mathewhe/aqua_rat huggingface dataset:
Question: A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
(A) 290
(B) 304
(C) 285
(D) 270
(E) 275
Rationale: In a month of 30 days beginning with a Sunday, there will be 4 complete weeks and another two days which will be Sunday and Monday.
Hence there will be 5 Sundays and 25 other days in a month of 30 days beginning with a Sunday
Average visitors on Sundays = 510
Total visitors of 5 Sundays = 510 × 5
Average visitors on other days = 240
Total visitors of other 25 days = 240 × 25
Total visitors = (510 × 5) + (240 × 25)
Total days = 30
Average number of visitors per day
=((510×5)+(240×25))/30
=((51×5)+(24×25))/3
=(17×5)+(8×25)=85+200=285
Answer is C.
Answer: (C) 285
Question: A circle in the coordinate plane passes through points (-3, -2) and (-1, -4). What is the smallest possible area of that circle?
(A) 13π
(B) 26π
(C) 262√π
(D) 52π
(E) 4π
Rationale: The distance between the two points is sqrt(8)
radius = sqrt(8)/2
Area= pi*(sqrt(8)/2)^2
E.4π
Answer: (E) 4π
Question: IT COSTS RE 1.TO PHOTOGRAPHY A SHEET OF PAPER. HOWEVER, 2% DISCOUNT IS ALLOWED ON ALL PHOTOCOPIES DONE AFTER FIRST 100 SHEETS.HOW MUCH WILL IT COST TO COPY 5000 SHEETS OF PAPER?
(A) RS.3920
(B) RS.3980
(C) RS.4900
(D) RS.4920
(E) NONE OF THESE
Rationale: TOTAL COST =RS.(1*100+(100-2)% OF 1*4000)
=RS.(10000+0.98*4000)=RS.(1000+3920)RS.4920
CORRECT OPTIONS: D
Answer: (D) RS.4920
Question: If Janice was 23 years old z years ago and Lisa will be 21 years old in p years, what was the average (arithmetic mean) of their ages 7 years ago?
(A) (z + p)/2
(B) (z - p + 30)/4
(C) (z - p + 20)/4
(D) (z + p + 40)/2
(E) (z - p + 30)/2
Rationale: Today, J = z+23 and L = 21-p
7 years ago, J = z+16 and L = 14-p
The average of their ages was (z-p+30) / 2
The answer is E.
Answer: (E) (z - p + 30)/2
Question: Jackson has $313,196 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,196 = 23 and 18 is divisible by 9.
Hence we need to subtract 5 to this number for it to be divisible by 9
Correct Option: E
Answer: (E) $5
Question: During a trip, joe traveled x percent of the total distance at an average speed of 30 miles per hour and the rest of the distance at an average speed of 40 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
(A) (180-x)/2
(B) (x+60)/4
(C) (300-x)/5
(D) 600/(115-x)
(E) 12000/x+300
Rationale: total distance =100 ;total time = T
t1 = x/30 t2 = 100-x /40
T =t1+t2 = x/30 + 100-x/40 = (40x + 3000- 30x)/1200
= (10x+3000)/1200
= x+300/120
av speed = 100*120/x+300 = 12000/x+300
E
Answer: (E) 12000/x+300
Question: An bus covers a certain distance at a speed of 200 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 920 km/hr
(B) 970 km/hr
(C) 996 km/hr
(D) 1021 km/hr
(E) 1000 km/hr
Rationale: Distance = (200 x 5) = 1000 km.
Required speed = 1000 km/hr
E
Answer: (E) 1000 km/hr
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 9.5km apart, if they walk in the same direction?
(A) 15 hours
(B) 16 hours
(C) 17 hours
(D) 18 hours
(E) 19 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 9.5 km
Time = Distance/Speed
Time= 9.5km / 0.5 kmph = 19 hrs
answer :E
Answer: (E) 19 hours
Question: There are 13 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 13 points that contain the point A?
