mathewhe/aqua_rat huggingface dataset:
Question: Find the sum of prime numbers lying between 60 and 72?
(A) 198
(B) 201
(C) 199
(D) 272
(E) None
Rationale: Solution
Required sum	= 61 + 67 + 71)
= 199.
Answer C
Answer: (C) 199
Question: Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?
(A) 400
(B) 600
(C) 500
(D) 700
(E) 800
Rationale: N * 50 = (325000 - 300000) = 25000
N = 25000 / 50
= 500
C
Answer: (C) 500
Question: What is the greatest power that 7 can be raised to so that the resulting number is a factor of 21!?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: the number of 7s in 21!= 21/7=3..
ans B
Answer: (B) 3
Question: In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 2kmph
(B) 3kmph
(C) 8kmph
(D) 9kmph
(E) 7kmph
Rationale: Speed in still water = (11+5)/2
= 8 kmph
Ans- C
Answer: (C) 8kmph
Question: A, B, C hired a car for Rs. 520 and used it for 7,8 and 11 hours respectively. Hire charges paid by B were :
(A) 160
(B) 180
(C) 220
(D) 225
(E) None
Rationale: Sol.
A : B : C = 7 : 8 : 11.
Hire charges paid by B = Rs. [520 * 8/26] = Rs.160
Answer A
Answer: (A) 160
Question: If [B] denotes the least integer greater than or equal to B and [B] = 0, which of the following statements must be true?
(A) B = 0
(B) 0 <= B < 1
(C) 0 < B <= 1
(D) -1 < B <= 0
(E) -1 <= B < 0
Rationale: The answer for this is 0 < = B < = 1
However it is not available in the options. The match to the above is-1 < B <= 0
Answer = D
Answer: (D) -1 < B <= 0
Question: The average of non-zero number and its square is 5 times the number. The number is:
(A) 9
(B) 7
(C) 8
(D) 5
(E) 3
Rationale: Let the number be x. Then,
(x + x2)/2 = 5x => x2 - 9x = 0
=> x(x - 9) = 0
=> x = 0 or x = 9
So, the number is 9.
Answer: A
Answer: (A) 9
Question: Pipe A can fill a tank in 6 hours. Due to a leak at the bottom, it takes 9 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 67
(B) 88
(C) 18
(D) 26
(E) 12
Rationale: Let the leak can empty the full tank in x hours 1/6 - 1/x = 1/9
=> 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18
=> x = 18. Answer:C
Answer: (C) 18
Question: If 7 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
(A) 588
(B) 263
(C) 120
(D) 160
(E) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 7c2
for vertical 8c2
total parallelogram is 7 c2*8c2=21*28
=588
ANSWER:A
Answer: (A) 588
Question: The least number which is a perfect square and is divisible by each of the numbers 16,20, and 24, is :
(A) 1600
(B) 3600
(C) 6400
(D) 11400
(E) None of these
Rationale: Solution
The least number divisible by 16, 20, 24
= L.C.M. of 16, 20, 24 = 240 = 2 × 2 × 2 × 2 × 3 × 5.
To make it a perfect square it must be multiplied by 3 × 5.
∴ Required number = 240 × 3 × 5 = 3600. Answer B
Answer: (B) 3600
Question: In 2triangle, the ratio of the areas is 4:3 and that of their heights is 3:4. Find the ratio of their bases?
(A) 10:8
(B) 11:8
(C) 16:9
(D) 17:19
(E) 17:10
Rationale: Given a1/a2 =4/3, h1/h2=3/4
also, we know that
a1/a2=(1/2×b1×h1)/(1/2×b2×h2)
on substituting in above equation, we get
b1/b2= 16/9
therefore b1:b2= 16:9
C
Answer: (C) 16:9
Question: My age is two year more than twice than of Ram. If I am 34 years old, how old is Ram?
(A) 18
(B) 14
(C) 16
(D) 20
(E) 12
Rationale: myage = 2 + 2*Ram
34 = 2 + 2*Ram
2(Ram) = 32
Ram = 16
ANSWER:C
Answer: (C) 16
Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to r% of stall’s revenue and accounted for s% of sales of juice tetra packs. Which of the following expresses r in terms of s?
