divelab/Sys2Bench huggingface dataset:
Question: A pipe can fill a cistern in 20 minutes whereas the cistern when fill can be emptied by a leak in 60 minutes. When both pipes are opened, find when the cistern will be full?
Options:
A)17 minutes
B)87 minutes
C)30 minutes
D)27 minutes
E)11 minutes
Rationale: 1/20 - 1/60 = 1/30
30 minutes
Answer:C
Answer: C
Question: In a survey about potential presidential candidates A and B, 35% of the public like A and 53% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
Options:
A)27%
B)34%
C)41%
D)22%
E)66%
Rationale: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
35% + 53% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 22% and 2x = 44%
100% = 22% + 44% + Neither
Neither = 34%
The answer is B.
Answer: B
Question: In a set of three numbers,the difference between the largest and the second largest numbers is added to the smallest number.The average of the largest,second largest and the new number formed exceeds the average of the original three numbers by 8.The largest number exceeds the second largest number by how much ?
Options:
A)5
B)10
C)15
D)30
E)60
Rationale: Let the numbers in increasing order be A<B<C...
since the new number(N) increase the average of new set of numbers by 5 after replacing the smallest number,A,
the new number,N, exceeds the smallest,A, by 3*5=15 orN=15+A..(1)
and what is the new number,N,----C-B (diff in the largest and second largest)+A...(2)...
from (1)(2) C-B=15
Answer:C
Answer: C
Question: A student completes a 3 part exam as follows. The student completes sections A in 6 minutes and takes an equal time to complete the two remaining sections. What is the ratio of time spent on section C to section A if the total duration is 1 hour?
Options:
A)7:1
B)9:2
C)8:3
D)5:2
E)6:1
Rationale: The time spent on section B and section C is 27 minutes each.
The ratio of C to A is 27:6 = 9:2
The answer is B.
Answer: B
Question: Average of six numbers comes out to be 3.95. Average of two of the numbers is 3.4 while the average of other two is 3.85. Determine the average of the two numbers left.
Options:
A)4.6
B)4.9
C)4.2
D)1.4
E)3.5
Rationale: Explanation:
In the given question we have taken average of 6 numbers taken 2 at a time which makes 3 numbers.
=> 3.95 (Average of 1st and 2nd number)
=> 3.85 (Average of 3rd and 4th number)
=> 3.4 (Average of 5th and 6th number)
3.95 = (3.4 + 3.85 + x)/3
x = 4.6
ANSWER: A
Answer: A
Question: How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)4 years
B)6 years
C)5 years
D)2 years
E)7 years
Rationale: P = Rs.900
SI = Rs.81
T = ?
R = 4.5%
T= 100×SIPR=100×81900×4.5=2 years
ANSWER:D
Answer: D
Question: If x > 0, x/50 + x/5 is what percent of x?
Options:
A)6%
B)25%
C)37 1/2%
D)60%
E)75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/50 + 100/5= 2+20 =25
25 is 25% of 100=B
Answer: B
Question: The salary of a person was reduced by 20%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
Options:
A)10%
B)15%
C)20%
D)25%
E)50%
Rationale: Let the original salary be $100
new salary = $80
increase on 80 = 20
increase on 100 = [(20/80)100]% = 25%
Answer is D
Answer: D
Question: Bob can fill Q cans of water in 5 minutes. If there are R cans of water in one gallon, how many gallons can Bob fill in 55 minutes?
Options:
A)5Q/R
B)11R/Q
C)11QR
D)11Q/R
E)5R/Q
Rationale: Bob can fill this number of cans in 55 minutes: (55/5)Q = 11Q.
One can is 1/R gallons.
Bob can fill 11Q*(1/R) = 11Q/R gallons of water in 55 minutes.
The answer is D.
Answer: D
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
Options:
A)1/3
B)1/2
C)1/5
D)1/6
E)1/8
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.Answer:B
Answer: B
Question: What inequality represents the condition 1<x<11?
