mathewhe/aqua_rat huggingface dataset:
Question: ram draws a card randomly among card 1-23 and keep it back.then sam draws a card among those.what is the prob than sam has drawn a card greatr than ram?
(A) 11/23
(B) 12/23
(C) 13/23
(D) 14/23
(E) 15/23
Rationale: Sum of probability of drowing a card greater than drawn by ram is (22/23)+(21/23)+.....(1/23)=253/23
but probability for choosing 1 card out of 23 is 1/23
therefore total probability is (253/23)*(1/23)=(11/23)
ANSWER:A
Answer: (A) 11/23
Question: Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together ?
(A) 100/11 min past 8
(B) 100/11 min past 9
(C) 100/11 min past 2
(D) 100/11 min past 1
(E) 100/11 min past 5
Rationale: Explanation:
In this type of problems the formulae is
x is replaced by the first interval of given time Here i.e 8
= min
Therefore the hands will be in the same straight line but not
together at min.past 8.
Answer: A) 100/11 min past 8
Answer: (A) 100/11 min past 8
Question: A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 87
(C) 26
(D) 21
(E) 44
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:E
Answer: (E) 44
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) Rs.287
(B) Rs.429
(C) Rs.480
(D) Rs.412
(E) Rs.482
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:C
Answer: (C) Rs.480
Question: How many three letter words are formed using the letters of the word TIME?
(A) 12
(B) 14
(C) 18
(D) 24
(E) 61
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer:D
Answer: (D) 24
Question: If chemistry book page and math book page ratio is 6:5.A child tore 25 page from chemistry book and 15 page from Math book.Now,ratio becomes 1:1.so,tell the initial no. of pages of chemistry.
(A) 50
(B) 60
(C) 70
(D) 80
(E) 40
Rationale: Chemistry pages=6x,Math pages=5x
6x-25/5x-15=1/1
6x-25=5x-15,6x-5x=10,x=10
chemistry pages=6x=60pages
answer B
Answer: (B) 60
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
(A) 12
(B) 16
(C) 24
(D) 48
(E) 50
Rationale: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 12 and 16.
L.C.M. of 12 and 16 = 48.
answer :D
Answer: (D) 48
Question: By selling 20 pencils for a rupee a man loses 30%. How many for a rupee should he sell in order to gain 30%?
(A) 8.56
(B) 10.75
(C) 14.5
(D) 16.5
(E) 11.4
Rationale: 70% --- 20
130% --- ?
70/130 * 20 = 10.75
Answer: B
Answer: (B) 10.75
Question: On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out
sand-dunes, 1 has treasure and only 2 out of 5 sand dunes formed have lucky coupons. Find
the probability that the blown-out sand dune will contain both the things.
(A) 2/25
(B) 4/75
(C) 7/75
(D) 3/5
(E) 4/5
Rationale: Probabilty of sand dune blown out = 2/3
Probabilty that it has treasure = 1/5
Probability that it has lucky coupon = 2/5
total probability = 2/3 * 1/5 * 2/5 = 4/75
ANSWER:B
Answer: (B) 4/75
Question: A car manufacturer sold 500 mini vans at $10000 each, 200 hatchbacks at $8000 each, and 220 sports utility vehicles at $18000 each. what percentage of the company's revenue is from the sale of sports utility vehicles?
(A) 27.5%
(B) 50.4%
(C) 37.5%
(D) 29.7%
(E) 39.5%
Rationale: Correct Answer: C
The company's total revenue from mini vans=500* $10000=$5 000 000
The company's total revenue from hatchbacks=200*$8000=$1 600 000
The company's total revenue from sports utility vehicles=220*$18000=$3 960 000
The combined total of all sales=$10560000
Therefore % of sports utility vehicles sales=3 960 000/10560000*100= 37.5%
Answer: (C) 37.5%
Question: A number x is 6 times another number y. The percentage that y is less than x is
(A) 12.5%
(B) 83.3%
(C) 80.5%
(D) 81%
(E) 1%
Rationale: Say y=1 and x=6.
Then y=1 is less than x=6 by (6-1)/6*100=5/6*100=83.3%.
Answer: B.
Answer: (B) 83.3%
Question: Rahul and Sham together can complete a task in 35 days, but Rahul alone can complete same work in 60 days. Calculate in how many days Sham can complete this work ?