(A) 100s/(150 – s)
(B) 200s/(250-s)
(C) 200s/(300-s)
(D) 250s/(400-s)
(E) 300s/(500-s)
Rationale: 1. Let the number of units sold be 100. Then n units of A are sold and (100-n) units of B are sold.
Total revenue= Revenue due to A + Revenue due to B
= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)
= s *1 + (100-s) *1.5
= s + (150-1.5s) --- (1)
2. But we know, revenue due to A = r%. of the total revenue --- (2)
3. To express r in terms of s we need to relate (1) and (2)
4. r% = s / ( s + (150-1.5s))
or r= 100s / 150-0.5s = 200s/(300-s)
C
Answer: (C) 200s/(300-s)
Question: In an animal behavior experiment, 50 tagged white pigeons and 300 tagged gray pigeons were released from a laboratory. Within one week, 88 percent of the white pigeons and 80.5 percent of the gray pigeons had returned to the laboratory. What percent of the total number of pigeons returned to the laboratory?
(A) 80.5
(B) 82
(C) 81.75
(D) 85
(E) 86.5
Rationale: Weighted mix method is best here....
Ratio is 1:6 for 88:80.5...
So the answer required = 80.5+ (88-80.5)*1/6=80.5+7.5*1/6
80.5+1.75=81.75
C
Answer: (C) 81.75
Question: The product of all the prime numbers less than 15 is closest to which of the following powers of 10?
(A) 10^2
(B) 10^4
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11,13
3*10^4
A
Answer: (A) 10^2
Question: What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
(A) Rs. 2.04
(B) Rs. 3.06
(C) Rs. 4.80
(D) Rs. 6.30
(E) Rs. 8.30
Rationale: As per formula it should be,
C.I. when interest = 5304-5000 = 304
compounded yearly
C.I. when interest is = 5306.04-5000 = 306.04
compounded half-yearly
Difference = Rs. (306.04 - 304) = Rs. 2.04
answer :A
Answer: (A) Rs. 2.04
Question: What is the smallest number W which when increased by 5 is completely divisible by 8, 11 and 24?
(A) 264
(B) 259
(C) 269
(D) 270
(E) 282
Rationale: This question includes a number of great Number Property shortcuts that you can take advantage of:
1) The question asks for the SMALLEST number that, when increased by 5 is divisible by 8, 11 and 24. Since the answers are numbers, we can TEST THE ANSWERS.
2) Any number that is divisible by 24 is ALSO divisible by 8, so we really just need to consider the 11 and the 24.
3) To be divisible by 24, the end number MUST be EVEN. Since we're adding 5 to get to that end number, the starting number MUST be ODD.
The last shortcut allows us to eliminate Answers A, D and E. Between Answers B and C, TESTING B first will prove that, when increased by 5, the end sum is divisible by both 11 and 24.
Final Answer:
B
Answer: (B) 259
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 142 m length?
(A) 82.1 sec.
(B) 12.6 sec
(C) 19.1 sec.
(D) 17.1 sec.
(E) 42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 142 = 252 m.
Required time = 252/20 = 12.6 sec.
Answer: B
Answer: (B) 12.6 sec
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 66. What is the largest among them?
(A) 21
(B) 24
(C) 25
(D) 36
(E) 57
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 66
3X = 57
X = 19
The numbers are 19, 22, 25
Therefore the largest number is 25
Answer C.
Answer: (C) 25
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
(A) 2207 ways
(B) 1440 ways
(C) 1220 ways
(D) 2810 ways
(E) 2760 ways
Rationale: Explanation:
In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2 = 1440 ways.
Answer: B
Answer: (B) 1440 ways
Question: A bike covers a certain distance at the speed of 16km/h in 2 hrs. If the bike was to cover the same distance in approximately 4 hrs, at what approximate speed should the bike travel?