Options:
A)|x|<3
B)|x-6|<5
C)|x-1|<9
D)|-5+x|<4
E)|3+x|<5
Rationale: 1<x<11 represents segment with
length: 11-1 = 10
center: (11+1)/2 = 6
For any |x-a|<b a is a center and b is a half of length. So, |x-6|<10/2 represents our inequality (answer B)
Answer: B
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
Options:
A)2988
B)2776
C)4400
D)2871
E)881
Rationale: X * (95/100) * (85/100) = 3553
X = 4400
Answer:C
Answer: C
Question: Ramanujan buys an old scooter for Rs. 5400 and spends Rs. 600 on its repairs. If he sells the scooter for Rs. 6600, his gain percent is :
Options:
A)20%
B)12%
C)10%
D)5%
E)None of these
Rationale: Explanation :
Solution: C.P. =Rs. (5400+600) =Rs. 6000; S.P. = Rs. 6600.
Gain% = (600*100/6000) = 10%.
Answer : C
Answer: C
Question: If a: b = 7: 5, b: c = 9: 11, find a: b: c?
Options:
A)63: 14: 55
B)63: 45: 55
C)14: 14: 15
D)7: 14: 15
E)9: 12: 17
Rationale: Explanation:
a: b = 7: 5
b: c = 9: 11
a: b: c = 63: 45: 55
ANSWER IS B
Answer: B
Question: What is the sum of the digits of integer k, if k = (10^40- 46)
Options:
A)351
B)360
C)363
D)369
E)378
Rationale: There are 41 digits in 10^4
When we subtract 46 from it, there will be 40 digits left.
10^4 can be written as 9999999....(40 times) + 1
So,
10^40 - 46 = 9999999....(40 times) + 1 - 46 = 9999999....(40 times) -45
Consider the last 2 digits,
99-45 = 54
The last 2 digits will be 54.
And our number would be 99999......99954 with 2 less 9s after subtraction.
Number of 9s left are 38 and the last two digits are 54
The sum of the digits will be
(38*9) + 5 + 4 =351
Answer:- A
Answer: A
Question: There are 5 physics books and 1 chemistry book on shelf P and 3 physics books on shelf Q. One book is moved from shelf P to shelf Q. A student picks up a book from shelf Q. What is the probability that the chemistry book is taken by the student?
Options:
A)1/42
B)1/36
C)1/30
D)1/24
E)1/18
Rationale: P(a chemistry book is moved to shelf Q) = 1/6
P(a chemistry book is then chosen from shelf Q) = 1/4
P(the student takes a chemistry book) = 1/6 * 1/4 = 1/24
The answer is D.
Answer: D
Question: In a game of 80 points; A can give B 5 points and C 15 points. Then how many points B
can give C in a game of 60 ?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: From the above information, A:B= 80:75 and A:C= 80:65
Now
B/C= (B/A)*(A/C)= (75/80)*(80/65)=15/13
B/C=15/13= 15*4/13*4= 60/52
In a game of 60, B can give C 8 points.
ANSWER:B
Answer: B
Question: Of the following values of n, the value of (-1/5 )^(-n) will be greatest for n =?
Options:
A)3
B)4
C)0
D)-4
E)-3
Rationale: imo -4
(-1/5)^-4=
1/(1/625)=625
oops i meant 4
B
Answer: B
Question: Meg and Bob are among the 8 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
Options:
A)2400
B)3000
C)20160
D)9000
E)1200
Rationale: Total # of ways the race can be finished is 8!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 8!/2=20160.
Answer: C.
Answer: C
Question: The average of 15 numbers is calculated as 20. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)30
B)26
C)16
D)97
E)12
Rationale: 15 * 20 + 36 – 26
= 300/10
= 30
Answer: A
Answer: A
Question: The initial price of an article is Rs.6000 which increases 40% increse in its price in the first year,a 20% decrease in the second year and a 20% increase in the next year. What is the final price of the article ?
Options:
A)Rs.5392
B)Rs.6392
C)Rs.8392
D)Rs.7392
E)Rs.9392
Rationale: The initial price of the article is Rs.6000. In the 1st year, price of the article = 6000 + 2400 = Rs. 8400. In the 2nd year, price = 8400 - 20% of 8400= 8400 - 1680 = Rs. 6720.
In the 3rd year, price = 6720 + 10% of 6720 = 6720 + 672 = Rs. 7392
Required price = = Rs.7392.
Answer:D
Answer: D
Question: If the first day of a year (other than leap year) was Monday, then which was the last day of that year?
Options:
A)Saturday
B)Friday
C)Tuesday
D)Monday
E)None of these
Rationale: Explanation :
Given that first day of a normal year was Monday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Monday+ 1 Odd day) = Tuesday
Therefore, last day of the mentioned year = Monday. Answer : Option D
Answer: D
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, ___?