(A) 84 days
(B) 82 days
(C) 76 days
(D) 68 days
(E) 60 days
Rationale: Explanation:
As Rahul and Sham together can finish work in 35 days.
1 days work of Rahul and Sham is 1/35
Rahul can alone complete this work in 60 days,
So, Rahul one day work is 1/60
Clearly, Sham one day work will be = (Rahul and Sham one day work) - (Rahul one day work)
=1/35-1/60
=1/84
Hence Sham will complete the given work in 84 days.
ANSWER IS A
Answer: (A) 84 days
Question: 7 teams compete in a track competition. If there are 12 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3(max wins) x 4 = 12 (4 teams win three events)
The answer is B.
Answer: (B) 4
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 40 days
(B) 20 days
(C) 30 days
(D) 60 days
(E) 40 days
Rationale: C
30 days
C = 1/5 – 1/6 = 1/30 => 30 days
Answer: (C) 30 days
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 54
(B) 90
(C) 64
(D) 92
(E) 98
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 16 sec. What is the length of the platform?
(A) 287 m
(B) 431.25 m
(C) 267 m
(D) 287.25 m
(E) 656 m
Rationale: Speed = 300/16 = 75/4 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 75/4
=> x = 731.25 m
Answer:B (431.25)
Answer: (B) 431.25 m
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Answer: (A) 1
Question: Ritesh and Co. generated revenue of Rs. 1,250 in 2006. This was 12.5% of its gross revenue. In 2007, the gross revenue grew by Rs. 2,500. What is the percentage increase in the revenue in 2007?
(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) None of these
Rationale: Explanation :
Given, Ritesh and Co. generated revenue of Rs. 1,250 in 2006 and that this was 12.5% of the gross revenue.
Hence, if 1250 is 12.5% of the revenue, then 100% (gross revenue) is:
=>(100/12.5)×1250.
=>10,000.
Hence, the total revenue by end of 2007 is Rs. 10,000. In 2006, revenue grew by Rs. 2500. This is a growth of:
=>(2500/10000)×100.
=>25%.
Answer : C
Answer: (C) 25%
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 51 kmph, find the speed of the stream?
(A) 15
(B) 17
(C) 14
(D) 18
(E) 16
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 51/3 = 17 kmph.
Answer:B
Answer: (B) 17
Question: If a, b, and c are integer and ab + c is odd, which of the must be true?
I. a + c is odd
II. b + c is odd
III. abc is even
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II and III only
Rationale: Personally I'd approach this question in another way.
ab+c=odd, means:
1. ab=even (which means that at least one of them is even) and c=odd
OR:
2. ab=odd (which means that both are odd) and c=even
We can see that in both cases at least one is even thus option III (abc=even) is always true.
Now, for I: if c=odd(case 1) and a=odd(so b=even) then a+c=even≠odd, so this option is not always true.
Exactly the same for option II: if c=odd (case 1) and b=odd (so a=even) then b+c=even≠odd, so this option is not always true.
Answer: C (III only).
Answer: (C) III only
Question: A number is missing from the number series below.
Can you find it ?
84, 155, 258, 399 ,?, 819.
(A) 275
(B) 350
(C) 399
(D) 584
(E) 449
Rationale: D
The missing number is 584.
84 = 4^3 + 3^2 + 4
155 = 5^3 + 5^2 + 5
258 = 6^3 + 6^2 + 6
399 = 7^3 + 7^2 + 7
819 = 9^3 + 9^2 + 9
Thus,
584 = 8^3 + 8^2 + 8
Answer: (D) 584
Question: What is the lowest positive integer that is divisible by 8 through 11, inclusive?
(A) 999
(B) 7811
(C) 6555
(D) 9200
(E) 7920
Rationale: The integer should be divisible by: 8, 9, 10 and 11. The least common multiple of these integers is LCM=8*9*10*11=7920
Answer: E
Answer: (E) 7920
Question: The sum of two numbers is 24 and their product is 148. Find the sum of the squares of that numbers.
(A) 250
(B) 280
(C) 230
(D) 290
(E) 250
Rationale: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=24ab=148 So, 24^2=a^2+b^2+2*148576=a^2+b^2+296a^2+b^2=280Ans B
Answer: (B) 280
Question: If 36 men can do a piece of work in 5 hours, in how many hours will15 men do it?
