RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: N, a set of natural numbers is partitioned into subsets S1 = {1}, S2 = {2,3}, S3 = {4,5,6}, S4 = {7,8,9,10} and so on. The sum of the elements of the subset S50 is
A.(a) 61250
B.(b) 65525
C.(c) 42455
D.(d) 62525
Answer: D.(d) 62525
Explanation: The question is based heavily on pattern-matching skills, and is far more 'layered' than what you would likely see on the Official GMAT on this subject. You'll likely find it easiest to define the patterns one-at-a-time, so that you can see how they impact the question.
To start, we're given information on the sub-sets of numbers:
-The 1st set has 1 number
-The 2nd set has 2 numbers
-The 3rd set has 3 numbers
Etc.
So the 50th set will have 50 numbers in it.
Since the numbers in the subsets are consecutive, we can figure out ALL of the numbers that show up BEFORE we get to the 50th set by usingbunching...
The 1st set has 1 number and the 49th set has 49 numbers....1 + 49 = 50 numbers
The 2nd set has 2 numbers and the 48th set has 48 numbers...2 + 48 = 50 numbers
Etc.
This pattern will continue all the way down to...
The 24th set has 24 numbers and the 26th set has 26 numbers...24 + 26 = 50 numbers
Thus, we have 24 'pairs' of 50 numbers and one set (the 25th set with 25 numbers) that doesn't have a 'pair-match'...
So 24(50) + 25 = 1225 consecutive numbers exist in the 49 sets BEFORE the 50th set - that's the numbers 1 to 1225, inclusive...
Thus, the 50th set starts with 1226 and ends with 1275. We can use 'bunching' again to figure out the sum of this group (although there's no 'middle term' this time)...
25(1226+1275) =
25(2501) =
62525
D
Question: A boy was asked to find 7/9 of a y. But he divided the y by 7/9, Thus he got 32 morethan theanswer. Find the y.
A.45
B.56
C.48
D.63
Answer: D.63
Explanation: x/7/9 = 9x/7 = 32 + y
Actualy he should do 7x/9 = y
y = (9x/7) - 32
y = (9x - 224)/7
(9x - 224)/7 = 7x/9
81y - 2016 = 49y
81y - 49y = 2016
32y = 2016
y = 63
D
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 8. What is the value of Z?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
X + 3Y + 3Z = 5Y + 8
Z+2+3Z+3+3Z = 5Z+5+8
2Z = 8
Z = 4
The answer is C.
Question: 8, 24, 12, 36, 18, 54, (....)
A.72
B.68
C.108
D.27
Answer: D.27
Explanation: 8 × 3 = 24
24 ÷ 2 = 12
12 × 3 = 36
36 ÷ 2 = 18
18 × 3 = 54
54 ÷ 2 = 27
Answer is D.
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 9 and 10. The larger of the two numbers is:
A.276
B.299
C.230
D.345
Answer: C.230
Explanation: Clearly, the numbers are (23 x 9) and (23 x 10).
Larger number = (23 x 10) = 230.
Answer: Option C
Question: What is the area of a square field whose diagonal of length 20 m?
A.228
B.271
C.200
D.277
Answer: C.200
Explanation: d2/2 = (20 * 20)/2 = 200
Answer:C
Question: In how many ways can the letters {U, R, U, R, R} be arranged?
A.10
B.20
C.120
D.720
Answer: A.10
Explanation: My answer : A
There is 5! ways to arrange those letters in total, however letter U repeats 2! times and letter R repeats 3! times
=> the way to arrange without repeating = 5!/ [2!x3!] = 10
Question: The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the school?
A.18
B.25
C.23
D.29
Answer: B.25
Explanation: 39x = 5 + 12 + 15 + 19 + (x – 4)44
x
= 25
Answer:B
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 27, what is the value of r-p?
A.20
B.10
C.34
D.40
Answer: C.34
Explanation: Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=54 ----eq2
Subtracting eq1 from eq2 we get: r-p=34
Hence, the correct answer is C
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
A.8925
B.8259
C.8529
D.8952
Answer: A.8925
Explanation: Sol.
Principal = Rs. [100 * 4016.25 / 9 * 5] = Rs. [401625 / 45] = Rs. 8925.
Answer A
Question: On the coordinate plane , points P and T are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?
A. (1.5,1)
B. (2,-5)
C. (0,0)
D. (1,1.5)
Answer: D. (1,1.5)
Explanation: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.
One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).
Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PT is the diameter of the circle.
There can be a case when PT is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.
If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D
Question: A and B start walking towards each other at 4pm at speed of 2kmph and 3kmph. They were initially 15km apart. At what time do they meet?
A.8pm
B.6pm
C.7pm
D.10pm
Answer: C.7pm
Explanation: Time of meeting = distance / relative speed = 15/3+2 = 15/5 = 3 hrs after 4pm = 7pm
Answer is C
Question: How many seconds will a 450 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?