(A) 8 km/h
(B) 9 km/h
(C) 7 km/h
(D) 6 km/h
(E) 10 km/h
Rationale: Ans.(A)
Sol. Total distance = 16 × 2 = 32 km
Now speed = 32/4 = 8 km/h
Answer: (A) 8 km/h
Question: A snooker tournament charges $40.00 for VIP seats and $15.00 for general admission (“regular” seats). On a certain night, a total of 320 tickets were sold, for a total cost of $7,500. How many fewer tickets were sold that night for VIP seats than for general admission seats?
(A) 212
(B) 200
(C) 220
(D) 230
(E) 240
Rationale: let no of sits in vip enclosure is x then x*40 +15( 320-x) =7500 or 25x = 7500 -4800 , x = 2700/25 =108
vip =108 general 212
A
Answer: (A) 212
Question: Mariah has decided to hire three workers. To determine whom she will hire, she has selected a group of 15 candidates. She plans to have one working interview with 3 of the 15 candidates every day to see how well they work together. How many days will it take her to have working interviews with all the different combinations of job candidates?
(A) 720
(B) 120
(C) 300
(D) 360
(E) 333
Rationale: 360.
Answer D
Answer: (D) 360
Question: When divided by 5, x has a remainder of 4 and y has a remainder of 3. Which of the following could be the remainder when x + y is divided by 10?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 0
Rationale: x = 5k+4 and y = 5j+3
x+y = 5(j+k) + 7
When divided by 10, the remainder is either 7 or 2.
The answer is B.
Answer: (B) 7
Question: Brandon has cans of both diet soda as well as regular soda. The ratio of diet soda to regular soda is 3 to 7. He has 12 more cans of soda than diet. How many cans of diet soda does he have left?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Let x equal the cans of diet soda, and y equal the cans of regular soda.
Since we want to solve for x (cans of diet soda), we convert the ratio from 3/7 to 7/3.
So, we know that y = 7/3x.
We also know that y = x + 12.
We can simplify:
x + 12 = 7/3x
To isolate x, we get:
4/3x = 12
And to solve for x, we get:
x = 9
Answer: D
Answer: (D) 9
Question: Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:
(A) 30 km/hr
(B) 45 km/hr
(C) 60 km/hr
(D) 75 km/hr
(E) 65 km/hr
Rationale: Let the speed of the slower train be x
and the faster train = 2x
Relative speed = x+2x = 3x
therefore (100+100)/8 = 3x
=> x = 25/3
So, Speed of the faster train = 2(25/3) = 50/3 m/s = (50/3*18/5)km/hr = 60km/hr
ANSWER:C
Answer: (C) 60 km/hr
Question: The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35.
ANSWER:C
Answer: (C) 35
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2.
A)
Answer: (A) 2
Question: A number is increased by 40% and then decreased by 40%, the final value of the number is ?
(A) decrease by 13%
(B) decrease by 12%
(C) decrease by 16%
(D) decrease by 14%
(E) decrease by 15%
Rationale: Here, x = 40 and y = - 40
Therefore, the net % change in value
= ( x + y + xy/100)%
= [40 - 40 + (40 * -40)/100]% or - 16%
Since the sign is negative, there is a decrease in value by 16%.
ANSWER: C
Answer: (C) decrease by 16%
Question: Of the people who responded to a market survey, 150 preferred Brand X and the rest preferred Brand Y. If the respondents indicated a preference for Brand X over Brand Y by ratio of 5 to 1, how many people responded to the survey?
(A) 80
(B) 180
(C) 240
(D) 360
(E) 480
Rationale: Ratio = 5:1 => 5x respondents preferred Brand X and x preferred Brand Y
Since, no. of respondents who preferred Brand X = 150 => 5x=150 => x=30
Hence Total no. of respondents = 150 + 30 = 180
Hence B is the answer.
Answer: (B) 180
Question: A bag consists of 20 marbles, of which 5 are blue, 7 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
(A) 3/4
(B) 2/4
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: bag consists of 20 marbles, of which 5 are blue, 7 are red
remainder are white. So, white = 20 - 5 - 7 = 8.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 7/20+8/20 = 15/20 = 3/4
Hence, answer will be A.
