divelab/Sys2Bench huggingface dataset:
Question: Anne, Markov, Peter line up at a ticket window. In how many ways can they arrange themselves so that Peter is first in line from the window?
Options:
A)a 24
B)b 12
C)c 9
D)d 2
E)e 3
Rationale: D
Peter's position is fixed. Now we need to arrange all others around Peter.
There are 2x1= 2 ways to arrange two people.
Answer: D
Question: When a merchant imported a certain item, he paid a 9 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $76.50, what was the total value of the item?
Options:
A)$1,250
B)$1,450
C)$1,650
D)$1,850
E)$2,050
Rationale: Let x be the value in excess of $1,000.
0.09x = 76.5
x = $850
The total value was $850 + $1,000 = $1,850.
The answer is D.
Answer: D
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 172 votes. Find the total number of valid votes?
Options:
A)430
B)436
C)477
D)439
E)537
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 172 => 4x/10 = 172
=> 4x = 1720 => x = 430.
Answer:A
Answer: A
Question: The greatest common divisor of (b-2)!,(b+1)!, and (b+4)! is 5040. what is the value of b?
Options:
A)8
B)10
C)12
D)9
E)6
Rationale: GCD of (b-2)!,(b+1)!, and (b+4)! is 5040. Find x.
Best way to find n is substitute each of the answer and find out the correct one.
Only option D gave the correct answer.
Option D: 9 and find GCD or 7!, 10! and 13!. 7! itself is 5040 and 7! which is contained in the other two factorials. This satisfies the condition, hence answer is 9.
Answer is D.
Answer: D
Question: By walking at 3/4th of his usual speed, a man reaches office 18 minutes later than usual. What is his usual time?
Options:
A)43min
B)54min
C)65min
D)60min
E)70min
Rationale: let T be the usual time.
time spent=4T/3
therefore, 4T/3=T+18
4T=3T+54...therefor T=54min
ANSWER:B
Answer: B
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train ?
Options:
A)230
B)777
C)267
D)288
E)277
Rationale: Explanation:
Relative speed = (120 + 80) km/hr
==
Let the length of the other train be x metres.
Then,
x + 270 = 500
x = 230.
Answer: A) 230 m
Answer: A
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 153 games will be played during the tournament. Find the number of participants.
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: If the number of participants is 3 (say A, B, C) the number of games played will be 2 (A plays against B and C) + 1 (B plays against C) = 3
Using the same logic, if the number of participants is n, the number of games played will be (n-1) + (n - 2) + (n - 3) + ... 3 + 2 + 1
Given that this sum = 153 = 1 + 2 + 3 + ... ( n - 1)
Sum of first m positive integers is given by m(m+1)/2. So sum of first (n-1) positive integers is (n-1)*n/2
153 = (n-1)*n/2
(n-1)*n = 306
17*18 = 306 (We know that 15^2 = 225 so the two consecutive numbers must be greater than 15. Also, 20^2 = 400 so the two numbers must be less than 20. The pair of numbers in between 15 and 20 whose product ends with 6 is 17 and 18)
So n = 18
Answer (D)
Answer: D
Question: A cab driver 5days income was $30, $50, $60, $65 , $70. Then his average income is?
Options:
A)A)$55
B)B)$42
C)C)$65
D)D)$48
E)E)$62
Rationale: avg = sum of observations/number of observations
avg income=(30+50+60+65+70)/5 = 55
Answer is A
Answer: A
Question: A wheel rotates 15 times every minute and moves 35 cm during each rotation. How many metres does the wheel move in one hour?
Options:
A)6 metre
B)12 metre
C)120 metre
D)315 metre
E)130 metre
Rationale: Number of times wheel moves in 1 hour = 15 * 60 = 900
:. Distance moves = (900 *35) cms = 31500 cms
In metres = 315 metre
ANSWER:D
Answer: D
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 8 AM, what will be the time at the end of 10 days?
