mathewhe/aqua_rat huggingface dataset:
Question: A taxi charges w dollars for the first two miles and c cents per quarter mile for every mile after the first two. Which equation describes cost of a taxi ride of n miles in dollars.
(A) wn – c/8(100)
(B) cw + 4n-8/200
(C) w + (4cn-8c)/100
(D) w + 100cn/4
(E) 4cw(n-2) – 100
Rationale: This is about as complicated as these types of problems come, but it is essentially the same as any problem which has an initial cost which is added to a dependent additional cost. Looking at the problem, we notice that the cost w is added to the mile dependent cost, which is some combination of the other terms listed in the problem. With just that knowledge we can eliminate all but two of the answer choices! Choices (A), (B), and (E) either do some strange calculation with the initial cost w, or subtract the additional cost from w. Both of these circumstances would be next to impossible if there is an initial cost being added to another cost. Thus, we only have to choose between choice (C) and choice (D). We can easily find the right answer by plugging in real numbers and checking which choice yields a correct answer. We can also see that answer choice (D) seems to be multiplying the cost in cents by 100, which, if the trip was 6 miles and the charge per mile was 25 cents, would make the taxi cost an additional $3750! This seems impossible, and leaves only the correct answer choice, (C).
Answer: (C) w + (4cn-8c)/100
Question: A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
(A) Rs. 7500
(B) Rs. 8000
(C) Rs. 8500
(D) Rs. 9000
(E) None of these
Rationale: Explanation:
Let B's capital be Rs. x.
Then,(3500x 12 / 7 )=2/3
14x = 126000
x = 9000.
Answer is D
Answer: (D) Rs. 9000
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 330 m long platform?
(A) 37 min
(B) 55 min
(C) 47 min
(D) 67 min
(E) 45 min
Rationale: E
45 min
Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +330)/ 36 * 5/18 = 45 min.
Answer: (E) 45 min
Question: Find the fourth proportion to 5,10,15
(A) 10
(B) 20
(C) 42
(D) 36
(E) 30
Rationale: Explanation:
5:10 :: 15:x
=> 5/10= 15/x
=> x = 15*10/5
=> x = 30
Answer:E
Answer: (E) 30
Question: In a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?
(A) 2 : 1
(B) 3 : 1
(C) 3 : 2
(D) 7 : 5
(E) None
Rationale: Sol.
For dividing 12 into two whole numbers, the sum of the ratio terms must be a factor of 12. So, they cannot be in the ratio 3 : 2.
Answer C
Answer: (C) 3 : 2
Question: 7, 26, 63, 124, 215, 342, (....)
(A) 481
(B) 511
(C) 421
(D) 391
(E) 515
Rationale: The series is (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1), ...
Hence, next number is (83 - 1) = 511
Answer is B
Answer: (B) 511
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum x of all the even integers between 99 and 301?
(A) 10,100
(B) 20,200
(C) 22,650
(D) 40,200
(E) 45,150
Rationale: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum x= Average*total count = 200*101 = 20,200
Answer is B
Answer: (B) 20,200
Question: A boat covers a certain distance downstream in 1 hour, while it comes back in 11⁄2 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
(A) 14 kmph
(B) 15 kmph
(C) 13 kmph
(D) 12 kmph
(E) None of these
Rationale: Explanation :
Let the speed of the water in still water = x
Given that speed of the stream = 3 kmph
Speed downstream = (x+3) kmph
Speed upstream = (x-3) kmph
He travels a certain distance downstream in 1 hour and come back in 11⁄2 hour.
ie, distance travelled downstream in 1 hour = distance travelled upstream in 11⁄2 hour
since distance = speed × time, we have
(x+3) × 1 = (x−3)(3/2)
=> 2(x + 3) = 3(x-3)
=> 2x + 6 = 3x - 9
=> x = 6+9 = 15 kmph. Answer : Option B
Answer: (B) 15 kmph
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
(A) 128
(B) 150
(C) 887
(D) 279
(E) 771
Rationale: 1/2 * 20(9 + 6) = 150 cm2
Answer: B
Answer: (B) 150
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 100, the dividend is:
(A) A)5322
(B) B)5330
(C) C)25100
(D) D)53400
(E) E)53420
Rationale: Divisor = (5 * 100) = 500
= 10 * Quotient = Divisor
=> Quotient = 500/10 = 50
Dividend = (Divisor * Quotient) + Remainder
Dividend = (500 * 50) + 100 = 25100.
