divelab/Sys2Bench huggingface dataset:
Question: How many different arrangements of A, B, C, D, and E are possible where A is adjacent to neither B nor D?
Options:
A)96
B)60
C)48
D)36
E)17
Rationale: Total # of permutation of 5 distinct letters will be 5!=120;
Glue A and B together, consider it to be one unit: {AB}{C}{D}{E} --> # of permutation of these 4 units will be 4!=24, A and B within its unit also can be arranged in 2 ways : {AB} or {BA}, so total # of ways to arrange A, B, C, D, and E so that A and B to be together will be 4!*2=48;
The same for A and D: total # of ways to arrange A, B, C, D, and E so that A and D to be together will be 4!*2=48;
Now, the above 48+48=96 cases will contain the arrangements when A is adjacent to both B and D, so we should subtract this cases to get rid of the double counting. The # of case when A is adjacent to both B and D will be: consider {BAD} {C}{E} --> # of permutation of these 3 units will be 3!, {BAD} also can be arranged in 2 ways: {BAD} or {DAB}, so total # of ways to arrange A, B, C, D, and E so that A is adjacent to both B and D will be 3!*2=12;
The # of arrangements when A is adjacent to neither B nor D will be total-(48+48-12)=120-84=36.
Answer: D.
Answer: D
Question: A boy asked a girl her name she replied your name is behind your scooty Behind the scooty is written 7.3 3.3 9.3 2.3 What is her name
Options:
A)RIAE
B)RIAF
C)RIAG
D)RIBF
E)SIAF
Rationale: 7.3=21=r
3.3 =9=i
9.3=27%26=1=a
2.3=6=f
ANSWER=RIAF
ANSWER:B
Answer: B
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)79.7
B)79.9
C)79.5
D)79.2
E)79.1
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: D
Answer: D
Question: A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the direction opposite to that in which the train is going ?
Options:
A)3.6sec
B)18sec
C)36sec
D)72sec
E)None
Rationale: Solution
Speed of train relative to jogger =(45-9)km/hr =36km/hr
(36*5/18)m/sec = 10 m/sec
Distance to be covered = (240 +120)m= 360m
∴ Time taken =(360/10)sec= 36 sec
Answer C
Answer: C
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
Options:
A)83.33%
B)83.93%
C)83.73%
D)83.23%
E)83.33%
Rationale: Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.AnswerE
Answer: E
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: Type R completes 1/24 of the job each hour.
Type S completes 1/12 of the job each hour.
Together R and S complete 1/24 +1/12 = 1/8 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/8) = 1 job completed
n = 4
The answer is B.
Answer: B
Question: How many ways are there to split a group of 10 students into two groups of 5 students each? (The order of the groups does not matter)
Options:
A)104
B)126
C)148
D)172
E)216
Rationale: 10C5 = 252
If we consider these groups, each group will be counted twice.
The number of ways to choose 2 groups of 5 is 252/2 = 126
The answer is B.
Answer: B
Question: In how many different number of ways 5 boys and 2 girls can sit on a shopa which can accommodate 5 persons?
Options:
A)1802
B)2500
C)2000
D)2100
E)None
Rationale: Option 'E'
7p5 = 7 × 6 × 5 x 4 x 3= 2520
Answer: E
Question: In a graduating class, 40 percent of the students are male. In this class, 40 percent of the male students and 30 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
Options:
A)0.66
B)0.72
C)0.78
D)0.84
E)0.9
Rationale: Let x be the total number of students.
The number students who are younger than 25 is 0.6*0.4x+0.7*0.6x = 0.66x
The answer is A.
Answer: A
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)5M
B)4M
C)9M
D)2M
E)6M
Rationale: Explanation:
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D
Answer: D
Question: How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)26 sec
B)30 sec
C)24 sec
D)19 sec
E)11 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 400 * 3/50
= 24 sec.
Answer:C
Answer: C
Question: In 2008, the profits of Company N were 8 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Options:
A)150%
B)105%
C)120%
D)124.2%
E)138%
Rationale: the profit 0f 2009 interms of 2008 = 0.8*15/8*100=150%
A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)298 m
B)178 m
C)197 m
D)150 m
E)167 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time
= 50/3 * 9
= 150 m
Answer:D
Answer: D
Question: How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?
Options:
A)254
B)100
C)132
D)503
E)50
Rationale: 1 million distinct 3 digit initials are needed.
