owner buys petrol at 7.50, 8.00 and 8.50 per litre for three successive years. What approximately is his average cost per litre of petrol if he spends 4000 each year?
Options:
A)8
B)9
C)7.98
D)7.98
E)None of the above
Rationale: Let average cost of petrol per litre be x
Then x = 12000 /4000/7.5+4000/8+4000/8.5
= 3 /2/15+1/8+2/17=6120/767= Rs. 7.98 per litre
Answer C
Answer: C
Question: What least number should be added to 1022, so that the sum is completely divisible by 25?
Options:
A)4
B)3
C)2
D)0
E)5
Rationale: 1022 Ã· 25 = 40 with remainder = 22
22 + 3 = 25.
Hence 3 should be added to 1022 so that the sum will be divisible by 25
Answer: Option B
Answer: B
Question: Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 2% per annum simple interest?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 2500 = D(100/2)2
D = 1
Answer: A
Answer: A
Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 9
Options:
A)1/2
B)7/18
C)5/13
D)5/12
E)6/17
Rationale: Total number of cases = 8*8 = 64
Favourable cases = [(2,8),(3,6),(3,7),(4,6),(4,7),(4,8),(5,5),(5,6),(5,7),(5,8),(6,4),(6,5),(6,6),(6,7),(6,8),(7,3),(7,4),(7,5),(7,6),(7,7),(7,8),(8,2),(8,3),(8,4),(8,5),(8,6),(8,7),(8,8)] = 28
So Probability = 28/64 = 7/18
Answer is B
Answer: B
Question: If 'x' is a positive integer exactly divisible by 6 or 15 but not divisible by 12.What could possibly be the value of 'x' ?
Options:
A)120
B)60
C)36
D)90
E)54
Rationale: 120 and 60 are both divisible by 6 and 15 but also by 12. so they are not the right answer.
36 and 54 are both clearly not divisible by 15(not correct)
90 is both divisible by 6 and 15 but not by 12.
answer : (D) 90
Answer: D
Question: The ration between the present ages of P and Q is 6:7. If Q is 4 years older than P, what will be the ratio of the ages of P and Q after 4 years?
Options:
A)2:3
B)7:8
C)11:13
D)9:13
E)1:2
Rationale: Let P's and Q's age be 6x and 7x
7x-6x = 4
x = 4
Required ratio = (6x+4):(7x+4) = 28:32 = 7:8
Answer is B
Answer: B
Question: How many R ways can Jason sit with his five friends in a row of six seats with an aisle on either side of the row, if Jason insists on sitting next to one of the aisles?
Options:
A)120
B)240
C)360
D)540
E)720
Rationale: Jason can select his seat in 2 Ways (two aisles)
His 1st of 4 friends have 5 seats to select =>
His 2nd of remaining 3 friends will have 4 seat to chose from...and so on
Total ways R=> 2*5*4*3*2*1 = 240.B
Answer: B
Question: The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
Options:
A)Rs. 8400
B)Rs. 8721
C)Rs. 8856
D)Rs. 9000
E)None of these
Rationale: Explanation:
Actual price = 95% of 90% of 85% of Rs. 12000
= 95/100 * 90/100 * 85/100 * 12000 = Rs. 8721.
ANSWER IS B
Answer: B
Question: If s is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
Options:
A)1
B)2
C)3
D)6
E)12
Rationale: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey s=4n, if it really wanted to convey so.
From other questions that I have seen, proper wordings could be:
If s is three times as large as n
OR simply,
If s is three times n.C
Answer: C
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.68?
Options:
A)5
B)6
C)4
D)3
E)8
Rationale: for the 1st no. there are 2 digits after decimal
for the 2nd no. there are 2 digits after decimal
total no. of decimals = 4
req. no. of digits=(n-1)=(4-1)=3
ANSWER :D
Answer: D
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)1410
B)1420
C)1360
D)1440
E)1540
Rationale: S.P. = 85% of Rs. 1600 = 85/100 x1600= Rs. 1360
answer : C
Answer: C
Question: The average earning of amechanic for the first 4days of a week is Rs.53 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
Options:
A)s. 10
B)s. 20
C)s. 30
D)s. 40
E)s. 50
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 53 + 4 x 22 -20
= Rs. 280
âˆ´ Average earning = 280/ 7
= Rs. 40
D
Answer: D
Question: A certain collage has total of 410 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
Options:
A)60
B)90
C)70
D)80
E)40
Rationale: Answer is B.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 410 seniors.
