mathewhe/aqua_rat huggingface dataset:
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 525 what is the least possible value of k?
(A) 10
(B) 14
(C) 15
(D) 21
(E) 25
Rationale: 525 = 3*5*5*7
Thus k must include numbers at least up to the number 10 so that there are two appearances of 5.
The answer is A.
Answer: (A) 10
Question: Three models (P, Q, and R) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model P, 17 cars of Model Q, and 15 cars of Model R. What is the maximum number of cars of model P in any showroom ?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13
Rationale: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17).
Moreover that the number of model P is maximum means that the numbers of model Q and R should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.
So Maximum number of model P is 17-2= 15.
The answer is (C)
Answer: (C) 15
Question: Find the average of first 60 natural numbers?
(A) 50.5
(B) 52
(C) 30.5
(D) 75
(E) 65
Rationale: Sum of first 100 natural numbers = 60*61/2 = 1830Required average = 1830/60 = 30.5Answer is C
Answer: (C) 30.5
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B.
(A) 240
(B) 288
(C) 277
(D) 390
(E) 361
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
13/21 * 630 = 390
Answer: D
Answer: (D) 390
Question: In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 2,400 circuit boards where 64 fail inspection?
(A) 72
(B) 356
(C) 200
(D) 256
(E) 264
Rationale: Total of 2,400 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.
From the 2,400 we know 64 fail. So 2,336 must pass. Of these 1/8 are faulty. 2,336 divided by 8 gives you 292.
What one must do now is to add to the 292 which were not detected the actually detected faulty ones, namely the 64.
Total faulty: 356.
Answer: B
Answer: (B) 356
Question: A, B and C start at the same time in the direction to run around a circular stadium. A completes a round in 252 seconds and C in 198 seconds, all starting at the same point. after what time will they meet again at the starting point ?
(A) 26 minutes 18 seconds
(B) 42 minutes 36 seconds
(C) 45 minutes
(D) 46 minutes 12 seconds
(E) 58 minutes
Rationale: Solution
L.C.M. of 252, 308 and 198 = 2772.
So, A, B and C will again meet at the starting point in 2772 sec. i.e, 46 minutes 12 seconds. Answer D
Answer: (D) 46 minutes 12 seconds
Question: Diana is painting statues. She has 7/16 of a gallon of paint remaining. Each statue requires 1/16 gallon of paint. How many statues can she paint?
(A) 7
(B) 20
(C) 28
(D) 14
(E) 19
Rationale: number of statues=all the paint÷amount used per statue
=7/16 ÷ 1/16
=7/16*16/1
=7/1
=7
Answer is A.
Answer: (A) 7
Question: A can do a piece of work in 30 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 30 days
(B) 65 days
(C) 86 days
(D) 45 days
(E) 17 days
Rationale: 10/30 + 10/30 + 10/x = 1
x =30 days
Answer:A
Answer: (A) 30 days
Question: In the new budget , the price of kerosene oil rose by 25%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
(A) 10
(B) 20
(C) 30
(D) 40
(E) None of them
Rationale: Reduction in consumption = [((R/(100+R))*100]%
=[(25/125)*100]%=20%.
Answer is B.
Answer: (B) 20
Question: If six coins are flipped simultaneously, the probability of getting at least one heads and at least one tails is closest to
(A) 3%
(B) 6%
(C) 75%
(D) 94%
(E) 97%
Rationale: Probability of getting no heads = 1/64
Probability of getting at least 1 head = 63/64
Probability of getting no tails = 1/64
Probability of getting at least 1 tail = 63/64
Probability of getting at least 1 head and at least 1 tail = 63*63/64*64
63/64 is greater than 98%... So squaring that should be greater than 96%. Answer is E.
Answer: (E) 97%
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 7 years, Arun's age will be 19 years. What is the age of Deepak at present?
(A) 16
(B) 14
(C) 12
(D) 9
(E) 15
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 7 = 19 => x = 12
Deepak's age = 3x = 9 years.