(A) 66
(B) 105
(C) 182
(D) 210
(E) 455
Rationale: Any 2 points out 12 points will create triangle with third point A, so the answer is 12C2=66.
Answer: A.
Answer: (A) 66
Question: Find out the C.I on Rs.1000 at 4% p.a. compound half-yearly for 1 1/2 years.
(A) A)Rs.41.20
(B) B)Rs.51.20
(C) C)Rs.61.20
(D) D)Rs.71.20
(E) E)Rs.81.20
Rationale: A = 1000(51/50)3
= 1061.20
1000
-----------
61.20
ANSWER:C
Answer: (C) C)Rs.61.20
Question: A car takes 6 hours to cover a distance of 324 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 65 Kmph
(D) 36 Kmph
(E) None
Rationale: Time = 6
Distence = 324
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 324/9 = 36 Kmph
D)
Answer: (D) 36 Kmph
Question: A baseball card decreased in value 10% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 19%
(B) 30%
(C) 32%
(D) 36%
(E) 72%
Rationale: consider the initial value of the baseball card as $100
After first year price = 100*0.9 = 90
After second year price = 90 *0.9 = 81
final decrease = [(100 - 81)/100] * 100 = 19%
correct answer - A
Answer: (A) 19%
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 46 years. What will be the age of the B ten years hence?
(A) 39
(B) 92
(C) 28
(D) 96
(E) 26
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 46 => b + c = 92 --- (2)
Answer: B
Answer: (B) 92
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
(A) If x>y
(B) X>=Y
(C) If x < y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Answer: (B) X>=Y
Question: Sarah is driving to the airport. After driving at 25 miles per hour for one hour, she realizes that if she continues at that same average rate she will be an hour late for her flight. She then travels 50 miles per hour for the rest of the trip, and arrives 30 minutes before her flight departs. How many miles did she drive in all?
(A) 100
(B) 175
(C) 210
(D) 245
(E) 280
Rationale: After driving at 25 miles per hourfor one hour, this distance left to cover is d-25. Say this distance is x miles.
Now, we know that the difference in time between covering this distance at 25 miles per hour and 50 miles per hour is 1+ 1/2 = 3/2 hours.
So, we have that x/25 - x/50 = 3/2 --> 2x/50 - x/50 = 3/2 --> x/50 = 3/2 --> x = 75.
Total distance = x + 25 = 100 miles.
Answer:A
Answer: (A) 100
Question: 12 men take 36 days to do a work while 12 women complete 3/4th of the same work in 36 days. In how many days 10 men and 8 women together will complete the same work?
(A) 6 days
(B) 12 days
(C) 27 days
(D) 28 days
(E) None of these
Rationale: Explanation:
1 man’s 1 day’s work = 1/ 36 × 12 = 1/432
10 men’s 1 day’s work = 10/432
12 women can finish the whole work in 4 × 36/3 = 48 days
1 woman’s 1 days work = 1/ 48 × 12 = 1/576
8 women’s 1 day’s work = 8/572 = 1/72
(10 men + 8 women)’s 1 day’s work = 10/432 + 1/72 = 10 + 6/432 = 16/432
= 1/27
Therefore, the required No. of days = 27 days.
Answer: Option C
Answer: (C) 27 days
Question: The ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250.The sum of the numbers is :
(A) 30
(B) 50
(C) 60
(D) 90
(E) 40
Rationale: Solution
Let the numbers be 3x,4x and 5x.Then,
9x2+6x2+25x2 = 1250=50x2= 1250=x2 = 25=x = 5.
∴ Sum of numbers = (3x+4x+5x) = 12 x =(12x5) = 60.
Answer C
Answer: (C) 60
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
(A) 229
(B) 787
(C) 144
(D) 128
(E) 121
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
Answer: C
Answer: (C) 144
Question: x^2 + sx + 72 = 0 has two distinct integer roots; how many values are possible for s?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
Rationale: For a quadratic equation ax^2+sx+c=0, we know that -s/a is sum of roots and c/a is product of roots.