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 29 + 9 = 38.
correct answer D)38
Answer: D
Question: A, B and C shared profits in ratio of 9 : 7 : 8. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?
Options:
A)10 : 49 : 45
B)20 : 49 : 64
C)10 : 19 : 64
D)20 : 29 : 64
E)36 : 29 : 63
Rationale: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
â‡’14 x = 9
â‡’ 8 x = 7
â‡’ 7x = 8
â‡’ Final investment ratio = 36 : 49 : 64
E
Answer: E
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
A)20
B)40
C)45
D)25
E)60
Rationale: 1: 2/5 = 5: 2
2/7 * 70 = 20
ANSWER A
Answer: A
Question: A garrison of 300 men had a provision for 31 days. After 28 days 280 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?
Options:
A)45 days
B)55 days
C)35 days
D)25 days
E)40 days
Rationale: 400 --- 31
400 --- 3
120 --- ?
300*3 = 20*x => x =45 days
ANSWER:A
Answer: A
Question: If 5400 mn = k^4, where m, n, and k are positive integers, what is the least possible value of 5m + n?
Options:
A)65
B)18
C)20
D)25
E)33
Rationale: k^4=5400∗mn
k^4=3^3.2^3.5^2.mn
In order to make RHS a perfect power of 4, we require it to be multiplied by 3, 2 & 5^2
mn=3.2.5^2
mn = 150 = 10 * 15 (Least possible)
Answer =5* 10 + 15 = 65
ANSWER:A
Answer: A
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
Options:
A)Rs.19,928.80
B)Rs.19,828.80
C)Rs.19,898.80
D)Rs.19,588.80
E)Rs.19,899.80
Rationale: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2
= (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08)
= 1360/0.08 = 17000 Principal + Interest = Rs. 19828.80
Answer:B
Answer: B
Question: In a company of 170 employees, 110 are females. A total of 80 employees have advanced degrees and the rest have a college degree only. If 25 employees are males with college degree only, how many employees are females with advanced degrees?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: The number of males is 170-110=60.
The number of males with advanced degrees is 60-25=35.
The number of females with advanced degrees is 80-35=45.
The answer is B.
Answer: B
Question: Car Dealership X, the total profit from sales increased by 12 percent over the previous years, while the number of cars sold decreased by 12 percent over the previous years. Approximately what was the average percent increase in profit per car over the previous year.
Options:
A)18%
B)20%
C)22%
D)27.27%
E)35%
Rationale: Let Profit be x and cars sold be y
Originally Profit/Car = x/y
Now it is 1.12x / 0.88 y = 112/88 (x/y)
Increase in profit per car = ((24/88) (x/y)) / (x/y) * 100 = 27.27%
Answer = D
Answer: D
Question: The number of sailors on a ship is 50% more than the number of officers. The ratio of sailors to officers would be
Options:
A)33:25
B)47:20
C)3:2
D)22:25
E)97:50
Rationale: Sailor = 1.50 * Officer
Sailor/Officer = 1.50/1 = 150/100 = 3/2
Answer will be C
Answer: C
Question: Two pipes A and B fill at a certain rate.B is filled at 10,20,40,80(10 in 1 hour,20 in 2 hours,40 in 3 hrs and so on). if 1/16 of B is filled in 17 hrs,what time it will take to get completely filled?
Options:
A)20 hrs
B)21 hrs
C)22 hrs
D)23 hrs
E)24 hrs
Rationale: 1/16 in 17 hrs
so 1/8 in 18 hrs
1/4 in 19 hrs
1/2 in 20 hrs
and complete tank in 21 hrs
ANSWER:B
Answer: B
Question: How many days per calendar year is the month a factor of the day
Options:
A)0
B)1
C)59
D)90
E)124
Rationale: Solution: 124
All 31 days in January, because 1 is a factor of all integers
14 of the 28 days in February (because every other day is divisible by 2)
10 of the 31 days in March (the multiples of 3 between 3 and 30)
7 days in April (the multiples of 4 between 4 and 28)
6 days in May (the multiples of 5 between 5 and 30)
5 days in June (the multiples of 6 between 6 and 30)
4 days in July (the multiples of 7 between 7 and 28)
3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)
3 days in September (9th, 18th, 27th)
3 days in October (10th, 20th,30th)
2 days in November (11th, 22nd)
2 days in December (12th, 24th)
And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!