Answer: D
Answer: (D) 9
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.10 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 399
(B) 272
(C) 732.6
(D) 277
(E) 311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.1 = 732.6 Answer: C
Answer: (C) 732.6
Question: The average of 65 numbers is 40. If two numbers, 83 and 30 are discarded, then the average of the remaining numbers is nearly
(A) 28.32
(B) 39
(C) 38.78
(D) 29
(E) 39.47
Rationale: Explanation :
Total sum of 63 numbers = (65 * 40) - (83 +30) = 2600 - 113= 2487
Average = 2487/63 = 39.47
Answer : E
Answer: (E) 39.47
Question: If W is the set of all the integers between 69 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 20
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Multiples of 2 from 69 to 99=Multiples of 2 from 1 to 99-Multiples of 2 from 1 to 68=[99/2]-[68/2]=49-34=15
Multiples of 3 from 69 to 99=Multiples of 3 from 1 to 99-Multiples of 3 from 1 to 68=[99/3]-[68/3]=33-23=10
Multiples of2 and 3 bothi.e.6 from 69 to 99=Multiples of 6 from 1 to 99-Multiples of 6 from 1 to 68=[99/6]-[68/6]=16-11=5
These 8 Numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3
i.e. Total Numbers in W = 15 + 10 - 5 = 20
Answer Option A
Answer: (A) 20
Question: Joshua and Jose work at an auto repair center with 2 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
(A) 1/15
(B) 1/12
(C) 1/9
(D) 1/6
(E) 1/3
Rationale: Two Methods
1) Probability of chosing Josh first = 1/4
Probability of chosing Jose second = 1/3
total = 1/12
Probability of chosing Jose first = 1/4
Probability of chosing Josh second = 1/3
Total = 1/12
Final = 1/12 + 1/12 = 1/6
D
Answer: (D) 1/6
Question: The average of 7 numbers is 25. If each number be multiplied by 5. Find the average of new set of numbers?
(A) A)110
(B) B)122
(C) C)120
(D) D)125
(E) E)145
Rationale: Explanation:
Average of new numbers = 25 * 5 = 125
Answer: Option D
Answer: (D) D)125
Question: Solve 2log53 X log9x + 1 = log53
(A) 3/5
(B) 4/5
(C) 4
(D) 4/6
(E) 5
Rationale: Solution:
We can rewrite the above equation in the below format
=> log532 X log9x = log53 - 1
=> log59 X log9x = log53 - log55
=> log59 X log9x = log5(3/5)
By Using the change of base rule in Left side we get
=> log5x = log5(3/5)
The value of X = 3/5
ANSWER IS A
Answer: (A) 3/5
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 22
(B) 28
(C) 98
(D) 37
(E) 13
Rationale: 36/7 r = 144
=> r
= 28
Answer: B
Answer: (B) 28
Question: If log1087.5 = 2.9421, then the number of digits in (875)10 is?
(A) 30
(B) 28
(C) 27
(D) 26
(E) 40
Rationale: X = (875)10 = (87.5 x 10)10
Therefore, log10X = 10(log2087.5 + 1)
= 10(2.9421 + 1)
= 10(3.9421) = 39.421
X = antilog(39.421)
Therefore, number of digits in X = 40.
ANSWER:E
Answer: (E) 40
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
(A) 9:22
(B) 9:20
(C) 9:25
(D) 9:26
(E) 9:21
Rationale: a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9:25
Answer:C
Answer: (C) 9:25
Question: For every positive odd integer n, the function h(n) is defined to be the product of all the odd integers from 1 to n, inclusive. If p is the smallest prime factor of h(100) +1, then p is?
(A) between 1 and 20
(B) between 10 and 20
(C) between 20 and 30
(D) between 30 and 40
(E) 1
Rationale: h(100) will have 0 in its unit digit because while doing the calculation of the function we are multiplying by 10 (and 100). So h(100)+1 will have 1 in the units digit so smallest prime factor is 1.
Answer: E
Answer: (E) 1
Question: Set S consists of numbers 2, 3, 6, 48, and 164. Number K is computed by multiplying one random number from set S by one of the first 10 non-negative integers, also selected at random. If Z=6^K, what is the probability that 678,463 is not a multiple of Z?
