mathewhe/aqua_rat huggingface dataset:
Question: The speed of a boat in still water is 60kmph and the speed of the current is 30kmph. Find the speed downstream and upstream?
(A) 40, 68 kmph
(B) 40, 30 kmph
(C) 90, 60 kmph
(D) 40, 60 kmph
(E) 90, 30 kmph
Rationale: Speed downstream = 60 + 30 = 90 kmph
Speed upstream = 60 - 30 = 30 kmph
Answer: E
Answer: (E) 90, 30 kmph
Question: Mary and Mike enter into a partnership by investing $800 and $200 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $1200 more than Mike did, what was the profit made by their business in that year?
(A) $3000
(B) $3500
(C) $4000
(D) $4200
(E) $4500
Rationale: Explanatory Answer
Let the profit made during the year be $3x
Therefore, $x would have been shared equally and the remaining $2x would have been shared in the ratio 8 : 2.
i.e., 80% of 2x would go to Mary and 20% of 2x would go to Mike.
Hence, Mary would get (80 - 20)% of 2x more than Mike
Or60% of 2x = $1200
i.e.,(60/100)*2x = 1200
or 2x = 2000.
Hence, the profit made by the company during the year $3x = $3000.
Answer : A
Answer: (A) $3000
Question: 8+2+2^2+2^3+2^4+2^5=？
(A) (2^3-1)(2^3+2)
(B) 2^6+1
(C) 2^5-1
(D) 2^5+1
(E) 2^5-2
Rationale: 8+2+2^2+2^3+2^4+2^5=64
(2^3-1)(2^3+2)=64
the correct answer is A.
Answer: (A) (2^3-1)(2^3+2)
Question: Anand and Deepak started a business investing Rs. 25,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
(A) 2777
(B) 2888
(C) 8050
(D) 2882
(E) 2781
Rationale: Ratio of their shares = 25000 : 35000 = 5:7
Deepak's share = 13800 * 7/12 = Rs. 8050.
Answer: C
Answer: (C) 8050
Question: In how many ways can the letters of the word RECPECT be arranged?
(A) 1800
(B) 1920
(C) 2520
(D) 3453
(E) 3500
Rationale: RECPECT has 7 words, but E is repeated two times. Thus ways = 7! / 2! = 2520 ways
C
Answer: (C) 2520
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 19
(B) 19.7
(C) 19.9
(D) 21.7
(E) 22.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
B)
Answer: (B) 19.7
Question: When positive integer w is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product w*n is 3..
this means w and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: (E) None of the above
Question: On a certain date, Pat invested $6,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $24,000, in how many years total will the total value of the investment plus interest increase to $48,000?
(A) 15
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: 24,000 = 6,000(1 + x)^10
4 = (1+x)^10 = 2^2
(1+x)^10 = ((1+x)^5)^2 = 2^2
Therefore, (1+x)^5 = 2
48,000 = 6000(1 + x)^n
(1+x)^n = 8
(1+x)^n = 2^3
(1+x)^n = ((1+x)^5)^3 = (1+x)^15
Therefore, n = 15.
The answer is A.
Answer: (A) 15
Question: What are the last two digits of 43*25*23*72*51*31?
(A) 54
(B) 75
(C) 00
(D) 45
(E) 32
Rationale: 43*25*23*72*51*31=
We have to focus on the last two digits only, so 43*25=75*23=25*72=00
51*00=00 therefore 31*00=00
Hence Answer is C
Answer: (C) 00
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?
(A) 18 days
(B) 27 days
(C) 26.67 days
(D) 16 days
(E) 12 days
Rationale: Answer
A can complete a project in 20 days. So, A will complete 1/20th of the project in a day.
B can complete a project in 30 days. So, B will complete 1/30th of the project in a day.
Let the total number of days taken to complete the project be x days.
B worked for all x days. However, A worked for (x - 10) days because A quits 10 days before the project is completed.
In a day, A completes 1/20th of the project.
Therefore, A would have completed x−10/20th of the project in (x - 10) days.
In a day, B completes130130th of the project.
Therefore, B would have completed x/30h of the project in x days.
∴ x−10/20+x/30= 1
Or x = 18.
