divelab/Sys2Bench huggingface dataset:
Question: which is the highest 3 digit number that divides nnumber 111....1(27 times ) perfactly without leaving remainder.
Options:
A)789
B)589
C)889
D)999
E)111
Rationale: 111....1(27 times )
divisble by 111
& 9 also as sum of digits = 27
reqd no. = 9*111 = 999
ANSWER:D
Answer: D
Question: What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 64.12 = ?
Options:
A)230
B)225
C)235
D)220
E)234
Rationale: ? = 33 1⁄3% of 768.9 + 25% of 161.2 – 64.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 64.12
= 256.3 + 40.3 – 64.12 ≈ 234
Answer E
Answer: E
Question: The average of 45 students in a class is 15 years. The average age of 25 students is 24. What is the average age of remaining 20 students?
Options:
A)30
B)25
C)20
D)15
E)35
Rationale: Sum of the ages of 14 students
= (20 * 45) - (24 * 25) = 900- 600= 300
Required average = (300/20) =15
Answer: 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.4500. How much third person will get?
Options:
A)2400
B)2878
C)2000
D)2662
E)1821
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 * 4500 = 2000
Answer: C
Answer: C
Question: A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 7 less, he would have gained 25%. Find the cost price of the article.
Options:
A)150
B)160
C)170
D)180
E)280
Rationale: Let the C.P. be 100
First S.P. = 115
Second C.P. = 90
Second S.P = 125% of 90 = 112.50
Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100
But actual difference is 7.
∴ C.P. = 100⁄2.50 × 7 = 280.
Answer E
Answer: E
Question: In a workshop there are 3 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Options:
A)A)168.
B)B)80.
C)C)60.
D)D)48.
E)E)16.
Rationale: ways to select one shelf = 2
ways to select one bed = 3
ways to select one of the following: a chair or a closet = 7+3 = 10
ways to select all of them together = 2*3*10 = 60
Answer : C
Answer: C
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
Options:
A)Rs.18000
B)Rs.15000
C)Rs.17000
D)Rs.14000
E)NONE
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
ANSWER:D
Answer: D
Question: What will come in place of the x in the following Number series? 49920, 4160, 416, 52, x
Options:
A)8.67
B)7.67
C)6.67
D)5.67
E)4.67
Rationale: 49920 /12 = 4160
3840 /10 = 416
416 /8 = 52
52/6 = 8.67
A
Answer: A
Question: Ajay's club with a total membership of 30 has formed 3 committees, M, S and R which have 8,12, and 5 members respectively. If no member of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees.
Options:
A)5
B)7
C)8
D)10
E)12
Rationale: Ajay's club with a total membership of 30 has formed 3 committees Given no member of committee M is on either of the other 2 committees -- hence (M n R) and (M n S) and (M n R n S) is zero.
Hence only M is 8. Now we need to consider only S, (S n R) and R.
(M U R U S) = M + R + S - (M n R) - (M n S) - (R n S) + (M n R n S) + Neither.
30 = 8 + (12 - x) + (5 - x) + 0 + 0 + x + 0 + Neither.
22 = (12-x) + (5-x) + x + Neither.
Now the max value of x could be 5 and the min value of x could be 0.
When x is 5 (max), Neither is 10.
When x is 0 (min), Neither is 5. We need maximum no of people who do not belong to any group. Hence max value of neither is 10.
Answer 10 (D).
Answer: D
Question: If P represents the product of the first 13 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 17
III. P is a multiple of 24
Options:
A)I only
B)II only
C)III only
D)None of the above
E)All of the above
Rationale: P = 13!
I It is a multiple of 2, so cannot be ODD
II. 17 is a prime number; cannot be multiple
III. 24 = 8 * 3; Yes it is a multiple	Answer = C) III only
Answer: C
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 24 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
Options:
A)6 2/3
B)15
C)20
D)25
E)26 2/3
Rationale: Here is how I did it:
The cyclist travels 24 miles in 60 mins, so in 5 mins he will travel [(24*5)/60] miles, which equals 2 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 2 miles, he will take [(60*2)/4] = 30 mins.
