mathewhe/aqua_rat huggingface dataset:
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
(A) 1/2
(B) 3/2
(C) 3/2
(D) 2/2
(E) 5/2
Rationale: A
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Answer: (A) 1/2
Question: A person want to give his money of $15800 to his 4 children A,B,C,D in the ratio 5:9:6:5. What is the A+C share?
(A) $4000
(B) $2890
(C) $3005
(D) $6952
(E) $6003
Rationale: A's share = 15800*5/25= $3160
C's share = 15800*6/25 = $3792
A+C = $6952
Answer is D
Answer: (D) $6952
Question: Pipe A can fill a tank in 3 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 1.1
(B) 1.3
(C) 1.5
(D) 1.7
(E) 1.9
Rationale: The part filled by A + B + C in 1 hour is 1/3 + 1/4 + 1/12 = 2/3
All the three pipes together will fill the tank in 1.5 hours.
The answer is C.
Answer: (C) 1.5
Question: If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.68 per litre then what is the rate of mixed oil per litre?
(A) Rs.49.17
(B) Rs.51.03
(C) Rs.56
(D) Rs.55.33
(E) None of the above
Rationale: 50*10 = 500
68*5 = 340
840/15 = 56
ANSWER:C
Answer: (C) Rs.56
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
(A) 22887
(B) 28779
(C) 27677
(D) 13500
(E) 17971
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer:D
Answer: (D) 13500
Question: Ashley and Betty start a business with $9000 each, and after 3 months, Betty adds another $5000. How should they share the profits at the end of the 24 months?
(A) 72:107
(B) 4:5
(C) 17:23
(D) 3:4
(E) 68:95
Rationale: Ashley invests $9000 for 24 months, but Betty invests $9000 for the first 3 months and then adds $5000. So, the investment of Betty for remaining 21 months is $14000.
Ashley:Betty
9000*24 : (9000*3) + (14000*21)
216000 : 321000
A:B = 72:107
Answer: A
Answer: (A) 72:107
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2 3/2 hours
(B) 2 1/3 hours
(C) 2 1/5 hours
(D) 2 9/2 hours
(E) 2 1/2 hours
Rationale: Required time
= (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer: E
Answer: (E) 2 1/2 hours
Question: The profit earned by selling an article for 872 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
(A) 960
(B) 990
(C) 1,200
(D) 920
(E) None of these
Rationale: Let the profit or loss be x
and 872 – x = 448 + x or, x = 424⁄2 = 212
\ Cost price of the article = 872 – x = 448 + x = 660
\ SP of the article = 660 × 150⁄100 = 990
Answer B
Answer: (B) 990
Question: x is the product of each integer from 1 to 75, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
(A) 8
(B) 7
(C) 6
(D) 9
(E) 10
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*75 = 50!
No. of trailing zeros in 75! = 75/5 + 75/5^2 = 15+3 = 18
100^k = 10^2k → k = 18/2 = 9
D
Answer: (D) 9
Question: Each of the numbers x1, x2...., xn, n > 4, is equal to 1 or –1.
Suppose, x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1 + xn–1xnx1x2 + xnx1x2x3= 0, then,
(A) n is even
(B) n is odd.
(C) n is an odd multiple of 3.
(D) n is prime
(E) None
Rationale: Explanation :
Every term of the eq : x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1 + xn–1xnx1x2 + xnx1x2x3= 0, would either be 1 or -1 (product of 1's and -1's would never be anything else).
Now for the equation to be true number of 1's would have to be equal to number -1's thus there would always be even number of terms in the equation. Now for that to be true n would have to be even.
Say for example n=6: x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + x6x1x2x3.
We see there are 4 terms in the equation, we can have 2 1's and 2 -1's. So , n is even.
Answer : A
Answer: (A) n is even
Question: A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even?
(A) 1/3
(B) 2/3
(C) 5/9
(D) 6/11
(E) 5/11
Rationale: Probability of getting an even number = 2/3
Probability of getting an odd number = 1/3
since the dice is biased.
