mathewhe/aqua_rat huggingface dataset:
Question: Every day, Fred takes the train to travel from his work back to Alkmaar, his place of residence. Usually, he arrives at the station of Alkmaar at six o'clock, and exactly at that moment, his wife picks him up by car. Yesterday evening, Fred took an earlier train, without informing his wife, and therefore he already was at the station of Alkmaar at five o'clock. He decided to walk part of the way to meet his wife. When he met the car with his wife, he drove home with her. In this way, they were home ten minutes earlier than normal. Fred's wife always drives the entire way between home and station at the same constant speed.How long did Fred walk yesterday evening?
(A) 55
(B) 45
(C) 58
(D) 65
(E) 59
Rationale: Fred's wife needed to drive ten minutes less than usual, which is five minutes less in the direction of the station and five minutes less back home. Therefore, Fred met his wife at five minutes to six. He had walked already since five o'clock, so he walked 55 minutes in total.
Answer A
Answer: (A) 55
Question: An article is bought for Rs.1200 and sold for Rs.800, find the loss percent?
(A) 16%
(B) 35%
(C) 33%
(D) 18%
(E) 12%
Rationale: 1200 ---- 400
100 ---- ? => 33%
Answer:C
Answer: (C) 33%
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. 48?
(A) A)Rs.3944
(B) B)Rs.3948
(C) C)Rs.3264
(D) D)Rs.3949
(E) E)Rs.3923
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 48 = Rs.3264.
Answer: C
Answer: (C) C)Rs.3264
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 8 months. At this time, the construction was behind schedule by how many projects?
(A) 34
(B) 96
(C) 198
(D) 164
(E) 504
Rationale: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*8 =272
Lag :272-108 = 164
D is the answer
Answer: (D) 164
Question: In an election, candidate A got 65% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
(A) 355600
(B) 355800
(C) 356500
(D) 309400
(E) 357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 65 %
Therefore, the number of valid votes polled in favour of candidate A = 65 % of 476000
= 65/100 × 476000
= 30940000/100
= 309400
D)
Answer: (D) 309400
Question: If xy = 2 and x^2 + y^2 = 12, then x/y + y/x =
(A) 6
(B) 3 1/7
(C) 5 1/3
(D) 7
(E) 60
Rationale: We can make simplifying of question and get it in view: (x^2 + y^2) / xy and as we know the meaning of this parts:
x^2 + y^2 = 12
xy = 2
we can calculate the answer 12/2 -> 6 so answer is A
Answer: (A) 6
Question: If $25,000,000 is the initial amount placed in an account that collects 7% annual interest, which of the following compounding rates would produce the largest total amount after two years?
(A)  compounding daily
(B)  compounding quarterly
(C)  compounding monthly
(D)  compounding annually
(E)  All four of these would produce the same total
Rationale: This will produce the maximum yield as the interest accured each day will be added the very next day to the Principal amount for further computation of interest.
This process will be repeated every day till the amount matures
Compounding annually will give least returns
Answer = A
Answer: (A)  compounding daily
Question: Each of the integers from 3 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into hat. If the slips are then drawn one at a time without replacement, how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Answer is 4. In the worst case, you could end up drawing 3,4,5. 7th draw will result in either of 6,7,8,9 which would result in the numbers adding to 10.
B
Answer: (B) 4
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 266
(B) 288
(C) 245
(D) 211
(E) 776
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer: C
Answer: (C) 245
Question: One fourth of one third of two fifth of a number is 10. What will be40% of that number
(A) A)140
(B) B)150
(C) C)120
(D) D)200
(E) E)220
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 10
then x = 10 * 30 = 300
40% of 300 = 120
Answer: Option C
Answer: (C) C)120
Question: The value of (2.502+0.064)^2 - (2.502-0.064)^2/2.502*0.064
(A) .25
(B) .235
(C) 4
(D) 3
(E) 2
Rationale: (2.502+0.064)2 - (2.502-0.064)2/2.502*0.064 = (a+b)2 - (a-b)/ab
= 4ab/ab
= 4
ANSWER:C
Answer: (C) 4
Question: A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:
(A) 588 apples
(B) 600 apples
(C) 672 apples
(D) 700 apples
(E) 720 apples
Rationale: Explanation:
Suppose originally he had x apples.
Then, (100 - 40)% of x = 420.
60	x x = 420
100
x =(420*100 /60)=700.
ANSWER IS D
Answer: (D) 700 apples
Question: What percentage of numbers from 1 to 95 have squares that end in the digit 0?
(A) 1
(B) 14
(C) 9.47
(D) 21
(E) 22
Rationale: 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 95 are 10,20,30,40,50,60,70,80,90.
Number of such numbers = 14.
Required percentage = (9/95 * 100) = 9.47%
ANSWER:C
Answer: (C) 9.47
Question: What is the angle between the 2 hands of the clock at 8:24 pm?
