mathewhe/aqua_rat huggingface dataset:
Question: Each of the 55 points is placed either inside or on the surface of a perfect sphere. If 60% or fewer of the points touch the surface, what is the maximum number of segments which, if connected from those points to form chords, could be the diameter of the sphere?
(A) 7
(B) 11
(C) 13
(D) 16
(E) 38
Rationale: Maximum number of points on the surface is 60%*55 = 33
Now note that if two points form a diameter, they cannot be part of any other diameter.
So in the best case we can pair up the points
We have 33 points, so at best we can form 16 pairs (32).
So, answer is (D)
Answer: (D) 16
Question: Two numbers have a H.C.F of 16 and a product of two numbers is 2560. Find the L.C.M of the two numbers?
(A) 140
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 2560/16 = 160.
ANSWER:C
Answer: (C) 160
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 6 months
(B) 8 months
(C) 4 months
(D) 2 months
(E) 5 months
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer:E
Answer: (E) 5 months
Question: The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q's present age and P's age afler 6 years is 2, what is the total of P's and Q's present ages?
(A) 46 years
(B) 48 years
(C) 52 years
(D) 56 years
(E) None
Rationale: Solution
Let the present ages of P and Q be 5x years and 7x years respectively.
Then	7x-(5x+6)=2
2x=8
x=4.
Required sum	= 5x+7x
=12x
=12×4
=48 years.
Answer B
Answer: (B) 48 years
Question: Of the 90 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?
(A) 15
(B) 20
(C) 30
(D) 40
(E) 60
Rationale: This is ratio problem solving question.
I will prefer to use RMV box.
R M V
Sales 2 30 60
Other 1 30 30
Total 3 30 90
Answer is 60. i.eE
Answer: (E) 60
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 16
(B) 30
(C) 88
(D) 26
(E) 12
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B
Answer: (B) 30
Question: There are 2 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
(A) A)10
(B) B)12
(C) C)24
(D) D)60
(E) E)100
Rationale: Using anagram method:
4_3_2_1
R_R_B_B
so..
4!/Number of repeated letters (2!)(2!) = 6
ANS:D
Answer: (D) D)60
Question: If the price has fallen by 15% what percent of its consumption be: increased so that the expenditure may be the same as before?
(A) 11 1/8%
(B) 11 1/5%
(C) 17 11/17%
(D) 18 7/9%
(E) 21 1/9%
Rationale: 100 â€“ 15 = 85
85------15
100------? => 17 11/17%
Answer: C
Answer: (C) 17 11/17%
Question: A worker is paid a regular rate of Rs.20 for completing a survey. The worker completes 100 surveys per week. For any survey involving the use of her cellphone, she is paid at a rate of that is 10% higher than her regular rate. If she completed 70 surveys involving the use of her cellphone, how much did she get that week?
(A) 2140
(B) 1140
(C) 550
(D) 650
(E) 750
Rationale: Amount earned using her cell phone = 70 * 22 = 1540
earned for remaining surveys = 30 * 20 = 600
Total earning = 2140
Answer : A
Answer: (A) 2140
Question: A certain music store stocks 800 cellos and 600 violas. Of these instruments, there are 110 cello-viola pairs, such that a cello and a viola were both made with wood from the same tree (each tree can make at most one viola and one cello, so there are no pairs other than these 90). If one viola and one cello are chosen at random, what is the probability that the two instruments are made with wood from the same tree?
(A) 11/48,000
(B) 1/8,100
(C) 3/1,600
(D) 1/90
(E) 2/45
Rationale: Solution provided by stanford2012 is correct: 110/800 choosing one of the cellos which has a pair viola, 1/600 choosing the viola which is the pair of chosen cello --> P=110/800*1/600=311/48,000.
Answer: A.
Answer: (A) 11/48,000
Question: Sourav walks 20 meters towards North. He then turns left and walks 40 meters. He again turns left and walks 20 meters. Further, he moves 20 meters after turning to
right. How far is he from his original position?
(A) 88
(B) 90
(C) 60 meters
(D) 27
(E) 91
Rationale: Explanation:
No explanation is available for this question!
ANSWER:C
Answer: (C) 60 meters
Question: A train having a length of 1/4 mile , is traveling at a speed of 75 mph. It enters a tunnel 3 ½ miles long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 3
Rationale: Total distance = 3 ½ + ¼ = 7/2 + ¼ = 15/4 miles
Speed = 75 mph
Time = distance/speed = (15/4) / 75 hr = 1/20 hr = 60/20 minutes = 3 minutes
Answer is E.
Answer: (E) 3
Question: A person's present age is two-fifth of the age of his mother. After 10years, he will be one - half of the age of his mother. How old is the mother at present ?