Options:
A)08:54:40 AM
B)08:56:24 AM
C)08:16:40 PM
D)08:54:24 AM
E)09:06:36 PM
Rationale: Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 09:54:24 am (Answer D)
Answer: D
Question: Judges will select 6 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
Options:
A)140
B)21
C)210
D)420
E)1,260
Rationale: First Select 5 from 7 contestants and then select top 3 from those 5 =
7C6*6C3 = 7 * 20 = 140
ANS:A
Answer: A
Question: A bicyclist's wheel has a circumference of 6 meters. if the bicyclist covers 180 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.
To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.=180/6*5 =6
Answer (E)
Answer: E
Question: What will come in place of the x in the following Number series? 68, 36, 20, 12, 8, x
Options:
A)6
B)4
C)2
D)1
E)0
Rationale: 6868 / 2 + 2 = 3636 / 2 + 2 = 2020 / 2 + 2 = 1212 / 2 + 2 = 88 / 2 + 2 = 6 A
Answer: A
Question: Today is Thursday. The day after 54 days will be?
Options:
A)Monday
B)Tuesday
C)Saturday
D)Sunday
E)wednesday
Rationale: Explanation:
54 days = 7 weeks 3 days = 5 odd days
Hence if today is Thursday, After 54 days, it will be = (Thursday + 5 odd days)
= Tuesday
Answer: Option B
Answer: B
Question: Amit and Ananthu can do a work in 15 days and 90 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
Options:
A)68 days
B)70 days
C)73 days
D)75 days
E)77 days
Rationale: Amit’s one day’s work= 1/15
Amit’s 3 day’s work = 1/15 *3 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/90
Ananthu can do work in = 4/5 *90 = 72 days
So total days = 72+3 = 75 days
ANSWER:D
Answer: D
Question: The ratio of three numbers is 4:2:5 and their sum is 121. The second number of the three numbers is?
Options:
A)22
B)26
C)27
D)29
E)30
Rationale: 4:2:5
Total parts = 11
11 parts --> 121
1 part ---->11
The second number of the three numbers is = 2 * 11= 22
Answer : A
Answer: A
Question: A family made a down payment of $100 and borrowed the balance on a set of encyclopedias that cost $400. The balance with interest was paid in 23 monthly payments of $16 each and a final payment of $9. The amount of interest paid was what percent of the amount borrowed?
Options:
A) 30%
B) 22%
C) 24%
D) 27%
E) 25.67%
Rationale: borrowings = 400-100 = 300
total pmt = 23x16 + 9 = 377
so int = 377 - 300 = 77
interest in terms of borrowing = 77/300 = 25.67%
Answer is E
Answer: E
Question: The product of the squares of two positive integers is 81. How many pairs of positive integers satisfy this condition?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Ans: C - 2 pairs
(xˆ2)(yˆ2) = 81 [square root both sides]
xy = 9
9 = 1x9, 9x1, 3x3
Cancel the repeats
This leaves us with exactly 2 options.
Hence, C
Answer: C
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)17
B)18
C)19
D)14
E)16
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer: Option A
Answer: A
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 36 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
Options:
A)22.5 km/hr
B)16 km/hr
C)27 km/hr
D)18 km/hr
E)None of these
Rationale: Explanation :
Total distance covered by B=36*6=216kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=216/8=27 km/hr
Answer : C
Answer: C
Question: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)2000
B)2887
C)2797
D)1172
E)1200
Rationale: Explanation:
Let C.P. be Rs. x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of Rs. 1600 = 125/100 * 1600 = Rs. 2000.
Answer:A
Answer: A
Question: Thabo owns exactly 160 books, and each book is either paperback fiction, paperback nonfiction, or hardcover nonfiction. If he owns 20 more paperback nonfiction books than hardcover nonfiction books, and twice as many paperback fiction books as paperback nonfiction books, how many hardcover books nonfiction books does Thabo own?
Options:
A)10
B)25
C)35
D)46
E)50
Rationale: I think we can use double-matrix method and solve using only one variable.