Choice A
Answer: (A) 18 days
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 14 liters
(B) 76 liters
(C) 10 liters
(D) 11 liters
(E) 12 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P =10 liters.
Answer: C
Answer: (C) 10 liters
Question: A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
(A) 8 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 18 days
Rationale: Explanation:
(A + B)'s 1 day's work =(1/15 + 1/10)=1/6
Work done by A and B in 2 days =(1/6 X 2)=1/3
Remaining work =(1-1/3)=2/3
Now,	1/15work is done by A in 1 day.
2/3work will be done by a in	(15 X 2/3)= 10 days.
Hence, the total time taken = (10 + 2) = 12 days.
ANSWER IS C
Answer: (C) 12 days
Question: Three grades of milk are 1 percent, 2 percent and 4 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 4 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?
(A) y + 5z
(B) (y +z) / 4
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z
Rationale: Based on the given information, the following equation could be dervied: 1% * x + 2% * y + 4% * z = 1.5% * (x+y+z) Then use algebra to figure out 0.5%*x = 0.5%*y + 2.5%*z. Thus, x = y + 5z.
A
Answer: (A) y + 5z
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
(A) 10
(B) 18
(C) 36
(D) 72
(E) 16
Rationale: Answer: Option C
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: (C) 36
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: x/2 – x/3 = 6 => x =6
3 + 6 = 9
ANSWER:D
Answer: (D) 9
Question: If 2 = (6x)/(x - xy/z) then which of the following is true?
(A) y = -2z
(B) y = 2z
(C) 2y = z
(D) -2y = z
(E) y = -z
Rationale: 2 = (6x)/(x - xy/z)
=> 2 = (6xz)/(x*(z - y))
=> 2x = (6xz)/(z - y)
=> (z - y) = 3z
=> y = -2z
Hence Ans is B
Answer: (B) y = 2z
Question: A bag contains 50 black balls and 10 white balls. One ball is drawn at random. What is the probability that the
ball is white?
(A) 1
(B) 1/6
(C) 1/3
(D) 1/2
(E) None of these
Rationale: Explanation:
Total cases = 50 + 10 = 60
Favourable cases = 10
So probability = 10/60 = 1/6
Answer: B
Answer: (B) 1/6
Question: In a survey, 56 percent of the people surveyed stated truthfully that they were married, while 30 percent of the people surveyed who were married at that time chose not to include that information in the survey. What percent of the people surveyed were actually married at the time of the survey?
(A) 20%
(B) 60%
(C) 40%
(D) 75%
(E) 80%
Rationale: Let the total survey population be 100x. Now, 56x are married.
Again, let the total no of married people in the survey be 100y. Thus, 30% of them lied about being married. Thus, 70% were honest about it.
Thus, 70y = 56x
And, therefore 100y = 80x.
Thus, 80% were actually married.
ANSWER:E
Answer: (E) 80%
Question: Which answer is closest to the √151?
(A) 12.1
(B) 12.2
(C) 12.3
(D) 12.4
(E) 12.5
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 151.
Answer C
Answer: (C) 12.3
Question: At a raffle, 20% of the attendees bought more than five tickets, 65% of the remaining bought four tickets or less. What percentage of the attendees bought five tickets?
(A) 28% of the attendees bought five tickets.
(B) 52% of the attendees bought five tickets.
(C) 20% of the attendees bought five tickets.
(D) 72% of the attendees bought five tickets.
(E) None of these.
Rationale: Explanation:Let total number of attendees be 100,Then, number of attendees who bought more than five tickets = 20.Number of attendees who bought four tickets or less= 65% of 80 = 52.Total number with five tickets = 100 – 20 – 52 = 28.Thus, 28% of the attendees bought five tickets.Answer: Option A.
Answer: (A) 28% of the attendees bought five tickets.
Question: Thomas and Matt has some money with them in the ratio of 3:4. If their father gives Rs.30 to each of them then the ratio becomes 4:5. What would be the ratio if Thomas spend Rs.40 and Matt spend Rs. 20 from what they have now?
