RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:9. If P invested the money for 5 months, find for how much time did Q invest the money?
A.9
B.17
C.13
D.10
Answer: A.9
Explanation: 7*5: 5*x = 7:9
x = 9
Answer: A
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
A.1/3
B.1/9
C.1/6
D.1/2
Answer: A.1/3
Explanation: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Question: A sum of money deposited at C.I. amounts to Rs.1820 in 4 years and to Rs.2402 in 5 years. Find the rate percent?
A.30%
B.31%
C.34%
D.19%
Answer: B.31%
Explanation: 1820 --- 582
100 --- ? => 31%
Answer: B
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
A.6:3
B.6:9
C.6:5
D.6:1
Answer: C.6:5
Explanation: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer:C
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. 80 percent of the distribution lies within one standard deviation d of the mean. If the shelf’s average life is 8.6 years and the standard deviation is 3.4 years, what percent of the distribution has more than 12.0 years as a shelf’s average life?
A.23%
B.22%
C.21%
D.20%
Answer: D.20%
Explanation: Average = 8.6
SD = 3.4
8.6 - 3.4 < 80% of distribution < 8.6 + 3.4
5.2 < 80% of distribution < 12.0
40% is outside this range.
Given: Distribution is symmetric. So 20% of distribution is less than 5.2 and the other 20% of distribution is greater than 12.0.
Answer: D
Question: The simple interest on a sum of money will be Rs. 600 after 10 years.If the principal is trebled after 5 years,what will be the total interest at the end of the tenth year ?
A.Rs. 600
B.Rs. 900
C.Rs. 1200
D.Rs. 1500
Answer: C.Rs. 1200
Explanation: Solution
22.22
Let the sum be Rs. x. Now, S.I. = Rs. 600,T = 10 years.
Rate = % = (100x600/X x 10)% =(6000/X)%
S.I. for first 5 years = Rs.(X x 5 x 6000/X x 100) = Rs. 300.
S.I. for first 5 years = Rs. (3X x 5 x 6000/X x 100)= Rs. 900.
∴ Total interest = Rs. 1200.
Answer C
Question: A hall 20m long and 15m broad is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at the rate of Rs.3.50 per sq. meter is
A.500
B.600
C.650
D.700
Answer: D.700
Explanation: Area of verandah = [(25Ãƒâ€”20)?(20Ãƒâ€”15)]mÂ²=200 mÂ²
Cost of flooring = Rs.(200Ãƒâ€”3.50) = Rs.700
Answer :D
Question: If the LCM of A and B is 72 and their HCF is 6, what is the product of A & B?
A.432
B.433
C.434
D.435
Answer: A.432
Explanation: The most important property of LCM (the least common multiple) and GCD (the greatest common divisors) is: for any positive integers x and y, x∗y=GCD(x,y)∗LCM(x,y) so AB=72*6=432.
ANSWER:A
Question: If a,b,c,d,e is an arithmetic sequence which of the following is also an arithmetic sequence?
I. 5a, 5b, 5c, 5d, 5e
II. a-6, b-6, c-6, d-6, e-6
III. a^8, b^8, c^8, d^8, e^8
A.I and II
B.II only
C.II and III
D.III only
Answer: A.I and II
Explanation: lets look at the three choices...
I. 5a, 5b, 5c, 5d, 5e
since the difference is constant, it is an arithmetic sequence...
II. a-6, b-6, c-6, d-6, e-6
since the difference is constant, it is an arithmetic sequence
III. a^8, b^8, c^8, d^8, e^8
since the difference is not constant it is not be an arithmetic sequence...
only l and ll.. ans A....
Question: Sonika bought a V.C.R. at the list price of 18,500. If the rate of sales tax was 8%, find the amount she had to pay for purchasing the V.C.R.
A.19,980
B.19,780
C.19,680
D.19,380
Answer: A.19,980
Explanation: Sol. List price of V.C.R. =18,500
Rate of sales tax = 8%
∴ Sales tax = 8% of 18,500
= 8⁄100 × 18500 = 1480
So, total amount which Sonika had to pay for purchasing the V.C.R. = 18,500 + 1480
= 19,980. Answer A
Question: The two lines y=x and x=-6 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
A.12
B.14
C.16
D.18
Answer: D.18
Explanation: The point of intersection is (-6,-6).
The triangle has a base of length 6 and a height of 6.
area = (1/2)*base*height = (1/2)*6*6 = 18
The answer is D.
Question: Find the simple interest on $10000 at 4% per annum for 12 months?
A.$400
B.$500
C.$650
D.$710
Answer: A.$400
Explanation: P = $10000
R = 4%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*4*1/100 = $400
Answer is A
Question: In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
A.16%
B.25%
C.30%
D.40%
Answer: C.30%
Explanation: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 45 are employed males, hence 19% are employed females.
