mathewhe/aqua_rat huggingface dataset:
Question: A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 4
(B) 5
(C) 6
(D) 76
(E) 7
Rationale: 2/5 + (2 + x)/10 = 1 => x = 4 days
\Answer: A
Answer: (A) 4
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 45 minutes. The total distance is?
(A) 1 km
(B) 2.87 km
(C) 3 km
(D) 4 km
(E) 5 km
Rationale: B
3 km
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 45/60
47x/60 = 45/60 => x = 0.95.
Total distance = 3 * 0.95 = 2.87 km.
Answer: (B) 2.87 km
Question: A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 45 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
(A) $15,360
(B) $17,360
(C) $18,000
(D) $21,360
(E) $29,160
Rationale: For every $3 earn above $9360, the recipient loses $1 of benefit.
OR
For every $1 loss in the benefit, the recipient earns $3 above $9360
If earning is; 9360+3x
Benefit = 12000-x
Or the vice versa
If benefit is 12000-x, the earning becomes 9360+3x
He lost 50% of the benefit;
Benefit Received= 12000-0.45*12000 = 12000-5400
x=6600
Earning becomes 9360+3x=9360+3*6600=29160
Ans:E
Answer: (E) $29,160
Question: If the range of the set of numbers {150, 90, 125, 110, 170, 155, x, 100, 140} is 90, which of the following could be x?
(A) 80
(B) 95
(C) 110
(D) 125
(E) 140
Rationale: The range of the other 8 numbers is 170-90 = 80, so x must be either the smallest number or the largest number in the set.
Then x = 170-90 = 80 or x = 90+90 = 180
The answer is A.
Answer: (A) 80
Question: If 1535/1038 = a+1/[b+1/{c+(d+ 1/e)}]. Find a*b*c*d*e?
(A) 165/2
(B) 175/2
(C) 178/3
(D) 187 by 2
(E) 197/2
Rationale: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Answer: (D) 187 by 2
Question: In order to complete a reading assignment on time, Terry planned to read 80 pages per day. However, she read only 40 pages per day at first, leaving 1000 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
(A) 18
(B) 19
(C) 17
(D) 16
(E) 15
Rationale: D=80*X - according to the plan, assignment to be completed on time reading 80 pages per day for next X days. But, Terry's plans changed so she read as follow:
40 pages for first Y days and 1000 pages for last 6 days, we get these equations:
40*Y+1000=80*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 40 pages per day and 6 leftover days used to complete a lump 1000 pages
From above we find that X=Y+6 and 40Y+1000=80Y+480 or 40Y=520 --->>>>> Y=13, hence X=19
Answer : B
Answer: (B) 19
Question: Age of a father and his son is in the ratio of 5 : 2. After two years, the ratio becomes 19 : 8. What are the present ages of father and son respectively ?
(A) 45 and 12
(B) 35 and 12
(C) 40 and 16
(D) 45 and 18
(E) 55 and 22
Rationale: Let present ages of father and son be 5x : 2x.
After two years:
(5x + 2) / (2x + 2) = 19 / 8
40x + 16 = 38x + 38 => 2x = 22 => x = 11.
Father = 5x = 5 x 11 = 55; Son = 2x = 2 x 11 = 22
Option E
Answer: (E) 55 and 22
Question: What is the sum of the prime factors of 121 and the prime factors of 7434
(A) 27
(B) 67
(C) 57
(D) 37
(E) 47
Rationale: The prime factors of 7434are 3*3*2*7
The prime factors of 121 are 11*11
3+3+2+7+11+11 = 37. D is the correct answer
Answer: (D) 37
Question: 15% people of a village in Sri Lanka died by bombardment, 25% of the remainder left the village on account of fear. If now the population is reduced to 4555, how much was it in the beginning?
(A) 7400
(B) 7145
(C) 7200
(D) 7323
(E) 6030
Rationale: X * (85/100) * (75/100) = 4555
X = 7145
Answer: B
Answer: (B) 7145
Question: A goods train runs at a speed of 72 kmph and crosses a 250 m long platform in 26 seconds.What is the length of the goods train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 270 m
(E) 250 m
Rationale: s=250+x/t
72*5/18=250+x/26
x=270
ANSWER:D
Answer: (D) 270 m
Question: Find the odd man out
1,5,14,30,50,55,91.