(A) 1:2
(B) 2:3
(C) 3:4
(D) 4:5
(E) 5:6
Rationale: Let money of Thomas and Matt be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x+30)/(y+30) = 4/5
=> 5x+150 = 4y+120 => 5x = 4y-30
But x = 3/4 y
5* 3/4 y = 4y-30
15y = 16y-120 => y = 120
=> x = 3*120/4 => x=90
Ratio of their money, if Thomas spend Rs.40 and Matt spend Rs. 20 => (90-40)/(120-20) = 50/100. => 1:2
Answer:A
Answer: (A) 1:2
Question: If 20! × 20!/20^n is an integer, what is the largest possible value of n?
(A) 20
(B) 16
(C) 8
(D) 4
(E) 1
Rationale: 20! × 20!/20^n is an integer.
Or 20! × 20!/(2^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 20! = [20/5] + [20/25] = 4
Since there are 2 20!'s, power of 4 in the numerator = 2*4 = 8
Hence the largest value of b for which 20! × 20!/20^n is integer = 8
ANSWER:C
Answer: (C) 8
Question: If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ?
(A) 141
(B) 200
(C) 624
(D) 391
(E) 412
Rationale: The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told that a, b and c are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...
A + (A+2) + (A+4) = 3A + 6
We know that 3A + 6 COULD equal one of those five answers; we just have to find it...
Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer
Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer
Could 3A + 6 = 624
3A =618
A = 206
This IS an EVEN INTEGER! The numbers would be 206, 208 and 210. This IS the answer
Final Answer:
C
Answer: (C) 624
Question: If each edge of a cube is increased by 50%, find the percentage increase in Its surface area
(A) 125%
(B) 129%
(C) 185%
(D) 725%
(E) 145%
Rationale: Let the edge = a cm
So increase by 50 % = =
Total surface Area of original cube =
TSA of new cube =
==
Increase in area = =
Increase % = = 125%
Answer: a
Answer: (A) 125%
Question: Find the least number which when divided by 5,6,7, and 8 leaves a remainder 3, but when divided by 9 leaves no remainder
(A) 1683
(B) 1684
(C) 1685
(D) 1582
(E) 1584
Rationale: Explanation :
L.C.M. of 5,6,7,8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Required number = (840 X 2 + 3)=1683
ANSWER IS A
Answer: (A) 1683
Question: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 hours a day?
(A) 4 days
(B) 3 days
(C) 7 days
(D) 2 days
(E) 9 days
Rationale: Sol. A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days
Ans: B
Answer: (B) 3 days
Question: If the perimeter of a rectangular garden is 800 m, its length when its breadth is 100 m is?
(A) 338 m
(B) 300 m
(C) 200 m
(D) 276 m
(E) 971 m
Rationale: 2(l + 100)
= 800 => l
= 300 m
Answer:B
Answer: (B) 300 m
Question: If a child walks at the rate of 5m/min from his home, he is 6 minutes late for school, if he walks at the rate of 7m/min he reaches half an hour earlier. How far is his school from his home ?
(A) 450 min
(B) 540 min
(C) 630 min
(D) 360 min
(E) none of these
Rationale: Let the distance between home and school is x.
Let actual time to reach be t.
Thus, x/5 = t + 6 ---- (1)
and x/7 = t - 30 -----(2)
Solving equation 1 and 2
x = 630 min
ANSWER:C
Answer: (C) 630 min
Question: Which of the following must be subtracted from 2^24 so that the resulting integer will be a multiple of 3?
(A) 2
(B) 3
(C) 1
(D) 4
(E) 5
Rationale: {4^1} / 3 =4/3 remainder 1
{4^2} / 3 = 16/3 remainder 1
{4^3} / 3 = 64/3 remainder 1
{4^4} / 3 = 256/3 remainder 1
Actually the same remainder keeps repeating .....
Try with a diff no, say 2
{2^1}/3 = remainder 2
{2^2}/3 = remainder 1
{2^3}/3 = remainder 2
{2^4}/3 = remainder 1
Answer : C
Answer: (C) 1
Question: In a class of 300 students, 150 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
(A) 50%
(B) 40%
(C) 30%
(D) 20%
(E) 10%
Rationale: No of students study french= 300- No of students study spanish = 300-150=150
% of the students study french but not spanish = (150/300)*100 % = 50 %
Answer: A
Answer: (A) 50%
Question: Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets?