(A) 100°
(B) 107°
(C) 106°
(D) 108°
(E) None of these
Rationale: Required angle = 240 – 24 × (11/2)
= 240 – 132 = 108°
Answer D
Answer: (D) 108°
Question: A man can do a piece of work in 9 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?
(A) 7 1/2 days
(B) 6 1/2 days
(C) 5 1/2 days
(D) 4 1/2 days
(E) None of these
Rationale: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily
get the other person work just by subtracting them. As
Son's one day work =
(1/3−1/9)=(6−2)/18=2/9
So son will do whole work in 9/2 = 4 1/2 days
Answer: D
Answer: (D) 4 1/2 days
Question: The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?
(A) 1
(B) 20
(C) 0
(D) 19
(E) 20
Rationale: Explanation:
Average of 20 numbers = 0
=> Sum of 20 numbers/20= =0
=> Sum of 20 numbers = 0
Hence at the most, there can be 19 positive numbers.
(Such that if the sum of these 19 positive numbers is x, 20th number will be- x)
Answer: Option D
Answer: (D) 19
Question: A meal cost $ 48.75 adn there was no tax. If the tip was more than 5 pc but less than 20pc of the price, then the total amount paid should be:
(A) 60-65
(B) 55-58
(C) 51-59
(D) 39-41
(E) 38-40
Rationale: 5%(48.75) = 2.4375
20%(48.75) = 9.75
total amount could have been 48.75+2.4375 and 48.75+9.75
=> could have been between 51.1875 and 58.5
=> approximately between 51 and 59
Answer is C.
Answer: (C) 51-59
Question: Solve below question 2x + 1 = -17
(A) -8
(B) -9
(C) -5
(D) -4
(E) 1
Rationale: 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
Answer: (B) -9
Question: The units digit of (35)^(87) + (93)^(46) is:
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
Rationale: Step 1: (35)^(87) can be broken up into (5)^87 x (7)^87. Each power of 7 ends in a units digit of either a 7,9,3 or 1. Each power of 5 ends in a 5. When you multiply 5 by any odd number you will end up with a units digit of 5.
Step 2: (93)^(46) can be broken up into (3)^46 x (31)^46. Each power of 31 ends in a units digit of 1. Each power of 3 ends in a units digit of either 3,9,7 and 1. Since there is a pattern here where every 4th power of 3 ends in a units digit of 3, the 46th power of 3 would end in a units digit of 9. When you multiply 1 by 9 you end up with a units digit of 9.
Therefore, the units digit we are looking for is 5 + 9 = 14. Units digit will be 4. Answer B.
Answer: (B) 4
Question: Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability T, that a book selected at random is either a hard cover book or a chemistry book?
(A) 1/10
(B) 3/20
(C) 1/5
(D) 1/4
(E) 9/20
Rationale: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, T=9 provide the desired outcome, making the answer E.
Answer: (E) 9/20
Question: 80% of the population of a village is 32000. The total population of the village is?
(A) 40000
(B) 24000
(C) 26682
(D) 29973
(E) 12312
Rationale: X * (80/100) = 32000
X = 400 * 100
X = 40000
Answer: A
Answer: (A) 40000
Question: What is the % change in the area of a rectangle when its length increases by 20% and its width decreases by 20%?
(A) 0%
(B) 20% increase
(C) 20% decrease
(D) 4% decrease
(E) Insufficient data
Rationale: (12/10)*(8/10) = 96/100 of original area
96/100 is a 4% decrease from 100/100 ->D
Answer: (D) 4% decrease
Question: In a class of 45 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
(A) 30
(B) 10
(C) 18
(D) 23
(E) 32
Rationale: Total=English+German-Both+Neither --> 45=English+22-12+0 --> English=35 --> Only English=English-Both=35-12=23.
Answer: D.
Answer: (D) 23
Question: A 160 meter long train crosses a man standing on the platform in 12 sec. What is the speed of the train?
(A) 48 kmph
(B) 54 kmph
(C) 92 kmph
(D) 86 kmph
(E) 76 kmph
Rationale: S = 160/12 * 18/5 = 48 kmph
ANSWER:A
Answer: (A) 48 kmph
Question: Two persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 63
(B) 10
(C) 28
(D) 27
(E) 12
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 700 / (15 + 25)5/18 = 700* 18 / 40 * 5 = 63 seconds.
Answer: A
Answer: (A) 63
Question: If a 10 percent deposit that has been paid toward the purchase of a certain product is $105, how much more remains to be paid?
(A) $945
(B) $965
(C) $1025
(D) $1050
(E) $1105
Rationale: 90% remains to be paid so the remaining amount is 9*105=$945.
The answer is A.
