divelab/Sys2Bench huggingface dataset:
Question: How many three digit numbers V greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?
Options:
A)72
B)48
C)120
D)96
E)76
Rationale: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.
Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.
Total possible choice 80 - 8 =72=V
Answer: A.
Answer: A
Question: Raju age after 55 years will be 5 times his age 5 years back, What is the present age of Raju
Options:
A)28
B)17
C)10
D)77
E)20
Rationale: Clearly,
x+55 = 5(x-5)
<=> 4x = 80 => x = 20
Answer:E
Answer: E
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 20 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)22
B)98
C)60
D)88
E)24
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/20 = 3x => x = 10/3.
So, speed of the faster train = 20/3 = 20/3 * 18/5 = 24 km/hr.
Answer:E
Answer: E
Question: The length of the room is 5.5m and width is 3.75m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq meter?
Options:
A)16500
B)16299
C)22898
D)12929
E)12091
Rationale: l=5.5m w=3.75m
area of the floor = 5.5 x 3.75 = 20.625 sq m
cost of paving = 800 x 20.625 = Rs. 16500
Answer: A
Answer: A
Question: What is the average of 120, 130, 140, 510, 520, 530, 1115, 1120, and 1125?
Options:
A) 419
B) 551
C) 601
D)590
E) 721
Rationale: Add 120, 130, 140, 510, 520, 530, 1115, 1120, and 1125
Grouping numbers together may quicken the addition
sum =5310
5310/9 =590
.D
Answer: D
Question: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 9 and 39 inclusive.
Options:
A)351
B)384
C)410
D)424
E)450
Rationale: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 9 to 39, inclusive. We're asked for the SUM of this group.
1) Start with the sum of the smallest and the biggest: 9 + 39 = 48
2) Now look at the 'next smallest' and the 'next biggest': 11 + 37 = 48
Now we have proof that there is no middle term. We have 8 bunches of 48
8(48) = 384
B
Answer: B
Question: SAKSHI CAN DO A PIECE OF WORK IN 20 DAYS. TANYA IS 25% MORE EFFICIENT THAN SAKSHI. THE NUMBER OF DAYS TAKEN BY TANYA TO DO THE SAME PIECE OF WORK IS:
Options:
A)15
B)16
C)18
D)25
E)NONE OF THESE
Rationale: RATIO OF TIMES TAKEN BY SAKSHI AND TANYA = 125:100 = 5:4
SUPPOSE TANYA TAKES X DAYS TO DO THE WORK;
5:4::20:X, X=(4x20/5), X=16 DAYS.
CORRECT OPTION: B
Answer: B
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 60 km downstream?
Options:
A)30/18 hours
B)37/13 hours
C)80/13 hours
D)12/5 hours
E)30/43 hours
Rationale: Speed downstream = 20 + 5 = 25 kmph.
Time required to cover 60 km downstream
= d/s = 60/25
= 12/5 hours.
Answer: D
Answer: D
Question: A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain?
Options:
A)20
B)40
C)60
D)80
E)90
Rationale: Suppose x bottles can fill the tin completely
Then4/5x-3/4x=6-4
X/20=2
X=40
Therefore required no of bottles =40
ANSWER B
Answer: B
Question: A can complete the job in 2 hours and B can complete the same job in 4 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
Options:
A)1/6
B)3/10
C)1/2
D)5/6
E)8/9
Rationale: A=1/6
Answer: A
Question: At the end of a business conference the 20 people present all shake hands with each other once. How many handshakes will there be altogether ?
Options:
A)20
B)45
C)55
D)190
E)95
Rationale: number of handshakes = 20C2= 20*19/2 = 190
ANSWER:D
Answer: D
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 6 pumps work to empty the tank in 1 day?
Options:
A)8
B)10
C)11
D)12
E)13
Rationale: 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 6 pumps then
48/6=8 hrs.
answer :A
Answer: A
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 15. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)395
Rationale: Clearly, the numbers are (23 x 13) and (23 x 15).
Larger number = (23 x 15) = 345.
