mathewhe/aqua_rat huggingface dataset:
Question: Maxwell leaves his home and walks toward Brad's house. One hour later, Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 54 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h. What is the total time it takes Maxwell before he meets up with Brad?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Total Distance = 54 kms
Maxwell Speed = 4 kms/hr
Maxwell travelled for 1 hour before Brad started , therefore Maxwell traveled for 4 kms in 1 hour.
Time taken = Total Distance / Relative Speed
Total Distance after Brad started = 50 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken to meet Brad after Brad Started = 50 / 10 = 5 hrs
Distance traveled by Maxwell = Maxwell's speed * time taken = 4 * 5 = 20+4 = 24 kms...
Therefore Total Time taken by Maxwell to meet Brad = Distance travelled by Maxwell / Maxwell's Speed = 24 /4 = 6 hrs ... Answer D
Alternatively ...
Total Time taken by Maxwell to meet Brad = Maxwell started 1 hour earlier to Brad + total time taken to meet brad after Brad started = 1+ 5 = 6 hrs... Answer D
Answer: (D) 6
Question: ine m lies in the xy-plane. The y-intercept of line m is -2, and line m passes through the midpoint of the line segment whose endpoints are (2, 4) and (6, -8). What is the slope of line m ?
(A) -3
(B) -1
(C) -1/3
(D) 0
(E) Undefined
Rationale: y intercept of line m is -2 ; i.e. one point on the line m is (0,-2)
Line m passes through the midpoint of (2,4) & (6, -8) i.e. ((2+6)/2 , (4+-8)/2) = (4, -2)
So two point on line m are (0,-2) and (4, -2) As the y coordinates of the two points are same, this is a line parallel to X axis.
So slope is zero.
Answer D
Answer: (D) 0
Question: Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $1,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?
(A) 23,500
(B) 24,500
(C) 25,500
(D) 26,500
(E) 27,500
Rationale: Let the weekly sales of both = x
550+(x−1000)8/100=10/100x
x = 23500
ANSWER:A
Answer: (A) 23,500
Question: If a: b = 11: 4, b: c = 15: 12, find a: b: c?
(A) 155: 50: 42
(B) 165: 60: 52
(C) 175: 70: 62
(D) 185: 80: 72
(E) 195: 90: 82
Rationale: a: b = 11: 4
b: c = 15: 13
a: b: c = 165: 60: 52
ANSWER:B
Answer: (B) 165: 60: 52
Question: It was intended that Rs. 585 be divided among P, Q and R in the ratio of 4 : 3 : 2, but by mistake the distribution was made in the proportion of 1/4 : 1/3 : 1/2. How much does 'R' gain by the error ?
(A) Rs. 99
(B) Rs. 126
(C) Rs. 140
(D) Rs. 152
(E) None of these
Rationale: Explanation:
Total amount = Rs. 585
on dividing it in the ratio of 4 : 3 : 2
Share of P = 4/9 * 585 = Rs. 260
Share of Q = 3/9 * 585 = Rs. 195
Share of R = 2/9 * 585 = Rs. 130
But the amount has been divided in the proportion of 1/4 : 1/3 : 1/2 i.e. 3 : 4 : 6
Share of P = 3/13 * 585 = Rs. 135
Share of Q = 4/13 * 585 = Rs. 180
Share of R = 6/13 * 585 = Rs. 270
Therefore, gain for R by virtue of error = Rs. 270 – Rs. 130 = Rs. 140
ANSWER C
Answer: (C) Rs. 140
Question: Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 1 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
(A) R-4
(B) R/(R+4)
(C) R/(R-2)
(D) 8/(R-8)
(E) 2R - 4
Rationale: Let T be the time thatAlexwill have been walking when Brenda has covered twice as much distance as Alex.
In T hours Alex will cover 4T miles;
Since Brenda begins her journey 1 hour later than Alex then total time for her will be T-1 hours, and the distance covered in that time will be R(T-1);
We want the distance covered by Brenda to be twice as much as that of Alex: 2*1T=R(T-1) --> 2T=RT-R --> T=R/(R-2).
Answer: C.
Answer: (C) R/(R-2)
Question: A money lender lent Rs. 1000 at 3% per year and Rs. 1400 at 3% per year. The amount should be returned to him when the total interest comes to Rs. 350. Find the number of years.
