divelab/Sys2Bench huggingface dataset:
Question: some 6th std students each bought a pencil paying a total of 143rs.some of the 26 fifth std students each bought a pencil and they paid a total of 165rs.how many more fifth std students than sixth std students bought a pencil
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: common factor between 165 and 143 is 11. (11*15=165, 11*13=143). so each pencil costs 11rs. and there was (13-11)=2 students more in fifth std than sith std
ANSWER:B
Answer: B
Question: The LCM and HCF of two numbers are 1000 and 100 respectively. Find the larger of the two numbers if their sum is 1100.
Options:
A)1000
B)10
C)567
D)57
E)678
Rationale: There are 2 approaches in solving this.
Methode 1.
HCF * LCM = The Actual Number.
1000* 100= 100000
So the answer which we are looking for has to be a factor of 100000.
So among the options shortlist the answers by eliminating those numbers which is not divisible by 100000. and then take the highest number as the answer as the question asks abt the highest number.
answer is A
Answer: A
Question: If n = 2p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
Options:
A) Two
B) Three
C) Four
D) Six
E) Eight
Rationale: If n = 2p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 2p have.
p = 3 --> 2p = 6--> 6 has 2 even divisors: 2, 6
Answer: A.
Answer: A
Question: How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)25
B)30
C)40
D)45
E)50
Rationale: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=500*3/50=30sec
ANSWER:B
Answer: B
Question: A hostel had provisions for 250 men for 32 days. If 50 men left the hostel, how long will the food last at the same rate?
Options:
A)30
B)40
C)50
D)60
E)65
Rationale: A hostel had provisions for 250 men for 32 days
If 50 men leaves the hostel, remaining men = 250 - 50 = 200
We need to find out how long the food will last for these 200 men.
Let the required number of days = x days
More men, Less days (Indirect Proportion)
(men) 250 : 200 :: x : 32
250×32=200x
5×32=4x
x=5×8=40
ANSWER B
Answer: B
Question: The population of a city is 160,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
A)268942
B)186935
C)179776
D)167425
E)None of these
Rationale: Explanation:
Population after n years = P [1 + (R/100)]2
Population after 2 years = 160000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 179776
ANSWER: C
Answer: C
Question: Consider a lady took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years she had to pay Rs. 9900 interest only for the period. The principal amount borrowed by her was
Options:
A)Rs. 2000
B)Rs. 27500
C)Rs. 15000
D)Rs. 20000
E)None of these
Rationale: Explanation :
Principal = Rs. (100×9900 / 12×3)
=> Rs. 27500.
Answer : B
Answer: B
Question: Jupiter travels around the Sun at an approximate speed of 7.8 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
Options:
A)40,500
B)42,600
C)44,700
D)46,800
E)48,900
Rationale: The speed is 7.8 miles/s. Then 7.8/0.6 = 13 km/s
13*3600 = 46,800 kph
The answer is D.
Answer: D
Question: A train running at the speed of 90 km/hr crosses a pole in 12 seconds. Find the length of the train?
Options:
A)150
B)872
C)287
D)288
E)300
Rationale: Speed = 90*(5/18) m/sec = 75/3 m/sec
Length of Train (Distance) = Speed * Time
(75/3) * 12 = 300 meter
Answer:E
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 852 grams per kg, what is his percent?
Options:
A)22%
B)25%
C)17.37%
D)99%
E)12%
Rationale: 852 --- 148
100 --- ? => 17.37%
Answer: C
Answer: C
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is:
Options:
A)20
B)30
C)32
D)34
E)46
Rationale: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
A)
Answer: A
Question: A certain kind of necklace is made from 9 yellow, 6 blue, and 3 silver beads. What is the maximum number of these necklaces that can be made from 63 beads of each color ?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Atleast 9 yellow breads are needed to make a necklace, so irrespective of the combinations of blue and silver beads, the number of necklaces that can be formed will be
63/9 =7
Answer:- A
Answer: A
Question: The number of positive integers valued pairs (x, y) satisfying 4x -17y = 1 and x <= 1000 (x is less than or equal to 1000) is
Options:
A)59
B)57
C)55
D)58
E)60
Rationale: We are asked to find integer solutions for x,y.
There is no need to apply Euclidian algorithm here, we can get particular solutions simply by plugging in some values.
As y reaches 3 we get:
y’ = 3 and x’ = 13. We need only to solve for x.
General solution for x will be:
x = x’ + bn = 13 + 17n
Hence lower limit for n is n ≥ 0.