Answer: (A) $945
Question: TATA company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
(A)  3,024
(B)  4,536
(C)  5,040
(D)  9,000
(E)  10,000
Rationale: TATA company plans to assign identification numbers to its employeeS.The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.
Total = 9*9*8*7 = something with the units digit if 6.
Answer: B.
Answer: (B)  4,536
Question: A first grade teacher uses eight cards, each numbered from 1 to 8, to teach her students to order numbers correctly. She has students choose four flash cards randomly, then arrange the cards in ascending order. One day, she removes the cards '2' and '4' from the deck. On that day, how many different correct arrangements of four randomly selected cards are possible?
(A) 70
(B) 15
(C) 60
(D) 45
(E) 33
Rationale: problem of combination 6C4 = 6!/4!*(6-4)! = 6*5*4!/4!*2! =15
B
Answer: (B) 15
Question: How much is 60% of 40 is greater than 4/5 of 25?
(A) 4
(B) 6
(C) 10
(D) 8
(E) 13
Rationale: 60/100) * 40 â€“ (4/5) * 25
24 - 20 = 4
Answer: A
Answer: (A) 4
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 10 days
(B) 5 days
(C) 6 days
(D) 24 days
(E) 18 days
Rationale: Explanation:
B = 1/8 – 1/2 = 1/24 => 24 days
Answer D
Answer: (D) 24 days
Question: Two friends P & Q started a business investing amounts in the ratio of 5 : 6. R joined them after six months investing an amount equal to that of Qâ€™s amount. At the end of the year 32% profit was earned which was equal to 98,000. What was the amount invested by R?
(A) 2,10,000
(B) 1,05,000
(C) 1,75,000
(D) Data inadequate
(E) 65625
Rationale: Ratio for amount invested by P, Q & R
= 5x Ã— 12 : 6x Ã— 12 : 6x Ã— 6
= 60x : 72x : 36x
= 5x : 6x : 3x
Profit = 98000 = 32% of T
where, T = Total amount
T = 306250
Amount received by
R = 3x /3x+6x+5x(306250)
= 65625
Answer E
Answer: (E) 65625
Question: Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
(A) 4800
(B) 6400
(C) 2280
(D) 3400
(E) 3490
Rationale: B
6400
Let the sum invested in Scheme A be x and that in Scheme B be (13900 - x).
Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2)/100 = 3508
28x - 22x = 350800 - (13900 x 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = (13900 - 7500) = 6400.
Answer: (B) 6400
Question: If P is a prime number greater than 7, what is the remainder when P^2 is divided by 8.
(A) 4
(B) 3
(C) 1
(D) 2
(E) Cannot be determined
Rationale: take square of any prime number
remainder will be 1
Ans C
Answer: (C) 1
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.35 – 6.35*?
(A) 0.35
(B) 0.5
(C) 6.25
(D) 0.25
(E) 6.0
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.35* =6 (the greatest positive even integer less than or equal to 6.35 is 6).
Hence, 6.35 – 6.35* = 6.35 - 6 = 0.35
Answer: A.
Answer: (A) 0.35
Question: Margaret is 9 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages
(A) 21yrs
(B) 20yrs
(C) 30yrs
(D) 40yrs
(E) 50yrs
Rationale: Let, age of son x=12
Margaret is 9 years more than twice the age of his son, y = 9+2(x)
=9+2(12)
=9+24
=33yrs
Difference = 33 - 12
=21yrs
ANSWER:A
Answer: (A) 21yrs
Question: The total marks obtained by a student in Mathematics and Physics is 70 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 40
(B) 45
(C) 27
(D) 28
(E) 22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 70 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (70 + 20) / 2 = 45.Answer:B
Answer: (B) 45
Question: There are 4 people who has to cross a stretch of 300 km. They normally run at a speed of 10 kmph. One of them has a bike that travels at 50 kmph. The bike first takes one person alone and crosses the stretch while the other two keep running. Then he comes back without wasting time and picks up from the way, drives him across the stretch, and does the same for the last person. How long does this whole process take?
(A) 24 hrs
(B) 16 hrs
(C) 56/3 hrs
(D) 58/3 hrs
(E) 48/3 hrs
Rationale: Time taken to carry 2nd person = 300/50 = 6 hrs.
Time taken to meet 3rd person =(300-6*10)/(50+10) = 4 hrs
Time taken to carry 3rd person = 4 hours
Time taken to meet 4th person = (300 –140)/60 = 8/3
Total time = 6+4+4+8/3+8/3 = 58/3 hours
ANSWER:D
Answer: (D) 58/3 hrs
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 3 minutes A is turned off. After how much more time will the cistern be filled?
(A) 8 1/7
(B) 8 1/1
(C) 8 1/4
(D) 8 1/2
(E) 8 3/7
Rationale: 3/12 + (3 + x)/15 = 1
x = 8 1/4
Answer: C
Answer: (C) 8 1/4
Question: A store reported total sales of $385 million for February of this year. If the total sales for the same month last year was $340 million, approximately what was the percent increase in sales?
