mathewhe/aqua_rat huggingface dataset:
Question: On the Richter scale, which measures the total amount of energy released during an earthquake, a reading of x-1 indicates one-tenth the released energy as is indicated by a reading of x. On that scale, the frequency corresponding to a reading of 9 is how many times as great as the frequency corresponding to a reading of 3?
(A) 40
(B) 50
(C) 10^4
(D) 10^5
(E) 10^6
Rationale: If Richter scale reading goes from X-1 to X it will be 10
if Richter scale reading goes from 3 to 4 it will be 10
if Richter scale reading goes from 4 to 5 it will be 10
if Richter scale reading goes from 5 to 6 it will be 10
Similarly if Richter scale reading goes from 6 to 7 it will be 10
and if Richter scale reading goes from 7 to 8 it will be 10
and if Richter scale reading goes from 8 to 9 it will be 10
so it will from 3 to 9 i.e 4,5,6,7,8,9 = 10*10*10*10*10*10 = 10^6
Answer is E
Answer: (E) 10^6
Question: In how many ways can 5 white and 2 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) 120
(B) 60
(C) 10
(D) 240
(E) 30
Rationale: 5 white chess pieces can be arranged in 5! ways and 2 black pieces can be arranged in 2 ! ways.
W_W_W_W
Number of ways = 5!*2! = 120 * 2 = 240
Answer D
Answer: (D) 240
Question: When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 85% of his regular speed, then
(A) Jack picks double the amount of olives Mac picks
(B) Mac picks 10 pounds more than Jack
(C) Jack picks 10 pounds more than Mac
(D) Mac picks 5 more pounds than Jack
(E) Jack picks 5 more pounds than Mac
Rationale: Let's say Jack's regular speed is J olives/hr and Mac's regular speed is M olives/hr
Given:
2*3J = 10 + 5*(4/5)M
3J = 5 + 2M
Question:if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed
Mac picks 2M and Jack picks 4*(3/4)J = 3J
They are asking you for the relation between 3J and 2M. You already know 3J = 5 + 2M
So Jack picks 5 pounds more olives than Mac.
E
Answer: (E) Jack picks 5 more pounds than Mac
Question: A, B and C have Rs.400 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
(A) A)150
(B) B)140
(C) C)130
(D) D)120
(E) E)110
Rationale: A+B+C = 400
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 400
----------------
C = 150
Answer:A
Answer: (A) A)150
Question: Three positive integers a, b, and c are such that their average is 28 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 28.
So, a+b+c3a+b+c3 = 84 or a + b + c = 84
a ≤ b ≤ c
Median = (a + 13)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 13
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 13) + (a + 13) = 84 (b and c are equal and b, the median, is a + 13)
Or 3a = 58 or a = 19.33
So, b = c = 19.33+ 13= 32.33
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 13) + (a + 14) = 84
Or 3a = 57or a=19 The value of the numbers is an integer.
If a = 19, b = 32 and c = 33.
The least value for c that satisfies all these conditions is 33
Correct answer is choice C.
Answer: (C) 33
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 35
(B) 34
(C) 36
(D) 32
(E) 31
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: C
Answer: (C) 36
Question: A store reduced the price of all items in the store by 8% on the first day and by another 10% on the second day. The price of items on the second day was what percent of the price before the first reduction took place?
(A) 80.0
(B) 80.9
(C) 81.0
(D) 81.1
(E) 82.8
Rationale: consider price of the all items as $100
after a initial reduction of 8% price becomes = 0.92 *100 = $ 92
after the final reduction of 10% price becomes = 0.9* 92 = $ 82.8
price of all items on second day is 82.8% of price on first day
correct answer option E
Answer: (E) 82.8
Question: Noelle walks from point A to point B at an average speed of 5 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 8 kilometers per hour?
(A) 6.75
(B) 7
(C) 7.25
(D) 7.5
(E) 20
Rationale: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
8= 2*5*x/5+x
x= 20
E is the answer
Answer: (E) 20
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 156
(B) 159
(C) 166
(D) 170
(E) 180
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: JAMES school has 2000 GIRLS and 5000 BOYS. What is the percentage increase from GIRLS to total attendance and BOYS to total attendance?
