mathewhe/aqua_rat huggingface dataset:
Question: A deer is standing 70 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 40 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?
(A) 160
(B) 240
(C) 520
(D) 190
(E) 720
Rationale: Let x be the length of the tunnel.
When the deer runs 70 meters west, the train goes 700 meters to a point 40 meters from the west entrance of the tunnel.
When the deer runs east, the deer runs x-70 meters while the train goes x + 700 + 40 meters.
x + 700 + 40 = 10(x-70)
9x = 1440
x = 160 meters
The answer is A.
Answer: (A) 160
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
(A) 10
(B) 20
(C) 40
(D) 50
(E) 60
Rationale: His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20
B
Answer: (B) 20
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150
(B) 160
(C) 180
(D) 170
(E) 190
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
Answer: Option A
Answer: (A) 150
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability ofhitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3,1.2 & 1.1 respectively. What is the probability that theplane is hit when all the four shots are fired?
(A) 0.6976
(B) 0.9753
(C) 1.5678
(D) 1.7454
(E) 2.6548
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: (A) 0.6976
Question: A 6" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
(A) 24
(B) 32
(C) 64
(D) 80
(E) 100
Rationale: The unpainted blocks are the interior blocks.
These blocks form a 4" cube on the inside.
The number of unpainted blocks is 4*4*4 = 64 blocks.
The answer is C.
Answer: (C) 64
Question: A shopkeeper purchased 85 kg of potatoes for Rs. 595 and sold the whole lot at the rate of Rs. 8 per kg. What will be his gain percent?
(A) 18 1/9 %
(B) 18 9/3 %
(C) 18 1/3 %
(D) 14 2/7 %
(E) 18 7/3 %
Rationale: C.P. of 1 kg = 595/85 = Rs. 7S.P. of 1 kg = Rs. 8Gain % = 1/7 * 100 = 100/7 = 14 2/7 %Answer: D
Answer: (D) 14 2/7 %
Question: What is the probability that a leap year has 53 Sundays and 52 Mondays?
(A) 1/8
(B) 1/7
(C) 1/4
(D) 1/3
(E) 1/5
Rationale: A leap year has 52 weeks and two days
Total number of cases = 7
Number of favourable cases = 1
i.e., {Saturday, Sunday}
Required Probability = 1/7
Answer:B
Answer: (B) 1/7
Question: A man spends 2/5 of his salary on house rent, 3/10 of his salary on food and 1/8 of his salary on conveyance. If he has $1400 left with him, find his expenditure on food.
(A) $400
(B) $1400
(C) $3400
(D) $2400
(E) $4400
Rationale: Part of salary left =1-(2/5+3/10+1/8)
=7/40
Let the monthly salary be $x
Then (7/40) of x=1400
X=8000
Expenditure on food=$2400
Option D
Answer: (D) $2400
Question: How many gallons of water must be mixed with 1 gallon of a 15% salt solution To obtain a 10% salt solution
(A) 5
(B) 67
(C) 1.0
(D) 1.5
(E) 2.00
Rationale: Since we are adding pure water then the amount of salt in both solutions will be the same, so 0.15*1=0.1*(1+x) --> x=0.5.
Answer: A.
Answer: (A) 5
Question: How many different positive integers are factors of 20?
(A) 6
(B) 8
(C) 4
(D) 10
(E) 12
Rationale: 2*10
4*5
Answer : C
Answer: (C) 4
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the 3rd digit of p, counting right to left from the units digit?
(A) 2
(B) 4
(C) 4
(D) 6
(E) 9
Rationale: --------------------------------------------------2
-------------------------------------------------22
-----------------------------------------------222
---------------------------------------------2,222
-------------------------------------------22,222
...
222,222,222,222,222,222,222,222,222,222
Total 30 numbers.
For the first digit (units place) we should add 30 2's --> 30*2=60, so 0 will be units digit and 6 will be carried over;
For the second digit (tens place) we should add 29 2's --> 29*2=58+6=64, so 4 will be written for this digit and 6 will be carried over;
for third digit (hundreth) we should add 28 2's --28*2=56+6 =62 2 will be written 6 will be carried over...
