mathewhe/aqua_rat huggingface dataset:
Question: A tank is filled in 5 hours by three pipes P, Q and R. The pipe R is twice as fast as Q and Q is twice as fast as P. How much time will pipe P alone take to fill the tank?
(A) 35 hrs
(B) 20 hrs
(C) 25 hrs
(D) 50 hrs
(E) 28 hrs
Rationale: Pipe P alone - x hrs to fill
then Q and R -> x/2 and x/4 hrs
then 1/x+2/x+4/x = 1/5
7/x=1/5
x = 33 hrs
ANSWER A
Answer: (A) 35 hrs
Question: A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %.
(A) 2%
(B) 3%
(C) 4%
(D) 5%
(E) 6%
Rationale: sol. cp=rs27.50, sp=rs 28.50
gain=rs(28.50 â€“27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%
ANSWER C
Answer: (C) 4%
Question: A sporting goods store sold 64 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $196 what is the fewest number of $4 Frisbees that could have been sold?
(A) 24
(B) 12
(C) 8
(D) 2
(E) 4
Rationale: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 64
3x + 4y = 196
x = 64 - y
3(64-y) + 4y = 196
192 - 3y + 4y = 196
y = 4
Answer: E
Answer: (E) 4
Question: A rectangular lawn of dimensions 70 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
(A) 2288
(B) 2779
(C) 2779
(D) 3900
(E) 3600
Rationale: Area = (l + b â€“ d) d
(70 + 60 â€“ 10)10 => 1200 m2
1200 * 3 = Rs.3600
Answer:E
Answer: (E) 3600
Question: John bought a total of 20 Mangoes and Oranges. Each Mango costs 80 cents and each orange costs 60 cents. If the average price of the 20 mangoes and oranges that John originally purchased was 65 cents, then how many oranges needs to return to raise the average price of his purchase to 72 cents?
(A) 4
(B) 5
(C) 6
(D) 9
(E) 12
Rationale: Let number of mangoes be x, number of oranges be 12-x
0.80x +(20-x)0.60/20 = 0.65
solving for x, we get x = 5 --> Mangoes 5, Oranges 15
Now, number of oranges to be returned be y
0.80*5 + (15-y)*0.60/20-y = 0.72
solving for y, y = 12
Ans: E
Answer: (E) 12
Question: If W = {1, 7, 18, 20, 29, 33}, how much less is the mean of the numbers in W than the median of the numbers in W?
(A)  1.0
(B)  1.5
(C)  2.0
(D)  2.5
(E)  3.0
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (1 + 7 + 18 + 20 + 29 + 33)/6 = 18
Median = (18 + 20)/2 = 19
Difference = 1
Option A
Answer: (A)  1.0
Question: If A and B are two prime numbers bigger than 2, which of the following can be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A- B is also a even number.
(A) 1 only.
(B) 1 and 3 only.
(C) 3 only.
(D) 2 and 3 only.
(E) 1, 2 and 3.
Rationale: Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : True
Ans :B
Answer: (B) 1 and 3 only.
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 16% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A) 5%
(B) 17%
(C) 16%
(D) 13%
(E) 30%
Rationale: 60-(x+16+z) + 50-(x+16+y) + 35-(z+16+y) + x + y + z +16 = 100
where x = people who bought MilkChicken
y = people who bought chickenApples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.
Hence solving the above equation we get,
113 -(x+y+z) = 100
Thus, x+y+z= 13
Answer: D
Answer: (D) 13%
Question: The simple interest at a% for a years will be $a on a sum of
(A) $ (1000)/a
(B) $(100)a^2
(C) $ a
(D) $ (100)/a
(E) $ 100a
Rationale: Principal =$(100*a)/(a*a)=$(100/a).
