mathewhe/aqua_rat huggingface dataset:
Question: Last year Department Store X had a sales total for December that was 5 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?
(A) 1/4
(B) 4/15
(C) 1/3
(D) 5/16
(E) 4/5
Rationale: Let avg for 11 mos. = 10
Therefore, Dec = 50
Year total = 11*10 + 50 = 160
Answer = 50/160 = 5/16 = D
Answer: (D) 5/16
Question: In a bouquet of flowers, all but two are roses, all but two are tulips, and all but two are daisies. How many flowers are in the bouquet?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: C
3
There are 3 flowers (1 rose, 1 tulip, and 1 daisy).
Answer: (C) 3
Question: Anthony and Michael sit on the six-member board of directors for company w. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: Soln: Let the commitees be I and II
Assuming that Anthony and Michael w go into commitee I, there is just one more place left to be filled in that commitee and it can be taken by any of the 4 remaining people. Thus 4 ways.
Since the Anthony and Michael can also go into commitee II, we get 4 ways for that commitee also.
So in total = 8 ways
Now total number of ways of choosing 3 from 6 people is
= 6C3
= 6 * 5 * 4/3!
= 20 ways
Therefore Probability is = (8 /20) * 100 = 40%
Answer: (C) 40%
Question: Two employees X and Y are paid a total of Rs. 570 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.259
(B) s.289
(C) s.299
(D) s.300
(E) s.389
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 570
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 570
⇒ y[12/10 + 1] = 570
⇒ 22y/10 = 570
⇒ 22y = 5700
⇒ y = 5700/22 = Rs.259
A)
Answer: (A) s.259
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 109, what is the product of b and c?
(A) 2652
(B) 2578
(C) 2970
(D) 3354
(E) 4234
Rationale: C
2970
Here d = a + 3
a + a + 3 = 109
2a = 106
a = 53
So, numbers are 53, 54, 55 and 56
∴ b × c= 54 × 55 = 2970
Answer: (C) 2970
Question: 3 persons are standing at the middle of edges of a Triangle.All the 3 persons starts moving at same time with same speed in random direction
What is the probability of meeting atleast 2 persons?
(A) 1/4
(B) 2/4
(C) 3/4
(D) 5/4
(E) 6/4
Rationale: no of times that they dont meet is 2
so they meet in 6 ways
so required probability is=6/8=3/4
ANSWER:C
Answer: (C) 3/4
Question: David obtained 36, 35, 42, 57 and 55 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
(A) 75
(B) 45
(C) 87
(D) 165
(E) 11
Rationale: Explanation:
Average = (36+ 35+ 42+ 57+ 55 )/ 5 = 225/5 = 45.
Answer:B
Answer: (B) 45
Question: Vasya wrote down several consecutive integers. Which of the following could not be the percentage of odd numbers among them
(A)  40
(B)  45
(C)  48
(D)  55
(E)  60
Rationale: what you have to check is if the (answer given: 100-answer given) is either equal or two consecutive values..
reason for this is that there are only three possiblities of numbers of odd numbers in consecutive integers
1) equal to number of even numbers
2)one more than number of even numbers
3)one more than number of even numbers
(A) 40:60=2:3possible
(B) 45:55=9:11not possible
(C) 48:52=12:13possible
(D) 50:50=1:1possible
(E) 60:40=3:2possible
ans D
Answer: (D)  55
Question: An student identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form?
(A) 211
(B) 216
(C) 1075
(D) 1080
(E) 2160
Rationale: An student identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating number is same as first digit number i.e. 2. and the third number is one of the remaining 9 numbers (we are rejecting 2 here, because it will result in 222, which is not acceptable as per the given condition). thus these two number can arrange themselves in two blank spaces in 2! ways. hence total number of numbers in which repeating digit is same as the first digit = 1.9.2! =18
now, suppose that repeating number is different than first digit. thus possible case in this case are 8 as listed below:
211
233
244
255
266
277
288
299
here again we have rejected 200( because number must be greater than 200) and 222 ( exactly two repeating digits are allowed)
thus total possible cases are 18 + 8 =26
case 2: number ranging from 300 to 999
here for first digit we have 7 cases (3,4,5,6,7,8,9)
now if the repeating number is same as the first number then we will have 18 cases ( same reasoning as mentioned in the previous case)
if the repeating number is different than first digit number then we will have 9 cases ( because here number ending with two zeros are allowed)
hence total number of ways = 7(18+9) = 189
thus different number of codes = 5(189+26) = 1075
hence C
Answer: (C) 1075
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr The man's speed against the current is
(A) 8.5 km/hr
(B) 9 km/hr
(C) 10 km/hr
(D) 12.5 km/hr
(E) None
Rationale: Solution
Man's rate in still water	= (15 - 2.5) km/hr
= 12.5 km/hr.