C
Answer: (C) C)25100
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 235
(B) 240
(C) 245
(D) 250
(E) 260
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (140 + x)/30 = 25/2 => 2(140 + x) = 750 => x = 235 m.
Answer: Option A
Answer: (A) 235
Question: The ages of 2 persons differ by 35 years. If 10 years ago the elder one be 6 times as old as the younger one, find the present age of elder person.
(A) 30
(B) 48.5
(C) 52
(D) 50
(E) 55
Rationale: age of the younger person = x
age of the elder person = x+35
6(x-10) = x+35-10
x= 15
age of elder person = 15+35=50
Answer is D
Answer: (D) 50
Question: A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 6.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y?
(A) (320 - y)/(5x)
(B) (y +190)/(5x)
(C) 5(80 - y)/(4x)
(D) (y + 400)/(4x)
(E) (4y + 320)/(5x)
Rationale: Ans B
Plug some numbers
Let y = 40 houses and x = 20
then they painted 20 houses per week
as painters were added to the group , the rate of the group increased to 6.25 x => 6.25 * 20 = 125 houses per week
total time they took = (40/20) + (40/125) = 2.3 weeks
Putting the values of x and y in equation B
(y +190)/(5x) = (40+190)/5*20 = 230/100 = 2.3
Answer: (B) (y +190)/(5x)
Question: What is the next number of the following sequence
2, 12, 4, 24, 8, 48, (...)
(A) 10
(B) 12
(C) 16
(D) 20
(E) 22
Rationale: The series is
2*6=12
12/3=4
4*6=24
24/3=8
8*6=48
48/3=16
ANSWER: C
Answer: (C) 16
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 188
(B) 200
(C) 277
(D) 266
(E) 121
Rationale: The number of ways to select two men and three women = ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer: B
Answer: (B) 200
Question: 15% of 75 is the same as vx% of 450.find x.
(A) 1
(B) 2.5
(C) 3
(D) 4
(E) 5
Rationale: 15%of 75=11.25
450*x/100=11.25
x=2.5
ANSWER:B
Answer: (B) 2.5
Question: In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit 9?
(A) 180
(B) 196
(C) 288
(D) 286
(E) 324
Rationale: We have to find the total number of 3-digit odd numbers not having 9 as a digit.
Units digits will be among 1,3,7,5
Tenth digits will be among 0,1,2,3,4,6,7,8,5
Hundredth digits will be among 1,2,3,4,6,7,8,5
So total numbers = 4*9*8 =288
Answer : C
Answer: (C) 288
Question: Can you deduce the pattern and find the next number in the series?
13, 24, 35, 46, __?
(A) 59
(B) 65
(C) 54
(D) 25
(E) 57
Rationale: Solution:
57
Explanation:
11+2=13
22+2=24
33+2=35
44=2=46
55+2=57
Answer E
Answer: (E) 57
Question: What is the perimeter of a triangle with sides 7 and 5 that has the maximum possible area?
(A) 12 + √7
(B) 12 + 4√7
(C) 12 + √47
(D) 12 + 4√47
(E) 12 + √74
Rationale: We can maximize the area of the triangle by making these two sides the base and the height of a right angle triangle. Then the third side is the hypotenuse with a length of √(49+25) = √74
The perimeter is 12 + √74
The answer is E.