Now we’ll find upper limit using given restriction x ≤ 1000. Plugging in general solution we’ll get:
13 + 17n ≤ 1000
17n ≤ 987
n ≤ 58
And our list of possible values of n has following representation:
0, 1,2, 3, ….. , 58
Total number of elements is 59.
ANSWER:A
Answer: A
Question: A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed against the current will be
Options:
A)11 kmph
B)12 kmph
C)14 kmph
D)17 kmph
E)None of these
Rationale: Explanation:
If you solved this question yourself, then trust me you have a all very clear with the basics of this chapter.
If not then lets solve this together.
Speed with current is 20,
speed of the man + It is speed of the current
Speed in still water = 20 - 3 = 17
Now speed against the current will be
speed of the man - speed of the current
= 17 - 3 = 14 kmph
Option C
Answer: C
Question: Fifteen runners from four different countries are competing in a tournament. Each country holds a qualifying heat to determine who its fastest runner is. These four runners then run a final race for first, second, and third place. If no country has more than one more runner than any other country, how many arrangements of prize winners are there?
Options:
A)24
B)384
C)455
D)1248
E)2730
Rationale: 1. We have runners by countries: 4 4 4 3
2. We choose 3 countries for all 3 "wining" places. 4 possibility: 4 4 4 and 3 times 4 4 3
3. Now we can choose any person from each country and take into account different positions (3!)
So, we get: (4*4*4)*3! + 3*(4*4*3)*3! = 3!*4*4*(4+3*3) = 1248 (D)
Answer: D
Question: A train of length 250 metres takes 45 seconds to cross a tunnel of length 350metres. What is the speed of the train in km/hr?
Options:
A)10 km/hr.
B)240 km/hr.
C)30 km/hr.
D)24 km/hr.
E)None
Rationale: Sol.
Speed = [250 + 350/ 45] m/sec = [600 / 45 * 18/5] km/hr = 24 km/hr.
Answer D
Answer: D
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Options:
A)1/6
B)1/9
C)1/5
D)1/6
E)1/3
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: C
Question: Two trains 140 m and 180 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)11.52 sec
B)10.1 sec
C)10.6 sec
D)10.8 sec
E)10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 180 = 320 m.
Required time = 320 * 9/250
= 11.52 sec.
Answer:A
Answer: A
Question: One woman and one man can build a wall together in half an hour, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them two hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
Options:
A)5/7
B)1
C)10/7
D)6/13
E)22/7
Rationale: Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 2/1-->(1) , w + 2g = 2/1-->(2) and m + g =1/2-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/6,m=1/3 and w=5/3.
So, n = 1/(13/6) = 6/13
Option, D
Answer: D
Question: Add: + 47 and -27
Options:
A)-30
B)+30
C)0
D)27
E)47
Rationale: The absolute values of +47 and -27 are 47 and 27 respectively; and their difference = 47 – 27 = 30.
(+47) + (-27) = +30
ANSWER :B
Answer: B
Question: If the population of a certain country increases at the rate of one person every 25 seconds, by how many persons does the population increase in 1 hour?
Options:
A)100
B)120
C)144
D)180
E)160
Rationale: Answer = 2.4 * 60 = 144
Answer is C
Answer: C
Question: A man speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man speed against the current is
Options:
A)7 km/hr [B] [C] [D]
B)8 km/hr
C)9 km/hr
D)6 km/hr
E)10 km/hr
Rationale: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
answer :E
Answer: E
Question: A watch which gains uniformly ,is 5 min,slow at 8 o'clock in the morning on sunday and it is 5 min 48 sec.fast at 8 p.m on following sunday. when was it correct?
Options:
A)10 min past 7pm on wednesday
B)20 min past 7pm on wednesday
C)20 min past 9pm on wednesday
D)26 min past 7pm on wednesday
E)20 min past 4pm on wednesday
Rationale: This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast. The watch gains min in a time of (7×24)+12 = 180 hours.
To show the correct time, it has to gain 5 min.
So the correct time will be shown on wednesday at 7:20 PM
Answer: B
Answer: B
Question: Pipes A and B can fill a tank in 10 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in
Options:
A)1 13/17 hours
B)2 8/11 hours
C)3 9/17 hours
D)5 5/11 hours
E)None
Rationale: Solution
Net part filled in 1 hour	= (1/10 + 1/6 -1/12)
= 11/60.
Therefore, the tank will be full in 60/11 hrs.	â€¹=â€º 5 5/11 hrs.