30-5=25 mins
D
Answer: D
Question: Meera purchased two three items from a shop. Total price for three items is Rs.5200/- She have given Rs. 6000/- What is the balance amount meera got?
Options:
A)650
B)400
C)350
D)800
E)750
Rationale: Total cost of Items : 5200/-
amount Paid : 6000/-
Balance receivable : 6000 - 5200 = 800/-
Answer is D
Answer: D
Question: Ramu bought an old car for Rs. 48000. He spent Rs. 14000 on repairs and sold it for Rs. 72900. What is his profit percent?
Options:
A)16%
B)17.5%
C)18.2%
D)58.5%
E)13%
Rationale: Total CP = Rs. 48000 + Rs. 14000
= Rs. 62000 and SP = Rs. 72900
Profit(%)
= (72900 - 62000)/62000 * 100
= 17.5%
Answer: B
Answer: B
Question: The class mean score on a test was 80, and the standard deviation was 15. If Jack's score was within 2 standard deviations of the mean, what is the lowest score he could have received?
Options:
A)30
B)31
C)50
D)90
E)89
Rationale: 1 SD from the mean is ADDING and Subtrating the amount if standard deviation from the mean one time. 2 SD from the mean is ADDING and Subtracting TWICE.
1SD from the mean ranges from 95 to 65, where 95 is within SD above the mean and 65 within 1SD below the mean
2SD=15 TWICE=30 from the the mean, which is 95 to 50, where 90 is within 2 SD above the mean AND 50 is within 2 SD below the mean.
Answer = C
Answer: C
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 2 years and that for 14 years?
Options:
A)3 : 2
B)1 : 7
C)2 : 3
D)3 : 1
E)2 : 1
Rationale: Explanation :
Simple Interest = PRT/100
Here Principal(P) and Rate of Interest (R) are constants
Hence, Simple Interest ∝ T
Required Ratio = Simple Interest for 2 years/Simple Interest for 14 years
=T1/T2
=2/14
=1/7
=1:7
Answer : Option B
Answer: B
Question: The S.I. on a certain sum of money for 5 years at 10% per annum is half the C.I. on Rs. 5000 for 2 years at 12% per annum. The sum placed on S.I. is?
Options:
A)1585
B)1454
C)1656
D)2458
E)1272
Rationale: C.I. = [5000 * (1 + 12/100)2 - 5000]= (5000 * 28/25 * 28/25 - 5000) = Rs. 1272.Sum = (636 * 100)/(5 * 10)= Rs.1272Answer:E
Answer: E
Question: There are 8 stores in town that had a total of 22 visitors on a particular day. However, only 12 people went shopping that day; some people visited more than one store. If 8 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 8 people visited 2 stores each for 16 visits.
To maximize the number of stores that one person visited, let's assume that 3 people visited 1 store each. The number of remaining visits is 22 - 16 - 3 = 3, which is the maximum that one person could have visited.
The answer is B.
Answer: B
Question: 2, 5, 10, 17, 26, ?
Options:
A)35
B)36
C)48
D)49
E)37
Rationale: The sequence is a series of squares+1,
1*1+1, 2*2+1, 3*3+1, 4*4+1, 5*5+1, 6*6+1=37
Answer : E.
Answer: E
Question: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?
Options:
A)22999
B)50000
C)26709
D)78766
E)17618
Rationale: Let the sum be Rs. x. Then,
(x * 25/2 * 1/100) - (x * 10 * 1)/100 = 1250
25x - 20x = 250000
x = 50000
Answer: B
Answer: B
Question: At a special sale, 12 tickets can be purchased for the price of 4 tickets. If 12 tickets are purchased at the sale, the amount saved will be What percent of the original price of the 12 tickets?
