mathewhe/aqua_rat huggingface dataset:
Question: A train having a length of 1/4 mile , is traveling at a speed of 75 mph. It enters a tunnel 3 ½ miles long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 3 min
(B) 4.2 min
(C) 3.4 min
(D) 5.5 min
(E) 5.7 min
Rationale: Explanation:
Total distance = 3 ½ + ¼ = 7/2 + ¼ = 15/4 miles
Speed = 75 mph
Time = distance/speed = (15/4) / 75 hr = 1/20 hr = 60/20 minutes = 3 minutes
Answer: Option A
Answer: (A) 3 min
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
(A) 1/9
(B) 1/6
(C) 1/5
(D) 1/0
(E) 1/1
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: (C) 1/5
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability R the piece ends no more than 7 spaces from the square numbered 49?
(A)  7%
(B)  8%
(C)  14%
(D)  15%
(E)  28%
Rationale: OA is E
required prob is 7 spaces any side of 49.
so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side
so total spaces = 28
probability R= 28%.E
Answer: (E)  28%
Question: Jacob is 12 years old. He is 3 times as old as his brother. How old will Jacob be when he is twice as old?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: j=12;
j=3b;
b=12/3=4;
twice as old so b=4(now)+(4)=8;
jacob is 12+4=16
ANSWER:D
Answer: (D) 16
Question: A train 100 m long crosses a platform 100 m long in 12 sec; find the speed of the train?
(A) 60 kmph
(B) 65 kmph
(C) 54 kmph
(D) 16 kmph
(E) 18 kmph
Rationale: D = 100 + 100 = 200
T = 12
S = 200/12 * 18/5 = 60 kmph
Answer:A
Answer: (A) 60 kmph
Question: A company consists of 10 senior and 10 junior staff officers. If a committee is created with 3 senior and 2 junior staff officers, in how many ways can the committee be formed?
(A)  4500
(B)  3500
(C)  4800
(D)  5400
(E)  2400
Rationale: Choose 3 senior from 10 senior and choose 2 junior from 10 junior:
10C3 * 10C2 = 120*45 = 5400
Ans: D
Answer: (D)  5400
Question: Can Z and can В are both right circular cylinders. The radius of can Z is twice the radius of can B, while the height of can Z is half the height of can B. If it costs $4.00 to fill half of can B with a certain brand of gasoline, how much would it cost to completely fill can Z with the same brand of gasoline?
(A)  $1
(B)  $2
(C)  $4
(D)  $8
(E)  $16
Rationale: Let x be the radius of b and 2h be the height of B. Therefore, radius of Z = 2x and height = h
Vol of b = 3.14*x^2*2h
Vol of a = 3.14*4x^2*h
cost to fill half of B = $4 --> cost to fill full B = $8
--> 3.14*x^2*2h = 8 --> 3.14*x^2*h = 4 --> 4*(3.14*x^2*h) = $16
Ans E
Answer: (E)  $16
Question: If annual decrease in the population of a town is 5% and the present number of people is 40000 what will the population be in 2 years?
(A) 24560
(B) 26450
(C) 36100
(D) 38920
(E) 45200
Rationale: Population in 2 years = 40000(1 - 5/100)^2 = 40000*19*19 / 20*20 = 36100
Answer is C
Answer: (C) 36100
Question: In Town P, 60 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town P are females?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: The percent of the population who are employed females is 60-45 = 15%
The percent of employed people who are female is 15% / 60% = 25%.
The answer is B.
Answer: (B) 25%
Question: If 12 ounces of a strong vinegar solution are diluted with 48 ounces of water to form a three-percent vinegar solution, what was the concentration of the original solution?
(A) 15%
(B) 18%
(C) 20%
(D) 21%
(E) 24%
Rationale: Let x be the concentration of the original solution.
12x = 0.03(60)
x = 0.15
The answer is A.
