divelab/Sys2Bench huggingface dataset:
Question: A wheel that has 2 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is:
Options:
A)49
B)4
C)12
D)3
E)27
Rationale: Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 2 :: 21 : x 14 * x = 2 x 21
x =	(2 x 21)/14
x = 3.
Answer is D.
Answer: D
Question: From below option 27 is divisible by which one?
Options:
A)A)4
B)B)8
C)C)9
D)D)10
E)E)911
Rationale: 27/9 = 3
C
Answer: C
Question: In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes T of the competition are possible?
Options:
A)18
B)20
C)54
D)84
E)120
Rationale: the ways the three teams can be selected is..
i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways..
ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60
total T=84 outcomes
D
Answer: D
Question: 30 pens and 75 pencils were purchased for 570. If the average price of a pencil was 2.00, find the average price of a pen.
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (570 – 150) = 360
∴ Average price of a pen = 420⁄60 = 14
Answer E
Answer: E
Question: A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: take the maximum mark in each sub as 100. qualify mark is 50.On a total dt fellow gets 60 x 5= 100.
We can write (10+9+8+7+6)a=300 => a=15/2
In 5 subjects he gets 75,67.5,60,52.5,45.
He passes in 4 subjects...
ANSWER:C
Answer: C
Question: The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people V who purchased only book A?
Options:
A)250
B)500
C)750
D)1000
E)1500
Rationale: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both,V= 1000 purchased A only. (This is much simpler to solve using the Venn diagram).
Correct answer is D. 1000
Answer: D
Question: Rs. 6000 is lent out in two parts. IN that One part is lent at 7% p.a simple interest and the second one is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)5 : 7
B)5 : 1
C)6: 1
D)7 : 1
E)5 : 3
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 10/100 (6000 - x) = 600 - 3x/100
=> 600 - 3/100 x = 450 => x = 5000
Amount lent at 10% = 1000
Required ratio = 5000 : 1000 = 5 : 1
ANSWER:B
Answer: B
Question: Out of 15 consecutive numbers, 2 are chosen at random. The probability that they are both odds or both primes is
Options:
A)1/6
B)1/9
C)1/3
D)1/7
E)1/1
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer: D
Answer: D
Question: If 0.5 : x :: 5 : 8, then x is equal to:
Options:
A)A)1.12
B)B)1.2
C)C)1.25
D)D)0.9
E)E)0.8
Rationale: (x * 5) = (0.5 * 8)
x = 4/5
x = 0.8
Answer = E
Answer: E
Question: If a trader sold two cars each at Rs. 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?
Options:
A)1.44% loss
B)14.4% profit
C)14.4% loss
D)0%
E)None of these
Rationale: SP of each car is Rs. 325475, he gains 12% on first car and losses 12% on second car.
In this case, there will be loss and percentage of loss is given by = [(profit%)(loss%)]/100 = (12)(12)/100 % = 1.44%
ANSWER:A
Answer: A
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
Options:
A)0998
B)2899
C)1889
D)1500
E)2881
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: D
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
Options:
A)5
B)8
C)4
D)9
E)2
Rationale: Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer:A
Answer: A
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 40.5 meters. How many times did the ball bounce?
Options:
A)3
B)6
C)7
D)8
E)9
Rationale: Division of total distance travelled will be 16+16+8+0.5
Ans:A
Answer: A
Question: In a particular state, 70% of the counties received some rain on Monday, and 50% of the counties received some rain on Tuesday. No rain fell either day in 20% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?
Options:
A)20%
B)40%
C)50%
D)60%
E)70%
Rationale: 70 + 50 + 20 = 140%
The number is 40% above 100% because 40% of the counties were counted twice.
The answer is B.
Answer: B
Question: Find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively
Options:
A)125
B)127
C)129
D)131
E)141
Rationale: Explanation:
In this type of question, its obvious we need to calculate the HCF, trick is
HCF of (1661 - 10) and (2045 -13)
= HCF (1651, 2032) = 127
Option B
Answer: B
Question: The price of a car is marked at $10,000. If the car has successive discounts of 25%, 20% and 5%, then at what price does a customer buy the car?
Options:
A)$5100
B)$5300
C)$5500
D)$5700
E)$5900
Rationale: 0.95*0.8*0.75*10000 = $5700
The answer is D.
Answer: D
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
Options:
A)s. Rs.10,500, Rs. 13,500, Rs. 16,500
B)s. 10,600, Rs. 13,500, Rs. 96,500
C)s. 10,500, Rs. 73,500, Rs. 16,500
D)s. 10,500, Rs. 18,500, Rs. 16,500
E)s. 40,500, Rs. 13,500, Rs. 16,500
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer:A
Answer: A
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140
B)287
C)1267
D)127
E)212
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: A
Answer: A
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)24
B)35
C)64
D)68
E)90
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Question: If 10% of x = 20% of y, then x:y is equal to?