(A) 3.5
(B) 3.75
(C) 4
(D) 4.25
(E) 4.86
Rationale: (1000xtx3/100) + (1400xtx3/100) = 350 â†’ t =4.86 answer E
Answer: (E) 4.86
Question: (A% of 5B + B% of A) is equal to ?
(A) A% of B
(B) B% of A
(C) 6% of AB
(D) AB% of 3
(E) None
Rationale: Answer
A% of 5B + B% of A =5AB/100 + AB/100
= 6AB/100 = 6% of AB
Correct Option: C
Answer: (C) 6% of AB
Question: If A = B/C, -1 < C < 0 and 4 < B, which of the following is correct?
(A) A > 4.
(B) 0 < A <4.
(C) -4 < A < 0.
(D) A < -4.
(E) A < -20.
Rationale: B is +veC is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take B=4.1A=-0.9
A=4.1/-0.9
A<-4
Ans D
Answer: (D) A < -4.
Question: On a track for remote controlled racing cars, racing car A completes the track in 56 seconds, while racing car B completes it in 35 seconds. If they both start at the same time after how many seconds will they be side by side again.
(A) 275
(B) 325
(C) 280
(D) 425
(E) None of these
Rationale: Time required in seconds will be LCM ( 35, 56 ) = 280
Hence, answer will be (C) 280
Answer: (C) 280
Question: On a purchase of $118, a store offered a payment plan consisting of a $18 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
(A) 16.7%
(B) 16.2%
(C) 16.5%
(D) 15.5%
(E) 15.3%
Rationale: 12*10 + 18 = 138
(18/118)* 100 = 15.3
Answer : E
Answer: (E) 15.3%
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 8
Rationale: Before stop 3, there were 2 passengers on the bus.
Before stop 2, there were 4 passengers on the bus.
Before stop 1, there were 8 passengers on the bus.
The answer is E.
Answer: (E) 8
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(A) 6 %
(B) 6.3 %
(C) 6.2 %
(D) 6.1 %
(E) 6.4 %
Rationale: Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (E) 6.4 %
Question: A mixture contains milk and water in the ratio 7:3. On adding 20 liters of water, the ratio of milk to water becomes 7:5. Total quantity of milk & water before adding water to it?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 140
Rationale: milk:water = 7:3
7x : 3x + 20 = 7 : 5
5[7x] = 7[3x + 20]
35x = 21x + 140
35x - 21x = 140
14x = 140
x = 10
The quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10
10x = 100
Option 'B'
Answer: (B) 100
Question: If 4 - (3/7)x = (x-3) / 7,
then what is the value of x ?
(A) 8
(B) 31
(C) 4
(D) 31/4
(E) -31/4
Rationale: 4 - (3/7)x = (x-3) / 7
=> 28 - 3x = x - 3
=> -4x = -31
=> x = 31/4
Answer: D
Answer: (D) 31/4
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/4 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
(A) 12 greater
(B) 17 fewer
(C) 28 fewer
(D) 36 fewer
(E) 52 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/4 * 480 =120
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 120-68 =52>>> therfore answer is 28 fewer
E
Answer: (E) 52 fewer
Question: If a + b > 5 and a - b < 3, which of the following must be true?
I. a > b
II. b > 1
III. a > 5
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I, II, and III
Rationale: I. Not true, example: a=3, b=4
II. True, add the equations together so that the greater parts are added. Thus, a + b + 3 > 5 + a - b. Combining like terms, we get 2b > 2. Thus, b > 1.
III. Not true, example: a = r, b = 4
Thus, II only so the answer if B.
Answer: (B) II only
Question: The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 4-hour period?
(A) 88
(B) 56
(C) 42
(D) 34
(E) 64
Rationale: Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.
4 hour = 240 minutes.
In 240 minutes operator can make 240/7=34 trips.
Answer: D.
Answer: (D) 34
Question: Of the teams competing in the world archery championships, Ten percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
(A) 13/20
(B) 16/20
(C) 13/15
(D) 17/20
(E) 13/17
Rationale: Half as manymeans half of EU, then
EU 10%
US 5%
AF 5%
the rest is 50%, answer B
Answer: (B) 16/20
Question: Drum X is 1/2 full of oil and drum Y, which has twice the capacity of drum X, is 1/4 full of oil. If all of the oil in drum X is poured into drum Y, then drum Y will be filled to what capacity?
(A) 1/2
(B) 2/3
(C) 3/4
(D) 5/6
(E) 7/8
Rationale: (1/2)X = (1/4)Y
(1/4)Y + (1/4)Y = (1/2)Y
The answer is A.