(A) 40%
(B) 10%
(C) .4%
(D) 50%
(E) 12%
Rationale: Ratio of GIRLS to total attendance (2/7)
Ratio of BOYS to total attendance (5/7)
percentage increase is (difference/initial quantity)*100
(2/7)/(5/7 )* 100= 40%
Correct answer is A
Answer: (A) 40%
Question: A train passes a platform in 22 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 40
(B) 50
(C) 60
(D) 30
(E) 20
Rationale: Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 12
=> 300+L = 15×22 = 330
=> L =330-300 = 30 meter
Answer is D.
Answer: (D) 30
Question: A box contains twelve bulbs out of which seven are defective. If seven bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/127
(B) 1/792
(C) 1/789
(D) 1/689
(E) 1/126
Rationale: Out of twelve, five are good and seven are defective. Required probability
= 7C7/12C7
= 1/792
Answer: B
Answer: (B) 1/792
Question: The remainder obtained when a prime number greater than 3 is divided by 3 is
(A) a) 1 or 3
(B) b) 2 or 4
(C) c) 3 or 5
(D) d) 4 or 5
(E) e) 5
Rationale: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 3, i.e. 7 and 5:
7/3 = 1 + remainder of 4
5/3 = 1 + remainder of 2
This is already sufficient to see that answer choice b) is correct.
B
Answer: (B) b) 2 or 4
Question: The number of livestock in a farm at the beginning of year 2015 was 100,000. During the year, the number increased by p%. During the next year 2016, there was a famine and the number decreased by q%. A census at the end of year 2016 revealed that the number of livestock in the farm was 100,000. Which of the following expressions is correct?
(A) q > p
(B) p > q
(C) p = q
(D) With the exception of 1 instance, p will be equal to q
(E) There is no relation between p and q
Rationale: Number plugging in will be best strategy for this question.
Let p = 5%,
Per the question 100000(1.05)(1-q/100) = 100000 ---> q = 4.7%. Thus p > q and hence B is the correct answer.
Answer: (B) p > q
Question: The average of 3 consecutive odd numbers is 30. What is the difference between the highest and lowest numbers?
(A) 5
(B) 6
(C) 8
(D) 4
(E) 3
Rationale: Let the numbers be x, x+2, x+4
Then, (x+ x+2+ x+4)/3 = 30
x = 28
Required answer is = 28+4-28 = 4
Answer is D
Answer: (D) 4
Question: x and y are positive integers of Q. If 1/x + 1/y < 2, which of the following must be true?
(A)  x + y > 4
(B)  xy>1
(C)  x/y + y/x < 1
(D)  (x - y)^2 > 0
(E)  None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: (B)  xy>1
Question: Which one of the following is a prime number?
(A) 55
(B) 2
(C) 74
(D) 25
(E) 21
Rationale: 2 is divisible by 1 and itself So, it is a prime number.
B
Answer: (B) 2
Question: If p^2 – 13p + 40 = a, and p is a positive integer between 1 and 10, inclusive, what is the probability that a < 0?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 3/10
Rationale: p2 – 13p + 40 = a
so (p – 8)(p – 5) = a
For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
The correct answer is B.
Answer: (B) 1/5
Question: What is the remainder when 47*50 is divided by 8?
(A)  1
(B)  3
(C)  13
(D)  5
(E)  14
Rationale: we can make use of the rule :
Remainder of { (a * b)/n}} = Remainder of (a/n) * Remainder of (b/n)
Here
Remainder of { 47 * 50)/8}} = Remainder of (47/8) * Remainder of (50/8) = 7 * 2 = 14
Answer :E
Answer: (E)  14
Question: Two numbers are in the ratio of 6 : 8. If 10 is subtracted from each, the new numbers are in the ratio 16 : 32. Find the smaller number.
(A) 22
(B) 12
(C) 38
(D) 15
(E) 17
Rationale: Explanation:
Let the number be 6x and 8x.
Then, (6x – 10) / (8x – 10) = 1 / 2
2 (6x – 10) = (8x – 10)
12x – 20 = 8x – 10
4x = 10
x = 2.5
The smaller number = (6 x 2.5) = 15
ANSWER D
Answer: (D) 15
Question: There are 6 ball in bag out of them 4 green and 2 red, randomly picked two boll one by one so find the probabilty atleast one picked boll will be red?