Answer: Option D
Answer: D
Question: If x*y = xy – 2(x + y) for all integers x and y, then 4* (–3) =
Options:
A)–14
B)–11
C)–4
D)4
E)16
Rationale: 4*(-3) = 4*(-3) - 2 (4 + (-3) ) = -12 -2 = -14
Option (A)
Answer: A
Question: one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago, and 5/8 of the workers have read the latest book by H. Kureishi. The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book. If there are 72 workers in the Palabras bookstore, how many of them have read both books?
Options:
A)13
B)12
C)9
D)8
E)4
Rationale: There are total 72 workers.
one-fourth of the workers in Palabras bookstore have read the latest book by J. Saramago,
So 18 have read Saramago.
5/8 of the workers have read the latest book by H. Kureishi.
So (5/8) * 72 = 45 have read Kureishi
The number of workers that have read neither book is one less than the number of the workers that have read the latest Saramago book and have not read the latest Kureishi book
If B workers have read both books, 18 - B have read Saramago but not Kureishi.
So, (18 - B - 1) have read neither.
Total = n(A) + n(B) - Both + Neither
72 = 18 + 45 - B + (18 - B - 1)
B = 4
Answer (E)
Answer: E
Question: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
Options:
A)$ 280,000
B)$ 320,000
C)$ 360,000
D)$ 450,000
E)$ 540,000
Rationale: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 40,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.
So the amount invested will get doubled thrice.
So, 40000 *2 = 80000
80000*2 = 160000
160000*2 = 320000
Hence, the answer is B.
Answer: B
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 4 :8. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
Options:
A)18 : 35 : 50
B)3 : 10 : 10
C)9 : 14 : 25
D)32 : 35 : 25
E)None of these
Rationale: Suppose the number of students studying Arts, Commerce and Science be 3x, 4x and 8x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 4x × 140% :
8x × 125% = 36 : 56 : 100
= 9 : 14 : 25
Answer C
Answer: C
Question: A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
Options:
A)8 km/hr
B)10 km/hr
C)12 km/hr
D)16 km/hr
E)None of these
Rationale: Distance covered by the car = 80 × 10 = 800 km
\ Speed = 800⁄8 = 100 km/hr
\ Speed gain = 100 – 80 = 20 km/hr
Answer E
Answer: E
Question: If Q is the least common multiple of 90,196, and 300, which of the following is NOT a factor of Q?
Options:
A)600
B)700
C)900
D)2,100
E)4,900
Rationale: IF Q is the least common multiple of 90,196 and 300, which of the following is NOT a factor of Q?
A- 600
B- 700
C- 900
D- 2100
E- 4900
90 = 2 * 3 * 3 * 5
196 = 2 * 2 * 7 * 7
300 = 2 * 2 * 3 * 5 * 5
LCM = 2 * 2 * 3 * 3 * 5 * 5 * 7 * 7
(TWO 2, TWO 3, TWO 5, TWO 7)
600 = 2 * 2 * 2 * 3 * 5 * 5
700 = 2 * 2 * 5 * 5 * 7
900 = 2 * 2 * 3 * 3 * 5 * 5
2100 = 2 * 2 * 3 * 5 * 5 * 7
4900 = 2 * 2 * 5 * 5 * 7 * 7=A
Answer: A
Question: Rectangular Floors X and Y have equal area. If Floor X is 10 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
Options:
A) 13 1/2
B) 20
C) 18 3/4
D) 21
E) 24
Rationale: The area of a rectangle is: Area = length x width
We are given that floor X is 10 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 10
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(10)(18) = 9n
(10)(2) = n
20 = n
Answer B.
Answer: B
Question: The figure above shows the dimensions of a semicircular cross section of a one-way tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit L on the height of vehicles that are allowed to use the tunnel?
Options:
A)5½ ft
B)7½ ft
C)8 ½ ft
D)9½ ft
E)10 ft
Rationale: Let's label the midpoint of the circle O. Since the base of the semi-circle is 20, we know that the diameter is 20 and, accordingly, the radius is 10.
We also know that the traffic lane is 12 feet long and there's an equal amount of space on either side, so the traffic lane extends 6 feet on either side of O. Let's call the leftmost point on the base of the traffic lane A. So, the distance OA is 6.