Man's rate against the current	= (12.5 - 2.5) km/hr
= 10 km/hr.
Answer C
Answer: (C) 10 km/hr
Question: A man ate 100 bananas in five days, each day eating 6 more than the previous day. How many bananas did he eat on the first day?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: let the number of bannanas in first day be x
for consecutive five days it will be like x,x+6,x+12,x+18,x+24
the sum of those are 100, 5x+60=100
so,x=8
ANSWER:C
Answer: (C) 8
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 288
(B) 267
(C) 190
(D) 150
(E) 123
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150
Question: The banker's discount on Rs. 1600 at 15% per year is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
(A) 3 months
(B) 4 months
(C) 6 months
(D) 8 months
(E) 7 months
Rationale: Simple Interest on Rs. 1600 = T.D. on Rs. 1680.
Therefore Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Therefore, Time = (100 x 80 / 1600 x 15)	year
= 1/3 year = 4 months.
Correct answer is B.
Answer: (B) 4 months
Question: If a man running at the speed of x km/hr travels a distance of y km, which of the following cannot be equal to the distance traveled?
(A) x-y km
(B) x/2 km
(C) (x-y)/2 km
(D) y-x km
(E) y/x km
Rationale: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.
We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).
We're given information on speed (X km/hour) and distance (Y km). We're asked which of the 5 answer choices CANNOT be the distance traveled.
IF....
X = 2 and Y = 1
Answers A (2-1 = 1) and B (2/2 = 1) are POSSIBLE. Eliminate A and B.
IF....
X = 3 and Y = 1
Answer C ([3-1]/2 = 1) is POSSIBLE. Eliminate C.
IF....
X = 1 and Y = 1
Answer E (1/1 = 1) is POSSIBLE. Eliminate E.
Final Answer:
D
Answer: (D) y-x km
Question: How many numbers can be formed by using digits 0 to 9, as the number should be divisible by 5 and it should be 4 digit one and no repitation is allowed on digits?
(A) 951 ways
(B) 952 ways
(C) 953 ways
(D) 954 ways
(E) 955 ways
Rationale: For a number to be divisbly by 5 we have two choices 0 or 5
case 1 : when choice is 0
_ _ _ 0 first digt can be filled in 9ways , 2nd in 8 ways, 3rd in 7 ways so 9 * 8 *7 = 504
case 2 : when choice is 5
_ _ _ 5 first digi can be in 8 ways (since 0 cannot come ) , 2nd in 8 ,3rd in 7 so 8*8*7 = 448
so it can be in 504 + 448 = 952 ways
ANSWER:B
Answer: (B) 952 ways
Question: A candidate who gets 30% of the marks fails by 50 marks. But another candidate who gets 45% marks gets 25 marks more than necessary for passing. Find the number of marks for passing?
(A) 199 Marks
(B) 200 Marks
(C) 188 Marks
(D) 188 Marks
(E) 176 Marks
Rationale: 30% ------------ 50
45% ------------ 25
----------------------
15% ------------- 75
30% -------------- ?
150 + 50 = 200 Marks
Answer:B
Answer: (B) 200 Marks
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 767 m
(B) 467 m
(C) 245 m
(D) 567 m
(E) 544 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2
=> 2(130 + x) = 750 => x = 245 m.