A
Answer: (A) 2
Question: In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 8 eggs. If the cost of each pound of rice is $0.33, then how many Q cents does a liter of kerosene cost? [One dollar has 100 cents.]
(A)  0.33
(B)  0.44
(C)  0.55
(D)  44
(E)  55
Rationale: Main thing to remember is answer is asked in cents, however when we calculate, it comes up as 0.44 $
Just multiply by 100, Answer Q= 44.D
Answer: (D)  44
Question: If the cost price of 50 articles is equal to the selling price of 15 articles, then the gain or loss percent is?
(A) 16
(B) 127
(C) 12
(D) 18
(E) 233
Rationale: Percentage of profit = 35/15 * 100 = 233%
Answer: E
Answer: (E) 233
Question: If # is an operation which results in adding the digits of integer until a single digit is left, what is the probability Q that a number picked up in first 90 positive integers will have the result of # as an odd digit ?
(A) (a) 4/10
(B) (b) 4/9
(C) (c) 1/2
(D) (d) 6/10
(E) (e) 5/9
Rationale: Here is how I did it. Probably there may be better way to do it.
First of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90.
That will be 17 (8+9+17) Why did I calculate this? I will come to that in a moment.
So to get an odd digit by carrying out the operation #, the sum of the digits of the integer should be 1, 3, 5, 7, 9, 10, 12, 14, and 16 (Why not 18? Because we know the maximum sum can be 17)
Number of integers, whose digits add to 1: 1 and 10 = 2
Number of integers, whose digits add to 3: 3, 12, 21, 30 = 4
Number of integers, whose digits add to 5: 5, 14, 23, 32, 41, 50 = 6
Number of integers, whose digits add to 7: 7, 16, 25, 34, 43, 52, 61, 70 = 8
Number of integers, whose digits add to 9: 10 multiples of 9 up to 90 = 10
Number of integers, whose digits add to 10: 19, 28, 37, 46, 55, 64, 73, 82 = 8
Number of integers, whose digits add to 12: 39, 48, 57, 66, 75, 84 = 6
Number of integers, whose digits add to 14: 59, 68, 77, 86 = 4
Number of integers, whose digits add to 16: 79, 88 = 2
So in total there are 2+4+6+8+10+8+6+4+2 = 50 such numbers
Probability Q= 50/90 = 5/9
Correct answer E
Answer: (E) (e) 5/9
Question: Chris mixed 3 pounds of raisins with 4 pounds of nuts. If a pound of nuts costs 4 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?
(A)  1/7
(B)  1/5
(C)  1/4
(D)  1/3
(E)  3/19
Rationale: 1 lbs of raisin = $1
3 lbs of raisin = $3
1 lbs of nuts = $4
4 lbs of nuts = $16
Total value of mixture = 16+3 = 19
Fraction of the value of raisin = 3/19
Ans:E
Answer: (E)  3/19
Question: 60% of a number is added to 120, the result is the same number. Find the number?
(A) 300
(B) 227
(C) 288
(D) 266
(E) 299
Rationale: (60/100) * X + 120 = X
2X = 600
X = 300
Answer: A
Answer: (A) 300
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 10
(B) 88
(C) 66
(D) 65
(E) 22
Rationale: Answer: Option D
Explanation:
lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer:A
Answer: (A) 10
Question: If 60% of 3/5 of a number is 72, then the number is?
(A) 80
(B) 100
(C) 75
(D) 90
(E) None of these
Rationale: Let the number be x. Then 60% of 3/5 of x=72
60/100*3/5*x=72
x=(72*25/9)=200
Required number=200.
Correct Option: E
Answer: (E) None of these
Question: Two trains 85 m and 75 m long are running in same direction with speeds of 62 km/hr and 44 km/hr respectively. In what time will the first train cross the second train ?
(A) 12 sec
(B) 32 sec
(C) 82 sec
(D) 92 sec
(E) 13 sec
Rationale: Explanation:
Given that,
1st train speed = 62 km/hr
2nd train speed = 44 km/hr
Hence the relative speed of two trains is 62-44 = 18 km/hr m/s = 5 m/s.