A.27 sec
B.30 sec
C.86 sec
D.16 sec
Answer: A.27 sec
Explanation: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 450 * 3/50
= 27 sec.
Answer: A
Question: If a man travels f miles an hour for m hours and r miles an hour for s hours, what is his average rate in miles per hour for the entire distance traveled?
A.fm + rs
B.(fm + rs)/2
C.m/f + s/r
D.(fm + rs)/(m + s)
Answer: D.(fm + rs)/(m + s)
Explanation: Average Speed = Total Distance /Total Time Taken
Total Distance travelled in m hours = fm
Total Distance travelled in s hours = rs
Total Time taken = m+s
Therefore , Average Speed = (fm+ms)/(m+s)
Answer D
Question: The average salary of 15 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $20,000 each. What is the average salary of the remaining employees?
A. $19,250
B. $15,800
C. $18,000
D. $15,850
Answer: B. $15,800
Explanation: total salary... 15*20k=300k
5 emp @ 25k =125k
4 emp @ 20k =80k
remaing 6 emp sal = 300k-125k-80k =95k
average=95k/6 = 15800
Ans:B
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 110 players took part in that tournament.
How many matches were played?
A.99 matches.
B.88 matches.
C.77 matches.
D.109 matches.
Answer: D.109 matches.
Explanation: Solution:
109 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 109 matches were played.
Answer D
Question: Rani is two years older than Banu who is twice as old as Chitra. If the total of the age of Rani, Banu and Chitra be 32 years, then how old is Banu ?
A.7 years
B.10 years
C.12 years
D.13 years
Answer: C.12 years
Explanation: Let Chitra's age be x years. Then, Banu's age = 2x years.Rani's age = (2x + 2) years.
(2x + 2) + 2x + x = 32
5x =30
x = 6
Hence, Banu's age = 2x = 12 years.
Answer : C
Question: The area of a parallelogram is 72sq m and its altitude is twice the corresponding base. Then the length of the base is?
A.6
B.9
C.7
D.62
Answer: A.6
Explanation: 2x * x = 72 => x= 6
Answer: A
Question: The unit digit in the product (891 * 781 * 912 * 463) is:
A.2
B.5
C.6
D.8
Answer: C.6
Explanation: Explanation:
Unit digit in the given product = Unit Digit in (1*1*2*3) = 6
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.36
B.50
C.28
D.26
Answer: B.50
Explanation: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] 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: B
Question: There are some people in party, 1/3rd left the party . Then 2/5th of the remaining left the party , then 2/3rd of the remaining left the party . At last 6 were remaining . How many people were in total ?
A.45
B.27
C.28
D.26
Answer: A.45
Explanation: Sol:
45
If x persons were there in total , then
x × (1 – 1/3)× (1 – 2/5) ×(1 – 2/3) = 6
x×2/3 × 3/5 × 1/3 = 6
x = 6 × 5 × 3/2 = 45
Answer:A
Question: What is the are of an equilateral triangle of side 14 cm?
A.66âˆš3 cm2
B.74âˆš3 cm2
C.64âˆš3 cm2
D.49âˆš3 cm2
Answer: D.49âˆš3 cm2
Explanation: Area of an equilateral triangle = âˆš3/4 S2
If S = 14, Area of triangle = âˆš3/4 * 14 * 14 = 49âˆš3 cm2;
Answer:D
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is?
A.20
B.30
C.40
D.43
Answer: A.20
Explanation: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
A)
Question: Ravi and sunil are partners in a business. Ravi invests Rs.10,000 for 8 months and Sunil invested Rs.12000 for 10 months then after one year ratio of their profits will be
A.1:3
B.2:3
C.3:2
D.3:1
Answer: B.2:3
Explanation: =(15000*8):(8000*10)
=80000:120000
=2:3
ANSWER:B
Question: The speed of a train is 120 kmph. What is the distance covered by it in 10 minutes?
A.26 kmph
B.20 kmph
C.28 kmph
D.30 kmph
Answer: B.20 kmph
Explanation: 120 * 10/60
=20 kmph
Answer: B
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
A.2208
B.2201
C.2200
D.2287
Answer: C.2200
Explanation: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs. 2200.Answer: C
Question: After allowing a discount of 15% on the marked price, the selling price is $6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
A.$5400
B.$5750
C.$5000
D.$7000
Answer: C.$5000
Explanation: C
$5000
Given SP = $6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = $8000
If SP = $8000, profit = 60%
CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = $5000
Question: If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?
A.25% loss
B.25% profit
C.20% loss
D.20% profit
Answer: C.20% loss
Explanation: Let the cost price of 1 article be $1.