Answer: (A) 3/4
Question: Exactly 36% of the numbers in set A are even multiples of 3. If 40% of the even integers in set A are not multiples of 3, what percent of the numbers in set A are not even integers?
(A)  76%
(B)  60%
(C)  50%
(D)  40%
(E)  24%
Rationale: Everything is correct except the red part with a typo: it should be N=0.6A --> even numbers are 60% of A --> 40% of A are not even integers.
Answer: D.
Answer: (D)  40%
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
(A) 4 hours
(B) 7 hours
(C) 8 hours
(D) 14 hours
(E) 15 hours
Rationale: Work done by the leak in 1 hour = (1/2 - 3/7) = 1/14
Leak will empty the tank in 14 hrs.
Answer = D
Answer: (D) 14 hours
Question: The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?
(A) 127
(B) 297
(C) 266
(D) 480
(E) 435
Rationale: 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48 = 480
Answer: D
Answer: (D) 480
Question: Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p + 5?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p + 5 is 6 + 5 = 11.
Answer: E.
Answer: (E) 11
Question: Walking with 4/5 of my usual speed, I arrive at the bus stop 6 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
(A) 20 min
(B) 22 min
(C) 15 min
(D) 18 min
(E) 24 min
Rationale: Let t = usual time = distance / usual speed
t + 6 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4
t = 24
The answer is E.
Answer: (E) 24 min
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) Rs.2.5
(B) Rs.2.7
(C) Rs.2.6
(D) Rs.7.5
(E) Rs.3.5
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer:A
Answer: (A) Rs.2.5
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 30 miles ahead of Joe?
(A) 150
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Joe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +30 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 30 miles in 120 mins
So answer 30+120= 150 mins. (ANSWER A)
Answer: (A) 150
Question: What is the square root of 81?
(A) 2
(B) 8
(C) 12
(D) 9
(E) 16
Rationale: 9X9 = 81
ANSWER D
Answer: (D) 9
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many D hours does it currently take Anne to clean the house on her own?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in D=3 hours)
Solving these 2 equations we can find B as 12
So, D
Answer: (D) 12
Question: The Malibu Country Club needs to drain its pool for refinishing. The hose they use to drain it can remove 60 cubic feet of water per minute. If the pool is 50 feet wide by 150 feet long by 10 feet deep and is currently at 80% capacity, how long will it take to drain the pool?
(A) 1000 min
(B) 1200min
(C) 1300 min
(D) 1400 min
(E) 1600 min
Rationale: volume of pool = 50*150*10 cu.ft , 80% full = 50*150*10*0.8 cu.ft water is available to drain.
draining capacity =60 cu.ft /min therefore time taken = 50*150*10*0.8/ 60 min= 1000min
A
Answer: (A) 1000 min
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $7 more than 1/4 of the fine and Peter paid $7 less than 1/3 of the fine, leaving pay $12 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
(A) $65
(B) $55
(C) $50
(D) $60
(E) $45
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 7] + [(1/3)F – 7] + [(1/2)F – 12]
F = (1/4)F + (1/3)F + (1/2)F – 12
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 144
12F = 13 F – 144
–F = – 144
F = 144
Well, if the fine cost $144, then Sam paid the part not covered by Joe or Peter. Half the fine is $72, and Sam paid $12 less than this: $60.
Answer = D
Answer: (D) $60
Question: A certain Dark Blue paint contains 40 percent blue pigment and 60 percent red pigment by weight. A certain green paint contains 40 percent blue pigment and 60 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
(A) 3.5
(B) 4
(C) 4.5
(D) 3
(E) 5
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.6 = 3 Grams of red pigment
Answer: (D) 3
Question: In a sale, a discount of 15% was available on all the articles. If Vinit purchased an article for Rs.4284 in the sale. What was the actual selling price of the article?
(A) Rs.5050
(B) Rs.5000
(C) Rs.5040
(D) Rs.4950
(E) Rs.4870
Rationale: Explanation:
i.e. Rs.4284 = 85% of SP
:. SP = 4284 x 100/84 = Rs.5040.