Answer: (E) 12 + √74
Question: A cistern is filled by a tap in 8 1/2 hours. Due to leak in the bottom of the cistern, it takes half an hour longer to fill the cistern. If the cistern is full how many hours will it take the leak to empty it?
(A) 133
(B) 143
(C) 153
(D) 163
(E) 173
Rationale: filling rate - leak rate = net rate
1/8.5 - leak rate = 1/9
leak rate = 2/17 - 1/9 = 1/153
The answer is C.
Answer: (C) 153
Question: If x + y = 11 and x – y = 3, then x^2 - y^2 =
(A) -4
(B) 4
(C) 10
(D) 33
(E) 40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 11
x – y = 3
Add the two equations to get: 2x = 14, which means x = 7
If x = 7, we can plug that value into either equation, to conclude that y = 4
If x = 7 and y = 4, then x² - y² = 33
Answer: D
Answer: (D) 33
Question: During a particular baseball game, the probability of a team's pitcher throwing a strike on each throw is 2/5. What is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50%.
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the pitcher throws a strike at least once in 2 guesses is 1- (3/5)^2 = 1 - 9/25 = 16/25 > 50%.
Answer: B
Answer: (B) 2
Question: In a box of 12 pens, a total of 6 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
(A) 1/6
(B) 5/22
(C) 6/11
(D) 9/16
(E) 3/4
Rationale: Method- 1
There are 9 fine pieces of pen and 6 defective in a lot of 12 pens
i.e. Probability of first pen NOT being defective = (6/12)
i.e. Probability of Second pen NOT being defective = (5/11) [11 pen remaining with 5 defective remaining considering that first was defective]
Probability of Both pen being NON-defective = (6/12)*(5/11) = 5/22
Answer: option B
Answer: (B) 5/22
Question: A train 125 m long passes a man, running at 15 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 60
(B) 50
(C) 28
(D) 26
(E) 29
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 15) km/hr. x - 15 = 45 ==> x = 60 km/hr
Answer: A
Answer: (A) 60
Question: What is the probability of rolling two normal six-sided dice and getting exactly one six?
(A) 1/36
(B) 1/6
(C) 5/18
(D) 11/36
(E) 1/3
Rationale: Possible pairs having exactly one six are (1,6), (2,6),(3,6),(4,6),(5,6),(6,1)...(6,5) = 10 pairs
Total number of possible pairs = 6*6 = 36
Therefore, probability of getting exactly one six = 1036=5181036=518
Answer: C
Answer: (C) 5/18
Question: A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?
(A) 1250
(B) 1280
(C) 1320
(D) 1340
(E) 1450
Rationale: Explanation:
Speed = 5 km/hr
Time = 15 minutes = 1/4 hour
Length of the bridge = Distance Travelled by the man = Speed × Time = 5×1/4 km
= 5 × 1/4 × 1000 metre=1250 metre
Answer: Option A
Answer: (A) 1250
Question: How many positive integers, from 2 to 100, inclusive, are not divisible by even integers greater than 1?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 50
Rationale: The no will be of the form 2^n to achieve this. Since any other form will have odd no in the prime factorization.
Hence we need to find solution of n for equation - 1< 2^n < 101.
2^6 = 64, 2^7 - 128
Hence n can take values from 1 to 6.
Hence Ans- (B) 6
Answer: (B) 6
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.9 sec
(B) 12.1 sec
(C) 17.9 sec
(D) 37.9 sec
(E) 12.8 sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20
= 12.1 sec.
Answer: B
Answer: (B) 12.1 sec
Question: Jerry, an electrician, worked 7 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 7? 12 months = 1 year
(A) 58.33%
(B) 68.33%
(C) 78.33%
(D) 88.33%
(E) 98.33%
Rationale: 1. Multiply the opposites
7 x 100 = 700
100=7/12
Divide by the remaining number
58.33
12)58.33/700.00
58.33% (rounded to hundredth)
correct answer A
Answer: (A) 58.33%
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 181?