There fore, the first train crosses the second train i.e (85+75)mts of distance with a speed of 5m/s in,
time = \frac{distance}{speed} \frac{(85+75)}{5} = 32 sec.
Answer: B
Answer: (B) 32 sec
Question: Stacy has a 63 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
(A) 9
(B) 8
(C) 10
(D) 8.5
(E) 21
Rationale: 63/3=21
Answer : E
Answer: (E) 21
Question: If p, q, and r are three different positive integers whose sum is prime, which of the following statements could be true?
(A) Each of p + 3, q + 3, and r + 3 is prime.
(B) Each of p, q, and r is prime.
(C) Each of p + q, p + r, and q + r is prime.
(D) The average (arithmetic mean) of p, q, and r is prime.
(E) p + q = r
Rationale: the question asks could be!!!!
this means that if at least one option works, it is the answer.
3, 7, 19 satisfies the condition, since 29 is a prime number. Since the question asks for a could be - we know automatically that B is the answer.
Answer: (B) Each of p, q, and r is prime.
Question: A furniture dealer purchased a desk for $150 and then set the selling price equal to the purchase price plus a markup that was 25% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) 40%
(B) 38%
(C) 36%
(D) 33.33%
(E) 35%
Rationale: Anyway, in this question, there is no discount but the mark up is given as 25% of the selling price. So it is not 25% of $150 but instead, 40% of Selling price which is obtained by adding mark up to $150.
So if selling price is S,
150 + 25% of S = S
S = 200
Profit = 50 which is calculated on cost price in % terms. So 50/150 * 100 =33.33% is profit.
D
Answer: (D) 33.33%
Question: The average of runs of a cricket player of 10 innings was 15. How many runs must he make in his next innings so as to increase his average of runs by 4?
(A) 87
(B) 16
(C) 10
(D) 76
(E) 59
Rationale: Average after 11 innings = 19
Required number of runs
= (19* 11) - (15* 10) = 209- 150
= 59.
Answer: E
Answer: (E) 59
Question: Insert the missing number. 2, 7, 8, 17, 16, 27, 22, 37
(A) 42
(B) 52
(C) 46
(D) 28
(E) 68
Rationale: Explanation :
There are two series here
2, 8, 16, 22, ... (Increase by 6)
7, 17, 27, 37 ... (Increase by 10)
Hence, next term is 22+6 = 28
Answer : Option D
Answer: (D) 28
Question: If x=kc and y=kt,then y-2x =?
(A) k(t-c)
(B) k(t-2c)
(C) c(k-t)
(D) t(k-c)
(E) k(1-t)
Rationale: Just put in the given values of y and x
y - x = kt - kc
Now take k common
y - x = k(t - c)
You get (B) as your answer.
Answer: (B) k(t-2c)
Question: If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle?
(A) 122 sq.cm
(B) 120 sq.cm
(C) 277 sq.cm
(D) 118 sq.cm
(E) 119 sq.cm
Rationale: let length = x and breadth = y then
2(x+y) = 46 x+y = 23
x²+y² = 17² = 289
now (x+y)² = 23²
x²+y²+2xy= 529
289+ 2xy = 529
xy = 120
area = xy = 120 sq.cm
Answer: B
Answer: (B) 120 sq.cm
Question: A person travelled from his house to office at 15km/hr and office to house at 25km/hr. Then find the average speed?
(A) 15km/hr
(B) 20km/hr
(C) 18.75km/hr
(D) 24km/hr
(E) 25km/hr
Rationale: Average speed = (2*15*25)/(15+25)
= 18.75km/hr
Answer is C
Answer: (C) 18.75km/hr
Question: In how many ways Chief Minister and Minister be elected from a team of 20 members?
(A) 128
(B) 131
(C) 132
(D) 380
(E) 145
Rationale: To do this, if captain is elected first, then we have 20 ways of doing this.
For election of vice-captain, we have only 19 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 20*19 = 380 ways.
Answer : D
Answer: (D) 380
Question: Ricky likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 00,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance travelled by each tyre?
(A) 20000
(B) 35000
(C) 70000
(D) 60000
(E) 80000
Rationale: E
80,000.
Explanation:
The distance travelled by each tyre:
4/5 * 1, 00,000 km = 80,000 km.