(A) 30
(B) 31
(C) 32
(D) 33
(E) 34
Rationale: Total price of 5 packet milk=5*20=100
Total price of 3 packet milk=3*12=36
Total price of 2 packet returned milk=100-36=64
Average price of 2 packet milk=64/2=32
Correct option Answer:C
Answer: (C) 32
Question: If log8p = 2.5, log2q = 5, then p in terms of q is?
(A) 3√q
(B) 2q
(C) q
(D) q/2
(E) None of these
Rationale: log8p = 5/2
=> p = 85/2 = 23(5/2) = (25)3/2
log2q = 5
=> q = 25
Therefore, p = q3/2.
ANSWER:A
Answer: (A) 3√q
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 520 ?
(A) 259
(B) 498
(C) 676
(D) 823
(E) 1,002
Rationale: slope of 2 and a y-intercept of 2
y-coordinate is 520
y = 2x + 2
518 = 2x
x = 259
Answer:
A. 259
Answer: (A) 259
Question: At a certain high school, the senior class is twice the size of the junior class. If 3/8 of the seniors and 1/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese?
(A) 1/2
(B) 2/3
(C) 1/4
(D) 1/3
(E) 3/4
Rationale: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (3/8)*200=75 and (1/4)*100=25. 75+25=100. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 100 total students in Japanese, so 100 students in Japanese / 300 total students equals 1/3 of the students in both classes that study Japanese.
Answer: D
Answer: (D) 1/3
Question: Evaluate: |8 - 8(3 - 12)| - |5 - 11| = ?
(A) 40
(B) 74
(C) 60
(D) 70
(E) 80
Rationale: According to order of operations, inner brackets first. Hence
|8 - 8(3 - 12)| - |5 - 11| = |8 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |8 + 72| - |5 - 11|
= |80| - |-6|
= 80 - 6 = 74
correct answer B)74
Answer: (B) 74
Question: A ship sails out to a mark at the rate of 23 kmph. and sails back at the rate of 16 kmph. The average rate of sailing is ?
(A) 5 km/hr
(B) 12 km/hr
(C) 12.5 km/hr
(D) 19 km/hr
(E) None
Rationale: Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 23 x 16 ) / (23 +16 ) km/hr.
= 19 km/hr.
Correct Option: D
Answer: (D) 19 km/hr
Question: 1 man or 2 women or 3 boys can do a work in 44days. Then in how many days will 1man, 1woman and 1 boy do the work?
(A) 20days
(B) 24days
(C) 30days
(D) 15days
(E) 10days
Rationale: number of days = 44*1*2*3/(1*2 + 2*3 + 1*3) = 24days
Answer is B
Answer: (B) 24days
Question: If 150!/10^n is an integer, what is the largest possible value of n?
(A) 38
(B) 47
(C) 32
(D) 36
(E) 37
Rationale: The question actually asks the highest power of 10 which divides 150! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
150 factorial will have 37 as -
150/5 = 30
30/5 = 6
6/5 =1
So answer will be (E) 37
Answer: (E) 37
Question: A car traveled 75% of the way from town A to town B at an average speed of 80 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?
(A) 16
(B) 20
(C) 25
(D) 30
(E) 37.5
Rationale: Total distance = 100 miles (easier to work with %)
75% of the distance = 75 miles
25% of the distance = 25 miles
1st part of the trip → 75/80 = 0.9375
2nd part of the trip → 25/S = t
Total trip → (75+25)/40 = 0.9375 + t » 100/40 = 0.9375 + t » 2.5 = 0.9375 + t » t = 1.5625
Back to 2nd part of the trip formula: 25/S = 1.5625 » S = 16
Ans A
Answer: (A) 16
Question: The average age of an adult class is 40years. 17 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
(A) 8
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Let original strength = y
Then , 40y + 17 x 32 = ( y + 17) x 36
â‡’ 40y + 544= 36y + 612
â‡’ 4y = 68
âˆ´ y = 17
D
Answer: (D) 17
Question: find the number
if 1 = 2
2 = 10
3 = 30
4 = 68
5 = ?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: 1^3+1=2
2^3+2=10
3^3+3=30
4^3+4=68
so 5 = 5^3+5=130
ANSWER:C
Answer: (C) 130
Question: A tank contains 7,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A)  4.77%
(B)  5.77%
(C)  6.77%
(D)  7.77%
(E)  8.77%
Rationale: We start with 7,000 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 7,000 = 350 gallons of sodium chloride.