The sum is even if
(even,even) or (odd,odd)
[P(even).P(even)] + [P(odd).P(odd)]
2/3 * 2/3 + 1/3 * 1/3 = 4/9 + 1/9 = 5/9
ANSWER:C
Answer: (C) 5/9
Question: Look at this series: 664, 332, 340, 170, ____, 89, ... What number should fill the blank?
(A) 85
(B) 97
(C) 109
(D) 178
(E) 112
Rationale: Answer: Option D
This is an alternating division and addition series: First, divide by 2, and then add 8.
Answer: (D) 178
Question: If the price has fallen by 12% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 11 1/8%
(B) 11 1/5%
(C) 11 1/9%
(D) 13 7/11%
(E) 21 1/9%
Rationale: 100 â€“ 12 = 88
88------12
100------? => 13 7/11%
Answer: D
Answer: (D) 13 7/11%
Question: What is the greatest 6-digit number when divided by 8 , 9, and 10 leaves a remainder of 6, 7, and 8 respectively?
(A) 456780
(B) 678918
(C) 997479
(D) 997916
(E) 997920
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so B is the only possible answer.
Answer: (B) 678918
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words?
(A) 5 to 4
(B) 3 to 2
(C) 42 to 1
(D) 5 to 1
(E) 6 to 1
Rationale: Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6
Number of ways to form 3-letter code: 10!/7! = 10*9*8
Ratio: 42 to 1
Answer : C
Answer: (C) 42 to 1
Question: Population of a city in 20004 was 1100000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 354354
(B) 545454
(C) 465785
(D) 456573
(E) 2384525/2
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 2384525/2
E
Answer: (E) 2384525/2
Question: After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount
(A) 22%
(B) 23%
(C) 21%
(D) 20%
(E) 17%
Rationale: Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
x=(100-80)=20
first discount = 20%
Option D
Answer: (D) 20%
Question: A 360 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 220 meter
(B) 225 meter
(C) 140 meter
(D) 235 meter
(E) None of these
Rationale: Explanation:
As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec
Let the length of other train is x meter then
x+360 /9=500 /9
=>x+360=500
=>x=140
So the length of the train is 140 meters
Option C
Answer: (C) 140 meter
Question: If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 1)?
(A) 3
(B) P + 2
(C) p – 1
(D) 2p – 1
(E) 2p + 1
Rationale: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+1)=pq+p is (pq+p-pq)-1=p-1.
Answer: C.
Answer: (C) p – 1
Question: The speed of a boat in still water is 15 km/hr and the rate of the current is 3 km/hr. The distance travelled downstream in 12 minutes is
(A) 1.2 km
(B) 1.8 km
(C) 2.4 km
(D) 3.6 km
(E) None
Rationale: Speed Downstream = (15 + 3) km/hr
= 18 km/hr.
Distance travelled = (18 x 12/60) hours
= 3.6km.
Answer D
Answer: (D) 3.6 km
Question: At what rate percent of simple interest will a sum of money double itself in 12 years?
(A) 8 1/6 %
(B) 8 1/3 %
(C) 8 8/3 %
(D) 8 3/3 %
(E) 8 1/2 %
Rationale: Let sum = x. Then, S.I. = x.
Rate = (100 * S.I.) / (P * T) = (100 * x) / (x * 12)
= 25/3 = 8 1/3 %.Answer: B
Answer: (B) 8 1/3 %
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
(A) 400
(B) 600
(C) 287
(D) 278
(E) 281
Rationale: Explanation:
Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5
= 600 ways.
Answer:B
Answer: (B) 600
Question: If a - b = 3 and a^2 + b^2 = 28, find the value of ab.
(A) 19
(B) 15
(C) 10
(D) 8
(E) 13
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 25 - 9 = 16
ab = 8.
Answer is D.
Answer: (D) 8
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) 70%
(B) 90%
(C) 80%
(D) 75%
(E) 85%
Rationale: A B C D
90 100 80 100
A D
90 ----- 100
360 ------ ? = 400
500 ------ 400
100 ------- ? => 80%
ANSWER:C
Answer: (C) 80%
Question: What will be the compound interest on a sum of Rs. 22,000 after 3 years at the rate of 12% p.a.?
