divelab/Sys2Bench huggingface dataset:
Question: There are 10 stamps from which two stamps will be selected. We have five stamps which are the same as five of the stamps which could be selected. What is the probability that the two stamps selected will be different from the stamps that we have?
Options:
A)7/17
B)5/12
C)4/11
D)3/10
E)2/9
Rationale: P(first stamp is different) = 5/10
P(second stamp is different) = 4/9
P(both stamps are different) = 5/10*4/9 = 2/9
The answer is E.
Answer: E
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
Options:
A)20%
B)30%
C)50%
D)70%
E)80%
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: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)22 1/8 days
B)22 1/2 days
C)22 6/2 days
D)72 1/2 days
E)23 1/2 days
Rationale: 1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 1/4 *2 = 22 1/2 days
Answer: B
Answer: B
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Options:
A)6
B)7
C)8
D)6
E)4
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min.Answer: A
Answer: A
Question: How many even numbers greater than 300 can be formed with digits 1,2,3,4,5 no digit being repeated ?
Options:
A)111
B)123
C)124
D)132
E)145
Rationale: Number can be 3, 4, or 5 digit (4 and 5 digit number will obviously be more than 300).
5 digit even numbers:
Last digit must be either 2 or 4 (for number to be even), so 2 choices. First 4 digits can be arranged in 4! # of ways. So total # of 5 digit even numbers possible is 4!∗2=484!∗2=48;
4 digit even numbers:
Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 3 digits out of 4 digits left when order of the digits matters is P34P43. So total # of 4 digit even numbers possible is P34∗2=48P43∗2=48;
3 digit even numbers:
Last digit again must be either 2 or 4, so 2 choices. # of ways to choose rest 2 digits out of 4 digits left when order of the digits matters is P24P42. So total # of 3 digit even numbers possible is P24∗2=24P42∗2=24.
But out of these 24 3-digit even numbers some will be less than 300, the ones starting with 1 or 2. There are 9 such numbers (1X2 and 3 options for the second digit X, so 3 plus 1X4 and 3 options for X, so 3 plus 2X4 and 3 options for X, so 3), which means that # of 3 digit even numbers more than 300 is 24−9=1524−9=15;
So total 48+48+15=11148+48+15=111.
ANS:A
Answer: A
Question: The inside dimensions of a rectangular wooden box are 4 meters by 5 meters by 6 meters. A cylindrical drum is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such drums that could be used, what is the volume, in cubic meters, of the one that has maximum volume?
Options:
A)20π
B)24π
C)25π
D)96π
E)100π
Rationale: You have three options here. Approach is to calculate volumes for all of them and see which one is greatest.
1. Cylinder's base rests on a 4x5 side of the box. So, height becomes 6 and the maximum possible radius becomes 4/2.
So, maximum volume = π.(4/2)^2.6=π24
2. Cylinder's base rests on a 5x6 side of the box. So, height becomes 4 and the maximum possible radius becomes 5/2.
So, maximum volume = π.(5/2)^2.4=π25
3. Cylinder's base rests on a 4x6 side of the box. So, height becomes 5 and the maximum possible radius becomes 4/2.
So, maximum volume = π.(4/2)^2.5=π20
Option 2 gives maximum value and so that should be the answer, π25.
ANSWER:C
Answer: C
Question: From a pack of 52 cards,two cards are drawn at random together at random what is the probability of both the cards being kings?
Options:
A)1/221
B)8/221
C)4/589
D)4/587
E)7/654
Rationale: let S be the sample space then
n(S)=52C2=(52*51)/(2*1)=1326
let E be the event of getting 2 kings out of 4
n(E)=4C2=(4*3)/(2*1)=6
P(E)=n(E)/n(S)=6/1326=1/221
Answer (A)
Answer: A
Question: Working alone, Mary can pave a driveway in 6 hours and Hillary can pave the same driveway in 6 hours. When they work together, Mary thrives on teamwork so her rate increases by 25%, but Hillary becomes distracted and her rate decreases by 20%. If they both work together, how many hours will it take to pave the driveway?
Options:
A)3 hours
B)4 hours
C)5 hours
D)6 hours
E)7 hours
Rationale: Initial working rates:
Mary = 1/6 per hour
Hillary = 1/6 per hour
Rate when working together:
Mary = 1/6+ (1/4*1/6) = 1/5 per hour
Hillary = 1/6 - (1/5*1/6) = 2/15 per hour
Together they work 1/5 + 2/15 = 1/3 per hour
So they will need 3 hours to complete the driveway. The correct answer is A.