(A) 12
(B) 38
(C) 60
(D) 88
(E) 72
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 15:36 ::5:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 5) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 5}{15}=12
Hence, 15 men can do it in 12 hours.
Answer: A) 12
Answer: (A) 12
Question: In the formula X = 1/(2y+1)^2, if y is halved, then X is multiplied by
(A) 25/9
(B) 25
(C) 1/9
(D) 1/25
(E) 9
Rationale: Say y=2 => X1 = 1/25
when y=1; X2 = 1/9
X2 = 25/9*X1.
Answer : A
Answer: (A) 25/9
Question: If y ¤ d = y^(2d) for all positive integers, then (3 ¤ 4) ¤ 2 =
(A) 3^8
(B) 3^12
(C) 3^16
(D) 3^24
(E) 3^32
Rationale: y ¤ d = y^(2d)
3 ¤ 4 = 3^(8)
(3 ¤ 4) ¤ 2 = (3^8) ¤ 2 = (3^8)^4 = 3^32
Correct Option: E
Answer: (E) 3^32
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 78 km downstream?
(A) 3 hours
(B) 33/13 hours
(C) 31/13 hours
(D) 30/13 hours
(E) 30/14 hours
Rationale: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 78 km downstream = d/s = 78/26
= 3 hours.
Answer:A
Answer: (A) 3 hours
Question: A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.
(A) 100 rs
(B) 150 rs
(C) 160 rs
(D) 180 rs
(E) 200 rs
Rationale: Gain in 2 years =
[(5000*6*2)/100]-[(5000*4*2)/100]
600-400=200
Gain in 1 year =(200/2)=100 rs
ANSWER:A
Answer: (A) 100 rs
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 35% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
(A) $15,840
(B) $17,820
(C) $16,335
(D) $19,800
(E) $21,780
Rationale: 10000 seats --> Full Price : Half Price = 6500 : 3500
Price when all seats are filled = 13000 + 3500 = 16500
100 seats are unsold --> Loss due to unfilled seats = 35 + 2*65 = 165
Revenue = 16500 - 165 = 16335
Answer: C
Answer: (C) $16,335
Question: If -1 < a < 0, which of the following must be true? I. a^9 < a^4 II. a^3 < 1 – a III. a^6 < a^3
(A) I only
(B) III only
(C) I,II,III only
(D) II only
(E) I,III only
Rationale: Answer : C
Answer: (C) I,II,III only
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 65 km/hr
(B) 17 km/hr
(C) 76 km/hr
(D) 50 km/hr
(E) 15 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer: D
Answer: (D) 50 km/hr
Question: In a class of 50 students, 20 play Baseball, 15 play Cricket and 11 play Football. 7 play both Baseball and Cricket, 4 play Cricket and Football and 5 play Baseball and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
(A) 10
(B) 46
(C) 67
(D) 68
(E) 446
Rationale: Notice that7 play both Baseball and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Baseball/Football.
[color=#ffff00]{Total}={Baseball}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS
[/color]
50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;
Those who play ONLY Baseball and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Baseball and Football are 5-2=3;
Hence, 5+2+3=10 students play exactly two of these sports.
Answer: A.
Answer: (A) 10
Question: The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the eldest boy?
(A) 6
(B) 9
(C) 16
(D) 4
(E) 21
Rationale: 3x + 5x + 7x = 45
x =3
7x = 21
Answer:E
Answer: (E) 21
Question: A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4. The number age of the family now is:
(A) 18
(B) 17
(C) 76
(D) 85
(E) 86
Rationale: Let the number of wickets taken till the last match be x. Then,
(12.4x + 26)/(x + 5) = 12
= 12.4x + 26 = 12x + 60
= 0.4x = 34
= x = 340/4 = 85.
Answer: D
Answer: (D) 85
Question: The salary of a person was reduced by 10%. By what percent should his
reduced salary be raised so as to bring it at par with his original salary?
(A) 100/9
(B) 100
(C) 110
(D) 98
(E) 100/11
Rationale: Let the original salary be $100. New salary = $90.