(A) s.8908.41
(B) s.1823.20
(C) s.6123.20
(D) s.10123.29
(E) s.10123.28
Rationale: Explanation:
Amount = [22000 * (1 + 12/100)3]
= 22000 * 28/25 * 28/25 * 28/25 = Rs. 35123.20
C.I. = (35123.20 - 22000) = Rs.8908.41
Answer:A
Answer: (A) s.8908.41
Question: What will be the area of a semi-circle of 14 metres diameter?
(A) 154 sq metres
(B) 77 sq metres
(C) 308 sq metres
(D) 22 sq metres
(E) None of these
Rationale: Area of semicircle = ½πr2
= ½ × 22⁄7 × 7 × 7 = 77 m2
Answer B
Answer: (B) 77 sq metres
Question: Median W of price of the car is 52,000. which could be the median of the other two.
35000, 44000, x, y, 57000.
(A) 38000
(B) 47000
(C) 48000
(D) 51,000
(E) 56,000
Rationale: Median of the car is 52,000 therefore 52,000 is the middle number. Assuming Y >= X, X will have to be the median value i.e. 52,000. Therefore the remaining value would have to be between 52,000 and 57,000 inclusive. The only answer choice that fits is W=56,000.E
Answer: (E) 56,000
Question: A man whose bowling average is 12.4, takes 6 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
(A) 113
(B) 114
(C) 115
(D) 116
(E) 117
Rationale: 12.4*x+26=(6+x)12
solve equation x=115
ANSWER:C
Answer: (C) 115
Question: Find the greatest number that, while dividing 47, 215 and 365, gives the same remainder in each case?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Calculate the differences, taking two numbers at a time as follows:
(215-47) = 168
(365-215) = 150
(365-47) = 318
HCF of 168, 150 and 318 we get 6, which is the greatest number, which while dividing 47, 215 and 365 gives the same remainder in each cases is 5.
ANSWER:C
Answer: (C) 5
Question: pipes P and Q would fill a cistern 18 and 24 minutes respectively. Both pipes being opened, find when the first pipe must be turned off so that the cistern may be just filled in 12 minutes?
(A) 6
(B) 9
(C) 5
(D) 4
(E) 1
Rationale: x/18 + 12/24 = 1
x = 9
Answer:B
Answer: (B) 9
Question: A set of football matches is to be organized in a "round-robin" fashion, i.e., every
participating team plays a match against every other team once and only once. If 6
matches are totally played, how many teams participated?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 2 ways to solve this problem..
summation(x)=n(n-1)/2
n(n-1)/2=6;
n^2-n-12=0
Ans : 4
ANSWER:A
Answer: (A) 4
Question: Pooja is selling her books at puzzles land at a strange price as
* she sells her book "Vanity" at $30
* she sells her book "Sybil" at $25
* she sells her book "xmen" at $20
At what price does she sell her book "twilight" ?
(A) 54
(B) 23
(C) 40
(D) 87
(E) 20
Rationale: C
40
Cost of each alphabet is 5
Answer: (C) 40
Question: Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 30 percent was planted with soybeans and 60 percent of the cleared land was planted with wheat. If the remaining 540 acres of cleared land was planted with corn, how many acres did the farmer own?
(A) 7200
(B) 6000
(C) 3500
(D) 5000
(E) 6200
Rationale: 30% od 90% = 27%, 60% 0f 90% = 54% so the remaining 90-27-54=9%=540 acres or 10% of 90%=9% --> 540/9*100=6000 acres Answer (B)
Answer: (B) 6000
Question: John spent 40 percent of his earning last month on rent and 30 percent less than what he spent on rent to purchase a new dishwasher. What percent of last month's earning did John have left over?
(A) 30%
(B) 32%
(C) 45%
(D) 68%
(E) 70%
Rationale: Say John's earning last month was $100.
John spent 40 percent of his earning last month on rent --> $40 on rent;
30 percent less than what he spent on rent to purchase a new dishwasher --> $40*0.7=$28 on the dishwasher.
Left over amount 100 - (40 + 28) = $32.
Answer: B.
Answer: (B) 32%
Question: A shopkeeper sells 600 metres of cloth for Rs. 36000 at a loss of Rs.10 per metre. Find his cost price for one metre of cloth?