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 6/5
Rationale: probality of selecting 1 red + probality of selecting 2 red =((2c1*4c1)/6c2)+((2c2)/(6c2))=3/5
ANSWER:C
Answer: (C) 3/5
Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is
(A) 400 kg
(B) 560 kg
(C) 600 kg
(D) 640 kg
(E) None
Rationale: Solution
ratio of 1st and 2nd parts = 4 : 6 = 2 : 3.
Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg.
Answer C
Answer: (C) 600 kg
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $29. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
(A) 180xy
(B) 261/(xy)
(C) 20xy
(D) 20xy/9
(E) xy/180
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 29 / (xy/9) = 261/(xy).
The answer is B.
Answer: (B) 261/(xy)
Question: Michael cashed a check for $1,170 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
(A)  $830
(B)  $800
(C)  $770
(D)  $730
(E)  $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1170 - 470 = 700.
Answer E
Answer: (E)  $700
Question: An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air ?
(A) 803km/hr
(B) 805km/hr
(C) 809km/hr
(D) 807km/hr
(E) 806km/hr
Rationale: Let the speed of the air plane in still air be x km/hr
And the speed of the wind be y km/hr.
Then speed of the airplane going with the wind = (x + y) km/hr
and speed of the airplane going against the wind = (x - y) km/hr.
We know that,
Distance = Speed × Time
or, Speed = Distance
Time
According to the problem,
An airplane travels 4362 km against the wind in 6 hours
x - y = 4362/6
or, x - y = 727 ----------- (1)
Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours
x + y = 5322/6
or, x + y = 887 ----------- (2)
Now add (1) and (2) we get,
x - y = 727
x + y = 887
2x = 1614
or, 2x/2 = 1614/2, (Divide both sides by 2)
or, x = 807
Now substitute the value of value of x = 807 in equation (2) we get,
807 + y = 887
-807 -807, (Subtract 407 from both sides)
y = 80
Answer: Rate of the plane in still air = 807 km/hr
correct answer D)807 km/hr
Answer: (D) 807km/hr
Question: A train covers a distance of 12 km in 10 min. If it takes 8 sec to pass a telegraph post, then the length of the train is?
(A) 100
(B) 110
(C) 160
(D) 130
(E) 140
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 8 = 160 m.
Answer: Option C
Answer: (C) 160
Question: You get 1 & -0.25 for each right and wrong answer. Answring 72 ques u get 47. How many ans were wrong?
(A) 10
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: let x be cort,thn 72-x are wrong.
x(1)+(72-x)(-1/4)=47
x=52,72-52=20.
so,20 are wrong.
ANSWER:B
Answer: (B) 20
Question: How many numbers are divisible by 4 between 1 and 100.
(A) 24
(B) 23
(C) 22
(D) 21
(E) 25
Rationale: Numbers divisible by 4 till 100=(100/4)=25
But we should not consider 100 as we are asked to find the number between 1 to 100 which are divisible by 4.
So answer is 24 numbers.
Option:A
Answer: (A) 24
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 215 m long?
(A) 40
(B) 46
(C) 88
(D) 77
(E) 21
Rationale: :
Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 215 = 575 m
Required time = 575 * 2/25 = 46 sec
Answer:B
Answer: (B) 46
Question: How many times are the hands of a clock at right angle in a day?
(A) 45
(B) 84
(C) 55
(D) 22
(E) 44
Rationale: Explanation:
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Answer is E
Answer: (E) 44
Question: You have been given a physical balance and 7 weights of 43, 45, 30, 33, 28, 37 and 55 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 145 kgs.
(A) 145
(B) 143
(C) 147
(D) 141
(E) 142
Rationale: 55 + 43 + 45 = 143
Answer: B
Answer: (B) 143
Question: If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 2?
(A) -1
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: Answer
x = 1 + √2
∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 2
= x2(x - 2)2 +2
= (1 + √2)2(1 + √2 - 2)2 + 2
=(√2 + 1)2 (√2 - 1)2 + 2
=[(√2)2 - (1)2]2 + 2
=(2 - 1)2 =1 + 2=3
Correct Option: E
Answer: (E) 3
Question: Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there?