Increase on 90=10 , Increase on 100=((10/90)*100)%
= (100/9)%
Answer A)100/9
Answer: (A) 100/9
Question: the hiker walking at a constant rate of 5 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour. the cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues to walk at her constant rate, how many minutes must the cyclist wait until the hiker catches up?
(A) 15
(B) 10
(C) 20
(D) 30
(E) 35
Rationale: After passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles/hour.
In those 5 mins the cyclist travels a distance of 5/3 miles.
In those 5 mins the hiker travels a distance of 5/12 miles.
So the hiker still has to cover 15/12 miles to meet the waiting cyclist.
The hiker will need 1/4 hours or 15 mins to cover the remaining 15/12 miles.
So the answer is A.
Answer: (A) 15
Question: An insect leaps 60 centimeters in 1.5 seconds. What is its speed?
(A) 9 centimeters per second
(B) 0.9 meters per second
(C) 4 meters per second
(D) 0.4 meters per second
(E) 4.4 centimeters per second
Rationale: 60 / 1.5 = 40 cm/s = 0.4 m/s
The answer is D.
Answer: (D) 0.4 meters per second
Question: (1^2+2^2+3^2+.....+10^2)=?
(A) 330
(B) 345
(C) 365
(D) 385
(E) None of them
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=10
=(1/6x10x11x21)
=385
Answer is D.
Answer: (D) 385
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $5.00 per hour and a standard tip rate of 25% of the cost of the orders she serves. If she worked four 9-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 540
(D) 350
(E) 400
Rationale: Jill earns 5 dollars/hour and the hourly tip is (1/4)*40.
Jill thus earns 5*9+9*10 per day(or 5(9)+10(9)=15(9)=135).
Jill has worked for 4 days -> 135*4=540.
This matches answer choice C.
Answer: (C) 540
Question: The result when a number subtracted from 100 is the same as the number added to 40. what is the number?
(A) 70
(B) 65
(C) 80
(D) 140
(E) 60
Rationale: Answer
Let the number be x.
Then, x - 40= 100- x
â‡’ 2x = 100+ 40= 140
â‡’ 2x = 140
âˆ´ x = 70
Correct Option: A
Answer: (A) 70
Question: In how many different number of ways 4 boys and 2 girls can sit on a bench such that girls always sit together.
(A) A)720
(B) B)240
(C) C)740
(D) D)780
(E) E)790
Rationale: 240
Option 'B'
Answer: (B) B)240
Question: What is the units' digit of the following expression (10)^5*(12)^5*(18)^5?
(A) 0
(B) 1
(C) 3
(D) 5
(E) 9
Rationale: We do not have to do any calculations or find units digit of remaining numbers...
all three terms - 10,12,18 - are EVEN and since the PRODUCT contains 0, the units digit of the product will remain 0
A
Answer: (A) 0
Question: The length of a rectangle is one- sixth of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1296 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
(A) 560 sq.units
(B) 360 sq.units
(C) 260 sq.units
(D) 460 sq.units
(E) 160 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1296 = 36units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 36 * 10 = 360 sq.units
Answer:B
Answer: (B) 360 sq.units
Question: Each child has 5 stickers and 8 candies. If there are 7 children, how many stickers are there in total?
(A) 12
(B) 38
(C) 48
(D) 21
(E) 35
Rationale: 5*7=35.Answer is E.
Answer: (E) 35
Question: If r and s are two different prime numbers, which of the following cannot be true?
(A) rs is odd.
(B) r + s is even.
(C) r + s is odd.
(D) rs is even.
(E) r/s is an integer
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (r/s=integer means that r is a multiple of s).
.
All other options are possible:
A. rs is odd --> r=3 and s=5;
B. r + s is even --> r=3 and s=5;
C. r + s is odd --> r=2 and s=3;
D. rs is even --> r=2 and s=3;
Answer: E
Answer: (E) r/s is an integer
Question: Dan read that an average snowfall of 10 inches yields 1 inch of water when melted. Very wet
snow will measure 5 inches for one inch of water, and very dry snow may measure 20 inches for an
inch of water. He made measurements for a storm that started with 5.3 inches of average snowfall.
The precipitation changed to wet snow and dropped another 4.1 inches. The weather continued to
warm up, and the storm finished with 1.5 inches of rain. What was the actual amount of water that fell
during the storm? Round your answer to tenths.