Answer: A
Question: A dishonest fruit seller professes to sell his goods at the cost price but weighs 800 grams for a kg weight. Find his gain percent.
Options:
A)100%
B)150%
C)50%
D)200%
E)None of these
Rationale: He gives 800 grams but charges the price of 1000 grams (1 kg) ⇒ on every 800 grams, he gains (1000 – 800) grams i.e. 200 grams.
∴ His gain % = 200⁄800 × 100% = 25%
Short cut : Gain % = error/true weight−error=100%
Answer A
Answer: A
Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is ?
Options:
A)4328
B)4322
C)4320
D)4332
E)4333
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways
= 6(6!)
= 4320
Answer: C
Answer: C
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 10800 ?
Options:
A)11
B)13
C)14
D)18
E)10
Rationale: Required difference = [3 ½ % of Rs.10800] – [3 1/3 % of Rs.10800]
= [(7/20-(10/3)]% of Rs.10800 =1/6 % of Rs.10800
= Rs. [(1/6)8(1/100)*10800] = Rs. 18.
Answer is D.
Answer: D
Question: Jake and Kay drive at constant speeds toward each other on a highway. Jake drives at a constant speed of 29 km per hour. At a certain time they pass by each other, and then keep driving away from each other, maintaining their constant speeds. If Jake is 155 km away from Kay at 6 am, and also 155 km away from Kay at 11 am, then how fast is Kay driving (in kilometers per hour)?
Options:
A)29
B)30
C)31
D)32
E)33
Rationale: Jake and Kay complete 310 km / 5 hours = 62 km/hour
Kay's speed is 62-29=33 km/hour
The answer is E.
Answer: E
Question: In a mixture there is ratio of alcohol and water is 4:3.if in this mixture we will add 3litre of water.then ratio become 4:5.then calculate the amount of alcohol?
Options:
A)4
B)5
C)6
D)8
E)9
Rationale: Let in mixture alcohol=4x litre,and water=3x litre
4x/3x+3=4/5
X=1.5
Amount of alcohol=(4×1.5)=6 litre
Answer C
Answer: C
Question: If a farmer wants to plough a farm field on time, he must plough 100 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
Options:
A)600
B)490
C)720
D)1400
E)1679
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 100â‹…x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
100x=85(x+2)+40
15x=210
x=14
So the farmer planned to have the work done in 6 days, and the area of the farm field is 100(14)=1400 hectares
correct answer D
Answer: D
Question: Which of the following statements is definitely false, if M is the sister of N and O. T is M's son and U is M's daughter?
Options:
A)N is T's uncle
B)O is T's uncle
C)N is U's brother
D)N is M's brother
E)O is M's uncle
Rationale: Explanation:
All the statements are true except C (N is U's brother), U is M's daughter that makes N her uncle, not brother.
Answer: C) Q is T's son
Answer: C
Question: If x is a positive integer with fewer than 3 digits, what is the probability R that x*(x + 1) is a multiple of either 4 or 5?
Options:
A)4/99
B)2/25
C)8/99
D)49/100
E)86/99
Rationale: Interesting question! Also one that we should be able to answer very quickly be keeping an eye on our best friends, the answer choices.
We know that x belongs to the set {1, 2, 3, ... , 99}. We want to know the probability R that x(x+1) is a multiple of either 4 or 5.
When will this happen? If either x OR (x+1) is a multiple of 4 or 5.
Since 4*5 is 20, let's look at the first 20 numbers to get a rough idea of how often this happens.
Out of the numbers from 1 to 20:
4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 20
So, 14 out of the first 20 numbers match our criteria. Since:
probability = (# of desired outcomes)/(total # of possibilities), we guesstimate the answer to be 14/20. Since (E) is the only answer greater than 1/2, we go with (E).
Answer: E
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 26 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)457 km
B)444 km
C)547 km
D)564 km
E)453 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 26 + 21 = 47
T = 12
D = 47 * 12 = 564
Answer:D
Answer: D
Question: If a = -0.5, which of the following is true?