The quadratic equation here is x^2 + sx + 72 = 0, where product of roots is 72.
If we find all the factors of 72, we have the answer.
By prime factorization, we get 72= 2^3*3^2.
We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D
Answer: (D) 12
Question: Look at this series: 8, 43, 11, 41, __, 39, 17, ... What number should fill in the blank?
(A) 22
(B) 33
(C) 14
(D) 16
(E) 18
Rationale: C
14
This is a simple alternating addition and subtraction series. The first series begins with 8 and adds 3; the second begins with 43 and subtracts 2.
Answer: (C) 14
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 750
(B) 7500
(C) 8500
(D) 1500
(E) 7503
Rationale: A : B : C = 20000*24 : 15000*24 : 20000*18 = 20*4 : 15*4 : 20*3
= 4*4 : 3*4 : 4*3
= 4:3:3
Answer is B
B's Share = (25000 * 3)/10 = 7500
Answer: (B) 7500
Question: A word is defined as a sequence of five dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
(A) 10
(B) 16
(C) 24
(D) 32
(E) 40
Rationale: 2^5 = 32
The answer is D.
Answer: (D) 32
Question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
(A) 8/3
(B) 2/1
(C) 8/5
(D) 5/8
(E) 5/3
Rationale: Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 450/3 = 150 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 150/75 = 2/1
Answer B
Answer: (B) 2/1
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $230, what were her original savings?
(A) $900
(B) $800
(C) $1000
(D) $920
(E) $1500
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $230. So 1 / 4 of her savings is $230. So her original savings are 4 times $230 = $920
correct answer D
Answer: (D) $920
Question: Find the largest number of four digits which is exactly divisible by 27,18,16,15
(A) 8600
(B) 8610
(C) 8620
(D) 8630
(E) 8640
Rationale: Explanation:
LCM of 27-18-16-15 is 2160.
After dividing 9999 by 2160 we get 1359 remainder.
So answer will be 9999-1359 = 8640
Option E
Answer: (E) 8640
Question: A train passes a station platform in 33 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 195 m
(B) 240 m
(C) 300 m
(D) 360 m
(E) 280 m
Rationale: Speed = 54 x	5/18	m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then,	(x + 300)/33	= 15
x + 300 = 495
x = 195 m.Answer: Option A
Answer: (A) 195 m
Question: A husband and wife can complete a certain task in 2 and 3 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 6 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task?
(A) a)15:46
(B) b)1:2
(C) c)12:23
(D) d)5:18
(E) e)10:3
Rationale: couples one hour work=1/2+1/3=5/6
so total time=6/5..
now, kids one hour work=1/4+1/6=5/12
so total time=12/5..
ratio=6/5:12/5=1/2
ans B
Answer: (B) b)1:2
Question: Murphy and Cooper are having the same amount of petrol in the petrol tanks of their respective cars. Murphy can drive for four hours with that amount whole Cooper can drive for five hours.
They both starts together and keep driving for a few hours. After some time, they find that the amount of petrol remaining in one car is four times that of the other car.
Using all these facts, can you find out how long they drove their cars?
(A) 2 3/4 hours.
(B) 3 3/4 hours.
(C) 4 3/4 hours.
(D) 5 3/4 hours.
(E) 6 3/4 hours.
Rationale: Solution:
3 3/4 hours
Explanation:
Suppose that the amount of petrol in each of the cars in the beginning was M.
Now, suppose that they drove for X hours.
In that case, the amount of petrol used by one car in X hours will be = M*X /4
The amount of petrol used by the other car will be = M*X/5
Therefore, the petrol left in one car = M - M*X / 4
Petrol left in the other car = M - M*X / 5
Now, according to the question,
M - M*X / 5 = 4 (M - M*X / 4)
=> X = 15 / 4 = 3 3/4 hours.
Therefore Murphy and Cooper drove for 3 3/4 hours.
Answer B
Answer: (B) 3 3/4 hours.