Our goal is to find the number of hardcover nonfiction books. Let that number be x. We are given that all 140 books are either paperback fiction, paperback nonfiction, or hardcover nonfiction. This implies that number of hardcover fiction books is 0.
Double-matrix: P = paperback; H = hardcover; F = fiction; NF = nonfiction
P H Total
F 2x+40 0
NF x+20 x
Total 3x+60 x 160
3x + 60 + x = 160
x = 25
Answer (B.)
Answer: B
Question: If x=1/7, which expression has the greatest value?
Options:
A)x^(1/3)
B)x^(1/2)
C)1/(2x)
D)x/.03
E)x^(-3)
Rationale: Options A and B are both less than 1.
Option C: 1/(2(1/7)) = 7/2 = 3.5
Option D: (1/7) / 0.03 = 1/0.21 which is about 4.76
Option E: (1/7)^(-3) = 7^3 = 343
The answer is E.
Answer: E
Question: In a manufacturing plant, it takes 36 machines 4 hours of continuous work to fill 8 standard orders. At this rate, how many hours of continuous work by 72 machines are required to fill 24 standard orders?
Options:
A)3
B)6
C)8
D)9
E)12
Rationale: the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times), = 4*48/72*24/8 = 6
Ans B
Answer: B
Question: A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)176
B)178
C)215
D)197
E)172
Rationale: Since each ring consists of six different letters, the total number of attempts possible with the three rings is
= 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 216 - 1 = 215.
Answer: C
Answer: C
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)1/98
B)1/2
C)1/6
D)1/2
E)1/9
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: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y + 1)
II. z<(x + 1)/(y + 1)
III. z>(x + 1)/(y - 1)
Options:
A)I only
B)I and II
C)II and III
D)II only
E)I and III
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y + 1) --> 2/3 > 1/4 --> True
II. z<(x + 1)/(y + 1) --> 2/3 < 3/4 --> True
III. z>(x + 1)/(y - 1) --> 2/3 > 3/2 --> False
Answer: B
Answer: B
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 50%?
I will see what is the quickest way to solve it then I will provide the explanation
Options:
A)3
B)7
C)9
D)10
E)11
Rationale: The following approach might be the easiest one and less error prone.
We need on-time departure rate to be higher than 5/10, so it should be at least 6/11, which means that 6 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 6-3=3 subsequent flights need to depart on-time.
Answer: A
Answer: A
Question: Find the remainder of the division (2^14)/7.
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Find the pattern of the remainders after each power:
(2^1)/7 remainder 2
(2^2)/7 remainder 4
(2^3)/7 remainder 1 -->this is where the cycle ends
(2^4)/7 remainder 2 -->this is where the cycle begins again
(2^5)/7 remainder 4
Continuing the pattern to (2^14)/7 gives us a remainder of 4
Final Answer:
D) 4
Answer: D
Question: A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be:
Options:
A)5
B)4
C)1
D)2
E)3
Rationale: Explanation:
Let x = 296q + 75
= (37 x 8q + 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1.
Answer C
Answer: C
Question: Six years ago Rahul was P times as old as Sachin was. If Rahul is now 17 years old, how old is Sachin now in terms of P ?
Options:
A)11/P + 6
B)P/11 +6
C)17 - P/6
D)17/P
E)11.5P
Rationale: let's call Sachin age six years ago is x
so six years ago Rahul was: 17-6 = 11 years old
and six years ago Rahul was P times as old as Sachin was
=> 11/x = P
=> x = 11/P
=> Now Sachin's age will be : x+6 = 11/P+6
=> the answer is A
Answer: A
Question: P, Q and R have Rs.7000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
Options:
A)Rs.3000
B)Rs.3600
C)Rs.2400
D)Rs.2800
E)None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(7000 - r) => 3r = 14000 - 2r
=> 5r = 14000 => r = 2800.
ANSWER:D
Answer: D
Question: A motorist travels to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. His average speed for the whole journey in km/hr is?
Options:
A)37.9
B)37.2
C)37.5
D)37.1
E)37.8
Rationale: Average speed = (2xy) /(x + y) km/hr
= (2 * 50 * 30) / (50 + 30) km/hr.