Answer D
Answer: D
Question: In 2005, 25 percent of the math department’s 60 students were female, and in 2007, 35 percent of the math department’s 65 students were female. What was the percent increase from 2005 to 2007 in the number of female students in the department?
Options:
A)15%
B)51.7%
C)62.5%
D)115%
E)160%
Rationale: Female students in 2005 = 25% of 60 = 15
Female students in 2007 = 35% of 65 = 22.75
Percentage increase = [(22.75- 15)/15] *100 % = 51.7%
Correct Option: B
Answer: B
Question: If b < 2 and 2x - 5b = 0, which of the following must be true?
Options:
A)x < 5
B)x < 2
C)x = 3
D)x < 3
E)D. x > 3
Rationale: 2x - 5b = 0
Therefore, 2x = 5b
As, b<2
2x < 5(2)
i.e x < 5
Answer : A
Answer: A
Question: The integer x is divisible by both 4 and 6. Which of the following must be an integer?
Options:
A)x/12
B)x/9
C)x/25
D)x/24
E)x/16
Rationale: Prime factorization of 4 = 2^2
Prime factorization of 6= 2*3
LCM of 4 and 6 = 2^2 * 3 = 12
Therefore x/12 must be an integer
Answer A
Answer: A
Question: IBM and KTC quote for a tender. On the tender opening day, IBM realizes that their quotations are in the ratio 7:4 and hence decreases its price during negotiations to make it Rs 1 Lakh lower than KTC's quoted price. KTC realizes that the final quotes of the two were in the ratio 3:4. What was the price at which IBM won the bid?
Options:
A)Rs. 7 lakh
B)Rs. 3 lakh
C)Rs. 4 lakh
D)Rs. 1.5 lakh
E)None of these
Rationale: Explanation :
IBM initially quoted Rs 7x lakh. KTC quoted 4x lakh.
IBM's final quote = (4x−1) Lakh.
Thus, (4x−1)/4=3/4
i.e x=1.
Hence, IBM's bid winning price = Rs 3 Lakh.
Answer : B
Answer: B
Question: If 25% of a number is subtracted from a second number, the second number reduces to its four-sixth. What is the ratio of the first number to the second number ?
Options:
A)5:3
B)4:3
C)6:3
D)3:4
E)5:4
Rationale: Explanation:
Let the numbers be p & q
q-p/4 = 4q/6
=> q-4q/6 = p/4
=> 2q/6 = p/4
=> p/q = 4/3
Answer B
Answer: B
Question: A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 63 liters of drink A to convert it to drink B?
Options:
A)7
B)14
C)21
D)28
E)35
Rationale: In 63 liters of drink A, there are 36 liters of milk and 27 liters of juice.
With 36 liters of milk, we need a total of 48 liters of juice to make drink B.
We need to add 21 liters of juice.
The answer is C.
Answer: C
Question: What is the next number of the following sequence
7, 0, 1, 8, 5, 12, 9, 26, 3, 2, 23, ?
Options:
A)28
B)29
C)30
D)31
E)32
Rationale: 7,0,1,8,5,12,9,26,3,2,23,X
(7,0,1,8),(5,12,9,26),(3,2,23,X)
7+0+1=8
5+12+9=26
3+2+23=X => X=28
ANSWER:A
Answer: A
Question: Meena wrote all the numbers from 1 to 69,999 inclusive. How many digits did she write in total?
Options:
A)278,889
B)308,889
C)338,889
D)368,889
E)398,889
Rationale: 1-9=>1*9 digits
10-99=>2*90=180 (numbers between 10-99 is 90 where each has 2 digits)
100-999=>3*900=2700
1000-9999=>4*9000 = 36,000
10000-69999=>5*60,000 = 300,000
The answer is 338,889
The answer is C.
Answer: C
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 3 man in committee ?
Options:
A)10/36
B)11/72
C)12/72
D)28/36
E)36/90
Rationale: We may have (3 men and 2 women) = (7C3 x 6C2) = 525
or (4 men and 1 woman) = (7C4 x 6C1) = 210
or (5 men only) = (7C5) = 21
Required ways = 756
Probability of having 3 man in committee = 525 / 756 =28/36
ans - D
Answer: D
Question: If the average of 37, 69, 47 and x is 46.5, what is x?
Options:
A)37
B)41
C)50
D)59
E)33
Rationale: x=33 because:
(37+69+47+x)/4=46.5
(37+69+47+x)/4*4=46.5*4
(37+69+47+x)=186
(37+69+47+x)-153=186-153
x= 33
Therefore, the answer is E, 33.