Answer: Option C
Answer: (C) Rs.5040
Question: A certain protective additive increases from 25 days to 30 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
(A) 25%
(B) 20%
(C) 50%
(D) 66 2/3%
(E) 75%
Rationale: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 30−25/25∗100=20
Answer: B.
Answer: (B) 20%
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 40 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A) A) 5.61
(B) B) 3.69
(C) C) 10
(D) D) 15
(E) E) 24
Rationale: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81
New time in minutes to cross 9 miles stretch = 9*60/40 = 9*3/2 = 13.5
Time difference = 3.69
Ans:B
Answer: (B) B) 3.69
Question: Solution A is 40% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
(A) 6:4
(B) 6:14
(C) 4:4
(D) 4:6
(E) 3:1
Rationale: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 40) = 3/1
So the volume of the two solutions will be equal. Answer has to be 3:1.
E
Answer: (E) 3:1
Question: How many integers between 334,700 and 458,600 have tens digit 1 and units digit 3?
(A) 10,300
(B) 10,030
(C) 1,353
(D) 1,352
(E) 1,239
Rationale: There is one number in hundred with 1 in the tens digit and 3 in the units digit:13, 113, 213, 313, ...
The difference between 334,700 and 458,600 is 458,600-334,700=123,900 - one number per each hundred gives 123,900/100=1,239 numbers.
Answer: E.
Answer: (E) 1,239
Question: Homer wants to read 2 books from his collection. He has 6 adventure books and 4 horror books. He chooses 2 books randomly and simultaneously. What is the probability that he chose 1 adventure book and 1 horror book?
(A) 16/25
(B) 24/45
(C) 7/8
(D) 12/105
(E) 10/24
Rationale: The probability is equal to the number of desired choices divided by the total number of possibilities.
Probability = Favorable/Total
Total = 10C2 = 10*9/2 = 45
Favorable:
Pick 1 adventure book out of 6 adventure books
AND
Pick horror book out of 4 horror books
6C1*4C1 = 6*4=24
P=24/45
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Thus,
Total Probability:
Probability of choosing an adventure book first AND Probability of choosing a horror book
OR
Probability of choosing a horror book first AND Probability of choosing an adventure book
Answer: B
Answer: (B) 24/45
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 87 Kmph
(B) 97 Kmph
(C) 72 Kmph
(D) 28 Kmph
(E) 108 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer: E
Answer: (E) 108 Kmph
Question: 90% of the labours of a factory is 2700. The total labours of the factory is?
(A) 2900
(B) 3000
(C) 3100
(D) 3050
(E) 2950
Rationale: X * (90/100) = 2700
X = 30 * 100
X = 3000
Answer: B
Answer: (B) 3000
Question: The probability of pulling a black ball out of a glass jar is 1/X. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
(A) 1/(XY)
(B) X/Y
(C) Y/X
(D) 1/(X+Y)
(E) 1/(X-Y)
Rationale: Probability of A and B:
When two events are independent, the probability of both occurring is the product of the probabilities of the individual events: P(A and B)=P(A)∗P(B)P(A and B)=P(A)∗P(B)
P(break & black) = P(break) * P(black) --> 1/y=P(break)*1/x --> P(break)=x/y.
Answer: B.
Answer: (B) X/Y
Question: At a meeting of 10 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?
(A) 263,320
(B) 271,180
(C) 282,240
(D) 291,470
(E) 308,560
Rationale: 10 people can be arranged around a table in 9! ways.
Consider the two chiefs who will not sit together as a single unit.
The number of ways to arrange 9 units around a table is 8!
We need to multiply this by 2 as the two people can be switched in each arrangement.
The total number of ways to arrange the chiefs is 9! - 2*8! = 7*8! = 282,240
The answer is C.
Answer: (C) 282,240
Question: In what time will a train 40 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 1.0 sec
(C) 7.5 sec
(D) 2.3 sec
(E) 1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 40/40
= 1.0 sec.
Answer:B
Answer: (B) 1.0 sec