37.5 km/hr.
Answer: C
Answer: C
Question: Let a,b,c,d,e,f be non-negative real numbers. Suppose that a + b + c + d + e + f = 1 and
ad + be + cf >= 1/18 . Find the maximum value of ab + bc + cd + de + ef + fa.
Options:
A)7/36
B)6/36
C)5/36
D)4/36
E)3/36
Rationale: We partially factor
ab + bc + cd + de + ef + fa = a(b + f) + c(b + d) + e(d + f):
Notice that the terms in the parenthesis are very close to (b+d+f), except each part is missing
one term. We can add ad + cf + eb to this expression to get
a(b + f) + c(b + d)e(d + f) + ad + cf + eb
= a(b + d + f) + c(b + d + f) + e(b + d + f)
= (a + c + e)(b + d + f)
Let x = a+c+e and y = b+d+f. We have x+y = 1, so AM-GM gives us x+y
2
p
xy, hence
(a + c + e)(b + d + f) - 1
4 . Subtracting away ad + be + cf - 1
18 gives us
ab + bc + cd + de + ef + fa -
1/4
-1/18
=
7/36
where equality holds when a + c + e = b + d + f = 1
2 and ad + be + cf = 1/18 . We can verify that
equality holds when a = e = 1/9 , b = d = 1/4 ,c = 5/18, f = 0.
correct answer A
Answer: A
Question: A basket contains 3 blue, 3 red and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?
Options:
A)2/21
B)3/25
C)1/6
D)9/28
E)11/24
Rationale: Probability of getting each color marble = (3C1*3C1*3C1)/9C3
= (3*3*3)/84
= 27/84 = 9/28
So answer is D
Answer: D
Question: You walk one mile to school every day. You leave home at the same time each
day, walk at a steady speed of 3 miles per hour, and arrive just as school begins. Today you
were distracted by the pleasant weather and walked the first half mile at a speed of only 2
miles per hour. At how many miles per hour must you run the last half mile in order to arrive
just as school begins today?
Options:
A)4
B)6
C)8
D)10
E)12
Rationale: Recall the formula s = v *t, where in this case, s is distance (in miles) traveled at a
constant speed of v (miles per hour), for a time of t hours. The first statement indicates that
it usually takes you only 20 minutes to go to school (solve for t in 1 = 3 * t and change units)
Today, it took you 15 minutes to cover the first half mile (solve for t in 1=2 = 2 * t and
change units). You only have 5 more minutes to arrive (that is 1/12th of an hour), and need
to cover another half mile. Solve for v in the equation 1/2 = (1/12) *v.
correct answer B
Answer: B
Question: In how many ways letters of the word LICENSING be arranged?
Options:
A)362880
B)12540
C)65320
D)48962
E)62458
Rationale: LICENSING has 9 letters, out of which I repeated 2 times, N repeated 2 times. Hence total ways = 10!/(2!*2!)= 362880 ways
A
Answer: A
Question: A ratio between two numbers is 3 : 4 and their L.C.M. is 180. The first number is
Options:
A)60
B)45
C)20
D)15
E)None
Rationale: Sol.
Let the required numbers be 3x and 4x. Then, their L.C.M. is 12x.
∴ 12x = 180⇔ x = 15. Hence, the first number is 45.
Answer B
Answer: B
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 50 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
A)70
B)65
C)60
D)75
E)80
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 50% of 50% i.e 25%. so he completed 50 +25 =75 % of total trip.
D
Answer: D
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
Options:
A)4:9
B)4:3
C)4:5
D)4:1
E)4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9
= 4:3
Answer:B
Answer: B
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 70kmph, find the rate at which the train B runs.
Options:
A)40
B)60
C)120
D)80
E)105
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 80 kmph, speed of B must be 70*(3/2) = 105 kmph
E
Answer: E
Question: A, B and C shared profits in ratio of 3 : 7 : 6. Theypartnered for 14months, 8months and 7months respectively. What was he ratio of their investments ?