(A) 20 toys
(B) 30 toys
(C) 40 toys
(D) 60 toys
(E) 50 toys
Rationale: x : the total number of toys
x/10 : the number of toys for first child
x/10 + 12 : the number of toys for second child
x/10 + 1 : the number of toys for the third child
2(x/10 + 1) : the number of toys for the fourth child
x/10 + x/10 + 12 + x/10 + 1 + 2(x/10 + 1) = x
x = 30 toys : solve for x
correct answer B
Answer: (B) 30 toys
Question: A, B and C work on a task. To complete the task alone, B takes twice the time that A would take to complete the task alone and 2/5rd the time that C would take to complete the task alone. If B actually worked for half the number of days that A worked and 3/2 times the number of days that C worked, what proportion of the total work was completed by B?
(A) 1/3
(B) 2/9
(C) 9/49
(D) 25/129
(E) 1/6
Rationale: The first thing to notice is that A is faster than B and B is faster than C.
Since work is proportional to time, in 1 day lets say if A does 2 works, B does 1 work and C does 2/3rd of a work.
If A works for 2 days, B works for 1 day and C works for only 2/3 of the day.
Therefore total work done = (2*2) + (1*1) + (2/5*2/5) = 129/25
Proportion of work done by B = (1*1) / (129/25) =25/129
Hence Answer D.
Answer: (D) 25/129
Question: A card player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many hearts as clubs and twice as many diamonds as hearts. How many spades does he hold?
(A) 6
(B) 5
(C) 8
(D) 2
(E) 9
Rationale: A
6
The player holds 1 club, 2 hearts and 4 diamonds.
As he holds 13 cards (or seven black cards), it follows that there must be 6 spades.
Answer: (A) 6
Question: A soccer store typically sells replica jerseys at a discount of 20 percent to 50 percent off list price. During the annual summer sale, everything in the store is an additional 20 percent off the original list price. If a replica jersey's list price is $80, approximately what percent of the list price is the lowest possible sale price?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Let the list price be 2x
for min sale price, the first discount given should be 50%, 2x becomes x here
now, during summer sale additional 20% off is given ie sale price becomes 0.8x
it is given lise price is $80
=> 2x = 80
=> x = 50
and 0.8x = 32
so lowest sale price is 32, which is 40% of 80
hence, E is the answer
Answer: (E) 50
Question: Two numbers are such that the ratio between them is 3 : 5, but if each is increased by 10, the ratio between them becomes 5:7. The numbers are
(A) 3, 5
(B) 7, 9
(C) 13, 22
(D) 15, 25
(E) None
Rationale: No's are in the ratio 3:5
Le the No's be 3x and 5x
ATQ. (3x+10) : (5x+10) = 5:7
? x = 5
No's are (15,25)
Answer: D.
Answer: (D) 15, 25
Question: If the average of 5 positive integers is 50 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
(A) 50
(B) 58
(C) 49
(D) 48
(E) 44
Rationale: Sum of 5 Integer (a, b, c, d, e) = 5*50 = 250
e - a = 10
i.e. e = a+10
For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers
i.e. a+a+a+a+(a+10) = 250
i.e. 5a = 240
i.e. a =48
i.e. Largest e = 48+10 = 58
Answer: option B
Answer: (B) 58
Question: A boy has nine trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
(A) 90
(B) 98
(C) 106
(D) 108
(E) 111
Rationale: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 10 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 10 = 90 ways
A)
Answer: (A) 90
Question: Find the value for m?
19(m + n) + 17 = 19(-m + n) - 97
(A) -3
(B) -1
(C) 1
(D) 2
(E) 3
Rationale: 19m + 19n + 17 = -19m + 19n - 97
38m= -114 => m = -3
A
Answer: (A) -3
Question: A can do a work in 24 days and B can do it in 16 days. In how many days A and B can do the work?