Answer: E
Question: What is the ratio F of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Options:
A)1/4
B)3/8
C)1/2
D)3/5
E)2
Rationale: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5 F.
Answer = D
Answer: D
Question: 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 81. How much wine did the cask hold originally?
Options:
A)18 litres
B)24 litres
C)32 litres
D)42 litres
E)52 litres
Rationale: Let the quantity of the wine in the cask originally be x litres.
Then, quantity of wine left in cask after 4 operations = x(1-8/x)^4 litres.
therefore, (x(1-8/x)^4)/x=16/81
=>(1-8/x)^4=(2/3)^4
=>x-8/x=2/3
=>3x-24=2x
=>x=24 litres.
ANSWER:B
Answer: B
Question: A box measuring 49 inches long by 42 inches wide by 14 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Options:
A)78
B)82
C)84
D)86
E)88
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
7 is the biggest number that could divide all three, 49, 42 and 14.
Thus side of cube must be 7, and total number of cubes = 49/7 * 42/7*14/7 = 84
Ans C.
Answer: C
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 10 sec. What is the length of the fast train?
Options:
A)27 7/6
B)27 7/5
C)27 7/2
D)500/9
E)27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 10= 500/9
= 27 7/9 m.
Answer:D
Answer: D
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
Options:
A)270
B)277
C)187
D)257
E)271
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer: A
Answer: A
Question: If you divide 7^102 by 5, which remainder do you get?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The units digit of 7^1 is 7.
The units digit of 7^2 is 9.
The units digit of 7^3 is 3.
The units digit of 7^4 is 1.
The units digit of 7^5 is 7.
etc...
The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}
The remainder of 102/4 is 2.
So the units digit of 7^102 is 9.
The remainder of 7^102 / 5 is 4.
The answer is E.
Answer: E
Question: Set A: {1, 3, 4, 6, 9, 12, 15}
If three numbers are randomly selected from set A without replacement, what is the probability that the sum of the three numbers is divisible by 3?
Options:
A)3/14
B)2/7
C)9/14
D)5/7
E)11/14
Rationale: Probability of an event = (# of favorable outcomes) / (total # of outcomes).
There are 5 numbers you can choose from (3, 6, 9, 12, 15) so that the sum to be divisible by 3 and there are total of 7 numbers so P=C35C37=27P=C53C73=27.
Answer: B.
Answer: B
Question: A sum of Rs.2000 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)2888
B)3120
C)2877
D)2999
E)1300
Rationale: Let A be the amount received at the end of the three years.
A = 2000[1 + 10/100][1 + 20/100][1 + 25/100]
A = (2000 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.3300
So the interest = 3300 - 2000 = Rs.1300
Answer: E
Answer: E
Question: How many two digit numbers of distinct digits can be formed by using digits 3, 4, 5, 6,7 and 8 such that the numbers are divisible by 9?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: CONCEPT: A number will be divisible by 9 if sum of all the digits of the number is divisible by 9
Here the Possible sum of the two distinct digits can be 9 only in order to satisfy the given condition
If sum of Digits = 9, No. = 36, 45, 54, 63 --- 4 Cases
Answer: option B
Answer: B
Question: A train 150 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
Options:
A)11 s
B)10 s
C)7 s
D)12 s
E)None of these
Rationale: We know from the formula Time = Distance/ Speed
Thus, Time = 150/ 54 x 5/18
or, Time = 10 sec.
ANSWER:B
Answer: B
Question: Rahul went to a shop and bought things worth Rs. 55, 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)A)19.7
B)B)19.9
C)C)21.9
D)D)40.9
E)E)49.7
Rationale: Total cost of the items he purchased = Rs.55
Given that out of this Rs.55, 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%
∴ (55−30/100−x)6/100 = 30/100
⇒ 6(55 −0.3 −x) = 30
⇒ (55 − 0.3 − x) = 5
⇒ x = 55 − 0.3 − 5 = 49.7
E)
Answer: E
Question: A car runs at the speed of 60 km per hour when not serviced and runs at 80 kmph when serviced. After servicing the car covers a certain distance in 4 hours. How much time will the car take to cover the same distance when not serviced?