Let the number of required alphabets in the language be ‘n’.
Therefore, using ‘n’ alphabets we can form n * n * n = n^3 distinct 3 digit initials.
Note distinct initials is different from initials where the digits are different.
For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.
This n^3 different initials = 1 million
i.e. n^3 = 106 (1 million = 106)
=> n^3 = (102)^3 => n = 102 = 100
Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.
Ans:B
Answer: B
Question: The sum of the present age of Henry and Jill is 43. What is their present ages if 5 years ago Henry was twice the age of Jill?
Options:
A)and 27
B)and 24
C)and 22
D)and 29
E)of these
Rationale: Let the age of Jill 5 years ago be x, age of Henry be 2x
x+5 + 2x+5 = 43
x = 11
Present ages will be 16 and 27
Answer : A
Answer: A
Question: Diana can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of M and T and N, what is the percent of the markup from her buy price to her sell price?
Options:
A)100-N/T
B)NMT/100
C)N-M/100T
D)100T/(NM)
E)NM/100T
Rationale: Algebraic Solution:If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/M *100 = 100T/(NM)
Answer : D
Answer: D
Question: The ratio of the arithmetic mean of two numbers to one of the numbers is 4:6. What is the ratio of the smaller number to the larger number?
Options:
A)1:5
B)1:4
C)1:3
D)1:2
E)2:3
Rationale: For two numbers, the arithmetic mean is the middle of the two numbers.
The ratio of the mean to the larger number is 4:6, thus the smaller number must have a ratio of 2.
The ratio of the smaller number to the larger number is 2:6 = 1:3.
The answer is C.
Answer: C
Question: If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 110 kilograms. What is the student's present weight in kilograms?
Options:
A)71
B)72
C)73
D)74
E)75
Rationale: Let x be the weight of the sister.
Then the student's weight is 2x+5.
x + (2x+5) = 110
3x = 105
x = 35 kg
Then the student's weight is 75 kg.
The answer is E.
Answer: E
Question: The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is :
Options:
A)120
B)123
C)125
D)128
E)130
Rationale: Time from 11 May to 10 September, 1987
=21+30+31+31+10 = 123 days
Time : 123 days = 123/365 year
S.I =(7300x123x5)/(365x100)=Rs.123
answer :B
Answer: B
Question: The average age of an adult class is 40years. 10new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
Options:
A)10
B)12
C)15
D)17
E)18
Rationale: Let original strength = y
Then , 40y + 10 x 32 = ( y + 10) x 36
â‡’ 40y + 320 = 36y + 360
â‡’ 4y = 40
âˆ´ y = 10
A
Answer: A
Question: The length of minute hand of a clock is 5.2 cm. What is the area covered by this in 10 minutes
Options:
A)15.27
B)14.15
C)17.27
D)18.27
E)19.27
Rationale: area of circle is pi*r^2
but in 10 minutes area covered is (10/60)*360=60 degree
so formula is pi*r^2*(angle/360)=3.14*(5.2^2)*(60/360)=14.15 cm^2
ANSWER:B
Answer: B
Question: A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?
Options:
A)22
B)37
C)30
D)27
E)18
Rationale: US = 25
DS = 35
M = (35 + 25)/2 = 30
Answer:C
Answer: C
Question: Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 45kmph.for how many min does the bus
stop per hr
Options:
A)12 min
B)11 min
C)13 min
D)19 min
E)17 min
Rationale: Due to stoppages,it covers 9km less.
time taken to cover 9 km is [9/54 *60] min = 10min
Answer is E.
Answer: E
Question: if a@b = a * b^(1/3) then 2@8 = ?
self made
Options:
A)2
B)6
C)3
D)8
E)4
Rationale: a@b = a * b^(1/3)
2@9 = 2*8^(1/3) = 2*2 = 4
Correct Option: E
Answer: E
Question: Sundar and Raju together can do a piece of work in 8 days. If Sundar alone can do the same work in 12 days, then Raju alone can do the same work in?
Options:
A)20 days
B)22 days
C)24 days
D)26 days
E)28 days
Rationale: Raju work = 1/8 - 1/2 = 1/24 => 24 days
ANSWER C
Answer: C
Question: Jamal had a bag of marbles. He had 12 yellow, 10 blue, 5 green and 1 black marbles. He decided to randomly select a ball from the bag. What is the proabilitly that he will draw a black marble?