(A) 5
(B) 50
(C) 55
(D) 91
(E) 1
Rationale: 50 is the odd man.. diff between sucessive no.s is a perfect square
ANSWER:B
Answer: (B) 50
Question: The edge of three cubes of metal is 3 dm, 4 dm and 5 dm. They are melted and formed into a single cube. Find the edge of the new cube?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: Explanation:
33 + 43 + 53 = a3 => a = 6
A)
Answer: (A) 6
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 870 in 4 years. The rate of interest per annum is?
(A) 2 1/2 %
(B) 8 3/4%
(C) 5%
(D) 6 2/3 %
(E) 6%
Rationale: S.I. on Rs. 800 for 1 year = (870 - 800) = Rs. 70 Rate = (100 * 70)/(800 * 1) = 8 3/4%
ANSWER:B
Answer: (B) 8 3/4%
Question: A waitress's income consists of her salary and tips.During one week ,her tips were 2/4 of her salary.What fraction of her income for the week came from tips?
(A) 1/9
(B) 1/6
(C) 1/3
(D) 4/9
(E) 5/9
Rationale: Her tips were 2/4 of her salary.
Let's say her salary =$4
This mean her tips = (2/4)($4) =$2
So, her TOTAL INCOME =$4+$2=$6
What fraction of her income for the week came from tips
$2/$6= 1/3
= C
Answer: (C) 1/3
Question: A father tells his son, "I was of your present age when you were born". If the father is 36 now, how old was the boy five years back ?
(A) 13
(B) 15
(C) 17
(D) 20
(E) 22
Rationale: F is fathers age and B is Boys age
F-B=B, F=2B
2B=36, B=18
Boys age 5 years back would be 13
ANSWER:A
Answer: (A) 13
Question: 34.94 + 240.016 + 23.98 = ?
(A) 298.936
(B) 298.694
(C) 289.496
(D) 289.469
(E) 298.964
Rationale: 34.94
240.016
+ 23.98
--------
298.936
Answer is A.
Answer: (A) 298.936
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
(A) 16 2/9%
(B) 16 4/3%
(C) 16 2/3%
(D) 16 3/3%
(E) 12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Answer: (C) 16 2/3%
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
(A) Rs.4082.67
(B) Rs.4082.99
(C) Rs.4082.29
(D) Rs.4082.40
(E) Rs.4082.12
Rationale: Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6
= Rs.4082.40
Answer:D
Answer: (D) Rs.4082.40
Question: How many different subsets of the set {10, 12, 17, 24} are there that contain an odd number of elements?
(A)  3
(B)  8
(C)  6
(D)  10
(E)  12
Rationale: Answer = B = 8
{10}
{12}
{17}
{24}
{10, 12, 17}
{12, 17, 24}
{10, 17, 24}
{10, 12, 24}
Answer: (B)  8
Question: A car travels from B at a speed of 20 km/hr. The bus travel starts from A at a time of 6 A.M. There is a bus for every half an hour interval. The car starts at 12 noon. Each bus travels at a speed of 25 km/hr. Distance between A and B is 100 km. During its journey ,The number of buses that the car encounter is ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Total journey = 100 km.
The bus travel starts from A at a time of 6 A.M. and each bus travels at a speed of 25 km/hr so time required for the bus to complete the journey = 4 hrs.
so the bus starts at 8:30 will meet with the car moving in opposite direction definitely.
Car travels from B at a speed of 20 km/hr so time of arrival of car at A is 5 P.M., it means the last bus which will meet with the car is that starts at 4:30 P.M.
so total bus ranges from 8:30 P.M. to 4:30 P.M. = 17
ANSWER:C
Answer: (C) 17
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.7, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.063
(B) 0.125
(C) 0.128
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.7
Therefore, probability of no rain = 0.3
0.3*0.3*0.7 = 0.063
Hence A
Answer: (A) 0.063
Question: John makes $40 a week from his job. He earns a raise and now makes $60 a week. What is the % increase?
(A) 16%
(B) 16.66%
(C) 18%
(D) 21%
(E) 50%
Rationale: Increase = (20/40)*100 = 50%.
E
Answer: (E) 50%
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his
bank balance doubled to $3420. What is the average monthly balance maintained by John in his
account during the year?
(A) 2840
(B) 5680
(C) 6840
(D) 7540
(E) 17100
Rationale: Soln:-
Bank balance is doubled with accumulation of interest to 3420..
this means INTEREST is 3420/2=1710 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 17100..