Options:
A)2:6
B)2:1
C)7:1
D)2:8
E)2:2
Rationale: 10% of x = 20% of y
10x/100 = 20y/100 => x/10 = y/5
x/y = 10/5 = 2/1
x:y = 2:1.
Answer:B
Answer: B
Question: What is x if x + 2y = 10 and y = 3?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Substitute y by 3 in x + 2y = 10
x + 2(3) = 10
x + 6 = 10
If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10. Hence
x = 4 correct answer B
Answer: B
Question: What is the total number of integers between 2 and 38 that are divisible by 4?
Options:
A)8
B)9
C)7
D)6
E)11
Rationale: 4, 6, 8, ..., 32,36
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (36 - 4) / (4)+ 1 = 32/4 + 1 = 8 + 1 = 9
Answer is B
Answer: B
Question: There are 18 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?
Options:
A)800
B)380
C)360
D)478
E)566
Rationale: The total number of stations= 20
From 20 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 20P2 ways.
20P2= 20*19= 380
ANSWER:B
Answer: B
Question: Running at the same rate, 8 identical machines can produce 560 paperclips a minute. At this rate, how many paperclips could 30 machines produce in 6 minutes?
Options:
A)1344
B)3360
C)8400
D)12600
E)67200
Rationale: 8 machines produce 560 in 1 min
8 machines produce 560* 6 in 6 min
30 machine produce 560*6*(30/8) in 6 minutes
560*6*30/8=12600 answer is D.
Answer: D
Question: The side of a square is increased by 5% then how much % does its area increases?
Options:
A)15.00 %
B)10.25 %
C)10.00 %
D)12.25 %
E)12.50 %
Rationale: a = 100 a2 = 10000
a = 105 a2 = 11025
----------------
10000 --------- 1025
100 -------? => 10.25 %
Answer:B
Answer: B
Question: The value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4)
Options:
A)8/(1-x^8)
B)4x/(1+x^2)
C)4/(1-x^6)
D)4/(1+x^4)
E)4x/(1-x^4)
Rationale: Highlighted part has mistake as the exponent of x must be 4 in last term
CORRECT QUESTION ISThe value of 1/(1-x) + 1/(1+x) + 2/(1+x^2) + 4/(1+x^4) = ?
Solution is as mentioned below...
one more way that could get the answer in the type of eqn and choices given is to substitute some value for x...
0 would be better as the eq has constant term free of term 'x'..
the Eq gives us 8 as the ans , as also only choice A..
Answer: A
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
A)7 sec
B)5 sec
C)9 sec
D)6 sec
E)1 sec
Rationale: T = 60/36 * 18/5
= 6 sec
Answer:D
Answer: D
Question: 987.650 - ? + 56.98 = 126.654
Options:
A)A)899.015
B)B)752.804
C)C)714.642
D)D)629.906
E)917.976
Rationale: Explanation:
917.976
Answer: Option E
Answer: E
Question: Pipes A and B can fill a tank in 5 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)4 1/2 hours
E)NONE
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12 = 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
ANSWER:C
Answer: C
Question: What percent of 5 letter combinations that can be made from the letters of the word SERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
Options:
A)20%
B)23.8%
C)25%
D)30.2%
E)35%
Rationale: a) noof combinations when all 5 letters are different = 7*6*5*4*3
b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3
b/a = 5/21= 0.238
B
Answer: B
Question: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 4x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 4x – 2 are ALLintegers
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers
When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 3(3) – 2.
When we evaluate these terms we get: 4, 6, 3, 5 and 10
Rearrange to get: 3, 4, 5, 6, 10. So, when x = 3, we getconsecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)
Answer:
C
Answer: C
Question: 1/2+[(2/6*6/32)+1]-9/16=
Options:
A)29/16
B)19/16
C)15/16
D)9/13
E)0
Rationale: 1/2 - [(2/6*6/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: E
Question: A baseball card decreased in value 20% in its first year and 30% in its second year. What was the total percent decrease of the card's value over the two years?
Options:
A)28%
B)30%
C)32%
D)36%
E)44%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.8 = 80
After second year price = 80 *0.7 = 56
final decrease = [(100 - 56)/100] * 100 = 44%
correct answer - E
Answer: E
Question: If A got 70 marks and B got 80 marks, then what percent of A's mark is B's mark?
Options:
A)A)60%
B)B)80%
C)C)65%
D)D)87.5%
E)of these
Rationale: A's marks =80 ; B's marks = 70.
Let x% of A = B => x/100 * 80 = 70
=> x = (70 * 100)/80 =87.5
B's marks is 87.5% of A's marks.
ANSWER:D
Answer: D
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
Options:
A)I only
B)II only
C)II only
D)I and II only
E)I, II, and III
Rationale: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1can not be ascertain as is not related to y directly ---not true
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, II are always true and hence answer is
C
Answer: C
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options:
A)Can't be determined
B)40
C)27
D)24
E)None of these
Rationale: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+3)/(4x+3)=119
⇒ 45x + 27 = 44x + 33⇒ 9(5x + 3) = 11(4x + 3)
⇒ 45x - 44x = 33 - 27
⇒ x = 6.