(A) 45
(B) 30
(C) 50
(D) 25
(E) 31
Rationale: Let the mother's present age be x years
Then the person's present age = 2x/5
(2x/5)+10 = 1/2(x+10)
2(2x+40) = 5 (x+10)
x = 50
Answer is C
Answer: (C) 50
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is?
(A) 5336
(B) 5345
(C) 5350
(D) 5356
(E) 5350
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336.
A)
Answer: (A) 5336
Question: On a certain Monday, john drove to work at an average speed of 50 miles per hour and home from work along exactly the same route at an average speed of 70 miles per hour. Which of the following is closest to his average speed for both trips combined?
(A) 54
(B) 55
(C) 58.33
(D) 56
(E) 57
Rationale: To solve the average speed questions, we need to know the total distance and the total time.
Let us assume that the distance from work = D
This will also be the distance from work to home
Hence total distance travelled = 2D
Time in going to work = D/50,
Time in coming back from work = D/70
Hence average speed of both the trips = 2D/ (D/50 + D/70)
= 2*350/12 = 58.33
C
Answer: (C) 58.33
Question: By selling a watch for Rs.640/-, a man loses 20% what is that watch cost price
(A) Rs. 700/-
(B) Rs. 800/-
(C) Rs. 900/-
(D) Rs. 1000/-
(E) Rs. 1100/-
Rationale: 80 % ------> 640 (80 * 8 = 640)
100 % ------>800 (100 * 8 = 800)
Cost price = Rs. 800/-
B
Answer: (B) Rs. 800/-
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
(A) 1/2
(B) 1/3
(C) 1/5
(D) 1/7
(E) None
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B)
Answer: (B) 1/3
Question: X, Y, and Z are consecutive numbers and X > Y > Z. Also, X + 3Y + 3Z = 5Y + 4. What is the value of Z?
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: If X, Y, and Z are consecutive numbers and X > Y > Z, then Y = Z+1 and X = Z+2.
X + 3Y + 3Z = 5Y + 4
Z+2+3Z+3+3Z = 5Z+5+4
2Z = 4
Z = 2
The answer is E.
Answer: (E) 2
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 113, what is the product of b and c?
(A) 2652
(B) 2578
(C) 2534
(D) 3192
(E) 4234
Rationale: Here d = a + 3
a + a + 3 = 113
2a = 110
a = 55
So, numbers are 55, 56, 57 and 58
∴ b × c= 56 × 57 = 3192
D
Answer: (D) 3192
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 750 resolutions?
(A) 277 m
(B) 704 m
(C) 278 m
(D) 288 m
(E) 1056 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 750 resolutions.
= 750 * 2 * 22/7 * 22.4 = 105600 cm
= 1056 m
Answer: E
Answer: (E) 1056 m
Question: A motorcyclist started riding at highway marker A, drove 120 miles to highway marker B, and then, without pausing, continued to highway marker C, where she stopped. The average speed of the motorcyclist, over the course of the entire trip, was 50 miles per hour. If the ride from marker A to marker B lasted 3 times as many hours as the rest of the ride, and the distance from marker B to marker C was half of the distance from marker A to marker B, what was the average speed, in miles per hour, of the motorcyclist while driving from marker B to marker C?
(A) 40
(B) 45
(C) 50
(D) 54
(E) 60
Rationale: A- B = 120 Miles
B - C = 60 Miles
Avg Speed = 50 Miles
Time taken for A-B 3t and B-C be t
avg speed = (120+60) / Total time
50 = 180/4t
t = 54
B-C = 54mph
Answer D
Answer: (D) 54
Question: A single discount equivalent to a series of 30%, 20%, and 10% is
(A) 50%
(B) 49.6%
(C) 49.4%
(D) 51%
(E) 52%
Rationale: Let the marked price be Rs. 100
Then S.P = 90% of 80% of 70% of 100
= ( 90/100*80/100*70/100*100 ) =50.4
Single discount = ( 100- 50.4 )% = 49.6%
ANSWER:B
Answer: (B) 49.6%
Question: Cost of 16 mirror and 8 comb is Rs.344 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
(A) 19
(B) 12
(C) 20
(D) 21
(E) 22
Rationale: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 344 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 152
=> m = 19
A
Answer: (A) 19
Question: How many ways can 9 friends be arranged around a circular dinner table?
(A) 5!
(B) 6!
(C) 7!
(D) 8!
(E) 9!
Rationale: The number of ways to order 9 people is 9!
However, around a circular table, each pattern would be repeated 9 times.
So the number of ways to seat 9 friends around a circular table is 8!
The answer is D.
Answer: (D) 8!
Question: Angelina walked 250 meters from her home to the grocery at a constant speed. She then walked 360 meters to the gym at double the speed. She spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Rationale: let the speed be X...
so time taken from home to grocery= 250/x..
the speed to gym = 2x..
so time taken = 360/2x=180/x..
its given 250/x-180/x=70..