Options:
A)20%
B)33.3%
C)40%
D)60%
E)66.6%
Rationale: let the price of a ticket be Rs.100, so 4 tickets cost 400 & 12 tickets cost 1200
12 tickets purchased at price of 4 tickets ie., for 400, so amount saved s Rs.800,
% of 5 tickets = (800 /1200)*100 =66.6 %
ANSWER:E
Answer: E
Question: Twelve machines, each working at the same constant rate, together can complete a certain job in 6 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 3 days?
Options:
A)14
B)12
C)15
D)16
E)18
Rationale: Rate of one machine = 1 job / (12*6) days
let X = number of machines needed to complete the job in 3 days
1/(12*6) * 3 * X = 1 job
X = 24
24-12= 12
ANSWER: B
Answer: B
Question: What is the units digit of 31! + 50! + 2! + 3!?
Options:
A)0
B)2
C)4
D)6
E)8
Rationale: For all N greater than 4, the units digit of N! is 0.
The sum of the four units digits is 0 + 0 + 2 + 6 = 8
The units digit is 8.
The answer is E.
Answer: E
Question: In how many ways can a group of 11 friends be seated round 2 tables if one of the tables can seat 7 and the other can seat 4 people?
Options:
A)11C6 * 9! *4!
B)11C3 * 6! *3!
C)15C4 * 9! *3!
D)15C2 * 10! *3!
E)16C5 * 10! *4!
Rationale: 7 people can be selected from 11 people in 11C7 ways.
Remaining 4 people can be selected from 4 people in 4C4 ways.
Now, arranging 7 people on a round table = (7-1) ! = 6!
Arranging 4 people on a round table = (4-1) ! = 3!
Hence, total number of ways = 11C7 * 6! * 4C4 * 3!
= 11C3 * 6! * 3!
B
Answer: B
Question: Divide Rs. 1800 among A, B and C so that A receives 2/5 as much as B and C together and B receives 1/5 as A and C together. A's share is?
Options:
A)400
B)500
C)375
D)450
E)600
Rationale: A+B+C = 1800
A = 2/5(B+C); B = 1/5(A+C)
A/(B+C) = 2/5
A = 1/6 * 3600=> 600
Answer: E
Answer: E
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
Options:
A)5
B)7
C)18
D)10
E)11
Rationale: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
5x = 45
x = 9.
Hence, B's age = 2x = 18 years.
Answer: Option C
Answer: C
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 231 but three tickets from city A to B and two tickets from city A to C cost Rs. 219. What are the fares for cities B and C from A ?
Options:
A)s. 4, Rs. 23
B)s. 13, Rs. 17
C)s. 15, Rs. 14
D)s. 17, Rs. 51
E)s. 39, Rs. 51
Rationale: If fares for cities B and C from A are x and y respectively, then
2x+3y=231 or 6x+9y= 693
3x+2y =219 or 6x+4y= 438
subtracting
5y = 255
y= Rs 51.
Hence E. Rs. 39, Rs. 51
ANSWER:E
Answer: E
Question: A trader purchases several articles at the rate of 13 for Rs. 10 and sells them at the rate of 10 for Rs. 13. What is his gain/loss?
Options:
A)69 % gain
B)56.25 % gain
C)56.25 % loss
D)25 % loss
E)None of these
Rationale: Explanation:
We have, C. P of 13 articles = Rs. 10
& S. P of 10 articles = Rs. 13
S. P of 13 articles = ?
= (13 * 13) / 10 = 16.9
Gain = [(16.9 – 10)/10] * 100 = 69 %
ANSWER: A
Answer: A
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 45 percent butterfat to obtain milk that is 20 percent butterfat?
Options:
A)6
B)12
C)14
D)16
E)20
Rationale: Equate the fat:
0.1x + 0.45*8 = 0.2(x + 8) --> x = 20.
Answer: E.
Answer: E
Question: The inverse ratio of 3: 2: 1 is?