(A) 20 days
(B) 10 days
(C) 6 days
(D) 9 3/5 days
(E) 7 days
Rationale: Explanation:
A's 1day's work = 1/24
B's 1day's work = 1/16
They work together = 1/24 + 1/16 = 5/48 = 48/5 = 9 3/5days
Answer: Option D
Answer: (D) 9 3/5 days
Question: In how many different ways can the letters of the word 'TAKING' be arranged in such a way that the vowels always come together?
(A) A)360
(B) B)480
(C) C)720
(D) D)5040
(E) of these
Rationale: The word 'TAKING' has 6 different letters.
When the vowels AI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters TKNG (AI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 2! = 2 ways.
Required number of ways = (120 x 2) = 360.
ANSWER:A
Answer: (A) A)360
Question: A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 12 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?
(A) 16
(B) 20
(C) 24
(D) 28
(E) 32
Rationale: Since the distance remains the same (we're just changing the rate and time), any increase in rate or time is met with a decrease in the other term. Decreasing the time by 1/3 would give us:
D = (R)(T) = (2T/3)(x*R)
x = 3/2 since (2T/3)(3R/2) = (R)(T) = D
3R/2 = R + 12
R/2 = 12
R= 24
The answer is C.
Answer: (C) 24
Question: In a hotel,8 items are served. The Limitation given by the hotel is customer eat only 5 items only.What are the possible ways to ate 5 items?
(A) 48
(B) 54
(C) 60
(D) 58
(E) 56
Rationale: The question is out of 8 items,5 items to be eaten (i.e)8C5
8C5=8!/5!*3!
=56 ways to ate 5 items.
Ans is option E
Answer: (E) 56
Question: The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:
.
(A) 28
(B) 32
(C) 40
(D) 64
(E) 68
Rationale: Let the numbers be 2x and 3x.
Then, their L.C.M. = 6x.
So, 6x = 48 or x = 8.
The numbers are 16 and 24.
Answer: Option C
Hence, required sum = (16 + 24) = 40.
Answer: (C) 40
Question: A dog takes 4 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 12:5
(B) 4:3
(C) 9:5
(D) 9:1
(E) 9:2
Rationale: Explanation:
Dog : Hare = (4*3) leaps of hare : 5 leaps of hare = 12 : 5.
Answer: A) 12:5
Answer: (A) 12:5
Question: A person travels from P to Q at a speed of 40 km/hr and returns by increasing his speed by 50%.
What is his average speed for both the trips ?
(A) 44 km/hour
(B) 46 km/hour
(C) 48 km/hour
(D) 50 km/hour
(E) None of these
Rationale: Explanation:
Speed while going = 40 km/hr
Speed while returning = 150% of 40 = 60 km/hr
Average speed =
2xyx+y=2
∗
40
∗
6040+60=4800100=48Km/hr
Answer: C
Answer: (C) 48 km/hour
Question: The cab company gets a discount at the fuel center when they fill up more than 2 cars at a time. The service is $1.05 per vehicle and .30 cents per liter of fuel. On Saturday , they will fill 2 vans and 3 smaller cars. The cars are 28 liters each and the vans are 80% bigger. How much will it cost to fill up all vehicles if they are empty?
(A) $68.00
(B) $60.69
(C) $71.27
(D) $72.36
(E) $57.22
Rationale: Lots of calculations.
1.05*5 + 3*28*.30+ 28*(9/5)*2*.30
Answer=$60.69
The correct option is B.
Answer: (B) $60.69
Question: Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
(A) 6
(B) 24
(C) 120
(D) 360
(E) 720
Rationale: Total arrangement of 6 = 6!. In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them). So, the needed arrangement is 6!/2=360.
Answer: D (360)
Answer: (D) 360
Question: A sun is divided among X, Y and Z in such a way that for each 2 rupees X gets, Y gets 80 paisa and Z gets 60 paisa. If the share of Y is RS. 40, what is the total amount?
(A) 160
(B) 155
(C) 150
(D) 170
(E) 165
Rationale: x:y:z = 200:80:60
10:4:3
4 --- 40
17 --- ? => 170
Answer: D
Answer: (D) 170
Question: If a number is subtracted from its square we get 272. Find the number?
(A) 7
(B) 21
(C) 19
(D) 15
(E) 17
Rationale: x^2 â€“ x = 272
=> x =17
Answer E
Answer: (E) 17