Now draw a line straight up from A to the top of the tunnel. Let's label the point at which the line intersects the circle B. The answer to the question will, therefore, be the height AB - .5 feet (we need to leave .5 feet of clearance).
Here's the key to solving the question: if we draw a line from O to B, that line is a radius of the circle and, therefore, has length 10. We now have right triangle OAB (the right angle is at point A), with leg OA=6 and hypotenuse OB=10. We can now solve for leg AB=8 (either by applying the pythagorean theorum or by applying the 3/4/5 special right triangle ratio).
Finally: AB=8, so the correct answer L is 8 - .5 = 7.5... choose (B)!
Answer: B
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (Y + X) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.
Options:
A)2 only.
B)3 only.
C)1 only.
D)2 and 3 only.
E)1, 2 and 3.
Rationale: Statement I is TRUE
Statement II is not TRUE
Statement III is not TRUE
Answer : C
Answer: C
Question: A soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 40 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
Options:
A)20
B)25
C)30
D)40
E)50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 20
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, A is the answer
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 80 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)24
B)35
C)36
D)37
E)38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (80 + 80)/12 => x = 6.66
Speed of each train = 10 m/sec.
= 6.66 * 18/5 = 24 km/hr.
Answer: Option A
Answer: A
Question: How many multiples of 4 are there between 4 and 64 ?
Options:
A)12
B)64
C)14
D)16
E)60
Rationale: It should be mentioned whether 4 and 64 are inclusive.
If 4 and 64 are inclusive, then the answer is (64-4)/4+1=16.
If 4 and 64 are NOT inclusive, then the answer is (60-8)/4+1=14.
Since OA is C, then we have NOT inclusive case.
Answer: C
Question: The simple form of the ratio 2/3:2/5 is?
Options:
A)5:8
B)5:5
C)5:9
D)5:3
E)5:1
Rationale: 2/3 : 2/5 = 10:6 = 5:3
Answer: D
Answer: D
Question: A cyclist rides a bicycle over a route which is 1/3 uphill, 1/3 level, and 1/3 downhill. If the cyclist covers the uphill part of the route at the rate of 6 km per hour and the level part at the rate of 9 km per hour, what rate in km per hour would the cyclist have to travel the downhill part of the route in order to average 9 km per hour for the entire route?
Options:
A)12
B)15
C)18
D)21
E)24
Rationale: Let V be the speed on the downhill section.
Let D be the distance of each of the three equal sections.
Total time T = T1+T2+T3 and 3D/T = 9 km/hour
3D / (D/6 + D/9 + D/V) = 9
1/3 = 1/6 + 1/9 + 1/V
1/V = 1/18 and so V = 18 km/h
The answer is C.
Answer: C
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 9 days, then C alone can do it in?
Options:
A)11
B)17
C)18
D)19
E)16
Rationale: C = 1/4 - 1/12 – 1/9 = 1/18 => 18 days'
Answer: C
Answer: C
Question: Submarine M and Submarine N are equipped with sonar devices that can operate within a 4,000 yard range. Submarine M remains in place while Submarine N moves 3,700 yards south from Submarine M. Submarine N then changes course and moves due east, stopping at the maximum range of the sonar devices. In which of the following directions can Submarine N continue to move and still be within the sonar range of Submarine M? I. North II. South III. West
Options:
A)I,II only
B)II,III only
C)II only
D)I and III only
E)III only
Rationale: It's evident if we make a diagram for the Movement of N respect to M.
From its South position to the east position, it has covered the maximum radius for the south direction. Similarly, it's east movement further will also make it out of range.
Thus it can only move north or west or anything in that curve.
Answer : D
Answer: D
Question: In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 1/8 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and straight
Options:
A)1/7
B)1/8
C)1/4
D)3/4
E)4/9
Rationale: Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
We're told that 1/8 of the garden is green, so, since all the flowers must be either green or yellow, we know that 7/8 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(straight) = 7/8 * 1/2 = 4/9, or E.
Answer: E
Question: A vessel contains a 105 ml mixture of milk and water. 3/7 of the mixture is alcohol, the remainder is water. An additional quantity of 105 ml of milk is poured into the mixture. What is the ratio of the volume of milk to water in the new mixture?