(A) 10%
(B) 25%
(C) 50%
(D) 90%
(E) 100%
Rationale: Probability of any random number being picked from set S = 1
Probability of kk not being 0 = 9/10 ( as there are total of 10 ways to pick up k and 9 ways for k not being 0)
Since it's an AND event , we will multiply the probabilities of both the events.
Hence total probability = 1∗9/10=90%. Answer:D
Answer: (D) 90%
Question: In a certain game, a player begins with a bag containing tiles numbered 1 through 15, each of which has an equal probability of being selected. The player draws one tile. If the tile is even, the player stops. If not, the player draws another tile without replacing the first. If this second tile is even, the player stops. If not, the player draws a third tile—without replacing either of the first two tiles—and then stops. What is the probability that at the conclusion of the game, the sum of the tiles that the player has drawn is odd?
(A) 5/18
(B) 13/36
(C) 3/8
(D) 5/8
(E) 23/36
Rationale: player begins with containing tiles 1 to 10 and have equal probability of selecting means
Proabability of selecting one number =1/10. here 5 even numbers and 5 odd numbers are there.
Next , player draws one title , if number is even player stops or otherwise title is odd without replacement
player draws second title.
If second title is even , player stops or title is odd without replacement player draws third title.
in third title , without replacement of first and second title, player draws and stops it.
the sum of tilte probability is odd. here two conditions are possible.
1st condition is
1st title is odd+ 2nd title is even stops= probability of selecting one title is 1/10*5c1.
Here are we are not selecting 1st condition as even stops because sum of tile is odd.
Here 5 odd numbers are there we can select 1out of 5 odd numbers.
without replacement of fist we select second tilte is even. is 5/10*5c1/9c1.
here we are selecting one number out of remaining 9 numbers. so probability is 5/18.
we are selecting 1 even number out of 5.
2nd condition is 1stodd without replacement,2nd odd without replacement and 3rd one also odd to get odd as sum of title.
Then probability is 5/10*4/9*3/8=1/12.
Finally sum of probability of two conditions is 5/18+1/12
=23/36.
so option E is correct.
Answer: (E) 23/36
Question: A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area Q of the triangle in terms of h?
(A) h/ √2
(B) h/2
(C) h/4
(D) (h)^2
(E) (h)^2/4
Rationale: IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA Q= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E
Answer: (E) (h)^2/4
Question: HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
(A) 36
(B) 66
(C) 132
(D) 264
(E) 152
Rationale: 12 * 396 = 36 * x
x = 132
ANSWER:C
Answer: (C) 132
Question: 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 8 pumps work to empty the tank in 1 day?
(A) 6
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 8 pumps then
48/8=6 hrs.
answer :A
Answer: (A) 6
Question: A bus leaves Los Angeles at 9:00 a.m. traveling north at 50 miles per hour. At 11:00 a.m. a plane leaves Los Angeles traveling north at 200 miles per hour. At what time will the plane overtake the bus?
(A) 11:40 a.m.
(B) 12:15 p.m.
(C) 10:00 a.m.
(D) 11:25 a.m.
(E) 10:40 a.m.
Rationale: At 11:00am, the bus is 100 miles ahead of plane
The plane travels at 200 mph, which gains 150 mph on bus
100/250=2/5 hours = 40 minutes
11:00 + 0:40 = 11:40
The plane will overtake bus at 11:40am
Answer:A
Answer: (A) 11:40 a.m.
Question: What is the smallest no. that should be added to 31110 to make it exactly divisible by 9?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 9
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 3+1+1+1+0=6, the next multiple of 9 is 9.
3 must be added to 31110 to make it divisible by 9
B
Answer: (B) 3
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 600 km/hr
(B) 720 km/hr
(C) 730 km/hr
(D) 750 km/hr
(E) 760 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Answer: (B) 720 km/hr
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
8, 28, 328, 4328, ?
(A) 29816
(B) 38291
(C) 54325
(D) 38290
(E) 54328
Rationale: See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54328
Answer : E
Answer: (E) 54328
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 300
(B) 230
(C) 245
(D) 250
(E) 260
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: Option C
Answer: (C) 245
Question: The curved surface of a sphere is 64 π cm2. Find its radius?