Answer:C
Answer: (C) 245 m
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
(A) 12 days
(B) 16 days
(C) 18 days
(D) 11 days
(E) 38 days
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.Answer: D
Answer: (D) 11 days
Question: The cost price of two types of tea are Rs. 180 per kg and Rs. 200 per kg respectively. On mixing them in the ratio 5:3, the mixture is sold at Rs. 210 per kg . In the whole transaction, the gain percent is
(A) 10%
(B) 11%
(C) 12%
(D) 13%
(E) 14%
Rationale: Exp. Let 5kg of first kind of tea be mixed with 3 kg of second kind
C.P of 8 kg of tea = Rs. ( 180*5 + 200*3 ) = Rs. 1500
S.P of 8 kg of tea = Rs. (210 * 8) = Rs. 1680
Gain = Rs. ( 1680 – 1500 ) = Rs. 180
Gain% = ( 180/1500*100 )% = 12%
ANSWER:C
Answer: (C) 12%
Question: Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both BG, with these two children immediately adjacent to here on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations Y are there for the children?
(A) 240
(B) 480
(C) 720
(D) 1440
(E) 3600
Rationale: MAGOOSHOFFICIAL SOLUTION:
First, we will consider the restricted elements — children ABG have to be in three seats in a row. How many “three in a row” seats are there in a row of seven seats?
X X X _ _ _ _
_ X X X _ _ _
_ _ X X X _ _
_ _ _ X X X _
_ _ _ _ X X X
There are five different “three in a row” locations for these three children. Now, for any given triplet of seats, we know A has to be in the middle, so the children could be seated B-A-G or G-A-B — just those two orders. This means the total number of configurations for these three children is 5*2 = 10.
Now, consider the non-restricted elements, the other four. Once ABG are seated, the remaining four children can be seated in any order among the remaining four seats — that’s a permutation of the 4 items —- 4P4 = 4! = 24. For any single configuration of ABG, there are 24 ways that the other children could be seated in the remaining seats.
Finally, we’ll combine with the Fundamental Counting Principle. We have 10 ways for the first three, and 24 ways for the remaining four. That’s a total number of configurations Y of 24*10 = 240.
Answer = A
Answer: (A) 240
Question: If an electricity bill is paid before due date, one gets a reduction of 4 % on the amount of the bill . By paying the bill before due date, a person got a reduction of Rs.13 . The amount of his electricity bill was
(A) Rs.125
(B) Rs.225
(C) Rs.325
(D) Rs.425
(E) None
Rationale: Answer
Let amount of electricity bill = ₹ N
∴ 4% of N = 13
⇒ (4 x N)/100 = 13
⇒ N = 13 x 25 = ₹ 325
Correct Option: C
Answer: (C) Rs.325
Question: A man is 24 years older than his son. In four years, his age will be twice the age of his son. The present age of the son is
(A) 14 years
(B) 18 years
(C) 20 years
(D) 22 years
(E) None
Rationale: Solution
Let the son's present age be x years .Then, man's present age	= (x+24)years.
Then	â€¹=â€º(x+24)+4= 2(x+4)
â€¹=â€ºx+28=2x+8
x= 20.
Answer C
Answer: (C) 20 years
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 23/113
(B) 36/145
(C) 21/117
(D) 11/154
(E) 21/115
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: In a certain parking lot, 2% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
(A) 4%
(B) 6%
(C) 8%
(D) 10%
(E) 12%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
2%*x = 20%*y
y/x = 1/10 = 10%
The answer is D.
Answer: (D) 10%
Question: Look at this series: 5000,1000, 200, ... What number should come next?
(A) 17
(B) 10
(C) 15
(D) 18
(E) 40
Rationale: E
40
This is a simple division series. Each number is divided by 5.
Answer: (E) 40
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
(A) 350
(B) 349
(C) 389
(D) 369
(E) 388
Rationale: x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p/17
The least value of p for which q =2 + 13p/17is a whole number is p = 26
x = (13 x 26 + 11)
= (338 + 11)
= 349
Answer B
Answer: (B) 349
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 76 sec
(B) 89 sec
(C) 87 sec
(D) 15 sec
(E) 16 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10
= 89 sec.
Answer:B
Answer: (B) 89 sec
Question: In how many ways can a committee of 6 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls?
(A) 67
(B) 64
(C) 65
(D) 66
(E) None of these
Rationale: There are 2 options: the selected groups have no girls or one girls.
-First case: 1 girl + 3 boys: 6C1 * 5C3 = 6*10 = 60
-Second case: 4 boys: 5C4 = 5
So there are 60 + 5 = 67 ways in total.
