MU-NLPC/Calc-aqua_rat huggingface dataset:
Approximately how many revolutions will be made by a car tire with a 10-inch diameter if the car travels 1⁄2 mile?
Choose the correct choice from the following answers.
A) 120
B) 180
C) 1003
D) 1000
E) 1,440

Solution: Diameter of car tire = 10 inches   Radius of car tire = 5 inches = 5*2.54= 
5*2.54 = 12.7
12.7 cm   Circumference of the car tire= 2*pi * 12.7 = 2 *3.14 *12.7= 79.76 cm   Distance traveled by car = .5 mile = .5 *1.6= 
.5 *1.6 = 0.8
.8 km= 800 m = 8 * 10^4 cm   Number of revolutions =Distance traveled / Circumference of tire = 8 * 10^4 / 79.76 = 1003   Since the answer choices are far apart we should use estimation in this question .   Ideally ,in the GMAT the conversion between units would be provided .   Answer 1003
Answer: C
Robin mixes two liquids, one blue in coloUr and other red in colour in the ratio 2:3 and sells the mixture at the rate of $20 per liter, thereby making a 25% profit on his outlay. The blue liquid costs Robin $5 per litre lesser than the red liquid. How much does a liter of red liquid cost?  Choose the most appropriate option: A) 12 B) 13 C) 14 D) 15 E) 16

Solution: Let x be the required cost per litre of red paint.   Take 5 litres of this mixture.   Sold at 100 with a profit of 1/4th of total cost. So, total cost will be 1/5th less than 100; total cost = 80.   2(x-5) + 3(x) = 80   x = 14   Answer is 14
Answer: C
A cricketer scored 136 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
Select
A) 46.2%  B) 54.54 %  C) 55.88%  D) 70%  E) None of these

Solution: Explanation :   Number of runs made by running = 136 - (12 x 4 + 2 x 6)   = 136 - (60)= 
136 - (60) = 76
76   Now, we need to calculate 72 is what percent of 136.=> 76/136 * 100 = 55.88 %   Answer : 55.88%
Answer: C
A set of numbers has the property that for any number t in the set, 2t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -3
II. 1
III. 6  Pick:
A) I only B) II only C) I and II only D) II and III only E) I, II, and III

Solution: The question is which of the followingmustbe in the set, notcouldbe in the set.   If -1 is in the set so must be   2*-1+2= 
  2*-1+2 = 0
0, as 0 is in the set so must be   0+2= 
  0+2 = 2
2, as 2 is in the set so must be   4+2= 
  4+2 = 6
6 and so on.   I onlynswer: I only.
Answer: A
John has on his shelf four books of poetry, three novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work? Choose one.
A) 1/6	B) 2/5	C) 3/10	D) 7/20	E) 8/45

Solution: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 3/9*2/8 + 2/9*3/8 = 1/6.   1/6nswer: 1/6.
Answer: A
The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is  Pick one:
A) 587 × 108 miles
B) 587 × 1010 miles
C) 587 × 10-10 miles
D) 587 × 1012 miles
E) 587 × 10-12 miles

Solution: The distance of the light travels in 100 years is:   5,870,000,000,000 × 100 miles.   = 587,000,000,000,000 miles.   = 587 × 1012 miles.   The answer is (587 × 1012 miles)
Answer: D
3 building 3 floors how many floors are in the 3 buildings?
Choose the most appropriate option.
A) 1  B) 6  C) 3  D) 9  E) 10

Solution: 3
Answer: C
Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 3,000, how much money did investors B and C earn in total?  Choose the correct choice from the following answers:
A) $4,000
B) $4,900
C) $5,600
D) $9,000
E) $10,500

Solution: Let profit for A = 5x   profit for B = 7x   profit for C = 8x   Investor A earned = 3000   5x = 3000=>x=600   Total profit for B and C = 7x+ 8x = 15x   Therefore , 15x 7 + 8= 
7 + 8 = 15
15x   Therefore , 15x= 15*600 = 9,000   Answer $9,000
Answer: D
What is the ratio G of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Choose one
A) 1/4
B) 3/8
C) 1/2
D) 3/5
E) 2

Solution: One side surface area of a cube = x*x = x^2   Total 6 sides = 6x^2   As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.   L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2   W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2   Total 6 sides = 8x^2 + 2x^2 = 10x^2   Ratio of cube area to rectangular area G= 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (3/5)
Answer: D
A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?  Choose the correct option:
A) Rs.45 B) Rs.45 C) Rs.55 D) Rs.60 E) None