Answer: (A) 15%
Question: The ratio of the present age of Sandy to that of Molly is 7:2. Twelve years from now, the ratio of the ages of Sandy to Molly will be 5:2. What was Sandy's age 6 years ago?
(A) 39
(B) 45
(C) 51
(D) 57
(E) 63
Rationale: Let the present age of Sandy be 7x years and that of Molly be 2x years.
(7x + 12) / (2x + 12) = 5 / 2
4x = 36
x = 9
Six years ago, Sandy's age was 7(9) - 6 = 57
The answer is D.
Answer: (D) 57
Question: Point (c,d) is on the circle represented by x^2+y^2=10, and c, d are integers. How many such points are possible?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: c^2+d^2=10 and c, d are integers means that 10 is the sum of two perfect squares.
10 is the sum of only one pair of perfect squares 1 and 9.
So, there can be 8 such points, 4 in each quadrant:
(1, 3);
(1, -3);
(-1, 3);
(-1, -3);
(3, 1);
(3, -1);
(-3, 1);
(-3, -1).
Answer: E.
Answer: (E) 8
Question: A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country X. If calls to country X are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country X in a certain month?
(A) $8.75
(B) $12
(C) $13.40
(D) $17.40
(E) $24.40
Rationale: Discount = 40% of spending
We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.
Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.
Saving = (Slightly less than 40) - 25 = Slightly less than 15 charged in X country
Answer (C)
Answer: (C) $13.40
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 5 screws and 1 nails?
(A) a. 4
(B) b. 5/2
(C) c. 2
(D) d. 3/2
(E) e. 5/4
Rationale: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 5s and 1n= 5s+1*5s=10s..
ratio= 15s/10s=15/10=3/2
D
Answer: (D) d. 3/2
Question: What is 15% of 2/3 of 0.5?
(A) 0.05
(B) 0.9
(C) 9
(D) 90
(E) None of the above
Rationale: The best way to solve these questions is to convert every term into fraction
(15/100)*(2/3)*(5/10) = 150/3000 = 0.05
Option A
Answer: (A) 0.05
Question: A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water?
(A) 2 litres
(B) 3 litres
(C) 5 litres
(D) 7 litres
(E) 8 litres
Rationale: Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water,
(87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
Answer:A
Answer: (A) 2 litres
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 298
(B) 150
(C) 2776
(D) 1888
(E) 177
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer:B
Answer: (B) 150
Question: we have 3 weights one of 2 kg one of 3 kg one of 5 kg by using only two weight how many wight u can weight
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: select 2 weight out of 3, 3C2=3
ANSWER:C
Answer: (C) 3
Question: shopkeeper bought 400 meter cloths at rs 40,000 and sell at 200 rs per one and half mtr cloths. what is the gain or loss percent?
(A) 34.33% Profit
(B) 33.33% Profit
(C) 36.33% Profit
(D) 39.33% Profit
(E) 43.33% Profit
Rationale: 400 mtr -- 40000
1 1/2 mtr -- ?
3/(2*400) * 40000 = 150rs
So he has bought 1 1/2 metres at 150 rs nd going to sold at 200 rs
So Gain = 200 - 150 = 50
Gain % = 50 * 100 /150
=> 5000/150 = 33.33%
ANSWER:B
Answer: (B) 33.33% Profit
Question: Which of the list following is a prime number ?
(A) 29
(B) 81
(C) 91
(D) 93
(E) 10
Rationale: A
29
Clearly, 29 is a prime number.
Answer is A
Answer: (A) 29
Question: A fast train takes 3 hours less than a slow train for a journey of 600 km, If the speed of the slow train is 10 km/hr less than that of the fast train, the speeds of the two trains are
(A) 60 km/hr and 70 km/hr
(B) 50 km/hr and 60 km/hr
(C) 40 km/hr and 50 km/hr
(D) None of these
(E) 30 km/hr and 40 km/hr
Rationale: =600/x - 600/x+10 = 3/1
Solving this, we get x = 40
Answer: C.