Answer: (E) 80000
Question: A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be
50 metres apart, then at what speed is the train travelling?
(A) 60 km/hr
(B) 100 km/hr
(C) 110 km/hr
(D) 120 km/hr
(E) None of these
Rationale: Explanation:
Number of gaps between 41 poles = 40
So total distance between 41 poles = 40*50
= 2000 meter = 2 km
In 1 minute train is moving 2 km/minute.
Speed in hour = 2*60 = 120 km/hour
Answer: D
Answer: (D) 120 km/hr
Question: The standard serial numbers for a bill are 2 letters followed by 5 digits. How many bills are possible if letters and digits can be repeated?
(A) 26 × 26 × 100 000
(B) 24³ × 10 ×10 000
(C) 26³ × 10 000
(D) 26 × 25 × 24 × 10
(E) 26 x 26 x 10 000
Rationale: OFFICIAL SOLUTION:
(A) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 options for the two letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of bills is 26 × 26 × 10 × 10 × 10 × 10 x 10 = 26 x 26 x 100 000.
The correct answer is choice (A).
Answer: (A) 26 × 26 × 100 000
Question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 20 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
(A) 64%
(B) 68%
(C) 72%
(D) 76%
(E) 80%
Rationale: Say May income = 100
L's income = 60 and rest of the family = 40
In June L's income = 60 * 120 /100 = 72
So 72 /72 + 40 = 64%
ANSWER:A
Answer: (A) 64%
Question: A trader bought a car at 25% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 118
(B) 110
(C) 105
(D) 113
(E) 115
Rationale: Original price = 100
CP = 75
S = 75*(140/100) = 105
100 - 105= 5%
Answer: C
Answer: (C) 105
Question: The sides of a triangle are in the ratio of
1/2:1/3:1/4. If the perimeter is 52 cm, then find the length of the smallest side.
(A) 12 cm
(B) 14 cm
(C) 16 cm
(D) 18 cm
(E) None of these
Rationale: Explanation:
Ratio of sides =1/2:1/3:1/4=6:4:3
Perimeter=52cm
So sides are =(52∗6/13)cm,
(52∗4/13)cm,
(52∗3/13)cm
a = 24 cm, b = 16 cm and c = 12 cm
Length of the smallest side = 12 cm
Option A
Answer: (A) 12 cm
Question: What is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1?
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Rationale: Since 1000=2^3*5^3 then a number can not have 2 and/or 5 as a factor.
The odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000.
We then need to eliminate the 100 numbers that end with 5, that is 5, 15, 25,...,995.
There are a total of 500 - 100 = 400 such numbers between 1 and 1000.
The answer is D.
Answer: (D) 400
Question: A reduction of 10% in the price of rice enables a lady to obtain 20kgs more for Rs.1000, find the original price per kg?
(A) 6.0
(B) 5.0
(C) 5.2
(D) 5.6
(E) 5.4
Rationale: Answer:	1000*(10/100) = 100 --- 20
? --- 1 => Rs.5
1000 --- 900
? --- 5 => Rs.5.6.Answer: D
Answer: (D) 5.6
Question: Set A = {1, 2, 3, 4, 5, 6, q}
Which of the following possible values for q would cause Set A to have the smallest standard deviation?
(A)  1
(B)  2.5
(C)  3
(D)  3.5
(E)  7
Rationale: I agree. The mean of the set q =1,2,3,4,5,6 is 3.5 . Now if we add one extra number to the set, in order for the standard deviation to be minimum, that number must be as close as possible to the original set (1,2,3,4,5,6). Therefore we have to choose the number closest to 3,5 from the options we have, leaving D as the best choice.
Answer D.
Answer: (D)  3.5
Question: If X = the product of five distinct prime numbers, how many factors does X have besides 1 and itself?
(A) 24
(B) 30
(C) 36
(D) 42
(E) 48
Rationale: Since X has 5 distinct prime factors, X has a total of 2^5 = 32 factors.
Besides 1 and itself, X has 30 factors.
The answer is B.