(employed females)/(total employed people)=19/64=30%
Answer: C.
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A.40 sec
B.29 sec
C.26 sec
D.27 sec
Answer: A.40 sec
Explanation: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25
= 40 sec
Answer: A
Question: If, for all positive integer values of n, P(n) is defined as the sum of the smallest n prime numbers, then which of the following quantities are odd integers?
I. P(10)
II. P(P(10))
III. P(P(P(10)))
A.I only
B.I and II only
C.I and III only
D.II and III only
Answer: C.I and III only
Explanation: 2 is the only even prime number. Now, the sum of first 10 prime numbers = 9*odd + 2 = odd. Thus P(10) = odd.
Again, the sum of the first n -odd primes = (n-1)*odd+2 = even.Thus, p(P(10)) = even.
Similarly, the sum of the first m - even primes = (m-1)*odd+2 = odd.
I and III.
ANSWER:C
Question: A beekeeper has 900,000 bees living in ten beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
A.18000
B.109756
C.46700
D.657587
Answer: B.109756
Explanation: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+9*(0.8)*x = 900,000 => 8.2x = 900,000 => x = 109756.
B is the answer.
Question: Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -9 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
A.-9,-9,-9
B.-9,9,9
C.1,1,1
D.-9,81,9
Answer: D.-9,81,9
Explanation: Mean: If all values are multiplied by -9 then their sum will also be multiplied by -9 so Mean will also get -9
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -9 then the difference between the mean and the individual values also gets multiplied by -9 and the square of that difference becomes 81. So, the variance gets multiplied by a factor of 81
SD:
Standard Deviation is the square root of variance so sqrt(81)=9. So SD gets multiplied by a factor of 9.
So, answer will be D.
Question: The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.35. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
A.A)0.8321
B.B)0.7
C.C)0.895
D.D)0.7531
Answer: C.C)0.895
Explanation: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.35*20 = 7.
So, out of 100 matches 60 + 7 = 67 are won.
It is known that the team has won the last match. Out of 67 matches won, Matt is in 60: 60/67 = 0.895...
Answer: C.
Question: Rs. 700 is divided among A, B, C so that A receives half as much as B and B half as much as C. Then C's share is
A.Rs 200
B.Rs 300
C.Rs 400
D.Rs 500
Answer: C.Rs 400
Explanation: Explanation:
Let C = x.
Then B = x/2
and A = x/4
A:B:C = 1:2:4.
C's share Rs.[(4/7)*700) = 400
Option C
Question: A company produces on an average 4000 items per month for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average of 4375 items per month over the whole?
A.4500
B.4600
C.4680
D.4710
Answer: A.4500
Explanation: Sol.
Required average = (4375 x 12) - (4000 x 3 ) / 9
⇔ 52500 - 12000 / 9
⇔ 40500 / 9
= 4500.
Answer A
Question: A number is increased by 30 % and then decreased by 30 %. Find the net increase or decrease per cent.
A.9%
B.8%
C.7%
D.3%
Answer: A.9%
Explanation: Let the number be 100.
Increase in the number = 30 % = 30 % of 100
= (30/100 Ã— 100)
= 30
Therefore, increased number = 100 + 30 = 130
This number is decreased by 30 %
Therefore, decrease in number = 30 % of 130
= (30/100 Ã— 130)
= 3900/100
= 39
Therefore, new number = 130 - 39 = 91
Thus, net decreases = 100 -91 = 9
Hence, net percentage decrease = (9/100 Ã— 100) %
= (900/100) %
= 9 %
Answer:A
Question: Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.10 minutes
B.20 minutes
C.15 minutes
D.12 minutes
Answer: A.10 minutes
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10
So, the tank becomes full in 10 minutes.
ANSWER:A
Question: The value of land increases by m% during June and decreases by n% during July. If the value of the land is the same at the end of July as at the beginning of June, what is n in terms of m?
A.200m/(100+2m)
B.100m/(100+m)
C.m(2+m)/(1+m)2
D.m(200+m)/10000
Answer: B.100m/(100+m)
Explanation: The simplest pairing is a 25% increase will be offset by a 20% decrease.
Here's the proof:
Starting value = 100
25% increase = 100 + (.25)(100) = 125
20% decrease = 125 - (.2)(125) = 100
Ending value = 100
So we would be looking for an answer that equals 20 when A=25. While the answers might appear 'complex', you can actually avoid much of the 'math' if you just fill in the parts and take a good look at what you have...
Answer A: (200)(25)/(150) ... since 200>150, this answer will be greater than 25. ELIMINATE A.
Answer B: (100)(25)/125) = (100)(1/5) = 20 This is a MATCH.