Options:
A)a < a^3 < a^2
B)a < a^2 < a^3
C)a^2 < a < a^3
D)a^3 < a < a^2
E)a^2 < a^3 < a
Rationale: a=-0.5;
a^2=0.25;
a^3=-0.125;
Answer : A
Answer: A
Question: A can do a work in 6 days. B can do the same work in 4 days. Both A&B together will finish the work and they got $2000 from that work. Find their shares?
Options:
A)600,400
B)500,500
C)300,700
D)800,1200
E)550,1450
Rationale: Ratio of their works A:B = 6:4
Ratio of their wages A:B = 2:3
A's share = (2/5)2000 = 800
B's share = (3/5)2000 = 1200
correct option is D
Answer: D
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
Options:
A)91.5 cm
B)91.6 cm
C)97.5 cm
D)51.5 cm
E)91.2 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42 = 91.5 cm
Answer: A
Answer: A
Question: In a circular racetrack of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite direction at 15 m/s. When will all the three meet for the first time on the track after the start?
Options:
A)After 4 s
B)After 50 s
C)After 100 s
D)After 200 s
E)None of these
Rationale: A takes (100m) / (10m/s) = 10s to finish one complete round.
B takes (100m) / (8m/s) = 12.5s to finish one complete round.
C takes (100m) / (15m/s) = (20/3)s to finish one complete round.
For them to meet, the time will be LCM of above three times i.e,
LCM(10,12.5,20/3) = LCM(10,25,20)/GCD(1,2,3)=100/1=100sec
ANSWER:C
Answer: C
Question: Lakshmi invested some money in 15% stock at 200.If Latha wants to invest in an equally good 30% stock ,he must purchase a stock worth of :
Options:
A)Rs. 300
B)Rs. 200
C)Rs. 450
D)Rs. 500
E)Rs. 400
Rationale: Solution
For an income of Rs. 15, investment = Rs. 200
For an income of Rs. 30, investment = Rs.(200/15x30) = Rs. 400
Answer E
Answer: E
Question: Two pipes A and B can separately fill a tank in 20 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)12min
B)14min
C)15min
D)13min
E)10min
Rationale: 4/20 + x/15 = 1
x = 12
ANSWER:A
Answer: A
Question: The average weekly salary per head of the entire staff
of a factory consisting of supervisors and the laborers
is Rs 60.The average salary per head of the supervisors
is Rs 400 and that of the laborers is Rs 56.Given that
the number of supervisors is 12.Find the number of
laborers in the factory
Options:
A)1000
B)1010
C)1020
D)1030
E)1040
Rationale: Average salary of laborerRs 56 Average salary of supervisors Rs 400
Average salary of entire staff Rs 60
340 4
Number of laborer / Number of Supervisors = 340 / 4=85/1
Thus,if the number of supervisors is 1,number of laborers =85.
Therefore if the number of supervisors is 12 number of laborers
85*12=1020.
ANSWER C
Answer: C
Question: Reduce
368/600
to the lowest terms
Options:
A)30/25
B)28/25
C)28/29
D)46/75
E)None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 600 which is 8
Step2: Divide both by 8, we will get the answer 46/75
Answer: Option D
Answer: D
Question: Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$600
B)$1000
C)$3800
D)$5300
E)$6200
Rationale: Pay out for plan A: Cost-$1,000 or Cost-0.5*Cost=0.5*Cost, when 0.5*Cost<$1,000;
Pay out for plan B: 0.8(Cost-$300);
The question is: for which of the following costs the pay outs are the same.
C-1,000=0.8(C-300) --> for C=3,800 and 0.5C=0.8(C-300) --> for C=800. As we have only $3,800 listed then it must be a correct answer.
Or you can use backsolving for this question:
A. C=$600: pay out for plan A will be 0.5*600=300 (as 0.5*600<1,000) and pay out for plan B will be 0.8*(600-300)=240;
B. C=$1000: pay out for plan A will be 0.5*1,00=500 (as 0.5*1,000<1,000) and pay out for plan B will be 0.8*(1,000-300)=560;
C. C=$3800: pay out for plan A will be 3,800-1,000=2,800 (as 0.5*3,800>1,000) and pay out for plan B will be 0.8*(3,800-300)=2,800 --> 2,800=2,800;
D. C=$5300: pay out for plan A will be 5,300-1,000=4,300 (as 0.5*5,300>1,000) and pay out for plan B will be 0.8*(5,300-300)=4,000;
E. C=$6200:pay out for plan A will be 6,200-1,000=5,200 (as 0.5*6,200>1,000) and pay out for plan B will be 0.8*(6,200-300)=4,720.