Options:
A)10/28
B)1/28
C)12/28
D)28/1
E)582/695
Rationale: B
Answer: B
Question: Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in
Options:
A)96 days
B)48 days
C)32 days
D)24 days
E)28 days
Rationale: jake 1 day work=1/16
paul 1 day work=1/24
j+p+h 1 ady work=1/8
1/16+1/24+1/x=1/8
1/x=1/48
x=48
so,Hari alone can dig the well in 48 days
ANSWER:B
Answer: B
Question: What is the 32nd word of "WAITING" in a dictionary?
Options:
A)AIWTNG
B)AGNTWI
C)AIGNWT
D)AGNTIWI
E)None of these
Rationale: Explanation :
Arranging the words of waiting in Alphabetical Order : A,G,I,I,N,T,W Start with A_ _ _ _ _ _ This can be arranged in 6!/2! ways=720/2=360 ways so can't be arranged starting with A alone as it is asking for 32nd word so it is out of range AG_ _ _ _ _then the remaining letters can be arranged in 5!/2! ways so,120/2=60 ways. Out of range as it has to be within 32 words. AGI_ _ _ _ Now the remaining letters can be arranged in 4! ways =24 AGN _ _ _ _ can be arranged in 4!/2! ways or 12 ways so,24+12 =36th word so out of range. So we should not consider all the words start with AGN now AGNI_ _ _can be arranged in 3! ways =6 ways so 24+6=30 within range Now only two word left so, arrange in alphabetical order. AGNTIIW - 31st word AGNTIWI - 32nd word
Answer : D
Answer: D
Question: A tradesman by means of his false balance defrauds to the extent of 32%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)74.5%
B)74.24%
C)84.6%
D)24.89%
E)45%
Rationale: g% = 32 + 32 + (32*32)/100
= 74.24%
Answer: B
Answer: B
Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Options:
A)xy2 – x2y + 2x2y2
B)xy2(1 – 2x) + x2y(2y – 1)
C)xy2(1 + x) – x2y(1 – y)
D)xy[y(1 + x) – x(1 – y)]
E)xy(y – x + 2xy)
Rationale: The other parts are equal to xy2 – x2y + 2x2y2.
Answer B
Answer: B
Question: The area of square ABCD above is 24. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
Options:
A)18−9/4∗π
B)24−9/2∗π
C)19+9/4∗π
D)24−6∗π
E)9/2−9/4∗π
Rationale: =Square - Quarter circle
=24- pi*24/4
=24- pi*6
ANSWER:D
Answer: D
Question: If an integer n is to be chosen at random from the integers 1 to 92, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)29/46
E)3/4
Rationale: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.
Thus when n is even, this whole expression will be divisible by 8.
from 1 to 96, there are 46 even integers.
Now when (n+1) is multiple by 8, we have 12 such values for (n+1)
probability that n(n+1)(n+2) will be divisible by 8
= (46 + 12)/92
= 58/96
= 29/46
Ans is D
Answer: D
Question: √[200√[200√[200……..∞]]] = ?
Options:
A)200
B)10
C)1
D)20
E)2
Rationale: Let √[200√[200√[200……..∞]]] = x ; Hence √200x = x
Squaring both sides 200x = x² Þ x (x – 200) = 0
Þ x = 0 or x – 200 = 0 i.e. x = 200
As x cannot be 0, x = 200.
ANSWER:A
Answer: A
Question: Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 36 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
Options:
A)8
B)7
C)6
D)5
E)9
Rationale: One way of approaching this question is by Relative speed method
1. Speed/ Rate of Donovan = Distance/ time => 400/45 =>80/9
2. Speed/ Rate of Michael = Distance/ time => 400/36 => 100/9
Relative Speed between them = 100/9 - 80/9 => 20/9 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)
In order to pass Donovan-
Distance to be covered = 400, Relative Rate = 20/9
Total Time taken by Micheal to surpass Donovan = Distance / rate => 400*9/20 => 3600/10 => 180
No. of laps taken by Michael = Total time / Michael's rate => 180/36 => 5
Hence correct answer is 5 Laps.
D
Answer: D
Question: If x/(9p) is an even prime number, where x is a positive integer and p is a prime number, what is the least value of x?
