mathewhe/aqua_rat huggingface dataset:
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.95 less, he could have gained 25%. What is the cost price?
(A) 372
(B) 375
(C) 278
(D) 475
(E) 288
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
95 ----- ? => 475
Answer:D
Answer: (D) 475
Question: At a local appliance manufacturing facility, the workers received a 25% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
(A) 83%
(B) 80%
(C) 20%
(D) 17%
(E) 12%
Rationale: Let's say he works usually 10 hours and earns 100 per hour.
10 * 100 = 1000
10 * 125 = 1250 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/125 = 8
So he can reduce his work by 2 hours. Which is 20%.
Answer C
Answer: (C) 20%
Question: 50% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 70
(B) 97
(C) 84
(D) 90
(E) 76
Rationale: Given, 50% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 50% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/50 =48
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (48 + 120)/2 = 84.
Answer:C
Answer: (C) 84
Question: The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 28 years. The ratio of their ages after 6 years will be
(A) 2 : 3
(B) 7 : 11
(C) 5 : 4
(D) 4 : 5
(E) 11 : 9
Rationale: Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 28
x = 4
Mini’s age = 16 years
And Minakshi’s age = 12 years
Ratio of their ages after 8 years = (16 + 6) : (12 + 6) = 22 : 18 = 11 : 9
ANSWER:E
Answer: (E) 11 : 9
Question: If −y ≥ x, and −x < −7, then which of the following must be true?
(A) y = −7
(B) y > −7
(C) −y > 7
(D) y ≤ −7
(E) y ≥ −7
Rationale: −y ≥ x, and −x < −7
y <= -x < -7
As '-x' is less than '-7' and Y is less than or equal to '-x'
we have y < -7 which is similar to -y > 7.
C) -y > 7
Answer: (C) −y > 7
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 11220, how much money did he borrow?
(A) 11000
(B) 80288
(C) 2668
(D) 2600
(E) 2781
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 11220
18x + 45x + 39x = (11220 * 100)
102x = 1122000 => x = 11000.
Answer:A
Answer: (A) 11000
Question: The owner of a furniture shop charges his customer 42% more than the cost price. If a customer paid Rs. 8300 for a computer table, then what was the cost price of the computer table?
(A) Rs. 5725
(B) Rs. 5845
(C) Rs. 6275
(D) Rs. 6725
(E) None of these
Rationale: CP = SP * (100/(100 + profit%))
= 8300(100/142) = Rs. 5845.
ANSWER:B
Answer: (B) Rs. 5845
Question: When Jack picks olives for two hours at three times his regular speed, he picks 20 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 75% 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.
D
Answer: (D) Mac picks 5 more pounds than Jack
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 3 seconds. What is the length of the fast train ?
(A) 27 7/9
(B) 16 2/3
(C) 29 7/9
(D) 30 7/9
(E) None of these
Rationale: Explanation:
As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length=50/9âˆ—3
=150/9
=16 2/3
Option B
Answer: (B) 16 2/3
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Poe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Poe?
(A) 15
(B) 60
(C) 75
(D) 90
(E) 105
Rationale: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Poe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins=D
Answer: (D) 90
Question: What is the average of four tenths and five thousandths?
(A) 0.2022
(B) 0.2012
(C) 0.2025
(D) 0.2021
(E) 0.2029
Rationale: Four tenths = 0.4
Five thousandths = 0.005
The average is (0.4 + 0.005)/2 = 0.2025
Answer: C
Answer: (C) 0.2025
Question: Find the area of the quadrilateral of one of its diagonals is 15 cm and its off sets 6 cm and 4 cm?
(A) 50 cm2
(B) 60 cm2
(C) 75 cm2
(D) 90 cm2
(E) 150 cm2
Rationale: 1/2 * 15(6 + 4)
= 75 cm2
Answer: C
Answer: (C) 75 cm2
Question: The number of ways in which ten candidates A1, A2, ...., A10 can be ranked so that A1 is always above A2 is
(A) 10!⁄2
(B) 10!