(A) 2%
(B) 17%
(C) 20%
(D) 65%
(E) 13%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 385 million
February sales last year = 340 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 385 million and the old value = 340 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(385 – 340)/340] x 100
65/340 x 100
≈ 13%.
The answer is E.
Answer: (E) 13%
Question: If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?
(A) 3 days
(B) 4 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself
A)
Answer: (A) 3 days
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations W of soloists can appear in the liner notes?
(A) 5!
(B) 10!/(5!5!)
(C) 10!/5!
(D) 10!
(E) 10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations W of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: (B) 10!/(5!5!)
Question: A business school club, Friends of Foam, is throwing a party at a local bar. Of the business school students at the bar, 40% are first year students and 60% are second year students. Of the first year students, 45% are drinking beer, 30% are drinking mixed drinks, and 25% are drinking both. Of the second year students, 30% are drinking beer, 30% are drinking mixed drinks, and 20% are drinking both. A business school student is chosen at random. If the student is drinking beer, what is the probability that he or she is also drinking mixed drinks?
(A) 2/5
(B) 4/7
(C) 11/18
(D) 17/24
(E) 17/10
Rationale: Suppose there are 100 students
Group A : 40% = 40 students
45% drink beer = 18
30% mixed = 12
25% both = 10
Group B 60% = 60
30% beer= 18
30% mixed = 18
20% both= 12
now we need both ( beer + mixed = both)
probability = total beer drinker = 18+18 =36 and both = 20
thus 22/36 = 11/18
Hence C
Answer: (C) 11/18
Question: Two employees X and Y are paid a total of Rs. 770 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) s.150
(B) s.200
(C) s.250
(D) s.350
(E) s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 770
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 770
â‡’ y[12/10 + 1] = 770
â‡’ 22y/10 = 770
â‡’ 22y = 7700
â‡’ y = 700/22 = 700/2 = Rs.350
D)
Answer: (D) s.350
Question: How many arrangements of the letters of the word ORANGES can be made, without changing the place of the vowels in the word?
(A) 22
(B) 29
(C) 24
(D) 28
(E) 30
Rationale: O,A,E fixed. Consonants can be arrangements in 4P4 = 4! = 24 ways
Option 'C'
Answer: (C) 24
Question: A single discount % equal to three successive discounts of 30%, 20% and 10%.
(A) 49.8
(B) 49.5
(C) 49.3
(D) 49.6
(E) 49.1
Rationale: Explanation:
Let the initial price be 100.
30% discount on 100 is 30
(100 – 30) = 70
20% discount on the 70 is 14
(70 – 14) = 56
10%discount on the 56 is 5.6
So the answer is 30 + 14 + 5.6 = 49.6
Answer: D
Answer: (D) 49.6
Question: 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women working together finish it ?
(A) 30 days
(B) 40 days
(C) 50 days
(D) 60 days
(E) 70 days
Rationale: Explanation:
Let 1 man's 1 day work = x
and 1 woman's 1 days work = y.
Then, 4x + 6y = 1/8
and 3x+7y = 1/10
solving, we get y = 1/400 [means work done by a woman in 1 day]
10 women 1 day work = 10/400 = 1/40
10 women will finish the work in 40 days
Option B
Answer: (B) 40 days
Question: A cube is divided into 64 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 30
Rationale: Each side of the cube has 4 x 4 = 16 cubelets.
Only the interior cubelets are painted one colour.
On each side, 2 x 2 = 4 cubelets are painted one colour.
Since the cube has six sides, the number of cubes with one colour is 6*4 = 24
The answer is D.
Answer: (D) 24
Question: In a college the ratio of the numbers of boys to the girls is 5:7. If there are 140 girls, the total number of students in the college is?
(A) 200
(B) 240
(C) 160
(D) 250
(E) 310
Rationale: Let the number of boys and girls be 5x and 7x
Then , 7x = 140
x= 20
Total number of students = 12x = 12*20 = 240
Answer is B
Answer: (B) 240
Question: 32 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
(A) 2√2
(B) 2√5
(C) 5
(D) 4√2
(E) 8
Rationale: Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 32
=> x/360*2*pi*r +2r= 32
=> 2A/r+2r=32
=> A= r16-r^2
= r16-r^2
We will now max using derivations
Max value of A will found at A=0
i.e 16-2r=0
r=8
E
Answer: (E) 8
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 200 meters, how long will it take to cross a railway platform 240 meters long
(A) 6 ½ sec
(B) 7 ½ sec
(C) 12 sec
(D) 8 ½ sec
(E) 9 sec
Rationale: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (200 + 240) m = 440 m.
Time taken =440×(3/110) sec =12 sec
Answer: Option C
Answer: (C) 12 sec