Options:
A) 22
B) 33
C) 44
D) 66
E) 99
Rationale: x/(11p) = even prime number
x = even prime number * 11p
Least value of x = Lowest even prime number * 11 * Lowest value of p
= 2 * 11* 2 = 44
Answer C
Answer: C
Question: If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between
Options:
A)0 and 3/20
B)3/20 and 1/5
C)1/5 and 1/4
D)1/4 and 3/10
E)3/13 and 1/2
Rationale: E. 3/13 and 1/2
Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.
Now you have excellent explanantion byscthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it.E
Answer: E
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Speed downstream = (13 + 4) km/hr = 17 km/hr.
Time taken to travel 68 km downstream =	68/17hrs = 4 hrs.
Answer: Option A
Answer: A
Question: Find the sum of prime numbers lying between 58 and 74?
Options:
A)198
B)201
C)252
D)331
E)None
Rationale: Solution
Required sum	= 59 + 61 + 67 + 71 + 73)
= 331.
Answer D
Answer: D
Question: 45 liters of mixture is created by mixing Liquid A and Liquid B in the ratio 3:2. How much more Liquid B must be added to make the ratio 9:11?
Options:
A)9 Litres
B)10 Litres
C)12 Litres
D)15 Lt
E)16 Litres
Rationale: In current ratio A = (3/5) * 45 = 27
B is 18
Suppose "b" amount of b is added
new ratio = 27/(b+18) = 9/11
=> b+18 = 33
=> b = 15
So, answer will be D
Answer: D
Question: During a recent track meet, Peter ran x meters of the 100 meter dash in 7 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?
Options:
A)7x/z
B)7zx
C)7z/x
D)7/xz
E)xz/7
Rationale: Speed of Peter = x/7 meters per second
Time needed to run z meters = DISTANCE/SPEED = z / (x/7) =7z/x
Option C
The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: C
Question: How many seconds will a train 250 meters long take to cross a platform 200 meters long if the speed of the train is 90 kmph?
Options:
A)18 sec
B)15 sec
C)21 sec
D)16 sec
E)20 sec
Rationale: D = 250+200 = 450
S = 90* 5/18 = 25 mps
T = 450/25 = 18 sec
A) 18 sec
Answer: A
Question: If n=10^100and n^n=10k what is the value of k?
Options:
A)200
B)10^100
C)10^102
D)100^100
E)1000^10
Rationale: There is a simple logic to this question.
(a^m)^n = a^mn
So, (10^100)^(10^100) = 10^(100*(10^100))
= 10^((10^2)*(10^100))
= 10^(10^102)
and this equals 10^k
So, k = 10^102
ANSWER:C
Answer: C
Question: In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?
Options:
A)80%
B)20%
C)40%
D)50%
E)None of these
Rationale: Number of students passed = 60% of 140 = 60/100 * 140 = 84
Number of students failed = 140 - 84 = 56.
Required percentage = 28/56 * 100 = 50%.
ANSWER:D
Answer: D
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. How far is the place?
Options:
A)2.29
B)2.88
C)2.2
D)2.12
E)2.14
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: B
Question: Approximately how many revolutions will be made by a car tire with a 15-inch diameter if the car travels 1⁄2 mile?
Options:
A)669
B)660
C)360
D)720
E)1,440
Rationale: Diameter of car tire = 15 inches
Radius of car tire = 7.5 inches = 7.5*2.54 cm = 19.05 cm
Circumference of the car tire = 2*pi * 19.05 = 2 *3.14 *19.05= 119.63 cm
Distance traveled by car = .5 mile = .5 *1.6 km = .8 km = 800 m = 8 * 10^4 cm
Number of revolutions =Distance traveled / Circumference of tire = 8 * 10^4 / 119.63 = 668.73
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer A
Answer: A
Question: How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?
Options:
A)720
B)24
C)None of these
D)120
E)247
Rationale: Explanation :
The word 'DELHI' has 5 letters and all these letters are different.
Total words (with or without meaning) formed by using all these
5 letters using each letter exactly once
= Number of arrangements of 5 letters taken all at a time
= 5P5 = 5! = 5 x 4 x 3 x 2 x 1 = 120. Answer : Option D
Answer: D
Question: If X,Y is 26%,30% smaller than Z then how much percentage is Y greater than X?