Options:
A)1:2:3
B)2:3:1
C)3:1:2
D)2:3:6
E)4:5:7
Rationale: Explanation:
1/3: 1/2: 1/1 = 2:3:6
ANSWER IS D
Answer: D
Question: What is the sum of all even numbers from 1 to 401?
Options:
A)122821
B)281228
C)281199
D)122850
E)40200
Rationale: Explanation:
400/2 = 200
200 * 201 = 40200
Answer: E
Answer: E
Question: ?% of 360 = 165.6
Options:
A)277
B)36
C)64
D)72
E)46
Rationale: ?% of 360 = 165.6
or, ? = 165.6×100/360=46
Answer E
Answer: E
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph. A man rows to place at a distance of 170 km and comes back to the starting point. The total time taken by him is:
Options:
A)12 hours
B)68 hours
C)36 hours
D)58 hours
E)None
Rationale: Sol.
Speed upstream = 3 kmph; Speed downstream = 15 kmph.
∴ total time taken = [105/7.5 + 105/10.5] hours = 68 hours.
Answer B
Answer: B
Question: One quarter of the workers at the factory is clerical, one fifth is technical, half are administrative and the other 25 are managerial. How many workers total are there in the factory?
Options:
A)250
B)366
C)400
D)500
E)2500
Rationale: 1/2x + 1/4x +1/5x = 19/20x
Remaining 1/20 x= 25
x= 25*20= 500
D is the answer
Answer: D
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)50 kmph
B)65 kmph
C)75 kmph
D)85 kmph
E)90 kmph
Rationale: Explanation:
S = (90 + 60)/2 = 75 kmph
C)
Answer: C
Question: The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
Options:
A)4/5
B)5/4
C)3/5
D)2/5
E)3/4
Rationale: Let the required fraction be x. Then 1/X - X = 9/20
(1-X^2)/X = 9/20 ==> 20 - 20X^2 = 9X
20X^2 + 9X - 20 = 0
20X^2 + 25X - 16X - 20 = 0
5X(4X + 5) - 4(4X + 5) = 0
(4X + 5)(5X - 4) = 0
X = 4/5 (neglecting -ve value)
Answer A)4/5
Answer: A
Question: An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
Options:
A)4.04
B)4.02
C)4.01
D)4.05
E)4.06
Rationale: Formula for Calculation of Percentage error is:
=(x−y−(xy)/100)%
=(2+2+(2×2)/100)%=4.04%
Answer is A.
Answer: A
Question: What percent of a day is 6 hours?
Options:
A)6.25%
B)20%
C)25%
D)12.5%
E)18%
Rationale: Total hours in a day = 24
Required percent
=6/24×100=25% Answer: Option C
Answer: C
Question: An author received $0.80 in royalties for each of the first 100,000 copies of her book sold, and $0.40 in royalties for each additional copy sold. If she received a total of $260,000 in royalties, how many copies of her book were sold?
Options:
A)130,000
B)300,000
C)380,000
D)550,000
E)420,000
Rationale: Total royalties for first 100.000 books = .8*100,000= 80,000
Total royalties for the rest of the books = 260,000-80,000 = 180,000
Remaining books = 180,000/0.4 = 450,000
Total books = 450,000+100,000 = 550,000 Answer D
Answer: D
Question: Out of a total of 1,000 employees at a certain corporation, 52 percent are female and 40 percent of these females work in research. If 55 percent of the total number of employees work in research, how many male employees do NOT work in research?
Options:
A) 520
B) 480
C) 392
D) 138
E) 88
Rationale: total number of female employees =52% =520
female employees working in research =(2/5)*520=208
Total no of employees working in research =55% =550
Total male employees =48%=480
male employees working in research =550-208=342
male employees not working in research =480-342=138
Answer D
Answer: D
Question: A man divides $8600 Among 5 Sons, 4 Daughters and 1 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
Options:
A)A)$200
B)B)$1000
C)C)$819
D)D)$1200
E)E)$400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 5*5X+4*4X+1*X=8600
25X+16X+X=8600
42X=8600, X=204.76.