Options:
A)3:7
B)3:4
C)5:2
D)1:1
E)2:5
Rationale: The amount of milk in the old mixture is 3/7 x 105 = 45 ml.
Further 105 ml milk is added.
Therefore, total milk in new mixture is 150 ml.
Water content is (105 -45) - 60 ml.
Milk to water ratio is 150: 60 or 5: 2
ANSWER:C
Answer: C
Question: An investor bought two shares of stock, which he sold for $84 each. If he had a profit of 20% on one of the shares and a loss of 20% on the other share, then on the sale of both shares combined, the investor had:
Options:
A)a profit of $10
B)a profit of $7
C)a loss of $7
D)a loss of $10
E)neither a profit nor a loss
Rationale: The cost of the first stock was 84/1.2=70, so the profit from it is 14.
The cost of the second stock was 84/0.8=105, so loss from it is 21.
Overall the loss is $7.
The answer is C.
Answer: C
Question: A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 15}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
Options:
A)15
B)16
C)19
D)20
E)36
Rationale: By looking at Set A, we can see that it's all primes. Thus, we should immediately break down the elements in Set B to their prime factors. That gives :
Set A = {2,3,5,7,11}
Set B = {2, 2x2, 3x2, 13}
Apart from 2x3x2 (taking 2 from set A) which is the same as 3x2x2(taking 3 from set A); there is nothing which can be repeated. Thus, the total unique product = 20-1 = 20.
D
Answer: D
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
Options:
A)4/9
B)4/5
C)4/1
D)4/2
E)4/3
Rationale: Explanation:
2/3 ---- 12
? ----- 8 ==> 4/9
Answer: A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 415 in 2 years and to Rs. 514 in 4 years. The sum is ?
Options:
A)Rs. 316
B)Rs. 251
C)Rs. 154
D)Rs. 294
E)Rs. 200
Rationale: Explanation:
S.I. for 2 years = (514 - 415) = Rs. 99
S.I. for 1 year = 99/2
Principal = (415 - 99) = Rs. 316.
ANSWER IS A
Answer: A
Question: What is the average of four tenths and five thousandths?
Options:
A)25002
B)2502
C)0.225
D)0.2025
E)0.02025
Rationale: (.4 + .005)/2 --> .405/2 --> .2025
D
Answer: D
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age six years back was?
Options:
A)13yr
B)15yr
C)20yr
D)25yr
E)30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 6 years back = 19-6 = 13 years
Answer is A
Answer: A
Question: A 400 meter long train crosses a man standing on the platform in 10 sec. What is the speed of the train?
Options:
A)144
B)108
C)278
D)126
E)112
Rationale: S = 400/10 * 18/5 = 144 kmph
Answer: A
Answer: A
Question: If a, b, and c are integers and ab^2/c is a positive even integer, which of the following must be true?
I. ab is even
II. ab > 0
III. c is even
Options:
A)I only
B)II only
C)I and II
D)I and III
E)I, II, and III
Rationale: ab2/c is positive which means a and C >0 or a and c<0 since b2 is positive
Case 1 - a=3 b=2 c=3 or c=6 where ab2 /2 would be even when c= 3 or c=6
lets see III option where C is even as per our assumption C can be even and odd, hence it is out.
lets see option II ab>0 a and b can positive or negative hence sign of ab cannot be determined hence it is out
So options B,C,D,E are gone and ans is A
Answer: A
Question: A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 5 cubic feet. If a large block has three times the width, twice the depth, and half the length of a normal block, what is the volume of cheese in a large block in cubic feet?
Options:
A)10
B)30
C)15
D)20
E)25
Rationale: Volume of cube=lbh=5
New cube l ,b, h are increases of 3b,2h and a decrease of .5l
New volume of cube =.5l*3b*2h=3*lbh
=3*5
=15
Answer: C
Answer: C
Question: Carol spends 1/4 of her savings on a stereo and 1/2 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
Options:
A)1/4
B)2/7
C)5/12
D)3/8
E)7/12
Rationale: Total Savings = S
Amount spent on stereo = (1/4)S
Amount spent on television = (1-1/2)(1/4)S = (1/2)*(1/4)*S = (1/8)S
(Stereo + TV)/Total Savings = S(1/4 + 1/8)/S = 3/8
Answer: D
Answer: D
Question: A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1551, What is the value of n?