E
Answer: E
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 60% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
Options:
A)1.8 lakh
B)1.2 lakh
C)1.9 lakh
D)8.1 lakh
E)6.1 lakh
Rationale: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.6 = 4.8 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 4.8 - 1.2 = 3.6 lakh
Average SP of all the 3 cars = 1.2 lakh
Answer: B)
Answer: B
Question: A person travels equal distances with speeds of 3km/hr, 4km/hr, 5km/hr. and takes a total time of 47minutes. Find the total distance ?
Options:
A)3
B)2
C)5
D)4
E)6
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/3)+(x/4)+(x/5) = 47/60
x=1
total distance = 3*1 = 3km
correct option is A
Answer: A
Question: The arithmetic mean of set M is zero. If N = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of M consisting of all those elements in M which are more than two but less than three standard deviations away from the arithmetic mean of M, what could be equal to the standard deviation of M?
Options:
A)0.54
B)0.77
C)0.82
D)0.97
E)1.62
Rationale: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and N = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of M
N consists of all those elements in M that are more than 2 but less than 3 MDs away from the arithmetic mean of M
If an element is 1 MD away from the mean, we can write it as either m + MD or m - MD
Similarly, if an element is 2 MDs away from the mean, we can write it as either m + 2*MD or m - 2*MD
So, if these elements lie within 2 and 3 MDs of mean, m=0
we can find which one of these values of MD satisfies each value within N
Only MD = 0.77 does
Answer : B
Answer: B
Question: If the price of a computer were reduced by 14 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
Options:
A)$844.10
B)$894.40
C)$1,053.50
D)$1,135.20
E)$1,259.90
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-14/100)------->X(43/50)=A(say)
means X=A*(50/43).....
so initial price to be integer(As per stem) final price must be multiple of 43
if we check options all were divisible by 43 except option (A)..which is Ans.
Ans A
Answer: A
Question: Gary started driving at 9:00 am from city A towards city B at a rate of 50 mph. At a rate that is 15 mph higher than Gary's, Thomas started driving at the same time as John from city B towards city A. If Gary and Thomas crossed each other at 11 am, what is the distance beween the two cities?
Options:
A)230 miles
B)240 miles
C)250 miles
D)260 miles
E)270 miles
Rationale: gary speed--->50mph
thomas speed---->65mph
both started at 9:00 am they crossed at 11:00 that means each travelled 2hrs so 50*2+65*2=230 miles
ANSWER:A
Answer: A
Question: Tim and Tom are workers in a department that has a total of 9 employees. Their boss decides that two workers from the department will be picked at random to participate in a company interview. What is the probability that both Jim and John are chosen?
Options:
A)1/35
B)1/34
C)1/33
D)1/36
E)1/37
Rationale: Probability = 2c2/9c2
= 1/36
Answer D
Answer: D
Question: If the number of white balls in a box are 6 times the black balls, which of the below is the total number of balls, if there are 8 black balls in the box?
Options:
A)A - 56
B)B - 57
C)C - 58
D)D - 59
E)E - 60
Rationale: Let the number of black balls = x and the number of white balls = 6x Then, total number of balls in the box = x + 6x = 7x i.e., the total number of balls must be a multiple of 7 From the given choices, only 56 is the multiple of 7. Hence, 56 are the number of balls in the box. Answer is A.
Answer: A
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
Options:
A)10
B)12
C)14
D)13
E)18
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: D
Question: Train X and train Y pass one another traveling in opposite directions. Sixty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
Options:
A)28
B)40
C)65
D)72
E)80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 1 hr
using RTD table, (2R+30) * 1 = 100 ==> R= 35 miles/hr
So the rate of train X is 65 miles/hr (since R+30)
The distance traveled by Train X in 60 min is R*T = 65 * 60/60 = 65 miles (C)
Answer: C
Question: Sam bought 50 candles and 3 lighters costing 2 dollars each. How was Sam's total?