Answer: (C) 40 km/hr and 50 km/hr
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses E at the restaurant? (Assume that all boxes are filled to capacity.)
(A) 96
(B) 240
(C) E=256
(D) E=384
(E) E=480
Rationale: Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: (E) E=480
Question: The area of the largest circle that can be drawn inside a rectangle with sides 18cm by 14cm is
(A) 237
(B) 154
(C) 2376
(D) 198
(E) 171
Rationale: Explanation:
The diameter is equal to the shortest side of the rectangle.
so radius= 14/2 = 7cm.
Answer: B) 154
Answer: (B) 154
Question: Ashok secured average of 76 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
(A) 38
(B) 27
(C) 99
(D) 17
(E) 86
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 76
Therefore total marks in 6 subjects = 76 * 6 = 456
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 456 – 370 = 86
ANSWER: E
Answer: (E) 86
Question: In expressing a length of 25.461 km as nearly as possible with the three significant digits, find the percentage error
(A) 0.353%
(B) 0.153%
(C) 0.035%
(D) 0.015%
(E) None of these
Rationale: Explanation:
Error = (25.5 - 25.461) = 0.039
Required percentage =
0.039/ 25.461Ã—100=0.153
Option B
Answer: (B) 0.153%
Question: Paul sells encyclopedias door-to-door. He earns $40 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?
(A) 13,200
(B) 14,800
(C) 14,900
(D) 15,600
(E) 19,600
Rationale: His pay check was $1320.
Out of this, $40 was his fixed salary so the total commission he earned was $1320 - $40 = $1280
He earns 10% on the sales of first $10,000 which gives a commission of $1000.
He earns 5% on every subsequent dollar. Since he earns another $280, he must have had sales of another 280*(100/5) = 5600
So his total sales must have been $10,000 + $5600 = $15,600
D
Answer: (D) 15,600
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 7
(B) 8
(C) 6
(D) 9
(E) 2
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: By how much is three-fifth of 380 greater than four-seventh of 210 ?
(A) 90
(B) 100
(C) 108
(D) 120
(E) 130
Rationale: Explanation:
3/5 of 380 - 4/7 of 210 = 228 - 120 = 108.
Answer: C
Answer: (C) 108
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 1/2
(B) 10/21
(C) 9/11
(D) 7/11
(E) 5/11
Rationale: Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5×4/2×1)/(7×6/2×1)=5×4/7×6=10/21
ANSWER:B
Answer: (B) 10/21
Question: there are 5 envelope and 5 letters placed at random. what is the probability that no single letter is placed in the right envelope
(A) 117/120
(B) 118/120
(C) 119/120
(D) 116/120
(E) 115/120
Rationale: probability that no single letter is placed in the right envelop is = 1- (placing all the letters in the right envelop)
i.e 5 letters will go in their right envelops in only 1 way, and total cases is 5!
so, 1-(1/5!) = 119/120
ANSWER:C
Answer: (C) 119/120
Question: kareena, Saif, and a puppy start walking down a road.
They start at the same time, from the same point, in the same direction.
The saif walks at 5 miles/hour
kareena at 6 miles/hour.
The puppy runs from saif to kareena and back again with a constant speed of 10 miles/hour.
The puppy does not slow down on the turn.
How far does the puppy travel in 1 hour?
(A) 10 miles
(B) 14 miles
(C) 12 miles
(D) 20 miles
(E) 30 miles
Rationale: A
10 miles
Speed us 10miles/hour
Answer: (A) 10 miles
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 46.24, the number of the member is the group is:
(A) 57
(B) 68
(C) 77
(D) 87
(E) 97
Rationale: Explanation:
Money collected = (46.24 x 100) paise = 4624 paise.
∴ Number of members = √(4624) = 68.
Answer: B
Answer: (B) 68
Question: For a construction,15 peoples are working. But constructor wants extra 3 people out of 5 people.What is possible selection?