70/x=70..
x=1m/secs..
so grocery to gym=2*1=2m/s...
Answer : A
Answer: (A) 2
Question: In a group of 7 boys and 8 girls , 5 members are to be selected. In how many different ways can they be selected such that at least 3 boys should be there ?
(A) 1200
(B) 1500
(C) 1281
(D) 1339
(E) 1296
Rationale: No of boys = 7
No of girls = 8
Therefore,
No of ways at least 3 boy can be selected = 7C5 * 8C0 + 7C4* 8C1 + 7C3*8C2
= 1281
Ans - C
Answer: (C) 1281
Question: If the product of two positive integers is 40, which of the following could be the LCM and HCF of the two numbers? a. LCM 20 : HCF 2 b. LCM 40 : HCF 5 c. LCM 20 : HCF 4
(A) b only
(B) c only
(C) a only
(D) a, c only
(E) a, b only
Rationale: a is the correct answer.
Answer : C
Answer: (C) a only
Question: A metal bar weighs 8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar? (round to the nearest thousandth)
(A) 5.580 ounces
(B) 7.580 ounces
(C) 8.560 ounces
(D) 4.480 ounces
(E) 9.880 ounces
Rationale: 93/100=x/8.15
Multiply the opposites:
93 x 8.15 = 757.95
Divide by the remaining number:
100)7.5795/757.9500
7.580 ounces
correct answer B
Answer: (B) 7.580 ounces
Question: Tom travels first 5 kilometers in 80km/hr and another 5 kilometers in 20km/hr. What is his average speed?
(A) 32km/hr
(B) 42km/hr
(C) 40km/hr
(D) 30km/hr
(E) 36km/hr
Rationale: Since the distance traveled is same, we can apply direct formula= 2XS1XS2/(S1+S2)
2X80X20/100= 32. 'A' is the answer.
Answer: (A) 32km/hr
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $94 per day. What was his wage on the 8th day?
(A) $83
(B) $90
(C) $92
(D) $97
(E) $104
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 94$
Wage on 8th day = 90*15 -( 87*7 + 94 *7)
= 1350 - (609 + 658)
=1350 - 1267
= 83
Answer A
Answer: (A) $83
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 13th, 13th, and 15th terms in the sequence?
(A) 2^18
(B) 3(2^17)
(C) 7(2^16)
(D) 3(2^16)
(E) 7(2^12)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 13th term will be 2^12
14th term 2^13
15th term 2^14
adding all three
we get
2^12+(2^12)*2+(2^12)*4
so answer is 2^15(1+2+4)=>7(2^12)
answer E
Answer: (E) 7(2^12)
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 20%
(B) 90%
(C) 80%
(D) 10%
(E) 50%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer:A
Answer: (A) 20%
Question: A man can row a boat at 21 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 70 km downstream?
(A) 11/9
(B) 5/7
(C) 3/2
(D) 5/3
(E) 5/2
Rationale: Speed downstream = 21 + 7 = 28 kmph.
Time required to cover 60 km downstream = d/s = 70/28
= 5/2 hours.
Answer: E
Answer: (E) 5/2
Question: 10% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
(A) 25
(B) 30
(C) 50
(D) 55
(E) 60
Rationale: I came up with (A) 25
Think of 100 people total:
From the first fact, 10 of these are women with fair hair.
From the second fact, these 10 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*10 equals the number of fair haired men, which is 15 men with fair hair.
Add this 15 to the 10 women and get 25 fair haired men and women out of 100 total men and women.
25%
A
Answer: (A) 25
Question: up to 20,how many no. are odd and prime both?
(A) 9
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: we have to calculate it manually.
odd 1,3,5,7,9,11,13,15,17,19
prime 2,3,5,7,11,13,17,19
common 3,5,7,11,13,17,19
total no. 7
answer D
Answer: (D) 7
Question: Selling an kite for Rs. 30, a shop keeper gains 30%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
(A) 8%
(B) 10%
(C) 11%
(D) 17%
(E) 20%
Rationale: Explanation:
Marked price = Rs. 30
C.P. = 100/130 * 30 = Rs. 23.07
Sale price = 90% of Rs. 30 = Rs. 27
Required gain % = 3.92/23.07 * 100 = 17%.
Answer: D
Answer: (D) 17%
Question: The area of circle O is added to its diameter. If the circumference of circle O is then subtracted from this total, the result is 6. What is the radius of circle O?
(A) –2/pi
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: pi*r^2 + 2r -2*pi*r =6
Simplifying the equation: pi*r(r-2)+2r=6
Without much algebraic: We can Test the answers quickly, then 3 is the only possible answer that will eliminate pi from equation.