(A) 3820
(B) 5740
(C) 6580
(D) 7360
(E) 9200
Rationale: 100 + 102 + ... + 180 =
100*41 + (2+4+...+80) =
100*41 + 2*(1+2+...+40) =
100*41 + 2(40)(41)/2 =
100*41 + 40*41 = 140(41) = 5740
The answer is B.
Answer: (B) 5740
Question: The value of a stock is X dollars. On Sunday the stock's value grew by third of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?
(A) X.
(B) X/2.
(C) 2X/3.
(D) X/3.
(E) 4X/9.
Rationale: Stock value= X
AT sunday end= x+X/3= 4X/3=1.3X
On monday the value drop to 1/3rd of its value on sunday
1.3x/3= 4X/9
E is the answer
Answer: (E) 4X/9.
Question: If a sum of money doubles itself in 15 years at simple interest, the ratepercent per annum is
(A) 12
(B) 12.5
(C) 6.67
(D) 13.5
(E) 14
Rationale: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 15) = 6.67
Option C
Answer: (C) 6.67
Question: If the diagonal of a rectangle is 17cm long and its perimeter is 46 cm. Find the area of the rectangle.
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: Explanation:
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
Question: A beekeeper has 100,000 bees living in five beehives. Among these beehives, the sizes of the beehives are proportional to the numbers of bees living in them. No beehive has less than 80% the number of bees of any other beehive. What is the maximum possible number of bees that the greatest beehive could have?
(A) 2381
(B) 24000
(C) 34000
(D) 26000
(E) 37000
Rationale: x be the # of bees in the hive with the max # of bees. Let other hives have same # of bees. So, x+4*(0.8)*x = 100,000 => 4.2x = 100,000 => x = 2381.
A is the answer.
Answer: (A) 2381
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 410 m long?
(A) 33 Seconds
(B) 22 Seconds
(C) 41 Seconds
(D) 24 Seconds
(E) 29 Seconds
Rationale: Distance travelled = 140 + 410m = 550m
Speed = 60 * 5/8 = 50/3m
Time = 550 * 3/50 = 33 Seconds
ANSWER A
Answer: (A) 33 Seconds
Question: Suzie’s Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $460. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $560. How much more do pairs of boots cost than pairs of shoes at Suzie’s Discount Footwear?
(A) 12
(B) 14
(C) 16
(D) 15
(E) 18
Rationale: Let X be pair of shoes and Y be pair of boots.
22x+16y = 460 ... eq1
8x +32y = 560....eq 2.
Now multiply eq 1 by 2 and sub eq 2.
44x = 920
8x = 560.
36x = 360 => x = 10.
Sub x in eq 2.... we get 80 + 32y = 560... then we get 32y = 480 then y = 15
Differenece between X and Y is 5
Answer : D
Answer: (D) 15
Question: If x/y=4 and y is not '0' what % of x is 2x-y
(A) 100%
(B) 125%
(C) 175%
(D) 185%
(E) 195%
Rationale: x/y=4
or,x=4y....(1)
"what % of x is 2x-y" means
what % of (4y)x is (2*4y-y)2x-y.
or,(7y/4y)*100=175%
ANSWER:C
Answer: (C) 175%
Question: It takes Megan 7 minutes to run a mile, and it takes Mike 8 minutes. If Megan and Mike both begin running at exactly 8:00 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
(A) 8:28 am
(B) 8:35 am
(C) 8:42 am
(D) 8:49 am
(E) 8:56 am
Rationale: Since Megan will run s miles after s × 7 minutes and Mike will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 7 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 7 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 7 and 8 is 56, so in the context of the question, this would be 56 minutes. Therefore, the first time they will finish running a mile at the same time is 8:00 + 56 minutes, or 8:56 a.m. The answer is (E).