(A) 9
(B) 8
(C) 4
(D) 5
(E) 6
Rationale: 4 πr2 = 64 => r = 4
Answer:C
Answer: (C) 4
Question: A card is drawn at random from a pack of 52 cards. What is the probability that it is neither a spade nor a jack?
(A) 9/13
(B) 4/13
(C) 2/13
(D) 6/13
(E) 5/13
Rationale: There are 13 spades including a jack and 3 more jacks of other suits.
Probability of getting spade or a jack:
= (13 + 3)/52
= 16/52
= 4/13
Therefore, the probability of getting neither a spade nor a jack:
= 1 − 4/13
= 9/13
ANSWER:A
Answer: (A) 9/13
Question: At a contest with 3000 participants, 1/2 of the people are aged 8 to 14. Next year, the number of people aged 8 to 14 will increase by 1/6. After this change, what percentage of the total 3000 people will the 8- to 14-year-olds represent?
(A) 53.33%
(B) 50%
(C) 58.33%
(D) 55.33%
(E) 68%
Rationale: I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 3000 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/6, we are multiplying it by 1 + 1/6 = 7/6, so the answer here must be (1/2)*(7/6) = 7/12 = 58.33 %.
Answer : C
Answer: (C) 58.33%
Question: Strawberries are purchased for $5/lb at the Farmer's Market. 4/5 of the strawberries will be used for making jam (1/5 of strawberries are rotten and thrown out). The strawberries are crushed and 1 lb of strawberries produces 2 cups of strawberry juice which is mixed with sugar to make the jam. If 3 cups of strawberry juice can make one jar of jam, how much money is needed to buy strawberries to make x number of jars of jam, in dollars?
(A) 2x
(B) 75x/8
(C) 8x/15
(D) 2x/3
(E) x/2
Rationale: Initial cost for 1 lb = $5, but ONLY 4/5 is used.
So the cost of 4/5 lb = $5, or 1 lb = $25/4,
and 1 lb of strawberries produces 2 cups of strawberry juice,so 2 cups of strawberry juice costs $25/4, but 3 cups are needed for 1 jar, so cost of 3 cups = $(25/4)(3/2) = $75/8.
If 1 jar costs $75/8, x number of jars will cost $75x/8..
Answer is B
Answer: (B) 75x/8
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square?
(A) 398
(B) 379
(C) 237
(D) 480
(E) 111
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: D
Answer: (D) 480
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
(A) 62%
(B) 18%
(C) 72%
(D) 12%
(E) 13%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer: D
Answer: (D) 12%
Question: If N is a positive integer and 14N/60 is an integer. What is the smallest Value of N for which N has exactly four different prime factors.?
(A) 30
(B) 60
(C) 180
(D) 210
(E) cannot be determined
Rationale: 14N/60 tells us that N must be multiple of 30.
Or N has at least 2 *3 * 5 in it.
To find out the smallest value of N such that it has 4 different prime factors, we will multiple 30 with next smallest prime factor which is 7 here.
So, Least value of N is 30 *7 =210 .
ANSWER:D
Answer: (D) 210
Question: The decimal 0.1 is how many times greater than the decimal (0.01)^4?
(A) 10^5
(B) 10^6
(C) 10^7
(D) 10^8
(E) 10^9
Rationale: 0.1 = 10^-1
(0.01)^4 = (10^-2)^4 = 10^-8
10^7 * 10^-8 = 10^-1
The answer is C.
Answer: (C) 10^7
Question: A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph of 3 edges and 3 points. The degree of a point is the number of edges connected to it. For, example, a triangle is a graph with 3 points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any through sequence of edges. The number of edges 'e' in the graph must satisfy the condition
(A) 11 ≤ e ≤ 66
(B) 10 ≤ e ≤ 66
(C) 11 ≤ e ≤ 65
(D) 0 ≤ e ≤ 11
(E) None
Rationale: Explanation :
The least number of edges will be when one point is connected to each of the other 11 points, giving a total of 11 lines. One can move from any point to any other point via the common point.