Answer is C
Answer: (C) 3
Question: Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio L of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?
(A) 5 to 1
(B) 10 to 7
(C) 1 to 5
(D) 7 to 10
(E) 9 to 10
Rationale: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:
We translate the exercise into the table:
R T W
X t/2 1
Y t 1
Z (t/2*3/2 =3t/4) 1
From this table we find the rates
Rx = 2/t
Ry = 1/t
Rz = 4/3t
The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)
Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t
Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t
The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio L is the inverse of work, the the answer is 7 to 10
CORRECT ANSWER D
Answer: (D) 7 to 10
Question: The digit in unit's place of the product 81 ×82×.....×89 is
(A) 0
(B) 2
(C) 6
(D) 8
(E) 4
Rationale: Solution
Required digit	= Unit digit
=(1×2×3×4×5×6×7×8×9)	=0.
Answer A
Answer: (A) 0
Question: There are 5 red shoes, 4 green shoes. If one drasw randomly a shoe what is the probability of
getting redshoe
(A) 1/9
(B) 2/9
(C) 3/9
(D) 4/9
(E) 5/9
Rationale: total shoes=9
probability of getting only red shoe=5/9
ANSWER:E
Answer: (E) 5/9
Question: There are 17 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 288
(B) 267
(C) 261
(D) 211
(E) 342
Rationale: The total number of stations = 19
From 19 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 19P₂ ways.
19P₂ = 19* 18 = 342.
Answer: E
Answer: (E) 342
Question: A man sells two articles for Rs.2250 each and he gains 24% on the first and loses 45% on the next. Find his total gain or loss?
(A) 9%loss
(B) 2%loss
(C) 7%loss
(D) 8%loss
(E) 11%loss
Rationale: Explanation:
(24*45)/100
= 11%loss
Answer:E
Answer: (E) 11%loss
Question: If each data point in a certain set Q is increased by a factor of 20, what happens with the set's standard deviation?
(A) Doesn't Change
(B) Decreases by Factor 20
(C) Can't be determined
(D) Increases by 20
(E) Increases by Factor 20
Rationale: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 20, the standard deviation will increase proportionately, giving us answer choice E
Answer: (E) Increases by Factor 20
Question: In the xy plane line m has the equation 4x + y = q. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
(A) -4/3
(B) 1/4
(C) -4
(D) 3/4
(E) 4/3
Rationale: The equation of line m is y=-4x+q. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Answer: (A) -4/3
Question: In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
(A) 360
(B) 480
(C) 720
(D) 5040
(E) None of these
Rationale: Explanation:
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
ANSWER IS C
Answer: (C) 720
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 4 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 = 4.
So, x = 65 ounces.
Water = (60 / 65) * (65) = 60 ounces.
Ans D
Answer: (D) 60
Question: Find the number of digits that are to be used in numbering a book of 400 pages.
(A) 1094
(B) 1093
(C) 1092
(D) 1099
(E) None of above
Rationale: Explanation:
One digit numbers from 1 to 9 = 9
Two digit numbers from 10 to 99 = 90
Three digit numbers from 100 to 400 = 301
.:Total numbers of digits that are to be used
=(9 x 1) + (90 x 2) + (301 x 3) = (9 + 180 + 903) = 1092
Answer: Option C
Answer: (C) 1092
Question: An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 10, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?
(A) a.	A - 10
(B) b.	B - 15
(C) c.	C – 22.5
(D) d.	D – 20
(E) e.	E – 67.5
Rationale: A --- 30/2 + 10 = 25 --- wrong
B --- 45/2 + 10 = not an integer --- wrong
C --- 22.5(3/2) + 10 = not an integer --- wrong
D --- 60/2+10 = 40 --- CORRECT
This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.
D
Answer: (D) d.	D – 20
Question: The cost of an article (which is composed of raw materials and wages) was 3 times the value of raw materials used. The cost of raw materials increased in the ratio 3 : 7 and wages increased in the ratio 4 : 9. Find the present cost of the article if its original cost was Rs. 18.
(A) Rs. 41
(B) Rs. 30
(C) Rs. 40
(D) Rs. 46
(E) Rs. 56
Rationale: Assume the raw materials’ cost as Rs.150, then the total cost will be Rs. 450, (Thus, wages cost is Rs. 300)
Since, the cost of raw materials goes up in the ratio of 3 : 7, the new raw material cost would become Rs. 350
The new wages cost would be in the ratio 4 : 9 as Rs. 675.
The new total cost would become, Rs. 1025.
Since Rs 450 become Rs. 1025 (change in total cost),
Unitary method calculation would give us that Rs. 18 would become Rs. 41.
ANSWER:A
Answer: (A) Rs. 41