Solution: Solution   A : B : C	=(10×7):(12×5):(15×3)   = 70 :60 :45   = 14 :12 :9   c's rent	=Rs.(175×9/35)   = Rs.45.   Rs.45nswer Rs.45
Answer: A
The sum of three consecutive even numbers is 42. Find the middle number of the three?	Pick.
A) 14  B) 15  C) 52  D) 25  E) 32

Solution: Answer: Option A   Three consecutive even numbers (2P - 2), 2P, (2P + 2).   (2P - 2) + 2P + (2P + 2) = 42   6P = 42 => P = 7.   The middle number is: 2P = 14.
Answer: A
A loan has a variable interest rate that fluctuates between 5% and 9% of the base payment per month. If base payments remain at $250 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month? Choose the correct choice from the following
A) $ 262.50 B) $ 265.13 C) $ 272.50 D) $ 275.23 E) $ 286.13

Solution: To find the maximum amount, select the maximum rate that is 9%. Therefore the combined amount is 272.5.   To this amount add 1% extra of it, as a surcharge.   This will be something close to 275.   ANSWER:$ 275.23
Answer: D
5020−(1004÷20.08)=? Answers
A) 4520
B) 4350
C) 4210
D) 4100
E) 4970

Solution: 4970xplanation:   =5020−(1004/2008×100)   =5020−50=4970   Option 4970
Answer: E
If a lies in the range (-4,3) then which of the following statements must be true?
Choose the correct choice from the following
A) a^4 >a^3 > a^2 > a  B) a > a^2 > a^3 > a^4  C) a^4 > a^2 > a^3 >a  D) a^2 > a^4 > a^3 >a  E) a^2 > a^4 > a > a^3

Solution: consider any number from the given range (-4,+3)..let a=-1/2   then a^2= 1/4   a^3=-1/8   a^4=1/16   so we have a^2>a^4>a^3>a   Ans a^2 > a^4 > a^3 >a
Answer: D
Half of the volume of the milk and water mixture of ratio 7:5 is converted into a mixture of ratio 3:1 by the substitution(or replacement method) the mixture of ratio 7:5 was formed from the mixture 7:3 by adding the water in it. if 240 L milk is required in the replacement method ,what it the total amount of water was added t6o prepare the mixture 7:5 ? Select:
A) 100 L
B) 50 L
C) 400 L
D) 300 L
E) 200 L

Solution: 2 actions have been done on the mix...   1)7:3 is converted into 7:5 mix..   2) half of the mix of 7:5 is converted in 3:1 by adding 240l milk..   let's start with 2 action as more info is given there..   let the mix common ratio be 2x..   so total sol = milk:water=7*2x:5*2x   240 l milk is added to half of it to make it 3:1..   so (7x+240)/5x =3:1..   we get x=30 or 2x=60..   so the sol is 7*60:5*60=420:300..   now we look at the first action ..   this was created from 7:3 mix...   so say x was added to get this ratio...   so 420/(300-x)=7/3..   here x =120..   but 120 does not seem to be a choice..   now why 120 has to be correct..   initial milk:water=420:180=7:3(this is given to us)..   120 l of water is added= 420:180+120=420:300=7:5(again this confirms with what has been given)   240 l of milk is removed from half the mixture..   half the mix=210:150..   add 240 l milk...   210+240:150=450:150=3:1(satisfies the given data in Q).   ANSWER:300 L
Answer: D
By selling 32 apples in a dollar, a man loses 40%. How many apples must he sell in a dollar to gain 20% profit?  Choose the correct option:
A) 16
B) 18
C) 20
D) 25
E) 28

Solution: This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 apples for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many apples he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of apples in half to double our returns (from 60% to 120%), yielding  32/2= 
 32/2 = 16
16 apples, or answer choice 16.
Answer: A
A and B together can do a work In 4 days. A alone can do it in 12days.what time B will take to do the work alone? Choose the correct answer.
A) 6 days  B) 8 days  C) 12 days  D) 10 days  E) 5 days