Daughter receives four times of nephew so 4 * 204.76= 819.
So Each Daughter receives $800. answer is option C) $819.
Answer: C
Question: You need to climb 10 stairs. At each support, you can walk one stair or you can jump two stairs.
In what number alternative ways you'll climb ten stairs?
Options:
A)99
B)79
C)55
D)89
E)66
Rationale: D
Answer: D
Question: The sale price sarees listed for Rs.175 after successive discount is 20% and 5% is?
Options:
A)187
B)133
C)142
D)178
E)175
Rationale: 175*(80/100)*(95/100)
= 133
Answer:B
Answer: B
Question: The radius of a semi circle is 7 cm then its perimeter is?
Options:
A)32.8
B)36
C)32.1
D)32.2
E)32.9
Rationale: Radius = 7 cm then Diameter = 14 cm
1/2*22/7*14+14 = 36
Answer : B
Answer: B
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 52, what is the compound interest on the same sum at the rate and for the same time?
Options:
A)s. 53.30
B)s. 53.22
C)s. 51.219
D)s. 53.18
E)s. 51.10
Rationale: Explanation:
Sum = (52 * 100) / (2 * 5) = Rs. 520
Amount = [520 * (1 + 5/100)2] = Rs. 573.3
C.I. = (573.3 - 520) = Rs. 53.30.
Answer:A
Answer: A
Question: What is the least positive integer that is not a factor of 30! and is not a prime number?
Options:
A)31
B)32
C)33
D)62
E)64
Rationale: A) 31 is prime and per the question stem we cannot use this
B) 32 = 2 * 16 - within 30! we have a 2 and 16 so 32 will be a factor of 30!
C) 33 = 3 *11 - again within 30! we have a 3 and an 11 so 33 will be a factor of 30!
D) 62 = 31 * 2 - Bingo 31 is not included in 30!
E) 64 = 16 * 4 - both 16 and 4 are multiplied in 30!
Answer is D!
Answer: D
Question: Find the slope of the line perpendicular to the line y = (1/2)x - 7
Options:
A)1
B)2
C)-2
D)4
E)5
Rationale: Two lines are perpendicular if the product of their slopes is equal to -1. The slope of the given line is equal to 1 / 2. If m is the slope of the line perpendicular to the given line, then
m × (1/2) = -1
Solve for m
m = - 2
correct answer C) -2
Answer: C
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)1350
B)1197
C)1927
D)1112
E)1921
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer: A
Answer: A
Question: There are 9 books on a shelf that consist of 4 paperback books and 5 hardback books. If 4 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?
Options:
A)88
B)99
C)110
D)121
E)132
Rationale: The total number of ways to select 4 books is 9C4 = 126
The number of ways which do not include any paperbacks is 5C4 = 5
The number of combinations with at least one paperback is 126-5 = 121
The answer is D.
Answer: D
Question: A man ran 20 miles in 2 hours 2 minutes. What was the average speed of the man in miles per hour?
Options:
A)9.72 miles / hour
B)9.73 miles / hour
C)9.75 miles / hour
D)9.78 miles / hour
E)9.79 miles / hour
Rationale: We first convert the time of 2 hours 2 minutes in minutes
2 hours 2 minutes = 2* 60 + 2 = 122 minutes
Average speed S is given by distance / time. Hence
S = 20 miles / 122 minutes = 0.163mile / minute
= 9.78 miles / hour
correct answer D
Answer: D
Question: The current birth rate per thousand is 37, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by?
Options:
A)2.6%
B)3.2%
C)3.9%
D)4%
E)5.1%
Rationale: Net growth on 1000 = 37-11 = 26
Net growth on 100 = 26*100/1000 = 2.6%
Answer is A
Answer: A
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1040
B)B)1045
C)C)1055
D)D)1060
E)E)1235
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 75 × 9 = 675.