Answer is D
Answer: (D) $ (100)/a
Question: {1/(4+√15)} =
(A) a. 16+16√15
(B) b. 31- 8√15
(C) c. 31+ 8√15
(D) d. 4- √15
(E) e. 32 + 4√15
Rationale: = 1 / (4 + root15)
Multiply numeratordenominator by (4 - root15)
= (4 - root15) / (16-15) = (4 - root15)
Answer = D
Answer: (D) d. 4- √15
Question: Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 36 meter head start. If Cristina runs at a pace of 4 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A)  15 seconds
(B)  18 seconds
(C)  25 seconds
(D)  36 seconds
(E)  45 seconds
Rationale: used pluging in method
say t is the time for cristina to catch up with Nicky, the equation will be as under:
for Nicky=N=3*t+36
for Cristina=C=5*t
@t=36, N=144 C=144 right answer
ans:D
Answer: (D)  36 seconds
Question: Two trains of length 100 m and 200 m are 200 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
(A) 21/9 sec
(B) 32/3 sec
(C) 20/7 sec
(D) 32/3 sec
(E) 40/7 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 200/35 = 40/7 sec.
Answer:E
Answer: (E) 40/7 sec
Question: If a, b, and c are positive numbers such that (a/(a+b))(10) + (b/(a+b))(20)=c and if a<b which of the following could be the value of c?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: The answer is D. For any positive a and b, c is a number between 10 and 20. Since a < b, weight of 10 is inferior of weight of 20 -> c is > 15 -> 18 is the answer.
Answer: (D) 18
Question: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 15 km/hr downstream and 7 km/hr upstream.
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) 11 kmph
Rationale: Speed in still water = (15 + 7)1/2 kmph = 11 kmph.
answer :E
Answer: (E) 11 kmph
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 878
(B) 2878
(C) 221
(D) 276
(E) 245
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:E
Answer: (E) 245
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is:
(A) 72
(B) 76
(C) 78
(D) 86
(E) 88
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86.
D
Answer: (D) 86
Question: If A and B are two events such that P (A) = 3/4, P (B) = 1/2 and P (A n B) = 3/8,
find P (not A and not B).
(A) 1/9
(B) 1/8
(C) 1/11
(D) 1/13
(E) 2/5
Rationale: P(not A and not B) = 1 - (P(A) + P(B) - P(AB))
which you might find somewhere in your text.
Substituting in our probabilities we get:
P(not A and not B) = 1 - (3/4 + 1/2 - 3/8)
P(not A and not B) = 1 - (7/8)
P(not A and not B) = 1/8.
B
Answer: (B) 1/8
Question: What is the unit digit in 8^100?
(A) 0
(B) 1
(C) 6
(D) 3
(E) 5
Rationale: Unit digit in 8^100 = unit digit in [(8^4)^25 ]But unit digit in 8^4=6unit digit 8^100= 6Answer is C
Answer: (C) 6
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 130 pages?
(A) 9 hours 45 mins
(B) 8 hours
(C) 9 hours
(D) 7 hours
(E) 6 hours
Rationale: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 130 pages when Anil and Suresh work together = 130 × 3 /40 = 39/4
= 9 3/4 hours = 9 hour 45 minutes
Answer is A.
Answer: (A) 9 hours 45 mins
Question: Given 2x + y + z = 3 and 5x + 3y + z = 9, what is the value of x + y - z?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: (1) 5x + 3y + z = 9
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 3
The answer is A.
Answer: (A) 3
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
(A) 20 litres
(B) 30 litres
(C) 15 litres
(D) 10 litres
(E) 25 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5 20x=4(3x+5)8x=20 x=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.
Option D
Answer: (D) 10 litres
Question: Which of the following are phases of 2-phase locking protocol?
(A) Intent to request locks
(B) Release the present locks and never asking for transmission
(C) Both (1) and (2)
(D) None of these
(E) DS
Rationale: Answer:C
Answer: (C) Both (1) and (2)
Question: Rani has only pennies, dimes, and nickels in a jar. The jar has at least 1 but no more than 4 pennies. If the jar has at least 1 nickel and 1 dime, which of the following could NOT be the total amount of money in the jar?
(A) 62
(B) 63
(C) 64
(D) 65
(E) 61
Rationale: Let there be a pennies , b nickels and c dimes
so total amount can be 1+5b+10c cents to 4+5b+10c
as you can see the equation of total whenever divided by 5 would leave a remainder from 1 to 4 ( as pennies can only be from 1 to 4 and hence a is limited to values from 1 to 4)
So the total can never be divisible by 5 and hence only 65 that is c is the option which is divisible by 5.
so answer is D
Answer: (D) 65
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 14/17
(D) (d) 17/35
(E) (e) 1/2
Rationale: This problem is very good example how easy and quick plug-in method might be.
Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 7*6=$42;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$42=$168;
Fraction of total revenue from large cups: 168/(36+168)=14/17.
Answer: C.
Answer: (C) (c) 14/17
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 5?
A. 48 kmph
(A) 33
(B) 52.5
(C) 28
(D) 27
(E) 16.6
Rationale: Let the distances between city A to B and B to C be 2x km and 5x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (5x)/60 = (6x + 10x)/120 = 16x/120 Average speed = (2x + 5x)/(16x/120) = 52.5 kmph.
Answer: B
Answer: (B) 52.5
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) 1055
(B) 1050
(C) 1057
(D) 1060
(E) 1070
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055.
A
Answer: (A) 1055
Question: Mathew is planning a vacation trip to London next year from today for 5 days, he has calculated he would need about $3,000 for expenses, including a round-trip plane ticket from L.A to London. He nets around $1,500 monthly in gross income, after all bills are paid, he is left with about $350 each month free for whatever he desires. How much money would Mathew need to evenly save from his $350 to have $3,000 in his bank within 12 months?
(A) $240
(B) $350
(C) $217
(D) $250
(E) $340
Rationale: Answer is (D). If Mathew is left with about $350 after all expenses each month, he would need to divide the total expense budget to London ($3,000) by 12 months to determine how much he would need to put away every single month to hit his target. $3,000/12 = $250.
Answer: (D) $250
Question: The greatest number by which the product of three consecutive multiples of 5 is always
(A) 54
(B) 81
(C) 750
(D) 243
(E) None of these
Rationale: Explanation:
5*10*15 = 750
Option C
Answer: (C) 750
Question: In a race where 16 cars are running, the chance that car X will win is 1/4, that Y will win is 1/12 and that Z will win is 1/7. Assuming that a dead heat is impossible, find the chance that one of them will win.
(A) 1/140
(B) 10/21
(C) 27/410
(D) 11/21
(E) 57/120
Rationale: Required probability = P(X) + P(Y) + P(Z) (all the events are mutually exclusive).
= 1/4 + 1/12 + 1/7
= 10/21
ANSWER:B
Answer: (B) 10/21
Question: An unbiased die is tossed. Find the probability of getting a multiple of 2.
(A) 1/2
(B) 1/3
(C) 2/3
(D) 1/4
(E) 1/6
Rationale: here s= {1,2,3,4,5,6}
let E be the getting of a multiple of 2.
then E = {2,4,6}
probability = 3/6 = 1/2
correct option is A
Answer: (A) 1/2
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.1205 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
(A) 22200
(B) 31897
(C) 48799
(D) 50000
(E) 52782
Rationale: P(11/10)^4 - P(6/5)^2 = 1205
P = 50000
Answer: D
Answer: (D) 50000
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.500 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 3999
(B) 7799
(C) 2500
(D) 2772
(E) 6250
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 500
B capital = 37500*1/6 = 6250.Answer: E
Answer: (E) 6250
Question: There are 12 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total?
(A) 58
(B) 62
(C) 66
(D) 70
(E) 74
Rationale: 12C2=66
The answer is C.
Answer: (C) 66
Question: A train ,130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is
(A) 235 m
(B) 245 m
(C) 247 m
(D) 249 m
(E) 252 m
Rationale: length of the bridge = x meter
Total distance covered = 130+x meter
total time taken = 30s
speed = Total distance covered /total time taken = (130+x)/30 m/s
= 45 × (10/36) = (130+x)/30
= 45 × 10 × 30 /36 = 130+x
= 45 × 10 × 10 / 12 = 130+x
= 15 × 10 × 10 / 4 = 130+x
= 15 × 25 = 130+x = 375
= x = 375-130 =245
Answer: (B) 245 m
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 187 cm
(B) 800 cm
(C) 216 cm
(D) 278 cm
(E) 272 cm
Rationale: Area of the square = s * s
= 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square
= 4 * 200
= 800 cm.