So e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f =90.
B
Answer: B
Question: The volumes of two cones are in the ratio 1 : 15 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)3:5
B)3:9
C)3:2
D)2:2
E)3:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r1^2 . h1/r2^2. h2 => 1/15
= (1)^2h1/(2)^2h2
=> h1/h2 = 3/5
i.e. h1 : h2 = 3:5
Answer: A
Answer: A
Question: What is the smallest no. which must be added to 27452 so as to obtain a sum which is divisible by 9?
Options:
A)7
B)2
C)9
D)4
E)6
Rationale: For 27452 , 2+7+4+5+2=20.
7 must be added to 27452 to make it divisible by 9.
Now , 2+7+4+5+9=27 => 27 is a multiple of 9 and hence 27452 is also divisible by 9
A
Answer: A
Question: The monthly rent of a shop of dimension 10feet × 10feet is Rs.1300. What is the annual rent per square foot of the shop?
Options:
A)43
B)156
C)68
D)87
E)92
Rationale: Sol. Monthly rent per square feet = 1300/(10*10) = 13
& Annual rent per square feet
=12*13=156
Answer : B
Answer: B
Question: For every integer n ≥ 3, the function h(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of h(102) – h(101)?
Options:
A)102
B)0
C)101
D)98
E)100
Rationale: h(101) = 1*3*5*7*9*...*99*101
h(102) = 1*3*5*7*9*...*99*101
They are going to be the same. Hence their difference will be 0
hence:B
Answer: B
Question: A boy swims downstream 48 km and upstream 12 km taking 6 hours each time; what is the speed of the current?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 48 --- 6 DS = 8
? ---- 1
12 ---- 6 US = 2
? ---- 1 S = ?
S = (8 - 2)/2 = 3
Answer: C
Answer: C
Question: Which of the following integers has the most number of divisors?
Options:
A)176
B)182
C)99
D)101
E)102
Rationale: Explanation:
99 = 1 × 3 × 3 × 11
=> Divisors of 99 are 1, 3, 11, 9, 33 and 99
101 = 1 × 101
=> Divisors of 101 are 1 and 101
182 = 1 × 2 × 7 × 13
=> Divisors of 182 are 1, 2, 7, 13, 14, 26, 91 and 182
176 = 1 × 2 × 2 × 2 × 2 × 11
=> Divisors of 176 are 1, 2, 11, 4, 22, 8, 44, 16, 88, 176
Hence 176 has most number of divisors.
Answer: Option A
Answer: A
Question: In western Europe, C bicycles were sold in each of the years 1990 and 1993. The bicycle producers of Western Europe had a 42 percent share of this market in 1990 and a 33 percent share in 1993. Which of the following represents the decrease in the annual number of bicycles produced and sold in Western Europe from 1990 to 1993?
Options:
A)9% of (x/100)
B)14% of (x/100)
C)75% of (x/100)
D)9% of x
E)14% of x
Rationale: Moreover is't question actually asking the the difference between the {(Quantity Produced + Quantity Sold ) C in 1990 - (Quantity Produced + Quantity Sold ) in 1993}
Though the Quantity sold in both the years is same it actually boils down to (Quantity Produced in 1990 ) in (Quantity Produced in 1993)=D
Answer: D
Question: In what ratio must tea at Rs. 62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be worth Rs. 64.50 per Kg?
Options:
A)3 :1
B)2:1
C)4:1
D)1:3
E)1:2
Rationale: C.P of a unit quantity of 1st kind = Rs. 62
C.P of a unit quantity of 2nd kind = Rs. 72
Mean price = Rs. 64.50
C.P of a unit quantity of 1st kind - Mean price =64.50-62= 2.50
C.P of a unit quantity of 2nd kind - Mean price = 72-64.50 =7.50
Required ratio = 7.50 : 2.50 = 3 : 1
Answer:A
Answer: A
Question: During a Thanksgiving weekend, a car rental company rented eight-tenths of their vehicles, including three-fifths of the 4WDs that it had. If 40% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
Options:
A)20%
B)30%
C)40%
D)60%
E)25%
Rationale: 2/10 of all the vehicles were not rented.
(2/5)(2/5) = 4/25 of all the vehicles are 4WDs that were not rented.