Total cost he has to pay = 560 + 675 = 1235.
E)
Answer: E
Question: The area of sector of a circle whose radius is 10 metro and whose angle at the center is 42Â° is?
Options:
A)36.7
B)52.9
C)52.8
D)52.1
E)52.2
Rationale: 42/360 * 22/7 * 10 * 10 = 36.7 m2
Answer: A
Answer: A
Question: A runs twice as fast as B and gives B a start of 64m.How long should the racecourse be so that A and B might reach in the same time?
Options:
A)75 m.
B)128 m.
C)150 m.
D)100 m.
E)None of the above
Rationale: ratio of speeds of a and b is 2:1
b is 64m away from a but we know that a covers 1 meter(2-1) more in every second than b
the time taken for a to cover 64m is 64/1=64m
so the total time taken by a and b to reach =2*64=128m
ANSWER:B
Answer: B
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)228
B)271
C)500
D)277
E)812
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.Answer: C
Answer: C
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?
Options:
A)5
B)4
C)3
D)2
E)6
Rationale: Work done by A and B in two hours, = First hour A + Second hour B = (1/4) + (1/12) = 1/3.
total time required to complete the work = 2 (3) = 6 days
ANSWER E
Answer: E
Question: If x, y, and z are positive integers and x = 4y = 7z, then the least possible value of x + y + z is
Options:
A)33
B)40
C)49
D)39
E)84
Rationale: x + y + z = x/4 + x + x/7
= (7 + 28 + 4 )x/28 =39x/28
39 is not divisible by 28, so for least value, x = 28
Answer - D
Answer: D
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)399
B)240
C)277
D)299
E)712
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: B
Question: At a certain company, two-thirds of the employees had cell phones and two-fifths had pagers. If one-third of the employees had neither cell phones nor pagers then what fraction of the employees had both cell phones and pagers?
Options:
A)7/5
B)6/11
C)2/5
D)1/3
E)4/15
Rationale: Let there be 15 employees
Cell Phone = 10
Pagers = 6
Neither Pager Nor Cell Phone = 5
So, 10 = 10 + 6 - x
Or, x = 6
So, fraction of the employees had both cell phones and pagers = 6/15 => 2/5
ANSWER:C
Answer: C
Question: Four of the five parts numbered (a), (b), (c), (d) and (e) are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
A)732.534 + 412.256 – 544.29
B)1256.214 – 355.514 – 300.2
C)246.86 + 439.38 – 80.74
D)1415.329 + 532.4 – 1347.229
E)398.14 – 239.39 + 441.75
Rationale: (c) = 605.5 whereas the other parts are equal to 600.5
Answer C
Answer: C
Question: On a test average (arithmetic mean) test score for 9 students is 80. What must be 10th student's score that average score for 10 students to be 82?
Options:
A)100
B)90
C)80
D)70
E)60
Rationale: (9*80+x)/10=82
x=(10*82)-(9*80)
x= 820 - 720
total score required 820 - 720=100
Correct answer is A
Answer: A
Question: What is the greatest value of m such that 4^m is a factor of 29! ?
Options:
A)12
B)5
C)4
D)3
E)2
Rationale: Pretty simple, really.
If m = 12, then 4m = 48, which is 24x2, both of which are included in 29!
Since 12 is the largest number here, its the answer.
Answer is A
Answer: A
Question: A train passes a platform in 40 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
Options:
A)280 meter
B)240 meter
C)200 meter
D)300 meter
E)None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/40 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 40
=> 300+L = 15×40 = 600
=> L = 600-300 =300 meter
Answer: Option D
Answer: D
Question: If PQRST is a parallelogram what it the ratio of triangle PQS & parallelogram PQRST
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)1/6
Rationale: area of parallelogram is=base*height----1
area of triangle=1/2(base*height)-------2
devide equation 2 by 1
1/2
ANSWER:A
Answer: A