Answer: (E) 8:56 am
Question: There r 4 prime numbers in ascending order. The multiplication of first 3 is 385 and that of last 3is 1001. what is the last number is
(A) 12
(B) 15
(C) 16
(D) 13
(E) 18
Rationale: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Answer: (D) 13
Question: A batsman hits a score of 78 runs in the 16th inning and thus increases his average by 4. Find his average after 16th inning.
(A) 13
(B) 18
(C) 27
(D) 39
(E) 40
Rationale: Explanation :
Let the average after 16th inning = x.
Average after 15th inning =(x-4).
=> 15(x-4)+78 = 16x
=> x = 18.
Answer : B
Answer: (B) 18
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
(A) 29
(B) 68
(C) 92
(D) 23
(E) 23
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer:B
Answer: (B) 68
Question: A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 8% p.a for 2 years. Find his gain in the transaction per year.
(A) 167.5
(B) 150
(C) 200
(D) 112.5
(E) 212.5
Rationale: Explanation :
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×4×2/100=400
He also lends it at 8% p.a for 2 years
Simple interest that he gets = PRT/100=5000×8×2/100=800
His overall gain in 2 years = Rs.800 - Rs.400 = Rs.400
His overall gain in 1 year = 400/2 = Rs.200
Answer : Option C
Answer: (C) 200
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units D digit of (a+2)^2?
(A) 1
(B) 3
(C) 5
(D) 6
(E) C. 14
Rationale: I also got A. By punching in numers:
D...7^2=...9
...8^2=...4
...9^2=...1.A
Answer: (A) 1
Question: The H.C.F. of two numbers is 28 and the other two factors of their L.C.M. are 12 and 15. The larger of the two numbers is
(A) 420
(B) 430
(C) 312
(D) 322
(E) None
Rationale: Solution
Clearly, the numbers are (28 x 12) and (28 x 15).
Larger number = (28 x 15)	= 420.
Answer A
Answer: (A) 420
Question: If n is a positive integer and n^2 is divisible by 36, then the largest positive integer that must divide n is
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=6, is n divisible by 48? No. So, n is not always divisible by 48.
A
Answer: (A) 6
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold a bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2a
II. y > a
III. y > 3
(A) I only
(B) II only
(C) I and II
(D) II and III
(E) I, II, and III
Rationale: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(a-12) where x is the total number of bikes sold (when a>12).
A = cycles sold last week
AS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2AS
lets test all statements with A=0;
AS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with A=1;
AS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with A=6;
AS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Answer: (D) II and III
Question: Find the number of ways of arranging the boy and 3 guests at a circular table so that the boy always sits in a particular seat?
(A) 3!
(B) 8!
(C) 11!
(D) 12!
(E) 14!
Rationale: Ans.(A)
Sol. Total number of persons = 4 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 3 places => 3! Ways ... The number of required arrangements = 3! x 1= 3! = 3! ways
Answer: (A) 3!
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 2 ounces of corn syrup, how many ounces of water does it contain?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 90
Rationale: Standard:
Fl: Corn S: Water = 1:12:30
Sport:
Fl: Corn S: Water = 3:12:180
This simplifies to 1:4:60
If the large bottle has a capacity of x ounces, then
4x / 65 = 2.
So, x = 32.5 ounces.
Water = (60 / 65) * (65/2) = = 30 ounces.
Ans B
Answer: (B) 30
Question: The incomes of two persons A and B are in the ratio 3:4. If each saves Rs.100 per month, the ratio of their expenditures is 1:2 . Find their incomes?
(A) 150,222
(B) 150,209
(C) 150,200
(D) 150,202
(E) 150,201
Rationale: The incomes of A and B be 3P and 4P.
Expenditures = Income - Savings
(3P - 100) and (4P - 100)
The ratio of their expenditure = 1:2
(3P - 100):(4P - 100) = 1:2
2P = 100 => P = 50
Their incomes = 150, 200
Answer: C
Answer: (C) 150,200