Options:
A)6 hours 12 minutes
B)5 hours 33 minutes
C)8 hours 15 minutes
D)7 hours 12 minutes
E)None
Rationale: Explanation :
Time = 80*4 / 60 = 5 hours 33 mins
Answer â€“ B
Answer: B
Question: When their father died, he left an Estate containing many assets, and a few expenses to his 6 children equally. His assets included: Investments, ($305,000), Life Insurance ($104,000), an old car (sold for $1900), an older house (sold for $75,000). His expenses included: Nursing Home Expenses ($6500) and Funeral Costs ($9300). How much would each child inherit?
Options:
A)80983
B)79001
C)75452
D)76767
E)78350
Rationale: In order to determine the total that each child would inherit, you must add all the assests and subtract all the expenses, and then divide by 6
305000 + 104000 + 1900 + 75000 - 6500 -9300 = 470100
470100 divided by 6 equals 78350
The correct answer is E
Answer: E
Question: The price of the jewel, passing through three hands, rises on the whole by 56%. If the first and the second sellers 20% and 25% profit respectively find the percentage profit earned by the third seller.
Options:
A)20
B)4
C)5
D)2
E)30
Rationale: Let the original price of the jewel be $ p and let the profit earned by the third seller be x% Then, (100+x)% of 125% of 120% of P =156% Of P ((100+X)/100*125/100*120/100*P)=(156/100*P)
==> (100+X)=(156*100*100)/(125*120)=104=>X=4%
Answer B)
Answer: B
Question: A sum of money at simple interest amounts to Rs. 835 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)s. 650
B)s. 690
C)s. 698
D)s. 700
E)s. 718
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (835 - 117) = Rs. 718.
Answer: Option E
Answer: E
Question: . A car covers a distance of 390 km in 4 hours. Find its speed?
Options:
A)104
B)55
C)66
D)98
E)100
Rationale: 390/4 = 98 kmph
Answer: D
Answer: D
Question: If 40% of (x-y) = 20% of (x+y), then what percent of x is y?
Options:
A)50.5%
B)44.4%
C)22.2%
D)33.3%
E)25%
Rationale: 40% of (x-y) = 20% of (x+y)
40/100 (x-y) = 20/100 (x+y)
x = 3y
Required percentage = y/x *100 = y/3y * 100 = 33.3%
Answer is D
Answer: D
Question: Set X consists of all two-digit primes and set Y consists of all positive even multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?
Options:
A) 87
B) 89
C) 90
D) 92
E) 95
Rationale: Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {10, 20, 30,..............., 70, 80, 90}
Combining two sets, say Set Z
Set Z = { 10,11, 13, 17, 20,30,..................., 70, 80, 83, 89, 90, 97}
Range = Max Value - Min Value
Range (Z) = 97 - 10 = 87
OA A is the answer.
Answer: A
Question: Prints a page 60 pg per min .If the printed for 1 hours except 10 min.Where there
was an paper jam,how many page did it print
Options:
A)10,880
B)12,880
C)3,000
D)8,880
E)18,880
Rationale: 60 pages ------->1 min
1 hrs except 10 mints means=1*60=60-10=50 mints
i.e.,50*60=3,000 pages printed.
ANSWER:C
Answer: C
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)10 2/8
B)10 2/9
C)10 2/3
D)10 2/2
E)10 2/5
Rationale: 2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer: C
Answer: C
Question: The probability is 1/2 that a certain coin turns up heads on any given toss. If the coin is tossed six times, what is the probability that the coin turns up tails on at least one of the tosses?
Options:
A)15/16
B)21/32
C)31/32
D)63/64
E)51/64
Rationale: P(6 heads)= 1/2*1/2*1/2*1/2*1/2*1/2=1/64.
P(at least one tail)=1-1/64=63/64.
The answer is D.
Answer: D
Question: A batsman in his 15th inning makes a score of 75 and their by increasing his average by 3. What is his average after the 15th inning?
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: 14x + 75 = 15(x + 3)
x = 30 + 3 = 33
Answer:C
Answer: C
Question: Which of the following equations represents a line that is perpendicular to the line described by the equation 2x + 3y = 12?
Options:
A)4x + 2y = 5
B)5x + y = 7
C)3x - 2y = 8
D)4x - 3y = 9
E)x + y = 10
Rationale: Perpendicular lines have slopes which are negative reciprocals of each other.
The line 2x + 3y = 12 in slope-intercept form is y = -(2/3)x + 4
The slope of this line is -2/3.
The slope of a perpendicular line is 3/2.
3x - 2y = 8 in slope-intercept form is y = (3/2)x - 4
The answer is C.
Answer: C