Anand's present age = 4x = 24 years.
Answer: D
Answer: D
Question: Of 60 children, 30 are happy, 10 are sad, and 20 are neither happy nor sad. There are 22 boys and 38 girls. If there are 6 happy boys and 4 sad girls, how many boys are neither happy nor sad?
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Venn diagrams are useful for multiple values of a single variable e.g. State of mind - happy/sad/neither. When you have two or more variables such as here where you have gender - boy/girl too, it becomes unwieldy. In this case, either use the table or logic.
Table method is shown above; here is how you will use logic:
There are 6 happy boys.
There are 4 sad girls but total 10 sad children. So rest 6 sad children must be sad boys.
We have 6 happy boys and 6 sad boys. Total we have 22 boys. So 22 - 6 - 6 = 10 boys must be neither happy nor sad.
Answer (E)
Answer: E
Question: How many ltrs of water must beadded to 16 ltrs of milk and water containing 10% water to make it 20% water in it?
Options:
A)1 liter
B)2 liter
C)3 liter
D)4 liter
E)5 liter
Rationale: By rule of alligation,
% Concentration
of water in pure water (100)	% Concentration
of water in the given mixture (10)
Mean % concentration
(20)
20 - 10 = 10	100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
=> Quantity of water =16×18=2 liter
B
Answer: B
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
Options:
A)6400
B)2400
C)5500
D)7400
E)3400
Rationale: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400
ANSWER:A
Answer: A
Question: A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 10 salespeople on staff, how many different arrangements of winners are possible?
Options:
A)1,728
B)1,440
C)1,320
D)220
E)720
Rationale: [quote=Bunuel]A company plans to award prizes to its top 3 salespeople, with the largest prize going to the top salesperson, the next-largest prize to the next salesperson, and a smaller prize to the third-ranking salesperson. If the company has 10 salespeople on staff, how many different arrangements of winners are possible?
10*9*8
=720
Answer : E
Answer: E
Question: There are 399 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
Options:
A)152
B)209
C)57
D)231
E)181
Rationale: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 399 = 231
ANSWER:D
Answer: D
Question: After decreasing 24% in the price of an article costs Rs.988. Find the actual cost of an article?
Options:
A)1667
B)6789
C)1300
D)6151
E)1421
Rationale: CP* (76/100)
= 988
CP= 13 * 100 => CP
= 1300
Answer: C
Answer: C
Question: 8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :
Options:
A)11/31
B)13/37
C)15/39
D)16/37
E)19/51
Rationale: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
= 15/39
C
Answer: C
Question: Mohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
Options:
A)Rs.598
B)Rs.594
C)Rs.596
D)Rs. 595
E)None of these
Rationale: Explanation:
Price of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390
Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208
Therefore, Total amount = Rs.390+Rs.208 = Rs.598.
Answer: Option A
Answer: A
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years. The age of the 15th student is
Options:
A)9 years
B)11 years
C)15 years
D)21 years
E)25 years
Rationale: Solution
Age of the 15th student	=[15x15-(14x7+16x7)]
= (225 - 210)
= 15 years.
Answer C
Answer: C
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
Options:
A)13 8/3 days
B)13 1/3 days
C)13 6/3 days
D)63 1/3 days
E)13 5/3 days
Rationale: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer:B
Answer: B
Question: David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
Options:
A)15
B)20
C)25
D)35
E)30
Rationale: Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 - 63x = 120x = 40
x = 1/3
Number of floors covered by David in (1/3) min. = (1/3 x 57)= 19.
So, their paths cross at (11 +19) i.e., 30th floor.
Answer is E.
Answer: E
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)42.3
B)560.45m
C)79m
D)26m
E)111.12m
Rationale: Explanation:
A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
ANSWER E
Answer: E
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:
A)2681
B)1892
C)1000
D)1345
E)1623
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
Answer: C
Answer: C
Question: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Options:
A)360
B)120
C)80
D)240
E)60
Rationale: Total number of arrangements = 6! = 720
In exactly half, Susan will be to the left of Tim, which gives us 360 arrangements
Option (A)
Answer: A
Question: A team of three entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
Options:
A)288
B)245
C)168
D)127
E)664
Rationale: Explanation:
3 * 84 = 252 - 7 = 245
Answer:B
Answer: B
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/6 + 6^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
Options:
A)1/4
B)1/5
C)1/6
D)1/7
E)1/8
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/4
Answer A
Answer: A
Question: The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h?
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24.
ANS :C
Answer: C
Question: The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?
Options:
A)32°
B)35°
C)38°
D)40°
E)None of these
Rationale: Explanation:
The temperature for first 4 days = 4 * 36 = 144
The temperature for last 4 days = 4 * 38 = 152
The difference between the temperatures is (152 – 144) = 8
The ratio of temperature between first and fifth day is 4 : 5
The temperature on fifth day is 5*8 = 40
ANSWER D
Answer: D