Answer: (B) 30
Question: Pipe P can drain the liquid from a tank in 3/4 the time that it takes pipe Q to drain it and in 3/3 the time that it takes pipe R to do it. If all 3 pipes operating simultaneously but independently are used to drain liquid from the tank, then pipe Q drains what portion of the liquid from the tank?
(A) 9/29
(B) 8/23
(C) 3/8
(D) 3/11
(E) 3/4
Rationale: Suppose Q can drain in 1 hr. So, rQ = 1/1 = 1
So, rP = 1/[(3/4)rQ] = 4/3
Also, rP = rR/(3/3) => 4/3 = rR/(3/3) => rR = 4/3
Let H is the time it takes to drain by running all 3 pipes simultaneously
So combined rate = rC = 1/H = 1 + 4/3 + 4/3 = 11/3= 1/(3/11)
Thus running simultaneously, Pipe Q will drain 3/11 of the liquid.
Thus answer = D.
Answer: (D) 3/11
Question: In Sam's hanger there are 23 boxes, 19 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.
Rationale: Total boxes = 23
Filled with toys = 19
Filled with appliance = 4
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 4 - 3 = 1
Correct Option: A
Answer: (A) 1.
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 2399
(B) 277
(C) 245
(D) 88
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30
= 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer: C
Answer: (C) 245
Question: In a factory, an average of 60 TV's are produced per day for the fist 25days of the months. A few workers fell ill for the next 5days reducing the daily avg for the month to 58 sets/day . The average production per day for day last 5days is ?
(A) 20
(B) 36
(C) 48
(D) 50
(E) 59
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
C
Answer: (C) 48
Question: What will be the day of the week 15th August, 2010?
(A) Sunday
(B) Saturday
(C) Monday
(D) Thursday
(E) Wednesday
Rationale: 15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2009
= 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day
Days from 1-Jan-2010 to 15-Aug-2010
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227
227 days = 32 weeks + 3 day = 3 odd day
Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday.
Answer is A
Answer: (A) Sunday
Question: Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Paul and 40% of his income to Quentin, Paul's new income would be what fraction of Quentin's new income?
(A) 	11/12
(B) 	13/17
(C) 	13/19
(D) 	15/11
(E) 	11/19
Rationale: MAKE R = 10
P = 0.6R = 6
Q = 0.8P = 4.8
S= 0.6P = 3.6
FOR THAT WE GET P = 12
AND Q 8.8
SO 12/8.8 = 3/ 2.2
Ans:D
Answer: (D) 	15/11
Question: If n is even, which of the following cannot be odd?
I	n + 3
II	3n
III	n^2 - 1
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Rationale: Let take a look at I
n + 3
we have this formula : even + odd = odd
=> n + 3 is odd
III: n^2 - 1
n^2 always be even
so n^2 - 1 is odd
=> only II is always even
=> answer is B
Answer: (B) II only
Question: In how many ways can 5 boys and 3 girls be seated on 7 chairs so that no two girls are together?
(A) 5760
(B) 14400
(C) 480
(D) 56
(E) 1440
Rationale: Let us take opposite of the constraint.
2 girls sitting together:	:
1 case is GGBGBBBB.
Total number of ways=3!*5!*5 with just shifting the rightmost girl.
Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.
So total number of ways = 3!*5!(5+4+3+2+1)=120*90=10800
Similarly another case is:
GBGGBBBB.
Using the above reasoning, the total number of cases is: 3!*5!*(15) =10800
Let us take 3 girls sitting together
GGGBBBBB
There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways
So total is 2*10800 + 4320=25920
The total number of possibilities = 8! Ways =40,320
Answer is 40320-25920=1440
Hence E.
Answer: (E) 1440
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) 1/2
(C) 8/15
(D) 9 by 20
(E) 9/24
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 by 20
Question: A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 49/64. How many marbles are in the bag?
(A) 24
(B) 48
(C) 60
(D) 96
(E) 84
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 49/64
-->(x-12)^2= 49/64
x^2
square rooting u have x-12/x = 7/8 or x = 96
D
Answer: (D) 96
Question: What least number must be added to 9599, so that the sum is completely divisible by 100 ?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: If we divide 9599 by 100 remainder is 99
100-99 =1
Answer : A
Answer: (A) 1