(A) 2.9" of water
(B) 3.9" of water
(C) 4.9" of water
(D) 7.9" of water
(E) 8.9" of water
Rationale: 5.3 ÷ 10 = .53" water from average snow
4.1 ÷ 5 = .82" water from wet snow
If you are unsure whether to multiply or divide, check your answer to see if it makes
sense. The actual snowfall in each case was less than what was needed to make
an inch of water, so division yields a sensible answer.
.53 + .82 + 1.5 = 2.85" rounds to 2.9" of water
correct answer A
Answer: (A) 2.9" of water
Question: The diagonals of two squares are in the ratio of 2:5 then find the ratio of its areas?
(A) 2:12
(B) 4:25
(C) 5:31
(D) 2:19
(E) 3:17
Rationale: Let the diagonals of the squares be 2x and 5x
Ratio of their areas = 1/2 (2x)^2 : 1/2 (5x)^2 = 4x^2 : 25x^2 = 4:25
Answer is B
Answer: (B) 4:25
Question: 20 people are there, they are shaking hands together, how many hand shakes possible, if they are in pair of cyclic sequence.
(A) 21
(B) 20
(C) 40
(D) 42
(E) 19
Rationale: n for cyclic hand shake and n-1 for linear handshake.
so here no of hand shake is 20.
ANSWER:B
Answer: (B) 20
Question: X starts a business with Rs.45000. Y joins in the business after 2 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 1:2
(B) 9:5
(C) 1:5
(D) 3:1
(E) 1:1
Rationale: Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000Ã—12:30000Ã—10
=45Ã—12:30Ã—10
=3Ã—12:2Ã—10
=9:5
Answer: Option B
Answer: (B) 9:5
Question: If x is an integer and (x)(x^2)(x^3)(x^8) is positive, which of the following could be negative?
(A) x^4
(B) (x)(x^3)
(C) (x)(x)
(D) x + x^9
(E) 3x^2
Rationale: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^9 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Answer: (D) x + x^9
Question: A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
(A) 720
(B) 900
(C) 1200
(D) 1800
(E) None of these
Rationale: Explanation:
2(15 + 12) × h = 2(15 × 12)
=> h = (180/27)m = 20/3 m.
Volume = (15 × 12 × (20/3)) m3 = 1200 m3
Answer: C
Answer: (C) 1200
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 50 km apart both 3 and 6 hours after start, then find the distance between the two stations.
(A) 190km
(B) 200km
(C) 220km
(D) 180km
(E) 150km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+50+ 50
2(R+S ) = R+S +100
R+S = 100
Hence distance between XY is R+S+ 50 = 100 +50 =150
Answer : E
Answer: (E) 150km
Question: A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 7.9
(B) 7.3
(C) 7.8
(D) 7.2
(E) 7.1
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
Answer :D
Answer: (D) 7.2
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $320,000?
(A) 30
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 10,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.
Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 40,000.00 takes the same (72/x) no of years to double 320,000.00.
72/x = 6 years.
So altogather:
10,000 - 20,000 = 6 years
20,000 - 40,000 = 6 years
40,000 - 80,000 = 6 years
80,000 - 160,000 = 6 years
160,000 - 320,000 = 6 years
total 30 years.
Answer: (A) 30
Question: A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of A
(A) 300
(B) 450
(C) 750
(D) 800
(E) None of them
Rationale: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (600 *4/8) = Rs.300, B's share = Rs. (600 *3/8) = Rs. 225.
C's share = Rs. [600 - (300 + 225») = Rs. 75.
Answer is A
Answer: (A) 300
Question: What percent is 120 of 80?
(A) 150 %
(B) 134 1/3 %
(C) 135 1/3 %
(D) 140 1/3 %
(E) 143 1/3 %
Rationale: 120/80 = 3/2
3/2 × 100 = 300/2 = 150 %
A
Answer: (A) 150 %
Question: Pomes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
(A) 40 minutes.
(B) 1 hour and 30 minutes.
(C) 1 hour.
(D) 1 hour and 40 minutes.
(E) 2 hours and 15 minutes.
Rationale: Rate =Output/Time
Pomes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Answer: (C) 1 hour.
Question: Which of the following must be subtracted from 2^72 so that the resulting integer will be a multiple of 3?
(A) 5
(B) 4
(C) 1
(D) 3
(E) 2
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