ANSWER:E
Answer: (E) 17100
Question: If 14 lions can kill 14 deers in 14 minutes how long will it take 100 lions to kill 100 deers?
(A) 1 minutes
(B) 14 minute
(C) 100 minutes
(D) 10000 minutes
(E) 1000 minutes
Rationale: we can try the logic of time and work,our work is to kill the deers so 14(lions)*14(min)/14(deers)=100(lions)*x(min)/100(deers)hence answer is x=14
ANSWER:B
Answer: (B) 14 minute
Question: The remainder obtained by the division of two numbers by a common divisor are 33 and 47 respectively. However when the sum of these two numbers is divided by the same divisor, the remainder obtained is only 30. What is the divisor?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 65
Rationale: Remainders are 33 & 47. So directly rule out the possibility of the divisor being 20, 30 & 40
Option A, B, C ruled out
Consider option D - 50
50+33 = 83 & 50+47 = 97
83+97 = 180
180/50 gives remainder = 30
Answer = D
Answer: (D) 50
Question: jess bakes 5 biscuits for 5 friends. 3 of the friend arrive early and eat 3 biscuits each. How many biscuits are left over if the other friends all have the same number of biscuits?
(A) 7
(B) 1
(C) 0
(D) 3
(E) 4
Rationale: jess made 5*5 biscuits = 25 biscuits. 3 friends eat 3 biscuits, leaving 16 remaining for 2 friends.
16 divisible by 2.
C is the correct answer
Answer: (C) 0
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
(A) 37
(B) 28
(C) 30
(D) 19
(E) 12
Rationale: Explanation:
There is a meal for 200 children. 150 children have taken the meal.
Remaining meal is to be catered to 50 children.
Now, 200 children = 120 men.
50 children = {\color{Blue} \left ( \frac{120}{200} \right )\times 50} =30men
Answer: C
Answer: (C) 30
Question: A dragon has 100 heads. A soldier can cut off 15, 17, 20 or 5 heads, respectively with one blow of his sword. In each of these cases, 24, 2, 14, 17 new heads grow on its shoulders. If all heads are cut off, the dragon dies. Can the dragon ever die?
(A) 61
(B) 3
(C) 5
(D) 6
(E) 1
Rationale: Here the difference in the cutoff heads and newly grown heads is 3. 100 is not divisible by 3. The dragon never die.
Answer:B
Answer: (B) 3
Question: Find the next number in the series
1, 6, 13, 22, 33, ......
(A) 44
(B) 45
(C) 46
(D) 47
(E) 48
Rationale: 1+5=6
6+7=13
13+9=22
22+11=33
33+13=46
ANSWER:C
Answer: (C) 46
Question: Which of the following is between 1/9 and 5/21?
(A) 2/13
(B) 3/8
(C) 1/2
(D) 5/8
(E) 7/9
Rationale: I see this as a POE (Process of Elimination) and Ballparking (Estimation) question. Not sure if this is the most efficient, but it worked:
1) I estimate 1/9 to be ~1/10 + (approximately slightly greater than 3/4)
2) I estimate 5/21 to be ~1/5+ (approximately slightly greater than 1/5)
3) So now I'm looking for an answer choice that is .1 < x < .2
Answer A - 2/13 ~ ..15 which is greater than .1 and less than .2
Answer: (A) 2/13
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.12 of money?
(A) 1200
(B) 1992
(C) 9921
(D) 2798
(E) 2789
Rationale: P = 12(100/10)2
=> P = 1200
Answer: A
Answer: (A) 1200
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1620 are infected, how manyworkersinhabit the colony?
(A) 1500
(B) 2500
(C) 2750
(D) 3000
(E) 3250
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1620
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1620
0,16s=640
64000:16= 4000 =s
In (2) 4000 + w = 7000
w= 3000 D
Answer: (D) 3000
Question: The below sequence is a bit tricky. Can you solve it to find the next number?
7, 25, 325, 4325, ?
(A) 29816
(B) 38291
(C) 54327
(D) 38290
(E) 55291
Rationale: See the pattern. With every digit, the previous numbers are added after that digit
So the next number in the series is 54327
Answer : C
Answer: (C) 54327
Question: Which of the following fractions W, if written as a decimal, would have a 2 in the thousandths place ?
(A)  3/11
(B)  7/9
(C)  1/8
(D)  4/7
(E)  1/6
Rationale: (A) W=3/11 = 0.2727272727....