When 2,500 gallons of water evaporate we are left with 4,500 gallons of solution. From here we can determine what percent of the 4,500 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(350/4,500) x 100 = ?
0.077 x 100 = ?
= 7.7%
Answer is D.
Answer: (D)  7.77%
Question: A starts 3min after B for a place 4.5 km distant B on reaching his destination immediately returns and after walking a km meets A. If A can walk 1km in 18min, then what is B's speed?
(A) 5kmph
(B) 4kmph
(C) 6kmph
(D) 3.5kmph
(E) 4.5kmph
Rationale: If speed of B is x kms/min, then
(4.5+1)/x= [3.5/(1/18)] +3
x=1/12 km/min= 5 kms/hr
ANSWER:A
Answer: (A) 5kmph
Question: In how many ways 4 Indians and 5 Englishmen can be seated in a row so that they are alternate?
(A) 1200
(B) 9600
(C) 3240
(D) 4250
(E) 2880
Rationale: number of ways = 4!*5! = 2880
Answer is E
Answer: (E) 2880
Question: 45 men can complete a work in 17 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
(A) 6.6
(B) 10
(C) 15
(D) 7
(E) 8
Rationale: 45*17 men can complete the work in 1 day
1 man's 1 day work = 1/765
45 men 6 days work = 6*1/17 = 6/17
remaining work = 1-6/17 = 11/17
75 men's 1 day's work = 75/765 = 5/51
11/17 work is done by them in 51/5 * 11/17 = 6.6 days
Answer is A
Answer: (A) 6.6
Question: Johnny borrows $30,000 from Tony at 3% daily interest compounded daily. How much does Johnny owe Tony after 4 weeks?
(A) 30000*0.02^56
(B) 30000*1.12
(C) 30000*2.12
(D) 30000*1.03^28
(E) (30000*1.02)^56
Rationale: A=A= P(1+r100)^n
So, A=30000(1+3/100)^7âˆ—4
So, A=A= 30000(1.03)^28
Hence answer will be (D)
Answer: (D) 30000*1.03^28
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 22 sec. What is the length of the goods train?
(A) 299
(B) 190
(C) 276
(D) 270
(E) 281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 22 sec.
Let the length of the train be x meters.
Then, (x + 250)/22 = 20
x = 190 m.
Answer: B
Answer: (B) 190
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.20000, find their shares?
(A) s.8000, Rs.12000
(B) s.8000, Rs.12700
(C) s.10000, Rs.12090
(D) s.8000, Rs.12003
(E) s.10000, Rs.12200
Rationale: The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 20000
= Rs.8000 Share of A in the total profit = 3/5 * 20000
= Rs.12000
Answer: A
Answer: (A) s.8000, Rs.12000
Question: Let y = 2g + x^2 and g = 4x + 1.
If g^2 = 625, then which of the following can be a value of 2y + 3g?
(A) 100
(B) 130
(C) 141
(D) 142
(E) 247
Rationale: 800score Official Solution:
First note that g can either be 25 or -25. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 25 and then g = -25. If g = 25, then x = 6. If g = -25, then x = -26/4. Since all of our solutions are whole numbers, we can dismiss -26/4. We use g = 25 and x = 6 to determine the value of y: y = 2(25) + 36 = 86. Finally, we substitute the values for y and g into the last expression to determine its value : 2(86) + 3(25) = 172 + 75 = 247;the correct answer is (E).
Answer: (E) 247
Question: For what value(s) of x is the following equation satisfied: 5x-9-4x = -4x+6+5x
(A) a. -5
(B) b. 0 only
(C) c. 5/2 only
(D) d. No value
(E) e. Any value
Rationale: 5x-9-4x = -4x+6+5x
k - 9 = k + 6
-9 = 6, which is false.
So, no k satisfies given equation.
Answer: D.
Answer: (D) d. No value
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 22:13
(C) 23:12
(D) 11:9
(E) 11:10
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
ANSWER:A
Answer: (A) 18:11
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 700 km/hr
(B) 720 km/hr
(C) 780 km/hr
(D) 800 km/hr
(E) 890 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Answer: (B) 720 km/hr