The maximum edges will be when a line exists between any two points. Two points can be selected from 12 points in 12C2 i.e. 66 lines.
Answer : A
Answer: (A) 11 ≤ e ≤ 66
Question: A train passes a station platform in 36 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) 177 m
(B) 176 m
(C) 240 m
(D) 187 m
(E) 186 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m.
Answer: C
Answer: (C) 240 m
Question: If m and n are positive integers such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
(A) 2m/n + 1
(B) 2n/m + 1
(C) 2n/(m+1)
(D) 2m/n
(E) 2n/m
Rationale: Lets say N=10, M=5
2N=20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: (E) 2n/m
Question: Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 12 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant?
(A) A)8/100
(B) B)9/100
(C) C)1/8
(D) D)4/5
(E) E)1/10
Rationale: Total letters 12, out of which the first letter is anything of 10 but N or X...
So there are 10 possible letters for first place..
And only one of them is correct..
So 1/10.
Answer: E
Answer: (E) E)1/10
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/458
(C) 1/453
(D) 1/456
(E) 1/454
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer: A
Answer: (A) 1/455
Question: For any real number x, the operatoris defined as:
(x) = x(5 − x)
If p + 1 =(p + 1), then p =
(A) −2
(B) 0
(C) 1
(D) 2
(E) 4
Rationale: (x) = x(5 − x)
(p + 1) = (p + 1)(5 - p - 1) = (4-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (4-p)(p+1) = (p + 1)
Or (p + 1) + (p-4)(p+1) = 0
(p + 1)(p-4) = 0
p = -1,p=4
Option E
Answer: (E) 4
Question: Last year Elaine spent 20% of her annual earnings on rent. This year she earned 20% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?
(A)  185.5
(B)  180.0
(C)  167.5
(D)  172.5
(E)  177.5
Rationale: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $20 of this on rent.
This year she earned 20% more, or $120
She would've spent 30% of this on rent, or $36
Do $36/$20
This will give you 180%
B is the correct answer.
Answer: (B)  180.0
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150m
(B) 157m
(C) 750m
(D) 850m
(E) 350m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A:
Answer: (A) 150m
Question: Calculate the average of all the numbers between 10 and 86 which are divisible by 9.
(A) 49.5
(B) 41.5
(C) 45.5
(D) 40.5
(E) 47.5
Rationale: Explanation:
numbers divisible by 9 are 18,27,36,45,54,63,72,81,
Average = (18+27+36+45+54+63+72+81,) / 8 = 396/8 = 49.5
ANSWER: A
Answer: (A) 49.5
Question: Two stations P and Q are 200 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
(A) 10 am
(B) 12 noon
(C) 10.30 am
(D) 12.30 am
(E) 11 am
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 200
=> 20x + 25(x-1) = 200
=> 45x = 225
=> x= 5
Means, they meet after 5 hours after 7 am, ie, they meet at 12 noon
Answer is B.
Answer: (B) 12 noon
Question: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 55 paise per sq m is
(A) Rs. 209.20
(B) Rs. 309.20
(C) Rs. 409.20
(D) Rs. 509.20
(E) None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)
= [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m
Cost of plastering = 744 Ã— (55/100) = Rs. 409.20 Answer: C
Answer: (C) Rs. 409.20
Question: Working at a constant rate, P can finish a job in 3 hours. Q, also working at a constant rate, can finish the same job in 15 hours. If they work together for 2 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?
(A) 30
(B) 36
(C) 40
(D) 45
(E) 48
Rationale: Each hour they complete 1/3 + 1/15 = 2/5 of the job.
In 2 hours, they complete 2(2/5) = 4/5 of the job.
The time for P to finish is (1/5) / (1/3) = (3/5) hour = 36 minutes
The answer is B.
Answer: (B) 36
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
(A) 2205
(B) 2229
(C) 2205
(D) 2984
(E) 2223
Rationale: A = 2000(21/20)2
= 2205
Answer:A
Answer: (A) 2205