Answer: (A) 1/2
Question: If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due?
(A) 8 months
(B) 11 months
(C) 10 months
(D) 9 months
(E) 12 months
Rationale: Explanation :
F = Rs. 498
TD = Rs. 18
PW = F - TD = 498 - 18 = Rs. 480
R = 5%
TD = (PW × TR)/100
⇒ 18 = (480 × T × 5)/100
⇒ 18 = 24 × T
⇒ T = 18/24 = 3/4 years = (12×3)/4 months = 9 months Answer : Option D
Answer: (D) 9 months
Question: if the price of a book is first decreased by 25% and then increased by 20%, then the net change in the price will be :
(A) 10
(B) 388
(C) 37
(D) 29
(E) 22
Rationale: Explanation:
Let the original price be Rs. 100.
New final price = 120 % of (75 % of Rs. 100) = Rs. (120/100 * 75/100 * 100) = Rs. 90.
Decrease = 10%
Answer: A) 10
Answer: (A) 10
Question: E and F represent two distinct digits. If the number 457E89F is divisible by 36, what is the value of (E+F)?
(A) a) 9
(B) b) 3
(C) c) 12
(D) d) 6
(E) e) 10
Rationale: A no. divisible by 36 means it is div by 49 .
to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only
similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find E could be either 1,4,7 only.
To be divisible by 9 only 1 works .(if we choose f=6 then E have to be 6 but as per condition EF are distinct) So
E=1
F=2
Ans:- 3.B
Answer: (B) b) 3
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order O? (1 cubic meter = 1,000 liters)
(A) 92
(B) 90
(C) 82
(D) 78
(E) 75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
O=12.5*6 = 75=E
Answer: (E) 75
Question: If x > 7, which of the following is equal to (x^2 + 4x + 4)/(x^2 - 4) ?
(A) (x + 4)/(4(x - 4))
(B) (x - 4)/(x + 4)
(C) (x - 2)/(x + 4)
(D) (x + 4)/(x - 4)
(E) (x + 2)/(x - 2)
Rationale: (x^2 + 4x + 4)/(x^2 - 4)
= (x + 2)(x + 2) / (x + 2)(x - 2)
=(x + 2)/(x - 2)
E. (x + 2)/(x - 2)
Answer: (E) (x + 2)/(x - 2)
Question: The C.P of 5 pens is equal to the S.P of 7 pens. Find his gain % or loss%?
(A) 25 4/7%
(B) 26 4/7%
(C) 28 4/7%
(D) 14 4/7%
(E) 23 4/7%
Rationale: 5CP = 7 SP
7 --- 2 CP loss
100 --- ? => 28 4/7%
Answer: C
Answer: (C) 28 4/7%
Question: A homeless man wins the lottery and winds up with $200,457,543. He wishes to share it equalling with 8 other homeless friends of his. How much more money does he need to be able to distribute the money equally?
(A) 7
(B) 0
(C) 6
(D) 1
(E) 4
Rationale: Using the rule on the divisibility of 9, we add all the digits together. The sum of those numbers is 30 and 36 is divisible by nine. Therefore, he needs 6 dollars.(option C)
Answer: (C) 6
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 87
(C) 26
(D) 21
(E) 14
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer:A
Answer: (A) 40
Question: A 45° -45° - 90° right triangle has hypotenuse of length h. What is the area of the triangle R in terms of h?
(A) h/ √2
(B) h/2
(C) h/4
(D) (h)^2
(E) (h)^2/4
Rationale: IF...each of the two shorter sides = 3, then the hypotenuse = H = 3(root2).
The AREA R= (1/2)(Base)(Height) = (1/2)(3)(3) = 9/2.
So we're looking for an answer that = 9/2 when H = 3(root2). There's only one answer that matches...
E
Answer: (E) (h)^2/4
Question: 30% of all students in a class commute by public transportation. If 40% of the students aspire to be scientists, which of the following can be the percentage of students who do not commute by public transportation and do not aspire to be scientists?
I.	5%
II.	40%
III.	50%
(A) I ONLY
(B) II ONLY
(C) III ONLY
(D) I AND III
(E) II AND III
Rationale: 30% Students use public transportation. This means 70% students do not use public transportation. 40% students aspire to be scientists means even if all these students use public transportation, minimum 70% - 40% = 30% students do not use public transportation and do not aspire to be scientists.This means correct answer is between 30% and 70%
Answer : E.