(4/25) / (2/10) = 4/5 is the fraction of non-rented vehicles that were 4WDs
1 - 4/5 = 20% of non-rented vehicles were not 4WDs.
The answer is A.
Answer: A
Question: The greatest number that divides 690 and 875 leaving remainders 10 and 25 respectively is:
Options:
A)170
B)130
C)150
D)120
E)180
Rationale: Explanation:
690 -10= 680, 875 – 25 = 850
Highest number that can divide 680 and 850 exactly is HCM of the numbers.
HCF of 680 and 850 = 170
Answer:A
Answer: A
Question: In a simultaneous throw of 2 dice, what is the probability of getting a total of 10 or 11?
Options:
A)2/7
B)1/4
C)1/2
D)7/36
E)5/36
Rationale: n(S) = 6*6 = 36
E = event of getting a total of 10 or 11 = {(4,6),(5,5),(6,4),(5,6),(6,5)}
probability = 5/36
Answer is E
Answer: E
Question: If a person walks at 14 miles/hr instead of 10 miles/hr, he would have walked 20 miles more. The actual distance traveled by him is:
Options:
A)20 miles
B)50 miles
C)30 miles
D)25 miles
E)35 miles
Rationale: Let the actual distance traveled be x km.
Then, X/10 = (X + 20)/14 ==> 14X = 10X + 200 ==> 4X = 200
X = 50.
Answer B) 50 miles.
Answer: B
Question: The first five numbers in a regular sequence are 4, 11, 25, 53, and 109. What is the next number in the sequence?
Options:
A)142
B)221
C)176
D)182
E)190
Rationale: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..
when we see the sequence 4, 11, 25, 53, and 109, we see that each succeeding number is some value more than twice the previous number..
10=2*4+3..
22=2*10+3..
and so on..
so next number= 2*109+3=221..
B
Answer: B
Question: A report consists of 20 sheets each of 55 lines and each such line consist of 65 characters. This report is retyped into sheets each of 65 lines such that each line consists of 70 characters. The percentage reduction in number of sheets is closest to
Options:
A)20
B)5
C)30
D)35
E)67
Rationale: Explanation :
Total no of characters= 20 * 55 * 65.
From the problem it is clear that 20 * 55 * 65 = x * 65 * 70.
we get x= 15.6 ∼ 16 because these are sheets.
therefore 4 less sheets.
Hencde, there is 20% decrease in number of sheets.
Answer : A
Answer: A
Question: How many seconds will a 800 m long train take to cross a man walking with a speed of 5 km/hr in the direction of the moving train if the speed of the train is 65 km/hr?
Options:
A)30
B)50
C)66
D)44
E)48
Rationale: Speed of train relative to man = 65-5= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 800 * 3/50 = 48 sec.
Answer: E
Answer: E
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
Options:
A)700
B)720
C)800
D)820
E)830
Rationale: Option 'B'
Answer: B
Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is?
Options:
A)625
B)827
C)657
D)726
E)634
Rationale: Let the sum be Rs. x. Then,
[x (1 + 4/100)2 - x] = (676/625 x - x)
= 51/625 x
S.I. = (x * 4 * 2)/100 = 2x/25
51x/625 - 2x/25 = 1 or x
= 625.
Answer: A
Answer: A
Question: In a certain city, 70 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:
Options:
A)45,000 to 90,000 inclusive
B)30,000 to 120,000 inclusive
C)60,000 to 90,000 inclusive
D)60,000 to 120,000 inclusive
E)90,000 to 120,000 inclusive
Rationale: The maximum percentage with both is 60% which is 90,000 households.
This means that every household with a recorder also has cable television.
The minimum percentage with both is 30% which is 45,000 households.
This means that 30% of households have only recorders but not cable television.
The other 30% of households with recorders have cable television.
The answer is A.
Answer: A
Question: A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 210 miles and spent a total of 12 hours traveling, what was her average speed on the second day?
Options:
A)5 mph
B)10 mph
C)20 mph
D)30 mph
E)40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Day 1 time = T1
Day 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Day 1 Rate = R1
Day 2 Rate = R2
R1 - R2 = 10 mph
i.e. R1 = 10 + R2
280 = 8R2 + 4R1
i.e. 280 = 8R2 + 4 (10 + R2)
i.e. R2 = 20 mph
ANSWER: D
Answer: D