Solution: Explanation:   6 days and B 1day's work = 1/4   6 days alone can do 1day's work = 1/12   what time B will take to do the work alone?   B = (6 days+B) - 6 days = (1/4) - (1/12) = 6 Days   6 daysnswer: Option 6 days
Answer: A
A store owner estimates that the average price of type A products will increase by 15% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?	Select
A) $14,305	B) $15,325	C) $16,000	D) $16,225	E) $17,155

Solution: cost of type $14,305 products next year = 1.15 * 4500= 
1.15 * 4500 = 5_175
5175   cost of type B products next year= 1.1 * 8300= 
1.1 * 8300 = 9_130
9130   total 5175 + 9130= 
5175 + 9130 = 14_305
14305 option $14,305
Answer: A
A precious stone weighing 35 grams worth Rs. 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight then find the loss incurred.  Options
A) Rs. 5750
B) Rs. 6000
C) Rs. 5500
D) Rs. 5000
E) Rs. 7000

Solution: The price varies as the square of the weight,   P = K x W2   12250 = K x 352   K = 10   Thus, P = 10W2   When the two pieces are in the ratio 2 : 5 (Weight wise) then we know that their weights must be 10g and 25g respectively.   Their values should be :   10g piece: 10 x 102 = Rs. 1000;   25g piece: 10 x 252 = Rs. 6250.   Total value of stone now, = 1000 + 6250 = Rs. 7250   Loss incurred = 12250 - 7250 = Rs. 5000   ANSWER:Rs. 5000
Answer: D
a man and a woman, walking together start out by boyh taking a step with the left foot.in order to keep together, the man whose stride is longer,takes two steps while the woman takes three.how many steps will the woman have taken they are both about to step out on the right foot for the first time together?	Choose the correct choice from the following answers.
A) 4  B) 5  C) 6  D) 7  E) 8

Solution: first man left and right, in that time woman has to do left,right and left. man and woman are ends with left and left.   next man left and right again, but woman has to start with right step. right,left,right. man and woman ends with right and right now.   hence solution is five.   ANSWER:5
Answer: B
If it takes Alex 20 minutes to walk from home to School and it takes him 10 minutes to walk from home to the supermarket, which of the following COULD be true?
I. The School is closer to Alex's home than the supermarket.
II. To walk to School, Alex will spend double the time it takes him to walk to the supermarket.
III. Alex will spend more time walking to the school than walking to the supermarket.
Select the correct option:
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III

Solution: Let’s check each statement.   Statement I:The School is closer to Alex's home than the supermarket. Alex spends 10 minutes to walk to the supermarket and spends 20 minutes to walk to school, it takes him longer time to get to school in which case Statement I can NEVER be true.   Statement II: To walk to School, Alex will spend double the time it takes him to walk to the supermarket. Alex spends 10 minutes to walk to school, double that time is 20 minutes. The time taken to walk to school is actually double the time taken to walk to the supermarket in which case Statement II is TRUE.   Statement III: Alex will spend more time walking to the school than walking to the supermarket. Alex spends 20 minutes walking to school and spends 10 minutes walking to the supermarket. Obviously more time is taken to walk to school than walking to the supermarket, in which case Statement III is TRUE.   Statement II and III are true.   So,the correct answer is II and III only.
Answer: D
A house is getting ready for dinner table. There are 15 members in the family, and the butler must assign 10 people to the following positions: 1 main chair, 4 on left side, 4 on right side, and 1 most further away seat. Only 3 of the family members are elderly enough to sit on the main chair, and they will not sit at any other place. The other members can sit on any seat. How many different groupings are possible? Choose the correct choice from the following options.
A) 64585 B) 100 C) 80 D) 59400 E) 789300

Solution: 3C1 select 1 for main chair from 3 elderly people;   12C4 select 4 people for left side chairs from 12 members (as 3 elderly would like to sit only on main chair  15-3= 
 15-3 = 12
12);   8C4 select 4 people for right side chair from 8 members (as 3 are elderly, and 4 we have already selected for left side  15-3-4= 
 15-3-4 = 8
8);   4C1 select 1 for the most further away chair from 4 people (again as as 3 are elderly, and 4 we have already selected for left side and 4 for right side chairs   15-3-4-4= 
  15-3-4-4 = 4
4)   Total # of selection=3C1*12C4*8C4*4C1=59400   Answer: 59400
Answer: D
A works twice as fast as B.If B can complete a work in 18 days independently,the number of days in which A and B can together finish the work is:  Options:
A) 4 days
B) 6 days
C) 8 days
D) 10 days
E) 12 days