Answer: B
Answer: (B) 800 cm
Question: A train 350 m long passed a pole in 35 sec. How long will it take to pass a platform 650 m long?
(A) 100 sec
(B) 89 sec
(C) 85 sec
(D) 16 sec
(E) 15 sec
Rationale: Speed = 350/35 = 10 m/sec.
Required time = (350 + 650)/10
= 100 sec.
Answer: A
Answer: (A) 100 sec
Question: If x is a positive, single-digit integer such that 4/3*x, 3x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: The big hints are thatx is a 1-digit integerAND (4/3)x, 3x, x, and x + 2, and 3x – 2 are ALLintegers
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers
When x =3, we get the following terms: (4/3)(3), 3(3),3,3+ 2, and 3(3) – 2.
When we evaluate these terms we get: 4, 9, 3, 5 and 7
Rearrange to get: 3, 4, 5, 7, 9. So, when x = 3, we getconsecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)
Answer:
C
Answer: (C) 5
Question: A and B are working on an assignment. A takes 6 hours to type 32 pages on a computer, while B takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
(A) 5 hours
(B) 6 hours
(C) 7 hours
(D) 8 hours
(E) 9 hours
Rationale: Number of pages typed by A in one hour=32/6=16/3
Number of pages typed by B in one hour=40/5=8
Number of pages typed by both in one hour=((16/3)+8)=40/3
Time taken by both to type 110 pages=110*3/40=8 hours.
Answer : D.
Answer: (D) 8 hours
Question: If 2x + y = 7 and x + 2y = 5, then 10xy/3 =?
(A) A) 10
(B) B) 2
(C) C) 17/5
(D) D) 18/5
(E) E) 4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(10*3*1)/3
= 30/3
=10
A
Answer: (A) A) 10
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 247
(B) 240
(C) 249
(D) 244
(E) 241
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer: B
Answer: (B) 240
Question: In a basketball contest, players must make 10 free throws. Assuming that Shmill O'Real has a 90% chance of making each of his shots, how likely is it that he will make all of his 10 shots in the contest?
(A) (9/10)^10
(B) (9/10)^2
(C) 9/10
(D) (8/9)^10
(E) (9/10)^9
Rationale: Probability of making to each of 10 shots = (9/10)*(9/10)*(9/10)*(9/10)*(9/10)*(9/10)*(9/10)*(9/10)*(9/10)*(9/10) = (9/10)^10
Answer: Option A
Answer: (A) (9/10)^10
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 20 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 9.45%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Rationale: The amount of chromium in the new 20+35=55 kg alloy is 0.12*20+0.08*35=5.2 kg, so the percentage is 5.2/55*100=9.2%.
Answer: A.
Answer: (A) 9.45%
Question: In a basket of 10 apples,John wants only 3 apples to give their 3 friends.In how many ways that john select apples from a basket?
(A) 120
(B) 150
(C) 30
(D) 100
(E) 50
Rationale: By the statement john wants 3 apples. He needs to select 3 apples out of 10 apples in a basket.
The probability to select is 10C3.
10C3=10!/7!*3!=10*9*8*7!/7!*3*2*1
=120
John have 120 ways to select 3 apples out of 10 apples.
The answer is option A
Answer: (A) 120
Question: A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
(A) 8 : 1
(B) 8 : 2
(C) 8 : 7
(D) 8 : 3
(E) 8 : 9
Rationale: Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
8:7
Answer:C
Answer: (C) 8 : 7
Question: If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is :
(A) 22
(B) 40
(C) 88
(D) 27
(E) 11
Rationale: Explanation:
Let the numbers are
By Hypothesis , ......(i)
Mean of new numbers =
By (i)
Answer: B) 40
Answer: (B) 40
Question: Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 20 percent. At the same time, it decreased its total working hours by 30 percent. By what percent did this factory increase its output per hour?
(A) 171.4
(B) 171.5
(C) 171.6
(D) 171.7
(E) None of the above
Rationale: Lets assume the initial production was 100 litres of beer for 100 hr.