Answer: A
Answer: (A)  3/11
Question: What will come in place of the question mark (?) in the following equation?
25(7.5) × 5(2.5) ÷ 125(1.5) = 5?
(A) 16
(B) 17.5
(C) 8.5
(D) 13
(E) None of these
Rationale: 25(7.5) × 5(2.5) ÷ 125(1.5) = 5?
or, 5(2 × 7.5) × 5(2.5) ÷ 5(3 × 1.5) = 5?
or 5(15) × 5(2.5) × 1⁄54.5 = 5?
or, 5(13)= 5? or, ? = 13
Answer D
Answer: (D) 13
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number is?
(A) 36
(B) 67
(C) 87
(D) 56
(E) 51
Rationale: (3x-9):(5x-9)
= 9:17
x = 12 => 3x
= 36
Answer:A
Answer: (A) 36
Question: For 1rs 6p interest
wat will be for 1000rs?
(A) 45Rs
(B) 50Rs
(C) 40Rs
(D) 30Rs
(E) 60Rs
Rationale: For 1rs , 4p interest
for 1000rs, x
x= 1000/1 * 6p ==> 6000 paise
To express in rs, 6000/100 = 60rs
ANSWER:E
Answer: (E) 60Rs
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are
(A) 4, 8, 12
(B) 5, 10, 15
(C) 10, 20, 30
(D) 12, 24, 36
(E) None of these
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12
The numbers are 12, 24, 36. Answer: D
Answer: (D) 12, 24, 36
Question: if i sell two articles, one at 20% profit for rs.100 and the other at 20% loss for rs.100, what is my net profit/loss?
(A) 4.16 profit
(B) 4.00 loss
(C) 8.33 profit
(D) 8.33 loss
(E) none
Rationale: 20/100=(100-CP1)/CP1
20/100=(CP2-100)/CP2
CP1 = 500/6 = 83.33
CP2 = 500/4 = 125
Total CP = 208.33
Total SP = 200
Loss = 8.33
Loss % = Loss x 100 / CP
833.33/208.33
4.0004 % loss
ANSWER:B
Answer: (B) 4.00 loss
Question: In a barrel of juice there is 30 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 2:1.
(C) 3:1.
(D) 4:3.
(E) 3:4
Rationale: Price of 30 L juice= 3x
1L= 3x/30
Price of 80 L beer= 4x
1L= 4x/80
Ratio of 1 L price = 3x/30/4x/80= 2:1
B is the answer
Answer: (B) 2:1.
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 7 years
(E) 6 years
Rationale: Explanation:
Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) = 42 years.
Required difference = (42 - 36) = 6 years.
Answer: Option C
Answer: (C) 6 years
Question: How many positive integers will divide evenly into 410?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 16
Rationale: The question is asking how many factors 410 has.
410 = 2*5*41
The number of factors is 2^3 = 8
The answer is C.
Answer: (C) 8
Question: The sum of money at compound interest amounts to thrice itself in 5 years. In how many years will it be 15 times itself?
(A) 8 years
(B) 9 years
(C) 10 years
(D) 25 years
(E) 3 years
Rationale: 100 ---- 300 --- 5
600 --- 5
900 ---5
1200 ---5
1500--- 5
25 years
Answer: D
Answer: (D) 25 years
Question: If the Average (mean ) of 9 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 8x
(B) 4x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Rationale: Let the 5 numbers be 1,2,3,4,5,..9 (since no restrictions are given). There mean is 4 (x).
Now the sum of greatest three would be 7+8+9=24
so the answer has to be 8x....that is option A
Answer: (A) 8x
Question: Factor: 2x4y3 â€“ 32y3
(A) A) 3y3(x2 + 4)(x + 2)(x -2)
(B) B) 2y3(x2 + 4)(x + 2)(x -2)
(C) C) 3y3(x2 + 4)(x + 2)(x -3)
(D) D) 3y3(x2 + 4)(x + 3)(x -2)
(E) E) 3y3(x2 + 4)(x + 2)(x -4)
Rationale: 2x4y3â€“ 32y3.
= 2y3(x4 â€“ 16).
= 2y3[(x2)2 - 42].
= 2y3(x2 + 4)(x2 - 4).
= 2y3(x2 + 4)(x2 - 22).
= 2y3(x2 + 4)(x + 2)(x -2).