(C) 9!
(D) 8!⁄2
(E) None of these
Rationale: Ten candidates can be ranked in 10! ways. In half of these ways A1 is above A2 and in another half A2 is above A1.
So, required number of ways is 10!⁄2
Answer A
Answer: (A) 10!⁄2
Question: The avg. age of a group of 16 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
(A) 22 years
(B) 23 years
(C) 24 years
(D) 25 years
(E) 26 years
Rationale: Total age of 16 students=16*20=320
If total age of 4 students=x
Then, (320+x)/(16+4) =(20+1), x=100
So average age of new students=100/4= 25 years
ANSWER:D
Answer: (D) 25 years
Question: M = {-6, -5, -4, -3, -2, -1}
T = {-5, -4, -3, -2, -1, 0, 1, 2}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
(A) 0
(B) 1/4
(C) 2/5
(D) 1/2
(E) 3/5
Rationale: We will have a negative product only if 1 or 2 are selected from set T.
P(negative product) = 2/8 = 1/4
The answer is B.
Answer: (B) 1/4
Question: A cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak empty it?
(A) 50hours
(B) 62hours
(C) 90hours
(D) 75hours
(E) 100hours
Rationale: Let the leak empty the full cistern in x hours
9x/x-9 = 9+1
x = 90 hours
Answer is C
Answer: (C) 90hours
Question: If the position of the first, sixth digits of the number 2796543018 are interchanged, similarly the positions of the the second and seventh digits are interchanged and so on, which of the following will be the left of seventh digit from the left end?
(A) 1
(B) 2
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
The new number formed is 4 3 0 1 8 2 7 9 6 5
The seventh digit from the left is 7, the 3rd digit from the left of 7 is 1
Answer: A) 1
Answer: (A) 1
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 30% lemonade syrup?
(A) 1.5
(B) 1.75
(C) 2.14
(D) 2.34
(E) 2.64
Rationale: Let the total solution is 150 L with 80 L water70 L syrup.
To make 30% syrup solution, the result solution must have 105 L syrup and 45 L syrup.
Therefore we are taking 25 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
25 L syrup in 53.6 L solution
We started by multiplying 10
Now to get to the result we need to divide by 25 => amount of solution to be replaced with water = (53.6/25) = 2.14.
Correct option : C
Answer: (C) 2.14
Question: Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of milk. The pattern repeats after she leaves the morsel of milk. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
(A) milk − wheat − wheat
(B) wheat − wheat − white
(C) white − milk − wheat
(D) white − white − white
(E) white − white − milk
Rationale: In a single round Lucy drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: (A) milk − wheat − wheat
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
(A) 3
(B) 4
(C) 5
(D) 7
(E) 8
Rationale: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
A
Answer: (A) 3
Question: If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc...
The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc...
The distances between marks are 3/12, 1/12, and 2/12.
The answer is C.
Answer: (C) 3
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 1 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
(A) 2.5 hours
(B) 4.5 hours
(C) 5.5 hours
(D) 1 hour
(E) None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 1 hours, Tank A and B can effectively fill 1⁄12 × 1 = 1⁄12 of the tank.
Time taken to fill the remaining 1−(1/12) = 11/12 of the tank = (11/12)/(1/6) = 5.5 hours. Answer : Option C
Answer: (C) 5.5 hours
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 149, what is the difference between the ages of Patrick and Monica?
(A) 27
(B) 64
(C) 45
(D) 72
(E) 18
Rationale: Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=149
x=4
Difference if ages of Pa and Mo=25x-9x=16x=16*4=64
Answer B
Answer: (B) 64
Question: What is the least number to be subtracted from 11, 15, 21 and 30 each so that the resultant numbers become proportional?
(A) 7
(B) 6
(C) 3
(D) 4
(E) 9
Rationale: Let the least number to be subtracted be 'x', then 11 - x, 15 - x, 21 - x and 30 - x are in proportion.