A
Answer: (A) 67
Question: If the radius of a circle decreased by 50% its area is decreased by:
(A) 75
(B) 79
(C) 72
(D) 70
(E) 80
Rationale: Original area = πr(power)2
New area = π(r/2)(power)2 = (πr(power)2)/4
Reduction in area = [(πr(power)2 - (πr(power)2)/4]2 = (3πr(power)2)/4
Reduction percent = ((3πr(power)2)/4 × 1/(πr(power)2 × 100) % = 75%
Answer is A.
Answer: (A) 75
Question: A certain psychologist charges $25 more for the first hour of therapy than for each additional hour. If the total charge to a patient who receives 5 hours of therapy is $250, what is the total charge to a patient who receives only 2 hours of therapy ?
(A)  $115
(B)  $135
(C)  $150
(D)  $165
(E)  $192
Rationale: Let the charge for first hour = x+25
then charge for each additional hour = x
x+25 + 4x = 250
=> 5x = 225
=> x = 45
Total charge for patient for 3 hours of therapy = x+25 + x = 2x+25
= 115 $
Answer A
Answer: (A)  $115
Question: A gym offers 11 levels of fitness classes, and in an attempt to reward those who progress toward higher levels of fitness it charges $50 less per course for each level of fitness. Jessica completed all 11 levels by taking one course at each level, and her total cost was $4675. What is the cost W for a course at the gym's highest level?
(A) $175
(B) $245
(C) $425
(D) $675
(E) $725
Rationale: Let the cost of a course in level 1 = x
=> Cost of level 2 = x-(50*1)... and so on
=> cost of level 11 = x-(50*10) = x-500
=> Total cost W of 1 course in each of the 11 levels = x+(x-50)+(x-100)+.....+(x-500)
= 11x -50 (1+2+....+10)
= 11x - (50*55)
=> 11x-2750 = 4675
11x = 7425
x= 675
x-500=175
Answer A
Answer: (A) $175
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
(A) 153
(B) 150
(C) 137
(D) 126
(E) 89
Rationale: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 126
=> x = 84
Verify. 84+ 42 = 126
Answer is D
Answer: (D) 126
Question: A salt manufacturing company produced a total of 1000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 1750
(B) 2789
(C) 2500
(D) 1550
(E) 2000
Rationale: Total production of salt by the company in that year = 1000+ 1100+ 1200+ .... + 2100= 18600.
Average monthly production of salt for that year = 18600/12 = 1550.
Answer: D
Answer: (D) 1550
Question: A farmer with 1,350 acres of land had planted his fields with corn, sugar cane, and tobacco in the ratio of 4:2:3, respectively, but he wanted to make more money, so he shifted the ratio to 2:2:5, respectively. How many more acres of land were planted with tobacco under the new system?
(A) 90
(B) 150
(C) 270
(D) 300
(E) 450
Rationale: Originally (3/9)*1350 = 450 acres were planted with tobacco.
In the new system (5/9)*1350 = 750 acres were planted with tobacco.
Thus 750-450 = 300 more acres were planted with tobacco.
The answer is D.
Answer: (D) 300
Question: The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is :
(A) 117.8
(B) 118
(C) 124.75
(D) 149
(E) 187
Rationale: For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
Answer: (C) 124.75
Question: A invested $300 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find A shares?
(A) $100
(B) $75
(C) $20
(D) $120
(E) $50
Rationale: A:B = 300*12:200*6
A:B = 3:1
A's share = 100*3/4 = $75
Answer is B
Answer: (B) $75
Question: Find the least number of complete years in which a sum of money put out at 13% compound interest will be more than double of itself?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 6 years
Answer: B
Answer: (B) 6
Question: 0.07 x 0.00112 is equal to:
(A) 6.48 x 10(power -5)
(B) 6.84 x 10(power -4)
(C) 4.68 x 10(power -4)
(D) 7.84 x 10(power -5)
(E) None of them
Rationale: 7 x 112 = 784. Sum of decimal places = 7
So, 0.07 x 0.00112 = 0.0000784 = 7.84 x 10(power -5)
Answer is D
Answer: (D) 7.84 x 10(power -5)
Question: If a town of 65,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
(A) a.66000
(B) b.67000
(C) c.68000
(D) d.69000
(E) e.70000
Rationale: 1% is quite small and hence the answer is A)
Answer: (A) a.66000
Question: For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 * 5 * 5. How many two-digit positive integers have length 6?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: The best (quickest) way I can think of to get the answer, is start with 2^6, then move on from there.