Answer: (E) II AND III
Question: Find the value of (875 233/899) × 899
(A) 786845
(B) 786857
(C) 786858
(D) 786859
(E) 786860
Rationale: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
C
Answer: (C) 786858
Question: ((-1.9)(0.6) – (2.6)(1.2))/3.0 = ?
(A) -0.71
(B) 1.0
(C) 1.07
(D) -1.42
(E) 2.71
Rationale: Dove straight into calculation
((-1.9)(0.6) – (2.6)(1.2))/3.0 = -1.42
Answer D
Answer: (D) -1.42
Question: A boat crossed a lake from North to South at the speed of 4 km/h, entered a river and covered thrice as much distance going upstream at 3 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Another way will be:
Total time for the trip = distance covered in Lake/speed in still water +distance covered upstream/upstream speed + distance covered downstream/downstream speed
If 7D is the total distance, then distance covered in lake = D, distance covered upstream = 3D and distance covered downstream = 3D
=>7D/3.8 = D/4 + 3D/3 + 3D/x (where x is the downstream speed)
=> 7/3.8 = 1/4 + 3/3 +3/x (div. both sides by D)
=> 1.84 = .25+1 +-59/x => x=5.05 ~ 5
option B
Answer: (B) 5
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
(A) Rs. 12
(B) Rs. 15
(C) Rs. 18
(D) Rs. 21
(E) Rs. 27
Rationale: Dividend on Rs. 20 = Rs(9/100)x20 = Rs 9/5
Rs. 12 is an income on Rs. 100.
Rs.9 is an income on Rs. (100/120)x(9/5)= Rs. 15.
ANSWER:B
Answer: (B) Rs. 15
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 5-cent stamps she could have bought ?
(A)  5
(B)  3
(C)  15
(D)  20
(E)  25
Rationale: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.05y
=> 2.65 = 0.30x + 0.20x + 0.05y
=> 265 = 50x + 5y
So Max value of 50x < 265 = 250
Hence y = 3
Answer - B
Answer: (B)  3
Question: S is the set of all fractions defined by the formula n/(n + 1), where n is a positive integer less than 20. What is the product C of all the fractions that are in S?
(A) 1) 1/20
(B) 2) 1/21
(C) 3) 1/2
(D) 4) 19/40
(E) 5) 19/20
Rationale: 1/2 * 2/3 * 3/4 * ... 19/20
= 1/20
Answer - A
Answer: (A) 1) 1/20
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 379
(B) 384
(C) 345
(D) 342
(E) 376
Rationale: Area of a parallelogram = base * height = 24 * 16 = 384 cm2
Area of a parallelogram = base * height = 24 * 16 = 384 cm2
Answer: Option B
Answer: (B) 384
Question: The weight of a glass of jar is 20% of the weight of the jar filled with coffee beans. After some of the beans have been removed, the weight of the jar and the remaining beans is 60% of the original total weight. What fraction part of the beans remain in the jar?
(A) 1/5
(B) 1/3
(C) 2/5
(D) 1/2
(E) 2/3
Rationale: Let weight of jar filled with beans = 100 g
Weight of jar = 20 g
Weight of coffee beans = 80 g
Weight of jar and remaining beans = 60 g
Weight of remaining beans = 40 g
Fraction remaining = 40/80 = 1/2
Answer is D.
Answer: (D) 1/2
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 60?
(A) 5
(B) 8
(C) 12
(D) 15
(E) 30
Rationale: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
60 = 4*3*5
The GCF is 12.
The answer is C.
Answer: (C) 12
Question: If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph, then the man’s rate along the current is
(A) 4.25 kmnph
(B) 6 kmph
(C) 6.5 kmph
(D) 8.5 kmph
(E) None
Rationale: Solution
Let the rate along the current be x kmph.
Then,	= (1 / 2(x+3.5))= 5
x= 6.5 kmph.
Answer C
Answer: (C) 6.5 kmph
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 179
(B) 208
(C) 210
(D) 223
(E) 229
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 – 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 208
2x = 358
x = 179 runs
ANSWER A
Answer: (A) 179
Question: A 75-liter solution of cool-drink is made from 10% jasmine water. If 3.5 liters of jasmine and 9.5 liters of water were added to the solution, what percent of the solution is jasmine?