Options:
A)300
B)103
C)56
D)106
E)55
Rationale: For this we need to add all items and multiple all items together
2x(50+3)=2x50+2x3=100+6=106
correct answer is D)106
Answer: D
Question: 2 identical circles intersect so that their centre and point at which they intersect form a square of 1 cm.the area of portion that is common two circles is
4
Options:
A)π2-1
B)4
C)√2-1
D)√5
E)π/2-1
Rationale: the area of the sector is pi*r^2*90/360 (as it is a square, so the angle is 90)
=pi*r^2/4
=pi/4 (as the area of the square is 1cm^2, so the sides are 1 cm each. the sides of the square are the radii of the circle)
now, the area of the triangle formed by two radii and a line which joins the point of intersection of the two circles = 0.5*1*1=0.5
So, half of the portion of our desired area= (pi/4 - 0.5)
therefore, the area of our desired portion is 2* (pi/4 - 0.5)
= pi/2 - 1
ANSWER:E
Answer: E
Question: In the first week of last month, Company X realized an average wholesale profit of $1428 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?
Options:
A)$3
B)$4
C)$7
D)$13
E)$51
Rationale: The key operator that everyone seems to have missed is the average. The average profit of $1428 per day is equivalent to a total profit of $9996 for the whole week.
Therefore, the difference between sale price and cost per unit is equal to $9996, which is divisible by all of the answer choices, except for 13.
So, D is the answer.
Answer: D
Question: Ritesh and Co. generated revenue of Rs. 1,500 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
Options:
A)12.5%
B)20.83%
C)25%
D)50%
E)None of these
Rationale: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,500 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1250 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1500.
=>12,000.
Hence, the total revenue by end of 2007 is Rs. 12,000. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/12000)×100.
=>20.83%.
Answer : B
Answer: B
Question: Two trains of equal lengths take 12 sec and 24 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)18 sec
B)12 sec
C)17 sec
D)21 sec
E)16 sec
Rationale: Speed of the first train = 120/12 = 10 m/sec.
Speed of the second train = 120/24 = 5 m/sec.
Relative speed = 10 + 5 = 15 m/sec.
Required time = (120 + 120)/15 = 16 sec.
Answer: E
Answer: E
Question: A student is ranked 17th from right and 5th from left. How many students are there in totality ?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: From right 17 , From left 5
Total = 17+5-1 = 21
ANSWER:D
Answer: D
Question: An ant walks an average of 500 meters in 60 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
Options:
A)1.0
B)0.5
C)0.75
D)0.425
E)0.3
Rationale: the ant walks an average of 500 meters in 60 minutes
500 meters in 1 hours
the beetle walks 15% less distance = 500-75=425 meters in 60 minutes
0.425 km in 1 hours
speed = 0.425*1 = 0.425 km/h
I guess option D should be 0.425
Answer: D
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)20
B)14
C)18
D)15
E)30
Rationale: 900 ---- 180
100 ---- ? => 20%
ANSWER A
Answer: A
Question: log42 - log82 + log16 2 -…. to ∞ is
Options:
A)e2
B)ln2+1
C)ln2-1
D)1-ln2
E)None of these
Rationale: Required sum = 1/2 - 1/3 +1/4 - … to ∞
Now, loge(1 + X) = X - X2/2 + X3/3 - …
Therefore, loge2 = 1-1/2 + 1/3 - … to ∞
=>1/2 - 1/3 + 1/4 .. to ∞ = 1 - loge2 = 1- ln2.
ANSWER:D
Answer: D
Question: A man wants to cross a home, which has 2 doors on one side and 1 door on other site. He has 2 x 1=2 ways for it.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The product of first ‘n’ natural numbers is denoted by n!.
n! = n(n-1) (n-2) ………………..3.2.1.
Ex. 5! = 5 x 4 x 3 x 2 x 1 =120
Note 0! = 1
Proof n! =n, (n-1)!
Or (n-1)! = [n x (n-1)!]/n = n! /n
Putting n = 1, we have
O! = 1!/1
or 0 = 1
A
Answer: A
Question: A candidate appearing for an examination has to secure 42% marks to pass paper I. But he secured only 42 marks and failed by 22 marks. What is the maximum mark for paper I?
Options:
A)110
B)120
C)130
D)152
E)150
Rationale: he secured 42 marks nd fail by 22 marks so
total marks for pass the examinatn=64
let toal marks x
x*42/100=64
x=152
ANSWER:D
Answer: D
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
Options:
A)25
B)13
C)40
D)20
E)30
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.
ANSWER:E
Answer: E