Answer: C.
Answer: C
Question: An assembly line produces 36 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
Options:
A)38
B)40
C)42
D)45
E)50
Rationale: The time to produce the first 60 cogs is 60/36 = 5/3 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / (8/3) hours = 45 cogs per hour.
The answer is D.
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 12 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)40
E)12
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)/12 = 3x => x = 50/9.
So, speed of the faster train = 100/9 = 100/9 * 18/5 = 40 km/hr.
Answer:D
Answer: D
Question: Square A has an area of 81 square centimeters. Square B has a perimeter of 32 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
Options:
A)17/64
B)17/81
C)16/25
D)3/5
E)6/25
Rationale: I guess it's mean that square B is placed within square Aentirely.
Since, the perimeter of B is 32, then its side is 32/4=8 and the area is 4^2=64;
Empty space between the squares is 81-64=17 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=17/81.
Answer: B
Answer: B
Question: A circular path of 12 m radius has marginal walk 2 m wide all round it. Find the cost of leveling the walk at 50p per m2?
Options:
A)Rs.49
B)Rs.40
C)Rs.81.72
D)Rs.42
E)Rs.43
Rationale: Explanation:
π (14^2 - 12^2) = 22/7 * 52 = 163.43
163.43 * 1/2 = Rs.81.72
Answer: Option C
Answer: C
Question: A man rows his boat 95 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream?
Options:
A)76 kmph
B)6 kmph
C)9 kmph
D)8 kmph
E)4 kmph
Rationale: Speed downstream = d/t = 95/(2)
= 48 kmph
Speed upstream = d/t = 60/(2)
= 30 kmph
The speed of the stream = (48 - 30)/2
= 9 kmph
Answer:C
Answer: C
Question: If (10^20) – 65 is written as a base 10 integer, what is the sum of the digits in that integer?
Options:
A)200
B)170
C)180
D)100
E)210
Rationale: We know that (10^20) is ending 00, so (10^20) – 65=9....9935
total number of digits in (10^20) – 65 is 20, or 18 digits of 9 and two digits 3 and 5.
answer choice is 18*9+(3+5)
18*9+8=170
Answer is B 170
Answer: B
Question: All the students of class are told to sit in circle shape. Here the boy at the 10 th position is exactly opposite to 40 th boy. Total number of boys in the class?
Options:
A)50
B)45
C)60
D)55
E)53
Rationale: As half the circle shape consist of 40-10=30 boys,
So total number of boys in full circle=2*30=60
ANSWER: C
Answer: C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 144km/h, what is the circumference of the tire?
Options:
A)2
B)1
C)4
D)6
E)5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 144,000 m : C is the circumference
C = 6 meters
correct answer D
Answer: D
Question: Albert invested Rs. 6500 in a scheme for 2 years at compound interest rate 6.5% p.a. How much amount will Albert get on maturity of the fixed deposit?
Options:
A)s.8829
B)s.7200
C)s.7200.5
D)s.4000
E)s.7372.46
Rationale: Amount = [6500 * (1 + 6.5/100)2]
= 6500 * 106.5/100* 106.5/100
= Rs.7372.46
Answer:E
Answer: E
Question: Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is
Options:
A)33
B)87
C)27
D)48
E)10
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 60 or x = (60 * 4) / 5 = 48.
Answer: D) 48
Answer: D
Question: In March, Kurt ran an average of 1.2 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June?
Options:
A)3590/60^2
B)2410/60^2
C)2390/60^2
D)3586/60
E)2990/60^2
Rationale: Kurt ran at an average of 1.2 miles/hour in march. So to run 1 mile he would take 1/1.2 hours = (60 * 60)/1.2 seconds = 3000 seconds.
If he increases his speed by 10 seconds, he will complete a mile in 2990 seconds. Converting in hours = 2990/(60 * 60) = 2990/(60^2)
ANSWER: E
Answer: E
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age 4 years back was:
Options:
A)12 years.
B)14 years.
C)17 years.
D)16 years.
E)19 years.
Rationale: Let the son's present age be x years. Then, (42 - x) = x
2x = 42.
x = 21
Son's age 5 years back (21- 4) = 17 years.
ANSWER :C
Answer: C
Question: In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
Options:
A)6! / 2!
B)3! * 3!
C)4! / 2!
D)(4! * 3!) / 2!