(A) 10
(B) 5
(C) 7
(D) 8
(E) 6
Rationale: 5C3=5!/2!*3!=5*4*3!/3!*2*1=10 possible ways to select the extra 3 people for construction
Answer is option A
Answer: (A) 10
Question: Of the 120 passengers on Flight 750, 60% are female. 10% of the passengers sit in first class, and the rest of the passengers sit in coach class. If 1/3 of the passengers in first class are male, how many females are there in coach class?
(A) 44
(B) 48
(C) 50
(D) 64
(E) 56
Rationale: Number of passengers on flight = 120
Number of female passengers= .6*120 = 72
Number of passengers in first class = (10/100)* 120 = 12
Number of passengers in coach class = (90/100)* 120 = 108
Number of male passengers in first class = 1/3 * 12 = 4
Number of female passengers in first class = 12-4 = 8
Number of female passengers in coach class = 72 - 8 = 64
Answer D
Answer: (D) 64
Question: John and Jacob set out together on bicycle traveling at 18 and 15 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 18 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
(A) 3
(B) 3 1/3
(C) 3 1/2
(D) 4
(E) 4 1/3
Rationale: John's speed - 18 miles/hr
Jacob's speed - 15 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 18x2/3 = 12 miles.
Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 15x5/3 = 25 miles.
Now, when John starts riding back, the distance between them is 13 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 18-15 = 3 miles/hr.
Thus, to cover 13 miles at 3 miles/hr, John will take 13/3 = 4 1/3 hours
Answer E
Answer: (E) 4 1/3
Question: #88
A necklace is made by stringing C individual beads together in the repeating pattern red bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then C could equal
(A) 16
(B) 32
(C) 41
(D) 54
(E) 58
Rationale: You can just write out the pattern and count: RGWBYRGWBYRGWBY... But to save time a good test taker will just look for a pattern. Min # is 3, because W is the third one. Then every 5 beads another white comes, so it must be 3+5+5+5.. and so on...
3+5 = 8
3+5+5 = 13
3+5+5+5=18
3+5+5+5+5=23
So you see it ends in either 8 or 3. 58 IS THE NO. E
Answer: (E) 58
Question: If the quantity (p − 25) is 5 times the quantity (q − 5), then what is the relationship between p and q?
(A) p = 5q + 30
(B) p = 5q − 30
(C) 5p = q + 20
(D) p = 5q
(E) p = 5q − 20
Rationale: p-25=5(q-5)
p-25=5q-25
p=5q
option D
Answer: (D) p = 5q
Question: Three cubes of metal whose edges are 9, 12 and 18 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
(A) 20.2
(B) 77
(C) 66
(D) 18
(E) 99
Rationale: 93 + 123 + 183 = a3 => a
= 20.2
Answer: A
Answer: (A) 20.2
Question: If 80 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 75 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?
(A) 60 %
(B) 65 %
(C) 70%
(D) 75%
(E) 80%
Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 80 + 75 - {Both correctly} + 5
{Both correctly} = 60.
Answer: A.
Answer: (A) 60 %
Question: 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
(A) 18
(B) 24
(C) 22
(D) 20
(E) 19
Rationale: Let the required number of days be x.
Less men,More days=27;36::18:x
27x=36*18
x=(36*18)/27
x=4*6
x=24 days.
Answer:B
Answer: (B) 24
Question: It takes Joey the postman 1 hours to run a 2 mile long route every day. He delivers packages and then returns to the post office along the same path. If the average speed of the round trip is 3 mile/hour, what is the speed with which Joey returns?
(A) 1
(B) 6
(C) 13
(D) 14
(E) 15
Rationale: let his speed for one half of the journey be 2 miles an hour
let the other half be x miles an hour
now,
avg speed =3 mile an hour
2*2*x/2+x=3
4x=3x+6=>x=6
B
Answer: (B) 6
Question: John,David and Xavier enter into partnership. John invests some money at the beginning, David invests double the amount after 6 months, and Xavier invests thrice the amount after 8 months. If the annual gain be Rs.24000. John's share is?