Solution: Explanation:   Ratio of rates of working of A and B =2:1. So, ratio of times taken =1:2   A's 1 day's work=1/9   6 days's 1 day's work=1/18   (A+6 days)'s 1 day's work=(1/9 + 1/18)=3/18=1/6   so, A and 6 days together can finish the work in 6 days   ANSWER IS 6 days
Answer: B
A train passes a station platform in 36 seconds and a man standing on the platform in 25 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Choose the correct choice.
A) 37 B) 240 C) 288 D) 267 E) 165

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 25)m = 375 m. Let the length of the platform be x meters. Then, (x + 375)/36 = 15 ==> x + 375 = 540 ==> x = 165 m.Answer: 165
Answer: E
The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?  Choose the correct choice from the following answers:	A) 18 2/61%	B) 18 2/11%	C) 18 2/81%	D) 18 2/12%	E) 18 2/21%

Solution: 13 CP = 11 SP   11 --- 2 CP   100 --- ? =>18 2/11%   Answer: 18 2/11%
Answer: B
If the difference of two numbers is 3 and the difference of their square is 39, then the larger number is: Choose the correct choice:
A) 9
B) 2
C) 12
D) 14
E) 8

Solution: Let the numbers be x and y   Then x2-y2=39   And x-y=3   We get x+y=13   Solving x-y=3, x+y=13   X=8, y=5   Larger number 8   ANSW8R 8
Answer: E
9 people decided to split the food order evenly. If the bill was $86.14 dollars, how much money should be removed with 1 cent as the smallest unit?	Choices:  A) $86.10  B) $86.11  C) $86.12  D) $86.13  E) $86.19

Solution: This is equivalent to finding the first number that is divisible by 9 that occurs after 8614.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of   8+6+1+4= 
  8+6+1+4 = 19
19. If you remove 1 , the number is divisible by 9 (19 -1). 18 is divisible by 9.   Hence, we need to remove 1 cent from this number for it to be divisible by 9.
Answer: D
How many words can be formed by using all letters of the word 'BIHAR'?
Pick one.
A) 720  B) 24  C) 120  D) 60  E) None of these

Solution: Explanation :   The word 'BIHAR' has 5 letters and all these 5 letters are different.   Total words formed by using all these 5 letters = 5p5 = 5!   = 5 x 4 x 3 x 2 x 1 = 120. Answer : Option 120
Answer: C
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:  Choose the most appropriate option:	A) 542	B) 546	C) 566	D) 548	E) 589

Solution: Least number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8= 
540 + 8 = 548
548.   ANSWER : 548
Answer: D
The least number which must be subtracted from 909 to make it exactly divisible by 9 is: Choose the correct answer: A) A)2 B) B)3 C) C)0 D) D)5 E) E)6

Solution: On dividing 909 by 9, we get remainder= 0   Therefore, required number to be subtracted= 0   Answer: 0
Answer: C
If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 50/r years. If Luke's parents invested $11,500 in a long term bond that pays 12 percent interest compounded annually, what will be the approximate total amount of the investment 12 years later, when Luke is ready for college?  Choose the correct choice.
A) 62,000 B) 85,500 C) 95,500 D) 100,500 E) 100,000

Solution: Answer equals C in 48 years. I thought by 50th year it would reach 95,500. Options should have been separated more widely for clarity.
Answer: C
Find the maximum value of n such that 50! is perfectly divisible by 2520^n  Choose one:
A) 7
B) 8
C) 9
D) 6
E) 5

Solution: 2520 = 2^3*3^2*5*7   Here, 7 is the highest prime,so find the no. of 7's in 50! only   no. of 7's in 50! = [50/7] + [50/7^2] = 7+1= 
7+1 = 8
8   ANSWER:8
Answer: B
A comic collector sells his memorabilia through an on-line distributor, which take a commission of 5% of the price set by the collector. The on-line store obtains the product from an artist at the price of $100 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 5% profit on the cost of the item? Choose the most appropriate option:
A) 98.42 B) 105.15 C) 110.53 D) 107.22 E) 66.68