Options:
A)5 15/37 %
B)13%
C)13 1/2%
D)14%
E)15%
Rationale: X = 74 %
Y = 70 %
Z = 100 %
X-Y/X × 100 = 4/76 × 100 = 5 15/37% greater than X
A)
Answer: A
Question: A can do 50% more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours ?
Options:
A)12
B)8
C)13 1⁄3
D)51⁄2
E)None of these
Rationale: B alone can do a work in 20 hours.
∴ A alone can do 3⁄2 of the work in 20 hours.
i.e., A alone can do the same work in 40⁄3 hours
∴ (A + B)’s one hour’s work = 3⁄40 + 1⁄20 = 5⁄40 = 1⁄8
⇒ A and B together can finish the whole work in 8 hours.
Answer B
Answer: B
Question: When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder?
Options:
A)11
B)13
C)15
D)Data inadequate
E)none of these
Rationale: Number= (31 * Q)+ 29.
Given data is inadequate.
ANSWER:D
Answer: D
Question: Speed of a boat in standing water is 8 kmph and the speed of the stream is 6 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
Options:
A)120 hours
B)240 hours
C)160 hours
D)480 hours
E)None
Rationale: Sol.
Speed upstream = 2 kmph; Speed downstream = 14 kmph.
∴ total time taken = [210/2 + 210/2] hours = 120 hours.
Answer A
Answer: A
Question: SCORE INTERVAL----------------NUMBER OF SCORES
50-59-------------------------- 2
60-69--------------------------10
70-79--------------------------16
80-89--------------------------10
90-99--------------------------18
The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 28 scores?
Options:
A)39
B)28th(50-79)
C)32
D)34
E)36
Rationale: Total scores= 2+10+16+10+18 =56, which is odd, therefore the median is the Floor(56/2)= 28th score. And the 37th score is in the 80-89 range, because 50-79 only reference 28 scores.
B
Answer: B
Question: Light glows for every 18 seconds . How many times did it between 1:57:58 and 3:20:47 am
Options:
A)281
B)277
C)283
D)384
E)385
Rationale: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/18 = 276.
so total 277 times light ll glow
ANSWER:B
Answer: B
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1344?
Options:
A)1200
B)2777
C)2889
D)27670
E)2771
Rationale: 1344 = P [1 + (5*12/5)/100]
P= 1200.Answer:A
Answer: A
Question: If the average marks of two sections of 40 and 45 students respectively is 75 and 60, then the average marks of all the students is:
Options:
A)53.33
B)67.05
C)75
D)None of these
E)Cannot be determined
Rationale: Explanation :
Required average = (40 x 75 + 45 x 60)/(40 + 45)
= (3000 + 2700)/85
= 5700/85
= 67.05
Answer : B
Answer: B
Question: A rectangular field has a length 10 meters more than it is width. If the area of the field is 231, what is the length (in meters) of the rectangular field?
Options:
A)21
B)23
C)25
D)27
E)29
Rationale: area = l * w = (L) * (L-10) = 231
trial and error:
20*10 = 200 (too low)
21*11 = 231
The length is 21 meters.
The answer is A.
Answer: A
Question: A manufacturing plant produces 2 products (hats and gloves). 25% of all products are colored red, the remaining products are colored blue. If the ratio of products made is 3:4, respectively, and the percentage of hats colored red is 55%, what percentage of gloves are colored blue?
Options:
A)87%
B)90.5%
C)97.5%
D)55.5%
E)96%
Rationale: Let H and G be number hats and gloves, and r and b represent red and blue, respectively.
H + G = total products.
H:G = 3:4
Hr/H = 55%
Gb/G = 100% - Gr/G = ?
[(3)(Hr/H) + (4)(Gr/G)]/(3 + 4) = 25%
[(3)(55%) + (4)(Gr/G)]/7 = 25%
Gb/G = 100% - 2.5% = 97.5%
Answer: C
Answer: C
Question: Let a, b, c, d and e be distinct integers such that (6-a)(6-b)(6-c)(6-d)(6-e) = 45. What is a+b+c+d+e?
Options:
A)5
B)17
C)25
D)27
E)30
Rationale: Since the prime factorization is 3*3*5
The constraint in the question is that they are distinct so the only possible way is 3,-3,5,1,-1
6-a = 3 => a=3
6-b = -3 => b=9
6-c = 5 => c=1
6-d = 1 => c=5
6-e = -1 => e = 7
Answer is C = 25
Answer: C