<=> (11 - x):(15 - x) = (21 - x):(30 -x)(21 - x)
From the options, when x = 3
=> 8 * 27 = 12 * 18 => then x = 3. => (11 - x)(30 - x) = (15 - x)(21 - x)
Answer: C
Answer: (C) 3
Question: A triangle has three angles all with the same ratio to each other, 1:1:1. What is the angle measurement?
(A) 45Â°
(B) 60Â°
(C) 75Â°
(D) 90Â°
(E) 105Â°
Rationale: If the ratio is 1:1:1, and the total angle measurement is 180Â°, then the equation is
x + x + x = 180Â°
3x = 180Â°
x = 60Â°
Therefore the answer is 60Â° or B.
Answer: (B) 60Â°
Question: Company C sells a line of 25 products with an average retail price of $1,200. If none of these products sells for less than $400, and exactly 12 of the products sell for less than $1,000, what is the greatest possible selling price of the most expensive product?
(A) 10,000
(B) 11.0
(C) 12,000
(D) 13,200
(E) 14,000
Rationale: The average price of 25 products is $1,200 means that the total price of 25 products is 25*1,200=$30,000.
Next, since exactly 12 of the products sell for less than $1,000, then let's make these 12 items to be at $400 each (min possible).
Now, the remaining 12 items cannot be priced less than $1,000, thus the minimum possible price of each of these 12 items is $1,000.
Thus the minimum possible value of 24 products is 12*400+12*1,000=$16,800.
Therefore, the greatest possible selling price of the most expensive product is $30,000-$16,800=$13,200.
Answer: D.
Answer: (D) 13,200
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 60 percent on clothing, 10 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A)  2.8%
(B)  3.6%
(C)  4.4%
(D)  5.2%
(E)  4.8%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2.4
Tax on others=2.4
Percentage= 4.8/100 =4.8%
Answer: E
Answer: (E)  4.8%
Question: What is the least number which when doubled will be exactly divisible by 12, 14, 18 and 22 ?
(A) 1386
(B) 1276
(C) 1566
(D) 1466
(E) 1577
Rationale: LCM of 12,14,18 and 22 = 2772
least no which will be exactly divisible by 12,14,18 and 22 = 2772
2772/2 = 1386
1386 is the number when doubled 2772
=>1386 is the least exactly divisible by 12,14,18 and 22.
ANSWER A
Answer: (A) 1386
Question: All of the stocks on the over-the-counter market are designated by either a 3-letter or a 4-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
(A) 27(26^3)
(B) 26(26^4)
(C) 27(26^4)
(D) 26(26^5)
(E) 27(26^5)
Rationale: Number of 4-letter codes: 26 * 26 * 26 = 26^3
Number of 5-letter codes: 26 * 26 * 26 * 26 = 26^4
Total Number of codes: 26^3 + 26^4 = 26^3 + 26*(26^3) = 27*(26^3)
Therefore, the answer is A: 27*(26^3).
Answer: (A) 27(26^3)
Question: One dog tells the other that there are two dogs in front of me.The other one also shouts that he too had two behind him. How many are they?
(A) 3
(B) 4
(C) 1
(D) 6
(E) 78
Rationale: Explanation:
Dog
Dog
Dog
So there are 3 dogs.
They are in circle.
Answer: A
Answer: (A) 3
Question: L29Q,L31S,P37U,R41W,T43U,?
(A) V43Y
(B) U47Y
(C) V47Z
(D) V47Y
(E) V46X
Rationale: L + Q = 29
L + S = 31
P + U = 37
R + W = 41
T + W = 43
29 , 31 , 37 , 41 , 43 ---> prime number number sequence
=> next number = 47
V + Y = 47 => V47Y
ANSWER:D
Answer: (D) V47Y
Question: A can do a work in 6 days , B can do a work in 8 days and C can do it in 12 days. B left work after 5 days. For how many number of days should A and C should work together to complete the remaining work ?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 4/3
(E) 5/2
Rationale: b work 1/8 * 5=5/8
remaining work =1-5/8=3/8
a and c work together =1/6+1/12=3/12=1/4
take remaining work is done in =8/3 *1/4=2/3 days
ANSWER:B
Answer: (B) 2/3
Question: An art gallery owner is hanging paintings for a new show. Of the eight paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
(A) 18
(B) 30
(C) 64
(D) 6720
(E) 216
Rationale: Arrangement means permutations questions..