(A) 12.5%
(B) 14%
(C) 15.5%
(D) 17%
(E) 18.5%
Rationale: The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume)
(0.1(75) + 3.5) / 88 = 11/88 = 1/8 = 12.5%
The answer is A.
Answer: (A) 12.5%
Question: workers decided to raise Rs.3 lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25 lacs. How many workers were they?
(A) 250
(B) 400
(C) 500
(D) 560
(E) 650
Rationale: N * 50 = (325000 - 300000) = 25000
N = 25000 / 50
= 500
C
Answer: (C) 500
Question: Carolyn bought 16 gumballs, Lew bought 14 gumballs, and Carey bought X gumballs. The average (arithmetic mean) number of gumballs the three bought is between 19 and 25, inclusive. What is the difference between the greatest number and the smallest number of gumballs Carey could have bought?
(A) 20
(B) 18
(C) 24
(D) 26
(E) 28
Rationale: Smallest gumballs = (19-16) + (19-14) +19= 27
Largest gumballs = (25-16) + (25-14) +25= 45
Difference = 45 - 27 = 18
B
Answer: (B) 18
Question: In a financial company investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
(A) 1.2
(B) 1
(C) 2
(D) 4
(E) 3
Rationale: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+34.1)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x
or in other words n = 4
D
Answer: (D) 4
Question: In a group of 12 engineers, 4 engineers have a PHD degree; the others have only an MS or BS degree. A team of 4 engineers is to be chosen which must have at least 1 engineer with a PHD, how many different teams can be chosen?
(A) 495
(B) 70
(C) 245
(D) 425
(E) 555
Rationale: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 12
r = 4
So, total teams is 12C4 = 12!/(4!(12 - 4)!) = 495, and
n = 12 - 4 = 8
r = 4
for teams without a PHD is 8C4 = 8!/(4!(8 - 4)!) = 70,
so, teams with at least 1 PHD = 495 - 70 = 425
Answer: D
Answer: (D) 425
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three WINDOWS of dimensions 4 feet * 3 feet each?
(A) 4000
(B) 3624
(C) 5673
(D) 4530
(E) 4566
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and WINDOWS, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 4 = Rs. 3624
Answer: Option B
Answer: (B) 3624
Question: During the past week, a local fish market tested N fish for two infections. If 1/10 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many fish did not have both infection A and B?
(A) N/15
(B) 4N/15
(C) 14N/15
(D) N/5
(E) 49N/50
Rationale: 1/10 of tested had infection A, thus N/10 had infection A;
Of those with infection A, 1/5 also had infection B, thus 1/5*N/10 = N/50 had both infections A and B.
Therefore, N - N/50 = 49/50 did not have both infection A and B.
Answer: E.
Answer: (E) 49N/50
Question: Vessel ‘A’ contains 150 litres of mixture of milk and water in the ratio of 3:1. Vessel ‘B’ contains 200 litres of the mixture in the ratio of 5:2. If the mixture from both the vessels are poured into vessel ‘C’, find the ratio of the resulting mixture.
(A) 15 : 7
(B) 8 : 3
(C) 15 : 2
(D) 143 : 53
(E) None of these
Rationale: Explanation:
As vessel A contains 150 litres of mixture of milk and water in the ratio 3:1, the quantity of milk is 3*150/4 litres, and that of water is 150/4 litres.
Similarly, as vessel B contains 200 litres of mixture of milk and water in the ratio 5:2, the quantity of milk is 5*200/7, and that of water is 2*200/7 litres.
After mixing the total quantity is 350 litres.
The quantity of milk is {(3*150/4) + (5*200/7)} = 7150/28
The quantity of water is {(150/4) + (2*200/7)} = 2650/28
The ratio of the resulting mixture = 7150/2650 = 143 : 53
ANSWER D
Answer: (D) 143 : 53
Question: One packet contains 2 black, 3 white and 2 red rubbers. 2 rubbers are drawn at random. What is the probability that none of the rubbers drawn is red?
(A) 10/21
(B) 21/23
(C) 23/25
(D) 21/20
(E) None
Rationale: Total number of rubbers = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 rubbers out of 7
= 7C2 `
=	(7 x 6)
(2 x 1)
= 21.
Let E = Event of drawing 2 rubbers, none of which is blue.
n(E)	= Number of ways of drawing 2 rubbers out of (2 + 3) rubbers.
= 5C2
=	(5 x 4)
(2 x 1)
= 10.
P(E) =	n(E)	=	10/21.
n(S)
A
Answer: (A) 10/21