(A) s.59
(B) s.58
(C) s.09
(D) s.70
(E) s.13
Rationale: SP per metre = 36000/600
= Rs. 60 Loss per metre
= Rs. 10 CP per metre = 60 + 10
= Rs.70
Answer: D
Answer: (D) s.70
Question: Double of Quarter of 6 percent written as a decimal is :
(A) 0.03
(B) 0.0005
(C) 0.25
(D) 0.005
(E) None of these
Rationale: Explanation :
Solution: (2)*(1/4)*6% = 0.03
Answer : A
Answer: (A) 0.03
Question: If x and y are positive, which of the following must be greater that 1/sqrt(x + y)?
I. sqrt(x + y)/2x
II. [sqrt(x) + sqrt(y)]/(x + y)
III. [sqrt(x) - sqrt(y)]/(x + y)
(A) None
(B) I only
(C) II only
(D) I and II
(E) III and II
Rationale: solving i ) Y > X ( which could be true or false)
sloving ii) 2 Sqrt(xy) > 0 ( which is true-given x and y are positive)
solving iii) -2 Squrt(xy) > 0 ( which is false)
Therefore C should be the answer.
Answer: (C) II only
Question: In a triangle, one side is 6 Cm and another side is 4 Cm. which of the following can be the perimeter of the triangle?
(A) 18.
(B) 25.
(C) 30.
(D) 32.
(E) 34.
Rationale: Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 18. Hence A.
Answer: (A) 18.
Question: A man buys s cycle for $100 and sells it at a loss of 10%. What is the selling price of the cycle?
(A) $50
(B) $60
(C) $70
(D) $80
(E) $90
Rationale: S.P. = 90% of the $100 = 90/100 * 100 = $90
Answer is E
Answer: (E) $90
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 3/7
(B) 4/7
(C) 6/7
(D) 7/11
(E) 8/11
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10)	= 4/7
B)
Answer: (B) 4/7
Question: A small college reduced its faculty by approximately 13 percent to 195 professors. What was the original number of faculty members?
(A) 182
(B) 208
(C) 224
(D) 254
(E) 302
Rationale: f x is the original number of faculty members, then after 13% reduction in faculty members number is .87x
but we are given .87x = 195
x = 224
So the original number of faculty members is 224
Correct Answer - C
Answer: (C) 224
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 1/2
(B) 2/5
(C) 8/5
(D) 9/20
(E) none of these
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) =	n(E)/n(S)	= 9/20.
ANSWER : D
Answer: (D) 9/20
Question: A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?
(A) 27.50,22.59
(B) 27.50,22.50
(C) 27.50,32.50
(D) 27.70,22.59
(E) 27.50,22.51
Rationale: Explanation:
Let the daily wage of a man be Rs. x.
Then, daily wage of a woman = Rs. (x - 5).
Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50.
Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50.
Answer: B) m:27.50 w:22.50
Answer: (B) 27.50,22.50
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 73
(B) 83
(C) 12
(D) 83
(E) 28
Rationale: Explanation:
T = 9/45 * 60 = 12
Answer: Option C
Answer: (C) 12
Question: At an elementary school, 60% of the faculty members are women and 60% of the faculty members are married. If 3/4 of the men are single, what fraction of the women are married?
(A) 5⁄7
(B) 7⁄10
(C) 1⁄3
(D) 7⁄30
(E) 5⁄6
Rationale: 2X2 table works perfect:
--------------------M------W--------Total
Marrried---------10-----50---------60
Not married-----30-----10---------40
Total-------------40-----60--------100
need married woman/total woman, so 50/60=5/6
E
Answer: (E) 5⁄6
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
Answer: Option B
Answer: (B) 30
Question: After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?
(A) 28.56%
(B) 35%
(C) 22.22%
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let Y be the Selling price.
So, x + (14.28x / 100) = y - (11.11y / 100).
Or y = 1.2856x
Or y = 128.56x/100
Or y = x + 28.56x/100
Hence, 28.56% above the cost price he marks his goods.
Answer : A
Answer: (A) 28.56%
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) Rs.600
(B) Rs.500
(C) Rs.250
(D) Rs.700
(E) Rs.800
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
ANSWER:A
Answer: (A) Rs.600
Question: The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 4500 pi cubic centimeters, what is hte surface area of the balloon in square centimeters?