Answer C: (25)(27)/(26)2 ... nothing 'cancels out', so this cannot = 20. ELIMINATE C.
Answer D: (25)(225)/10000... the 'units' digit of the numerator is a 5; when dividing by 10,000, this won't end in a 0. ELIMINATE D.
Answer E: (50/25) + 50 = 52. ELIMINATE E.
B
Question: If a rectangular room measures 8 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
A.24,000
B.16,000,000
C.2,400,000
D.24,000,000
Answer: B.16,000,000
Explanation: B. 160,000,000
8*100*5*100*4*100 = 160,000,000
Question: In 26 minutes, the minute hand gains over the hour hand by
A.116°
B.125°
C.143°
D.158°
Answer: C.143°
Explanation: In one hour, the hour hand moves 30°, which is 0.5° each minute.
In one hour, the minute hand moves 360°, which is 6° each minutes.
The minute hand gains 5.5° each minute.
In 26 minutes, the minute hand gains 26 * 5.5° = 143°.
The answer is C.
Question: The total of 342 of 20 paise and 25 paise make a sum of Rs. 71. The no of 20 paise coins is
A.238
B.290
C.278
D.200
Answer: B.290
Explanation: Explanation:
Let the number of 20 paise coins be x. Then the no of 25 paise coins = (342 - x).
0.20 * (x) + 0.25 (342 - x) = 71 => x = 290..
Answer: B) 290
Question: Ben earns $12,800 a year. About 15% is taken out for taxes.
How much is taken out for taxes?
A.$19200
B.$11920
C.$1920
D.$19820
Answer: C.$1920
Explanation: 15/100=x/12.800
Divide by the remaining number:
1920/192000
100
$1920
correct answer C
Question: Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent?
A.11 1/8%
B.11 1/5%
C.11 1/9%
D.11 12%
Answer: C.11 1/9%
Explanation: 900 --- 100
100 --- ? => 11 1/9%
Answer: C
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 50%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
A.100% decrease
B.50% decrease
C.40% decrease
D.40% increase
Answer: C.40% decrease
Explanation: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 50%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer C.
Question: By selling an Shirt for $300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
A.9%
B.2%
C.8%
D.5%
Answer: C.8%
Explanation: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Question: A number whose fifth part increased by 3 is equal to its fourth part diminished by 3 is ?
A.120
B.180
C.200
D.220
Answer: A.120
Explanation: Answer
Let the number be N.
Then, (N/5) + 3 = (N/4) - 3
â‡’ (N/4) - (N/5) = 6
â‡’ (5N - 4N)/20 = 6
âˆ´ N = 120
Option: A
Question: One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 50 of the attendees are neither female nor students, what is the total number of attendees at the convention?
A.600
B.300
C.400
D.500
Answer: B.300
Explanation: Let no. of Attendee are A.
Now As per the condition of the problem stated above .
We have following population in the convention as Attendee.
Total no. of females = [2/3]*A
Total no. of females as student : [1/6]*A
Total no. of students = [1/3]*A
Total no. of male as student = [1/6]*A
Total no. of males = A - [2/3]*A = [1/3]A
No. of males which are not student = [1/3]A - [1/6]*A = 50
Hence A =300
Total no of males who are not student will be the answer as it states it should be neither female nor student
So Answer is B
Question: Tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?
A.3/10
B.3/20
C.2/5
D.1/2
Answer: A.3/10
Explanation: S={1,2,3,….20}
E={3, 6,9,12,15,18}
P(E)=6/20
=3/10
Option A
Question: Twelve people are planning to share equally the cost of a rental van. If one person withdraws from the arrangement and the others share equally the cost of the rental van, then the share of each of the remaining people will increase by...?
A.1/12
B.1/8
C.1/11
D.12/11
Answer: C.1/11
Explanation: Let P = total cost of the rental van.
The original share per person is P/12.
The new share per person is P/11.
P/11 = P/12 * 12/11 = (1 + 1/11)*original share
The answer is C.
Question: In a trapezium ABCD, AB is parallel to DC, AB = 3*DC, and the diagonals of the trapezium intersect at O. The ratio of the area of ∆OCD to the area of ∆OAB is:
A. 1:9
B. 1:3
C. 3:1
D. 1:10
Answer: A. 1:9
Explanation: triangles are similar , so ratio will be 1:9
A
Question: There are 5 red shoes, 4 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
A.1/9
B.2/9
C.5/9
D.4/9
Answer: C.5/9
Explanation: total 9 from take one.
9c1=9
red 5 from one
5c1=5
5/9
ANSWER:C
Question: The average (arithmetic mean) monthly income of four workers is $3,000. After one worker’s income increases by 20 percent the new average income is $3,300. What was the original income of the worker whose monthly income increased?