(A) 7500
(B) 7250
(C) 8000
(D) 8200
(E) 8100
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 24000 = 8000
Answer: C
Answer: (C) 8000
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
(A) 18
(B) 76
(C) 12
(D) 17
(E) 13
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer:A
Answer: (A) 18
Question: Maths, Physics and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books. Among all the books, 12 books are soft cover and the remaining are hard-cover. If there are a total of 7 hard-cover books among the maths and physics books. What is the probability R, that a book selected at random is either a hard cover book or a chemistry book?
(A) 1/10
(B) 3/20
(C) 1/5
(D) 1/4
(E) 9/20
Rationale: First phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf. To do so, you have the equations:
m + p + c = 20 (since 4/5 of the 25 spots are full of books)
m = 2p
p = 4 + c
From that, you can use Substitution to get everything down to one variable.
c = p - 4
m = 2p
p = p
Then (p - 4) + 2p + p = 20, so 4p = 24 and p = 6. That means that there are 12 math, 6 physics, and 2 chemistry books on the shelf.
With those numbers, you also know that there are 8 total hardcovers, 1 of which is chemistry. So if your goal is to get either a hardcover or a chemistry, there are 9 ways towin- either one of the 7 hardcovers that aren't chemistry or the two chemistry books. So out of the 20 total, R=9 provide the desired outcome, making the answer E.
Answer: (E) 9/20
Question: The average mark obtained by 23 candidates in an examination is 45. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?
(A) 26
(B) 45
(C) 90
(D) 80
(E) 65
Rationale: It is clear that 23 x 45 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 45
Answer:B
Answer: (B) 45
Question: When asked what the time is,a person answered that the amount of time left is 1/2 of the time already completed.what is the time.
(A) 2 PM
(B) 9 PM
(C) 3 PM
(D) 4 PM
(E) 6 PM
Rationale: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=1/2x⇒x=16
Time is 4 PM
Answer:D
Answer: (D) 4 PM
Question: If x is to be chosen at random from the set {5,6,7,8} and y is to be chosen at random from the set {3,4,5}, what`s the probability that xy will be even?
(A) 1/6
(B) 1/3
(C) 1/2
(D) 5/6
(E) 2/3
Rationale: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: E.
Answer: (E) 2/3
Question: How many prime numbers between 50 to 100?
(A) 11
(B) 10
(C) 15
(D) 14
(E) 12
Rationale: primes are of the form 6n+1 or 6n-1
Put n=9
6n+1=6*9+1=55 where 55 is not prime
for n=9
6n-1=6*9-1=53
for n=10 , 6n-1= 59 and 61
for n=11 , ==> 67
for n =12 ==> 73 and 71
for n =13 ==> 79
for n =14 ==> 83
for n=15 ==> 89
for n =16 ==> 97
therefore total number of prime numbers = 10
Ans - B
Answer: (B) 10
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 7hrs if the speed of the bike is twice speed of the tractor?
(A) 400 km
(B) 500 km
(C) 360 km
(D) 550 km
(E) 630 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 7 h is
90 × 7 = 630 km
Ans.(E)
Answer: (E) 630 km
Question: A,B,C together can do a work in 12 days. A alone can do the work in 45 days and B alone can do the same work in 55 days. Find in what time C alone can do that work?
(A) 28.80days
(B) 17days
(C) 23.29days
(D) 30days
(E) 33.20days
Rationale: The required answer is = 12*45*55 / 45*55-12(45+55)
= 29700/1275 = 23.29days
Answer is C
Answer: (C) 23.29days
Question: There are 1200 military people in a division of the army. There is one Officer for every 15 soldiers in that division. Now the question is how many officers are in the division?
(A) 22
(B) 35
(C) 37
(D) 73
(E) 75
Rationale: E
75
15 soldiers + 1 officer makes a group of 16 people. Now number of such groups = 1200/16 = 75.
Answer: (E) 75