(A) a. 40
(B) b. 100
(C) c. 400
(D) d. 1,000
(E) e. 2,000
Rationale: The surface area is 4.pi.r^2 (its area remember not volume)
as 4/3.pi.r^3=4500pi
r=15
so area = 4.pi.r^2= 900.pi= 900 x 3.14 = 2000 (approx)
E
Answer: (E) e. 2,000
Question: By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Sol:
(SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%
option D
Answer: (D) 50
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is :
(A) 48
(B) 52
(C) 58
(D) 66
(E) None
Rationale: Sol.
Relative sped = (60 + 90) km/hr
= [150 * 5/18] m/sec = [125 / 3] m/sec.
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = [2000 * 3/125] sec = 48 sec.
Answer A
Answer: (A) 48
Question: The length of the longest rod that can fit in a cubical room of 4 m side is?
(A) 7.256 m
(B) 6.928 m
(C) 8.524 m
(D) 10.256 m
(E) 11.823 m
Rationale: 4 root(3)= 6.928 m
ANSWER B
Answer: (B) 6.928 m
Question: A mixture contains alcohol and water in the ratio 4:3. If 5liters of water is added to the mixture, the ratio becomes 4:5. Find the quality of alcohol in the given mixture.
(A) 10
(B) 8
(C) 7.5
(D) 6
(E) 3.5
Rationale: Let the quantity of alcohol and water be 4x and 3x
4x/(3x+5) = 4/5
20x = 4(3x+5)
x=2.5
Quantity of alcohol = 4*2.5 = 10liters.
Answer is A
Answer: (A) 10
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3
(B) 1/5
(C) 1/0
(D) 1/2
(E) 1/1
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: (A) 1/3
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
(A) 6/11
(B) 6/13
(C) 6/15
(D) 7/11
(E) 7/13
Rationale: Part filled by (A + B + C) in 3 minutes = 3 1	+	1	+	1 = 3 x	11 =	11	.
30	20	10	60	20
Part filled by C in 3 minutes =	3	.
10
Required ratio = 3/10	x	20/11 =	6/11	.
Answer A)
Answer: (A) 6/11
Question: If a fair die is rolled six times, what is the probability that a 3 occurs on at least one roll?
(A) 25/36
(B) 125/216
(C) 425/639
(D) 11/36
(E) 36/216
Rationale: Questions such as these that talk aboutat leastormaximumorminimumin probability questions should make sure realize that probability of any event (N) to occur = 1- P(Not N)
Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6)(5/6)(5/6)(5/6)(5/6) = 1-214/639 =425/639.
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
C is thus the correct answer.
Answer: (C) 425/639
Question: What is the greatest positive integer n such that 3^n is a factor of 36^150?
(A) 100
(B) 200
(C) 300
(D) 600
(E) 900
Rationale: 36 = 3^2 * 2^2.
36^150 = 3^300 * 2^300
The answer is C.
Answer: (C) 300
Question: Annie has 100 cards numbered 1 through 100. If she deals nine cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?
(A) 95!/100!
(B) 9!/100!
(C) (92! X 9!)/100!
(D) (96! X 5!)/100!
(E) (97! X 4!)/100!
Rationale: Alex to get 9 consecutive cards in ascending order, to have 9 consecutive at the end is good enough.
There are 92 consecutive numbers in 100: {1, 2, 3, 4, 5,6,7,8,9}, {2, 3, 4, 5, 6,7,8,9,10}, ..., {92,93,94,95,96, 97, 98, 99, 100};
Total ways to pick 9 cards out of 100 is {9!*92!}{100!}.
Answer: C.
Answer: (C) (92! X 9!)/100!
Question: If -1<x<0, what is the median K of these six numbers listed below
1/x^3,1/x^2, 1/x,x, x^2,x^3
(A) 1/x
(B) x^2
(C) x^2(x+1)/2
(D) K=x(x^2+1)/2
(E) x^2/2x
Rationale: My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows:
-8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that.
median will be between -0.5 and -0.125.
So, (x^3+x)/2 (D).
Answer: (D) K=x(x^2+1)/2