Question: If e is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
(A) √n + 1
(B) n + 1
(C) n^2 + 1
(D) e + 2√e + 1
(E) n^2 + 2n + 1
Rationale: If n is the square of a positive integer, which of the following must be equal to the square of the next positive integer?
e = (x)^2 where x is a positive integer
To calculate -
(x+1)^2 = x^2 + 2x + 1
root(e) = x
Ans - e + 2 root(e) + 1
This should beD
Answer: (D) e + 2√e + 1
Question: What is the positive difference between the sum of the squares of the first 5 positive integers and the sum of the prime numbers between the first square and fourth square?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
the sum of the squares of the first 4 positive integers = 1^2 + 2^2 + 3^2 +4^2+5^2 = 55
the sum of the prime numbers between the first square(=1) and fourth square(=16) = 2+3+5+7+11+13=41.
So the difference between 41 and 55 is 14.
So the answer is (D).
Answer: (D) 14
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum X of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A)  6x
(B)  4x
(C)  5x/3
(D)  3x/2
(E)  3x/5
Rationale: Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<X<5x --> only option B fits.
Answer: B.
Answer: (B)  4x
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 6
(B) 5
(C) 7
(D) 9
(E) 2
Rationale: C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days
Answer:D
Answer: (D) 9
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 8 years
(C) 10 years
(D) 12 years
(E) 14 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years. Answer: Option A
Answer: (A) 4 years
Question: A computer program assigns consecutive numbers to the days of the week. Sunday is 1, Monday is 2, ..... and Saturday is 7. Every day, the computer program calculates the value of parameter D according to the following definition: D is the number of the day times the value of D on the previous day. If the computer calculated D to be 16 on Wednesday, what would be the value of D calculated on the following Saturday?
(A) 2520
(B) 2940
(C) 3360
(D) 3780
(E) 4150
Rationale: On Saturday, the value would be 7*6*5*16 = 3360
The answer is C.
Answer: (C) 3360
Question: which of the following could be the greatest common factor of positive integers a and b?
I. 1
II. a
III. a-b
(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III
Rationale: It could be 1 if a and b are co-prime, for example, 1 and 2, 11 and 13...
It could be a itself if a is a factor of b, for example, 2 and 4, 5 and 15...
It could be a-b, for example, when a=b+1: a=2 and b=1, a=3 and b=2...
Answer: E.
Answer: (E) I, II and III
Question: At an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?
(A) 239
(B) 700
(C) 278
(D) 260
(E) 1711
Rationale: Explanation:
Let the total votes are 100x. Then winning candidate got 84x, and losing candidate got 16x.
⇒ 84x – 16 x = 476
⇒ 68 x = 476
⇒ x = 7
Total votes are 700.
Answer: B
Answer: (B) 700
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
(A) 144º
(B) 150º
(C) 168º
(D) 180º
(E) 190º
Rationale: Angle traced by the hour hand in 6 hours =360/12x 6º= 180º.
Answer: Option D
Answer: (D) 180º
Question: A cistern which could be filled in 4 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
(A) 76 hrs
(B) 99 hrs
(C) 55 hrs
(D) 20/3 hrs
(E) 11 hrs
Rationale: 1/4 - 1/x = 1/10
=> 20/3 hrs
Answer: D
Answer: (D) 20/3 hrs
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
(A) 1:96
(B) 1:97
(C) 1:99
(D) 1:28
(E) 1:29
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144
= 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas
= 3x : 12x2 = 1 : 4x
= 1:96.
Answer:A
Answer: (A) 1:96
Question: The average mark obtained by 22 candidates in an examination is 45. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
(A) 2
(B) 0
(C) 9
(D) 8
(E) 6
Rationale: It is clear that 22 x 45 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 0
Answer:B
Answer: (B) 0
Question: If the product of the integers a, b, c and d is 770, and if 1 < a< b< c< d, what is the value of a+ d?