With the 20% increase the total amount of beer production will be 120 litres and with 30 % decrease in total hours will be reduced to 70 hr.
100hr ----> 100 lts
1hr -----> 1 lts
70hr -----> 120 lts
1hr -----> 1.714 lts
Total Increase in production for 1 hr = 171.4%
Answer A
Answer: (A) 171.4
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 51. What is that number?
(A) 3.5
(B) 6
(C) 8
(D) 7
(E) 4
Rationale: Let the number be x. Then,
3(2x + 9) = 51
2x = 8 => x = 4
ANSWER:E
Answer: (E) 4
Question: All the students of class are told to sit in circle shape. Here the boy at the 10 th position is exactly opposite to 45 th boy. Total number of boys in the class?
(A) 65
(B) 68
(C) 72
(D) 70
(E) 58
Rationale: As half the circle shape consist of 45-10=35 boys,
So total number of boys in full circle=2*35=70
ANSWER: D
Answer: (D) 70
Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:
(A) 91/2
(B) 3/6
(C) 4/5
(D) 2/91
(E) 8/9
Rationale: Let S be the sample space.
Then, n(S)	= number of ways of drawing 3 balls out of 15
= 15C3
=	(15 x 14 x 13)
(3 x 2 x 1)
= 455.
Let E = event of getting all the 3 red balls.
n(E) = 5C3 = 5C2 =	(5 x 4)/(2 x 1)= 10.
P(E) =	n(E)/n(S)=10/455=2/91.
Ans:D
Answer: (D) 2/91
Question: Ron cycles his way up on a hill side and back. He takes the exact same route both ways. On the trip out he cycles an average speed of 5 miles per hour. On the trip back, downhill cycling at an average speed of 100 miles per hour, he is quick to return back. What is his approximate average speed for the round trip in miles per hour?
(A) 8
(B) 9.52
(C) 10
(D) 11.7
(E) 20
Rationale: Average speed = total distance/total time
Here distance to hill top and back is same as he takes the same route.
D = 5T1 and D=100T2
Therefore, T1 = D/5 and T2 = D/100
T1+T2 = 21d/100
Therefore, average speed = 2d/21d/100 =2d * 100/21d
Answer is 9.52 Since, the options are far away we need not solve till the decimal points
So correct answer is option B
Answer: (B) 9.52
Question: A certain Maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight. A certain green paint contains 10 percent blue pigment and 90 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
(A) 1.5
(B) 2
(C) 2.5
(D) 3
(E) 3.5
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.3 =1.5 Grams of red pigment
Answer: (A) 1.5
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 63
(B) 72
(C) 14
(D) 50
(E) 25
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
ANSWER A
Answer: (A) 63
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {6, 6, 6, 14, 14, 14}, standard deviation = P
Set II = {10, 10, 10, 10, 10, 10}, standard deviation = Q
Set III = {7, 8, 9, 11, 12, 13}, standard deviation = R
Rank these three standard deviations from least to greatest.
(A) P, Q, R
(B) P, R, Q
(C) Q, P, R
(D) Q, R, P
(E) R, Q, P
Rationale: SD is minimum when the terms are closer to the mean.
In set 2, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 1 and Set 3, Set 3 has terms more closer to mean than set 1. hence, Set 1 Sd is the highest.
So, Answer is D
Answer: (D) Q, R, P
Question: What is the perimeter of an isosceles right angled triangle. The area of the isosceles right angled triangle is 50.
(A) 25
(B) 36
(C) 25
(D) 30
(E) 34.14
Rationale: An isosceles right angled triangle has both the base and height same.
The area of an isosceles triangle = 1/2 * base * height
since height = base
1/2 * height * height = 1/2 * height ^2 = 50
height ^ 2 = 100
height = 10 = base
Since we know the base and height. We will calculate the hypotenuse using Pythagoras
Base ^ 2 + Height ^ 2 = Hypotenuse ^ 2
10^2 + 10^2 = Hypotenuse^2
Hypotenuse^2 = 200
Hypotenuse = 14.14
Perimeter of the triangle = 10 + 10 + 14.14 = 34.14
Ans: E
Answer: (E) 34.14