Answer: (B) 2y3(x2 + 4)(x + 2)(x -2)
Answer: (B) B) 2y3(x2 + 4)(x + 2)(x -2)
Question: If there are 6 seats and 2 students, in how many ways can they be seated?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: The first student has 6 choices and the second student has 5 choices.
The number of ways to sit is 6*5 = 30.
The answer is B.
Answer: (B) 30
Question: David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
(A) 75
(B) 77
(C) 28
(D) 29
(E) 26
Rationale: Explanation:
Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5 = 75.
Answer: A) 75
Answer: (A) 75
Question: A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 11 hours longer than the first half, how many hours did it take the runner to run the second half?
(A) 14
(B) 15
(C) 18
(D) 22
(E) 33
Rationale: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+11
T1 = 11 and so T2 = 22.
The answer is D.
Answer: (D) 22
Question: On a scale that measures the intensity of a certain phenomenon, a reading of f+1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of f. On that scale, the intensity corresponding to a reading of 8 is how many times as great as the intensity corresponding to a reading of 3?
(A)  5
(B)  50
(C)  10^5
(D)  5^10
(E)  8^10 - 3^10
Rationale: To solve this problem we need to examine the information in the first sentence. We are told that “a reading of f + 1 corresponds to an intensity that is 10 times the intensity corresponding to a reading of f.”
Let’s practice this idea with some real numbers. Let’s say f is 2. This means that f + 1 = 3. With the information we were given we can say that a reading of 3 is ten times as great as the intensity of a reading of 2.
Furthermore, we can say that a reading of 4 is actually 10 x 10 = 10^2 times as great as the intensity of a reading of 2.
Increasing one more unit, we can say that a reading of 5 is 10 x 10 x 10 = 10^3 times as great as the intensity of a reading of 2.
We have found a pattern, which can be applied to the problem presented in the stem:
3 is “one” unit away from 2, and thus a reading of 3 is 10^1 times as great as the intensity of a reading of 2.
4 is “two” units away from 2, and thus a reading of 4 is 10^2 times as great as the intensity of a reading of 2.
5 is “three” units away from 2, and thus a reading of 5 is 10^3 times as great as the intensity of a measure of 2.
We can use this pattern to easily answer the question. Here we are being asked for the number of times the intensity corresponding to a reading of 8 is as great as the intensity corresponding to a reading of 3. Because 8 is 5 units greater than 3, a reading of 8 is 10^5 times as great as the intensity corresponding to a reading of 3.
Answer C.
Answer: (C)  10^5
Question: Michelle leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Michelle, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Michelle is 30 km\hr, find the speed of his son.
(A) 15km/hr
(B) 6 km/hr
(C) 4.28 km/hr
(D) 9 km/hr
(E) 4.12 km/hr
Rationale: Michelle leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Michelle, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Michelle is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here, Michelle would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
Answer: (C) 4.28 km/hr
Question: Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
(A) 5 days
(B) 7 days
(C) 8 days
(D) 6 days
(E) 4 days
Rationale: 2M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
70M + 105W = 84M +84M
21W = 14M => 2M = 3W
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
Answer:A
Answer: (A) 5 days
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.17 per cubic meter?
(A) 2998
(B) 2799
(C) 2890
(D) 1683
(E) 2780
Rationale: 22/7 * 14 * 3/2 * 3/2
= 99 m2
99 * 17
= 1683
Answer:D
Answer: (D) 1683
Question: In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a14?
(A) 100
(B) 55
(C) 27
(D) 19
(E) 1
Rationale: As stated above, (a1+a2+a3......+a10)/10=10
therefore a1+a2+a3.......a14=196 (1)
using the same logic, we got a1+a2+a3..........+a13=169 (2)
(2)-(1) we got a14=27
C
Answer: (C) 27
Question: If s and t are positive integers, and 3 is not a factor of t, then t may be which of the following?
(A) (s−1)·s·(s+1)
(B) (s−3)·(s−1)·(s+1)
(C) (s−2)·s·(s+2)
(D) (s−1)·s·(s+2)
(E) (s−3)·(s+1)·(s+2)
Rationale: Plugged in values :
let s=5
A. (s−1)·s·(s+1) --> divisible by 3
B. (s−3)·(s−1)·(s+1) --> divisible by 3
C. (s−2)·s·(s+2) --> divisible by 3
D. (s−1)·s·(s+2) --> not divisible. Hence the answer.
Answer: (D) (s−1)·s·(s+2)