2^6=64
2^5*3=96
Obviously 2^5*5 will be more than 2 digits, as will 2^4*3^2. So 64 and 96 are it.
Answer is 2 (C).
Answer: (C) Two
Question: Three small cruise ships, each carrying 8 passengers, will dock tomorrow. One ship will dock at Port A, another at Port B, and the third at Port C. At Port A, two passengers will be selected at random and each winner will receive one gift certificate worth $50. At Port B, one passenger will be selected at random to receive a gift certificate worth $35, and at Port C, one passenger will be selected at random to receive a gift certificate worth $25. How many different ways can the gift certificates be given out?
(A) 9,832
(B) 10,752
(C) 11,364
(D) 12,548
(E) 13,786
Rationale: The number of ways for the ships to go to the ports is 3! = 6.
At Port A, the number of ways to choose two winners is 8C2 = 28.
At Port B, the number of ways to choose one winner is 8.
At Port C, the number of ways to choose one winner is 8.
The total number of ways to give out gift certificates is 6*28*8*8 = 10,752
The answer is B.
Answer: (B) 10,752
Question: If I walk at 8 km/h, I miss the bus by 14 minutes. If I walk at 9 km/h, I reach 16 minutes before the arrival of the bus. How far I walk to reach the bus stand ?
(A) 3.4 km
(B) 2.9 km
(C) 2.4 km
(D) 2.6 km
(E) 2.8 km
Rationale: d = product of speed difference of time /difference of speed
d = 8 X 9/60[14âˆ’(âˆ’16)/9-8]
[Here, â€“ve sign indicates before the schedule time]
â‡’ d = 2.4 km
Answer C
Answer: (C) 2.4 km
Question: A shopkeeper sells one radio for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. What is his total gain or loss percentage?
(A) 6 15/17%
(B) 5 15/17%
(C) 3 15/17%
(D) 4 15/17%
(E) 5 15/18%
Rationale: selling price of first radio=840
gain =20%
cost price of first radio=840×100/120=700
selling price of second radio =960
loss =4%
cost price of second radio =960×100/96=1000
total cost price =700+1000=1700
total selling price =840+960=1800
total gain =1800−1700=100
total gain percentage =100*100/1700=100/17%=5 15/17%
Answer : B
Answer: (B) 5 15/17%
Question: On a certain Monday, Carlos drove to work at an average speed of 10 miles per hour and home from work along exactly the same route at an average speed of 20 miles per hour. Which of the following is closest to his average speed for both trips combined?
(A) 17
(B) 16
(C) 15
(D) 14
(E) 13.33
Rationale: To solve the average speed questions, we need to know the total distance and the total time.
Let us assume that the distance from work = D
This will also be the distance from work to home
Hence total distance travelled = 2D
Time in going to work = D/10,
Time in coming back from work = D/20
Hence average speed of both the trips = 2D/ (D/10 + D/20)
= 2*20/3 = 13.33
E
Answer: (E) 13.33
Question: J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r?
(A) 93.5
(B) 90
(C) 6.75
(D) 6.25
(E) 2
Rationale: Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables.
Let, P = 400
then J = (75/100)*400 = 300
also J = (80/100)*T
i.e. T = 300*100/80 = 375
and T = [1-(r/100)]*P
i.e. 100-r = 100*T/P = 100*375/400 = 93.75
i.e. r = 6.25
Answer: Option D
Answer: (D) 6.25
Question: Jennifer had $120 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
(A) $16
(B) $14
(C) $5
(D) $15
(E) $0
Rationale: 1/5 x $120 = $24 for sandwich
1/6 x $120 = $20 for museum
1/2 x $120 = $60 for book
$24 + $20 + $60 = $104 spent
$120 - $104 = $16 left over
correct answer A
Answer: (A) $16
Question: In Football game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4
Rationale: In Football game,Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
Answer: C.
Answer: (C) 5/9