8P3 = 8!/3! = 6720
.
ANS option D is correct answer..
Answer: (D) 6720
Question: How many randomly assembled people are needed to have a better than 50% probability that at least 1 of them was born in a leap year?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (C) 3 , with 2 we will have exactly 50%, so for more than 50% should be 3.
Answer: (C) 3
Question: Find the no. of ways in which 8 different flowers can be stung to form a garland so that 4 particular flowers are never separated.
(A) 3!x3!
(B) 7!x3!
(C) 7!x4!
(D) 8!x4!
(E) 4!x4!
Rationale: Condsidering the 4 particular flowers as one unit we have 5 flowers, which can be arranged in garland in 4! ways. But the flowers can be arranged in 4! ways. Therefore required no. of ways is 4!x4!. Ans:(E )
Answer: (E) 4!x4!
Question: X and Y invested in a business. They earned some profit which they divided in the ratio of 2 : 6. If X invested Rs.5,000. the amount invested by Y is
(A) Rs.45,000
(B) Rs.50,000
(C) Rs.60,000
(D) Rs.15,000
(E) None
Rationale: Solution
Suppose Y invested Rs.y
Then,	5000 /y = 2 / 6
â€¹=â€º y=(5000Ã—6 / 2).
â€¹=â€º y=15000.
Answer D
Answer: (D) Rs.15,000
Question: If f(a)=2a, what is the value of (f(a-b)+f(a))/b ?
(A) 4a/b
(B) 3a+4b/b
(C) (4a-2b)/b
(D) 5a-6b*b
(E) 8a-7b/b
Rationale: f(a)=2a
f(a-b)= 2(a-b)
(f(a-b)+f(a))/b = (2(a-b)+2a)/b = (4a-2b)/b
Answer is C
Answer: (C) (4a-2b)/b
Question: How many factors does 36^2 have?
(A) 2
(B) 8
(C) 24
(D) 25
(E) 26
Rationale: 36^2 = 2^4 3^4
total factors = (4+1)(4+1) = 25.
Answer is D.
Answer: (D) 25
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Explanation:
=> 3(2x+9) = 75
=> 2x+9 = 25
=> x = 8
Option A
Answer: (A) 8
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 9 miles?
(A) 27/5
(B) 26/5
(C) 23/5
(D) 22/5
(E) 21/5
Rationale: 1 km is approxmately equal to 0.6 miles
So 9 km = 9*0.6 = 5.4 miles . Multiple & divide by 10
i.e 5.4*10/10 = 54/10 = 27/5
Answer : A
Answer: (A) 27/5
Question: Machine T takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine T to make 40 widgets?
(A)  5
(B)  6
(C)  8
(D)  10
(E)  12
Rationale: i approached this one by plugging in numbers...started with C.
if 40 are made in 8 hours, then 20 are made in 4 hours. so time of T is 4, and time of B is 2.
rate together: 20/4 + 20/2 = 5+10 = 15. so in 1 hour, together make 15 widgets. in 3 hours = 45. way too much. we can eliminate right away C, B, and A - because B and T reduces the time - the total # of widgets made will be even higher.
now between D and E -> try only one ..if it doesn't work, then the other one is the answer.
i picked E:
12h to make 40 widgets, and 6 hours to make 20. this is the time of T. time of B=4 hours.
20/6 + 20/4 = 10/3 + 20/4
find LCM of 3 and 4 = 12. multiply first by 4, and second by 3:
40+60/12 = 100/12
divide by 4:
25/3
so this is the rate given.
E is the correct answer
Answer: (E)  12
Question: A train is 400 meter long is running at a speed of 60 km/hour. In what time will it pass a signal post?