Options:
A)12 : 49 : 64
B)20 : 49 : 64
C)10 : 19 : 64
D)20 : 29 : 64
E)30 : 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 = 3
â‡’ 8 x = 7
â‡’ 7x = 8
â‡’ Final investment ratio = 12 : 49 : 64
A
Answer: A
Question: Machine A can put caps on a set of bottles in 8 hours at a constant rate. If Machine A does the job for 6 hours and Machine B does the rest of the job, which works at 1/4 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?
Options:
A)4hrs
B)6hrs
C)8hrs
D)10hrs
E)16hrs
Rationale: machine A will do 6/8 in 6 hrs, so A does 3/4 of the work ..
Therefore, B will do the remaining 1/4 th work alone..
As the speed of B is 1/4 rate of A, B will do the 1/4th work in same time that A takes to complete full job...
ans 8
C
Answer: C
Question: If x is an integer, then x(x - 1)(x - v) must be evenly divisible by three when v is any of the following values EXCEPT
Options:
A)-4
B)-2
C)-1
D)2
E)5
Rationale: here's another approach
x(x - 1)(x - v)
all three are consecutive, so the product MUST be a multiple of 3
we don't know the value of v just yet ... so let's extend the series ... the extension itself reveals the answers
..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..
we can see the possible values of v too from the series
v = 2 OR 2+3n [25]
v = -1 OR -1+3n [-1-4]
B i.e. -2 does not fit in any value of v
so B it is
Answer: B
Question: One fourth of one third of two fifth of a number is 35. What will be40% of that number
Options:
A)A)140
B)B)420
C)C)180
D)D)200
E)E)220
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 35
then x = 35 * 30 = 1050
40% of 1050 = 420
Answer: Option B
Answer: B
Question: An internet service provider charges $3.10 for the first 1/5 of a day plus $0.40 for each additional 1/5 of a day. What would this company charge for an internet usage that was 8 days long?
Options:
A)$15.60
B)$16.00
C)$17.80
D)$18.70
E)$19.10
Rationale: first 1/5 day = $3.10
rest of the days = 8 - (1/5) = 39/5
charge for the rest of the days = 39 *0.4 = 15.6
total charge = 3.10+15.6 = 18.7
Answer is D.
Answer: D
Question: The ratio of sodium chloride to ammonium in 100 kg of mixed ammonium normally used by three chemists is 1: 3. The amount of sodium chloride to be added to 100 kg of mixed ammonium to make the ratio 9 :25 is
Options:
A)2 kg
B)6.625 kg
C)6.25 kg
D)6.35 kg
E)6.55 kg
Rationale: sodium chloride in 100 kg = 1/4 x 100 = 25 kg
ammonium in 100 kg = 3 / 4 x 100 = 75 kg
Now 75 is 25 parts out of (25 + 9) = 34 parts.
Hence 9 parts = 9/25 x 75 = 27
Amount to be added = 27 - 25= 2 Kg
ANSWER:A
Answer: A
Question: There are 172 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
Options:
A)83
B)85
C)87
D)79
E)89
Rationale: Editing my solution:
Number of switches = 172
Number of switches turned on by A: 3, 6, ... 171 = 57
Number of switches turned on by B: 5, 10, ....170 = 34
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off.
Number of switches that are turned on = (57- 6) + (34 - 6) = 79
Answer: D
Answer: D
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 4% sugar by weight. To make a delicious and healthy mixture that is 6% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
Options:
A)2:9
B)2:7
C)1:6
D)1:4
E)1:2
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (6 - 4)/(10 - 6) = 2/4 = 1/2
So they should be mixed in the ratio 1:2
Answer - E
Answer: E
Question: What is the measure of the angle W made by the diagonals of the any adjacent sides of a cube.
Options:
A)30
B)45
C)60
D)75
E)90
Rationale: C.. 60 degrees
All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.C
Answer: C
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
Options:
A)48.55
B)49
C)51
D)61
E)62
Rationale: Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55
Answer is A
Answer: A