A.$6,500
B.$6,400
C.$6,000
D.$6,200
Answer: C.$6,000
Explanation: Increase in total income was 300*4=$1200, we know that this increase was 20% (1/5th) of the workers original income, thus his/her original income was 1200*5=$6,000.
Answer: C
Question: Find the one which does not belong to that group ?
A.36
B.49
C.64
D.81
Answer: B.49
Explanation: Explanation:
36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102.
36, 64, 81 and 100 are squares of composite numbers, but not 49.
ANSWER IS B
Question: A can give B 100 meters start and C 150 meters start in a kilometer race. How much start can B give C in a kilometer race?
A.10.55 meters
B.11.55 meters
C.33.55 meters
D.55.55 meters
Answer: D.55.55 meters
Explanation: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 850 meters.
Therefore, B runs 900 meters while C runs 850 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 850)/900 = 944.44 meters
Thus, B can give C (1000 - 944.44) = 55.55 meters start
Answer:D
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a.for the next five years and 13% p.a.for the period beyond eight years If the total interest paid by him at the end of eleven years is 8160, how much money did he borrow?
A.8000
B.10,000
C.12,000
D.Data inadequate
Answer: A.8000
Explanation: Let the sum be x. Then,
(x×6×3/100)+(x×9×5/100)+(x×13×/)=8160
⇒ 18x + 45x + 39x = (8160 × 100)
⇒ 102x = 816000
⇒ x = 8000.
Answer A
Question: What percent of 5 letter combinations that can be made from the letters of the word FERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
A.23.8%
B.20%
C.25%
D.30.2%
Answer: A.23.8%
Explanation: a) noof combinations when all 5 letters are different = 7*6*5*4*3
b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3
b/a = 5/21= 0.238
A
Question: A childrens identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
A.211
B.216
C.1075
D.1080
Answer: C.1075
Explanation: A childrens identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18
now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299
here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)
thus total possible cases are 18 + 8 =26
case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)
if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)
hence total number of ways = 7(18+9) = 189
thus different number of codes = 5(189+26) = 1075
hence C
Question: The length of the bridge, which a train 150 m long and traveling at 45 km/hr can cross in 30 sec is?
A.377
B.225
C.237
D.245
Answer: B.225
Explanation: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (150 + x)/30 = 25/2
x = 225 m.
Answer: B
Question: A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets W be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .
A.(J - 50)/3
B.3(J + 20)/x
C.(J + x - 50)/3
D.(J - x + 60)/3
Answer: D.(J - x + 60)/3
Explanation: here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
= (J - X)/3 + 20
W= (J - X + 60)/3=D
Question: If John takes 7 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?
A.420xz
B.7z/x
C.420z/x
D.7xz
Answer: C.420z/x
Explanation: It will take (z/x)(7) minutes which is (z/x)(7)(60) seconds = 420z/x seconds.
The answer is C.
Question: The average of first 25 natural numbers is?
A.14
B.13
C.15
D.18
Answer: B.13
Explanation: Sum of 25 natural no.
= 650/2 = 325
Average = 325/25
= 13
Answer:B
Question: The distance from Steve's house to work is 30 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
A.5.
B.10.
C.14.
D.15
Answer: D.15
Explanation: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 30 km => Speed = 15 kmph
ANSWER:D
Question: Two men, Vikas and Vishal, working separately can mow a field in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Vikas beginning at 8 a.m, when will the mowing be finished?
A.232
B.787
C.2369
D.277
Answer: B.787
Explanation: Answer:B
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
A.334
B.224
C.667
D.2678
Answer: B.224
Explanation: Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km
Answer: B
Question: The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the width and the length of the garden.
A.80
B.90
C.100
D.70
Answer: C.100
Explanation: Let L and W be the length and width of the garden. The statement "the length of a rectangular garden is 2 feet longer than 3 times its width" may be formulated by
L = 2 + 3 W
The formula for the perimeter is given by
P = 2 L + 2 W
Substitute P and L in the above equation by 100 and 2 + 3 W respectively to obtain
100 = 2(2 + 3 W) + 2 W
Solve for W and L
W = 12 and L = 2 + 3 W = 38.
Check that the perimeter of the rectangular garden is 100
P = 2 L + 2 W = 76 + 24 = 100
Answer C
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A.45 km/hr
B.55 km/hr
C.35 km/hr
D.50 km/hr
Answer: D.50 km/hr
Explanation: Speed of the train relative to man =125/10	m/sec
25/2	m/sec.
25/2	x 18/15	km/hr
= 45 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 x = 50 km/hr. Answer : D
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
A.1/20
B.1/26
C.1/23
D.1/50
Answer: B.1/26
Explanation: Total no of cases = 52
fav cases = 2
prob = 2/56 = 1/26
ANSWER B