Therefore, cost price of 20 articles = 20 * 1 = $20
The selling price of 25 articles = cost price of 20 articles = $20.
Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.
Cost price of 25 articles = 25 * 1 = $25.
Therefore, profit made on sale of 25 articles = Selling price of 25 articles - cost price of 25 articles
= 20 - 25 = -$5.
As the profit is in the negative, the merchant has made a loss of $5.
Therefore, % loss = loss/cp * 100
% loss = -5/25 * 100 = 20% loss.
ANSWER:C
Question: I. x2 + 9x + 20 = 0,
II. y2 + 5y + 6 = 0 to solve both the equations to find the values of x and y?
A.If x < y
B.If x > y
C.If x ≤ y
D.If x ≥ y
Answer: A.If x < y
Explanation: I. x2 + 4x + 5x + 20 = 0
=>(x + 4)(x + 5) = 0 => x = -4, -5
II. y2 + 3y + 2y + 6 = 0
=>(y + 3)(y + 2) = 0 => y = -3, -2
= x < y.
ANSWER:A
Question: At a certain conference, 72% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
A. 18.0%
B. 62.0%
C. 79.2%
D. 80.0%
Answer: D. 80.0%
Explanation: 0.72A -> At least 2 weeks in advance and paid conference fee in full.
FA -> Paid the conference fee in full
0.10FA -> Not 2 weeks in advance paid but conference fee in full
=> 0.90FA -> 2 Weeks in advance and paid the conference fee in full
0.90FA = 0.72A
FA/A = 72/90 * 100
= 80%
Answer - D
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?
A.6.06%
B.6.07%
C.6.08%
D.6.09%
Answer: D.6.09%
Explanation: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09%
ANSWER:D
Question: The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 44 kg more than the weight of the third boy, what is the weight of the lightest boy?
A.87.2 kg
B.35.2 kg
C.98.2 kg
D.65.2 kg
Answer: B.35.2 kg
Explanation: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 44
=> 5k = 44 => k = 8.8
Therefore the weight of the lightest boy
= 4k = 4(8.8) = 35.2 kg.
Answer:B
Question: Find the odd man out
4, 8, 12, 16, 20, 24, 27, 32
A.8
B.27
C.24
D.32
Answer: B.27
Explanation: 27 is odd man out
as
all numbers in
4, 8, 12, 16, 20, 24, 27, 32 series are even except 24 which is even number.
ANSWER:B
Question: How many 4-digit positive integers are multiple of each integer from 1 to 10
A.1520
B.2520
C.3520
D.5140
Answer: B.2520
Explanation: Least No which could be divisible by integers [ 1,2,3,4,5,6,7,8,9,10] is the LCM of the said integers.
LCM [1,2,3,4,5,6,7,8,9,10] = 2520
No the Nos which are divisible by 2520 will be divisible by [1,2,3,4,5,6,7,8,9]
There are 3 values possible between 1000 to 9999
They are 2520 x 1= 2520
2520 x 2 = 5040
2520 x 3 = 7560
ANSWER:B
Question: John bought 2 shares and sold them for $84 each. If he had a profit of 20% on the sale of one of the shares but a loss of 20% on the sale of the other share, then on the sale of both shares John had
A.a profit of $10
B.a profit of $7
C.a loss of $7
D.a loss of $10
Answer: C.a loss of $7
Explanation: Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 84*2 = $168
Total Cost Price = 168/(0.96) = $175
Loss = 175-168 = $7
Answer: Option C
Question: A shopkeeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is:
A.45:56
B.45:51
C.47:56
D.47:51
Answer: A.45:56
Explanation: Solution: Let the CP be 100.
Hence, SP = 100 + 12% of 100 = 112.
If the marked price be X, then
90% of X = 112
=>	X = (112*100)/90 = Rs. 1120/9
Hence,
Required ratio = 100:1120/9 = 900:1120 = 45:56.
Answer: Option A
Question: A certain set of numbers has an average (arithmetic mean) of 50 and a standard deviation of 50.5. If b and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the sum of b and n?
A.-200
B.-130
C.-104
D.51
Answer: D.51
Explanation: 2 standard deviations from the average is frommean - 2*SDtomean + 2*SD, thus from 50-2*50.5=51 to 50+2*50.5=151:
-51 < b < 151
-51 < n < 151
-102 < b+n < 302.
Only option D is in this range.
Answer: D.
Question: The batting average for 40 innings of a cricket palyer is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is
A.165 runs
B.170 runs
C.172 runs
D.174 runs
Answer: D.174 runs
Explanation: Since scores are differ by 172
let us consider the highest as x+172
lowest score would be x
x+ 172 + x=176
2x=4
x=2
so x+172=174
ANSWER:D
Question: If the cost price is 40% of selling price. Then what is the profit percent.