Options:
A)22
B)38
C)62
D)94
E)672
Rationale: Factorise 1551.. 3*11*47..
So n has to be a multiple of largest prime number,61..
So n=2*47=94..
Ans :D
Answer: D
Question: If a person having Rs. 2000 and he want to distribute this to his five children in the manner that each son having Rs. 30 more than the younger one , what will be the share of youngest child ?
Options:
A)Rs. 175
B)Rs. 325
C)Rs. 340
D)Rs. 260
E)Rs. 230
Rationale: Explanation:
Assume first child (the youngest) get = Rs. x
According to the question ;
each son having Rs. 30 more than the younger one
Second child will get = Rs. x + 30
Third child will get = Rs. x + 30 + 30 = x + 60
Forth child will get = Rs. x + 30 + 30 + 30 = x + 90
Fifth child will get = Rs. x + 30 + 30 + 30 + 30 = x + 120
Total amount they got = Rs. 2000
x + (x+30) + (x+60) + (x+90) + (x+120) = 2000
5x + 300 = 2000
5x = 1700
x = Rs. 340
So the youngest child will get Rs. 340.
ANSWER IS C
Answer: C
Question: It takes Joey the postman 1 hours to run a 7 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 8 mile/hour, what is the speed with which Joey returns?
Options:
A)11
B)12
C)13
D)8
E)15
Rationale: let his speed for one half of the journey be 7 miles an hour
let the other half be x miles an hour
now,
avg speed =8 mile an hour
2*7*x/7+x=8
14x=8x+56=>x=8
D
Answer: D
Question: Each Machine of type A has 2 steel parts and 2 chrome parts. Each machine of type B has 6 steel parts and 5 chrome parts. If a certain group of type A and type B machines has a total of 20 steel parts and 22 chrome parts, how many machines are in the group
Options:
A)2
B)3
C)4
D)6
E)7
Rationale: Look at the below representation of the problem:
Steel Chrome total
A 2 2 20 >>no. of type A machines=20/4=5
B 6 5 22 >>no. of type B machines=22/11=2
So the answer is 7 i.e E.
Hope its clear .
Answer: E
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Options:
A)40%
B)30%
C)50%
D)60%
E)70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
Question: Find the sum and number of divisors of 544 excluding 1 and 544.
Options:
A)589
B)599
C)618
D)659
E)648
Rationale: if N = p^a * q^b *r^c *...
total no. of factors of N = (a+1)*(b+1)*(c+1)*... &
sum of all of the factors of N =(1+p+p^2+...+p^a)*(1+q+..+q^b)*(1+r+r^2+...+r^c)
544 = 2^5 * 17
number of divisors of 544 excluding 1 and 544 = (5+1)*(1+1) - 2 = 10
sum of divisors of 544 excluding 1 and 544 = (1+2+2^2+2^3+2^4+2^5)*(1+17)-1-544
= 589
ANSWER:A
Answer: A
Question: A computer program generates a single digit by a random process, according to which the probability of generating any digit is directly proportional to the reciprocal of one more than that digit. If all digits are possible to generate, then the probability Q of generating an odd prime digit is between
Options:
A)0 and 1/6
B)1/6 and 1/3
C)1/3 and 1/2
D)1/2 and 2/3
E)2/3 and 5/6
Rationale: K (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9+ 1/10) =1
Note that 1/10 is least value and is equal to 0.1 so we can write above series as
K (1+0.5+0.3+0.25+0.2+0.16+0.5+residual) = 1
K=1/3+
P (3 or 5 or 7) =K*13/24
Required probability Q= 13/24 × 1/3+ = 4+/24 > 1/6
Answer should be B
P.s. 3+ denotes a value little greater than 3 .
Same for 4+.
Answer: B
Question: In what time will a railway train 56 m long moving at the rate of 39 kmph pass a telegraph post on its way?
Options:
A)3 sec
B)4 sec
C)5 sec
D)6 sec
E)7 sec
Rationale: T = 56/39 * 18/5 = 5 sec
ANSWER:C
Answer: C