E)(3! * 3!) / 2!
Rationale: Explanatory Answer
Step 1: Group the vowels as one unit and rearrange
ABACUS is a 6 letter word with 3 of the letters being vowels.
Because the 3 vowels have to appear together, let us group the AAU as one unit.
There are 3 consonants in addition to one unit of vowels.
These 4 elements can be rearranged in 4! ways.
Step 2: Rearrange the letters within the unit containing the vowels
The 3 vowels can rearrange among themselves in 3!/2! ways as "a" appears twice.
Hence, the total number of rearrangements in which the vowels appear together is 4!∗3!/2!
Choice D
Answer: D
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
Options:
A)4630
B)4920
C)5120
D)7960
E)8960
Rationale: l = (48 - 16)m = 32 m,
b = (36 -16)m = 20 m,
h = 8 m.
Volume of the box = (32 x 20 x 8) m3 = 5120 m3.
answer :C
Answer: C
Question: Which one of the following numbers is exactly divisible by 12?
Options:
A)A)12
B)B)13
C)C)14
D)D)15
E)E)16
Rationale: 12/12=1 answer is A
Answer: A
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
Options:
A)5
B)6
C)9
D)7
E)3
Rationale: 7 * 8 : 9 * x = 8:9
=> x= 7
Answer: D
Answer: D
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. 72 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 7.6 years and the standard deviation is 2.6 years, what percent of the distribution has more than 10.2 years as a shelf’s average life?
Options:
A)17%
B)16%
C)15%
D)14%
E)13%
Rationale: Average = 7.6
SD = 2.6
7.6 - 2.6 < 72% of distribution < 7.6 + 2.6
5.0 < 72% of distribution < 10.2
28% is outside this range.
Given: Distribution is symmetric. So 14% of distribution is less than 5.0 and the other 14% of distribution is greater than 10.2.
Answer: D
Answer: D
Question: Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?
Options:
A)5/221
B)55/221
C)45/221
D)59/221
E)1/221
Rationale: 2 cards drawn from 52 cards,so chances are 52C2
chances for drawing both black cards=26C2
chances for drawing both queen=4C2
so we will be having 2 queens in black cards,thus it is 2C2 which is 1
probability=(325+6-1)/1326=55/221
ANSWER:B
Answer: B
Question: A man swims downstream 36 km and upstream 48 km taking 6 hours each time, what is the speed of the man in still water?
Options:
A)5
B)24
C)7
D)42
E)6
Rationale: 36--- 6 DS = 6
? ---- 1
48 ---- 6 US = 8
? ---- 1 M = ?
M = (6 + 8)/2 = 7
Answer: C
Answer: C
Question: The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 33 ?
Options:
A)440
B)512
C)550
D)620
E)650
Rationale: Large numbers are made in two ways:
Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.
31*2 = 62 (large prime number)
2^6 = 64 (many small prime numbers)
To get a sum as large as 33 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.
You are left with 620 which is 31*2*2*5 (sum greater than 33)
Answer (D)
Answer: D
Question: Curious Elva asked her father what he would gift for her nineteenth birthday. Father replied that it would depend on the day of the week and be one of SUNglasses, MONeybag, ..., FRIedcake, and SATchel. Please help Elva find the day of the week on 08-Jan-2029
Options:
A)Monday
B)Tuesday
C)Thursday
D)Saturday
E)Sunday
Rationale: at year 2000 there is 0 odd day as it is multiple of 400.
from 2001 to 2028 there are 28 years in which 28/4 = 7 are leap years and 21 are ordinary days.
Odd day in 7 leap years = 7*2 = 14
Odd day in 21 ordinary days = 21
total odd day till 31 dec 2028 = 14+21 = 35/7 = 0
hence 1jan 2029 will be Monday.
&
8jan 2029 will also be monday
ANSWER:A
Answer: A
Question: If the mean of weight of students in a class of weight 38, 50, 70, 88 and 110 is 71.5 kg, what is the mean of the class if student of weight 50 kg left the class i.e state whether what will happen to original mean value ?
Options:
A)increase
B)decrease
C)remains unchanged
D)can't say
E)none of the above
Rationale: Given mean of class = M1 = 71.5 kg
Mean = (Sum of all weights in class)/(no. students)
M2 = (38+70+88+110)/(4)
= 76.5 kg
since, M1 < M2
Answer =A
Answer: A