(A) 10
(B) 13
(C) 16
(D) 18
(E) 21
Rationale: 770 = 2 * 5 * 7 * 11
So a= 2, x = 5, c= 7, d= 11
a+ d= 2 + 11 = 13
Answer - B
Answer: (B) 13
Question: If a2 - b2 =11 and a*b = 5, find a4 + b4.
(A) 62
(B) 181
(C) 170
(D) 171
(E) 50
Rationale: a2 - b2 = 11 : given
a4 + b4 - 2a2b2 = 112 : square both sides and expand.
a*b = 2 : given
a2b2 = 52 : square both sides.
a4 + b4 - 2(25) = 121 : substitute
a4 + b4 = 171
correct answer D
Answer: (D) 171
Question: What number should replace the question mark?
16, 23, 19, 22, 15, 25, ?
(A) 10
(B) 18
(C) 11
(D) 22
(E) 26
Rationale: C
11
There are two alternate sequences: +3 and -4.
Answer: (C) 11
Question: At 1:00 pm, there were 10.0 grams of bacteria. The bacteria increased to x grams at 4:00 pm, and 16.9 grams at 7:00 pm. If the amount of bacteria present increased by the same fraction during each of the 3-hour periods, how many grams of bacteria were present at 4:00 pm?
(A) 13.0
(B) 13.3
(C) 13.6
(D) 13.9
(E) 14.2
Rationale: Let x be the factor by which the bacteria increases every three hours.
At 4:00 pm, the amount of bacteria was 10x and at 7:00 pm it was 10x^2.
10x^2 = 16.9
x^2=1.69
x=1.3
At 4:00 pm, the amount of bacteria was 10(1.3)=13 grams.
The answer is A.
Answer: (A) 13.0
Question: In a certain Gun shooting competition prizes were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points . No other points were awarded. John participated several times in the competition. The product of all the points he received was 84700. How many times did he participate in the competition.
(A) 7
(B) 5
(C) 3
(D) 2
(E) cannot be determined
Rationale: 84700 = 2*2*5*5*7*11*11
If the question stated that John atleast came 4th each time he participated, then we can say that John participated 7 times.
But, it is not stated how many times did John come fifth, sixth, seventh, etc.
Hence, Answer will be E.
Answer: (E) cannot be determined
Question: If each of 3 digit code is formed of integers from 1 to 25, inclusively, and each of the digits are different, how many possible codes are there?
(A) 13600
(B) 13500
(C) 13400
(D) 13800
(E) 13900
Rationale: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 25 possibilities
Second digit can have 24 possibilities
Third digit can have 23 possibilities
Total number of possible codes = 25*24*23 = 13800
Answer: D
Answer: (D) 13800
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?
(A) 3
(B) 4
(C) 5
(D) 2
(E) 7
Rationale: 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) 2
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.82 per glass on the first day, what was the price per glass on the second day?
(A)  $015
(B)  $0.20
(C)  $0.30
(D)  $0.40
(E)  $0.55
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.82=3*x --> x=$0.55.
Answer: E.
Answer: (E)  $0.55
Question: A car starts 2/5 of a mile behind a bus that is traveling at 60 miles per hour. If the car catches up to the bus after 2 minutes, how many miles does the car travel in that time?
(A) 2 1/10
(B) 2 2/5
(C) 2 1/2
(D) 2 7/8
(E) 3
Rationale: Car is travelling at a speed of 2/5 miles per 2 mins faster than the bus
i.e 12 mph faster than the buse
= 72 mph
So in 2 mins = 72 * 2/60 = 2.4
Answer is B.
Answer: (B) 2 2/5
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 28 seconds
(B) 27 seconds
(C) 40 seconds
(D) 128 seconds
(E) 18 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer: C
Answer: (C) 40 seconds
Question: Find the odd man out
74, 24, 82, 61, 10, 4
(A) 61
(B) 24
(C) 10
(D) 82
(E) 74
Rationale: 61 is the only odd number in the series.
ANSWER:A
Answer: (A) 61