(A) 28 seconds
(B) 30 seconds
(C) 40 seconds
(D) 24 seconds
(E) 18 seconds
Rationale: Speed = 60 Km/hr = 60*(5/18) m/sec = 150/9 m/sec
Total distance = 400 meter
Time = Distance/speed
= 400 * (9/150) = 24 seconds
Answer: D
Answer: (D) 24 seconds
Question: The product of the squares of two positive integers is 900. How many pairs of positive integers satisfy this condition?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Ans: E - 4 pairs
(xˆ2)(yˆ2) = 900 [square root both sides]
xy = 30
20 = 1x30, 3x10, 6x5, 5x6, 10x3, 30x1, 15x2, 2x15
Cancel the repeats
This leaves us with exactly 4 options.
Hence, E
Answer: (E) 4
Question: An archer is shooting arrows from various distances. She shoots at a target from 40 yards, 50 yards, and 60 yards. The probability that she hits within the bullseye from 40 yards is 4/5, the probability that she hits within the bullseye from 50 yards is 3/4, and the probability that she hits within the bullseye from 60 yards is 2/3. What is the probability that she hits the bullseye at least once in three shots, one from each distance listed.
(A) 39/40
(B) 49/50
(C) 59/60
(D) 9/10
(E) 14/15
Rationale: The probability that she hits the bullseye at least once = 1 - (the probability that she misses the bullseye every shot)
The probability that she misses every shot = (prob that she misses from 40 yards)*(prob that she misses from 50 yards)*(prob that she misses from 60 yards)
Prob that she misses from 40 yards = 1 - 4/5 = 1/5; Prob that she misses from 50 yards = 1 - 3/4 = 1/4; Prob that she misses from 60 yards = 1 - 2/3 = 1/3
Thus the probability that she misses all shots = (1/5)*(1/4)*(1/3) = 1/60
Thus the probability that she makes at least one shot = 1 - (1/60) = 59/60
C
Answer: (C) 59/60
Question: How many seconds will a 600 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 25
(B) 36
(C) 40
(D) 45
(E) 50
Rationale: Relative speed of the train=63-3=60kmph=60*5/18=50/3 m/sec
t=600*3/50=36sec
ANSWER:B
Answer: (B) 36
Question: Fortunes, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms?
(A) 34 km per hour
(B) 54 km per hour
(C) 49 km per hour
(D) 65 km per hour
(E) 67 km per hour
Rationale: Given that the diesel consumption is at the rate
1400×[1000x+x]1400×[1000x+x]
Cost of diesel = Rs 35 per litre
Payment to the driver = Rs 125 per hour.
Also given that the SUV is driven at the speed of xx km per hour.
Total cost (c)(c)
=1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x
=70000x+70x+100000x=70000x+70x+100000x
Now differentiating both sides in the above equation with respect to xx.
dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0
⇒ x=49 km per hour.
C
Answer: (C) 49 km per hour
Question: Find the annual income derived by investing $ 6800 in 40% stock at 136.
(A) 550
(B) 2000
(C) 250
(D) 3000
(E) 400
Rationale: By investing $ 136, income obtained = $ 40.
By investing $ 6800, income obtained = $ [(40/136)*6800] = $ 2000.
Answer B.
Answer: (B) 2000
Question: Express the following as a Decimal 6%
(A) 0.6
(B) 6.0
(C) 0.006
(D) 6.6
(E) 0.06
Rationale: 6% = 6/100
=0.06
Answer is E.
Answer: (E) 0.06
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 8 minutes more to walk to work than to ride his bike to work, then x equals?
(A) 4
(B) 7
(C) 12
(D) 15
(E) 20
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 480 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=480 ----> 40x=480--> x = 12.
Option C
Answer: (C) 12
Question: At an examination in which full marks were 500. A got 10% less than B, B got 25% more than C and C got 20% less than D. If A got 360marks, what percentage of full marks was obtained by D?
(A) 40%
(B) 44%
(C) 80%
(D) 90%
(E) 100%
Rationale: Explanation:
A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
Answer: Option C
Answer: (C) 80%