A.150%
B.120%
C.130%
D.200%
Answer: A.150%
Explanation: Explanation:
Let the S.P = 100
then C.P. = 40
Profit = 60
Profit% = (60/40) * 100 = 150%. Answer: A
Question: Debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Debanshu averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
A.135
B.105
C.95
D.75
Answer: D.75
Explanation: Debanshu normally drives to work in 45 minutes at an average speed of 40 miles per hour.
Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Question: A river boat leaves Silver Town and travels upstream to Gold Town at an average speed of 6 kilometers per hour. It returns by the same route at an average speed of 8 kilometers per hour. What is the average speed for the round-trip in kilometers per hour?
A.6.8
B.7.1
C.7.2
D.7.5
Answer: A.6.8
Explanation: Pick a number which is LCM of 8 and 6 = 24.
Upstream time = 24/6 = 4 hrs
Downstream time = 24/8 = 3 hrs
Total time = 7 hrs
Total distance = 48
Average Speed = 48/7 =6.8km/hr
Question: If x^2 - y^2 = 2xy, then (x+y)^2 =
A.2x^2
B.3x^2
C.4xy
D.2y^2
Answer: A.2x^2
Explanation: Its B
x^2 -y^2 = 2xy
x^2 = 2xy + y^2
Add x^2 on both sides we get
x^2 +x^2 = x^2 +y^2 +2xy
2x^2 = (x+y)^2
Correct Option : A
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?
A.Rs.3944
B.Rs.3948
C.Rs.3942
D.Rs.3965
Answer: A.Rs.3944
Explanation: 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: A
Question: Dacid obtained 81, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
A.29
B.38
C.76
D.37
Answer: C.76
Explanation: Average = (81 + 65 + 82 + 67 + 85)/5
= 76.
Answer: C
Question: The smallest number which when diminished by 6, is divisible 12, 14, 16, 18 and 22 is:
A.11099
B.11094
C.11091
D.10323
Answer: B.11094
Explanation: Required number = (L.C.M. of 12, 14, 16, 18, 22 ) + 6
= 11088 + 6
= 11094
Answer: Option B
Question: While working alone at their respective constant rates, server G uploads 480 files in 4 hours and server Y uploads 480 files in 8 hours. If all files uploaded by these servers are the same size, how long would it take the two servers, working at the same time and at their respective constant rates, to process a total of 480 files?
A. 2 hr
B. 2hr 20 min
C. 2hr 40 min
D. 5 hr 40 min
Answer: C. 2hr 40 min
Explanation: Server G processes 480/4 files per hour = 120 per hour
Server Y processes 180/8 files per hour = 60 per hour
Total files processed per hour when G and Y work together = 120+60 per hour = 180 files per hour
480/180 = 2 2/3 hours=C
Question: 4, 2, -4, -8, 32, 26, -156, ?
A.-134
B.-144
C.-154
D.-164
Answer: D.-164
Explanation: 4 - 2 = 2,
2 * -2 = -4,
-4 - 4 = -8,
-8 * -4 = 32,
32 - 6 = 26,
26 * -6 = -156,
-156 - 8 = -164
ANSWER:D
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?
A.22%
B.88%
C.20%
D.94%
Answer: C.20%
Explanation: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers = 14.
Required percentage
= (14/70 * 100) = 20%
Answer:C
Question: A Fruit store sells four varieties of Mangoes. A,B,C & D. IF A Costs 20% less than B, and C costs 25% less than A,and D costs 35% less than C what percent of B's cost is D?
A.40%
B.39%
C.44%
D.36%
Answer: B.39%
Explanation: Soln:-
B=100
A 20% less than B = 80
C 25% less than A = 60
D 35% less than C = 39
D is what percent of B = D/B * 100
= 39/100 * 100 = 39%
ANSWER:B
Question: If six persons sit in a row, then the probability that three particular persons are always together is?
A.1/5
B.1/4
C.1/9
D.1/6
Answer: C.1/9
Explanation: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer:C
Question: Marla is hanging a banner diagonally across a rectangular room. The length of the room is 3 feet shorter than its width. If the total area of the room is 130 square feet, what is the length of the banner (in feet)?
A.between 16 and 17
B.between 17 and 18
C.between 18 and 19
D.between 19 and 20
Answer: A.between 16 and 17
Explanation: To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have
x(x - 3) = 130. By putting the equation in standard form, we get x^2-3x-130=0. By using the quadratic formula, we get roots of -10 and 13. We know that x is the width, and x-3 is the length, so by using the roots, we get 13 as the width (x), and 10 as the length (x-3).
Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=13^2+10^2
=169+100
=269
The square root of 269 is less than 17, since 17^2 = 289. Going down a number, we can compute 16^2 = 256 < 269. Therefore, the length of the diagonal must be between 16 and 17.
The correct answer is A.