Solution: 110.53ollector price = $100;The on-line distributor wants to maintain a 5% profit on the cost of the memorabilia, thus he must get $ 100*1.05= 
 100*1.05 = 105
$105 after the distributor takes a commission of 5% of the final price --> (final price)*0.95= $105 --> (final price) = $110.53.Answer: 110.53.
Answer: C
The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is
Pick.
A) 1.2 km
B) 1.8 km
C) 2.4 km
D) 3.6 km
E) 1.6 km

Solution: B = 15km/hr, S= 3km/hr, Downstream B+S = 15+3= 
15+3 = 18
18 km/hr   down stream time t= 12 min, we have to change it to hours so t = 12/60=1/5 hrs.   Distance = Speed*time = 18*1/5= 
18*1/5 = 18/5 = around 3.6
3.6 km.   ANSWER:3.6 km
Answer: D
A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?  Options
A) 425 miles
B) 625 miles
C) 325 miles
D) 225 miles
E) 625 miles

Solution: During each hour, the car travels 65 miles. For 5 hours it will travel   65 + 65 + 65 + 65 + 65 = 5 *65= 
5 *65 = 325
325 miles correct answer 325 miles
Answer: C
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?  Pick:
A) 32 years	B) 36 years	C) 40 years	D) 48 years	E) None

Solution: Solution   Let the mother's present age be x years.Then, the person's present age	= (2/5 x) years.   Therefore	=[2/5x+8]   = 1/2(x+8)   = 2(2x+40)   =5(x+8)   = 40 year   Answer 40 years
Answer: C
If 4 people are selected from a group of 7 married couples, what is the probability that none of them would be married to each other?
Choose the correct choice from the following answers.
A) 1/33  B) 2/33  C) 1/3  D) 16/33  E) 47/84

Solution: If we are to select 4 people from 7 couples WITHOUT any restriction, how many ways can we make the selection? 14!/4!10! =1001   If we are to select 4 people from 7 couples WITH restriction that no married couple can both make it to the group, only a representative?   7!/4!3! = 35   But we know that to select a person from each couple, take 2 possibilities     35*2*2*2*2= 
  35*2*2*2*2 = 560
560   Probability= Desired/All Possibilities = 560/1001 = 47/84   Answer: 47/84
Answer: E
A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red? Select the correct option:
A) 5/21
B) 5/24
C) 5/26
D) 5/31
E) 6/29

Solution: P(Both are red),   =65/262135/262=65/262135/262   =5/26   5/26
Answer: C
There are 8 orators A, B, C, D, E, F, G and H. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.  Pick:  A) 8! / 3!  B) 8! / 6!  C) 5! x 3!  D) 8! / (5! x 3!)  E) 8! / (5! x 4!)

Solution: Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C.   The remaining 5 people have to be arranged in 5 places.   Thus, 8C3 x 5! = 56 x 120 = 67200 = 8! / 3!   8! / 3!NSWER:8! / 3!
Answer: A
A copy machine, working at a constant rate, makes 40 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ? Choose the most appropriate option
A) 90
B) 2,700
C) 4,500
D) 5,400
E) 2,850

Solution: Together the two machines make 40+55= 
40+55 = 95
95 copies per minute. So, in half an hour they will make 95*30=2,850 copies.   Answer: 2,850.
Answer: E
The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 12 years more than twice the age of the son. Find the present age of the father.  Select the correct option:
A) 33  B) 39  C) 29  D) 40  E) 48

Solution: if the present age be x years.   father's will be (3x+3)years..   so, (3x+3+3)=2(x+3)+12   or, x=12   so the fathers present age =(3x+3)=(3*12+3)= 
(3*12+3) = 39
39years..   ANSWER : OPTION 39
Answer: B
Two unbiased coins are tossed.What is the probability of getting at most one head? Choose the correct choice from the following options:
A) 2/3	B) 1	C) 3/4	D) 2	E) 1/2

Solution: s={hh,tt,ht,th}   e=event of getting at most one head.   e={tt,ht,th}.   p(e)=n(e)/n(s)=3/4   Answer is option 3/4
Answer: C
A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
Select
A) 2277 B) 1640 C) 2977 D) 2991 E) 2771

Solution: (x*8*3)/100 = ((2665 - x)*3*5)/100   24x/100 = 39975/100 - 15x/100   39x = 39975 => x = 1025   Second sum = 2665 – 1025 = 1640   Answer: 1640
Answer: B
An alloy weighing 24 ounces is 70 percent gold. How many ounces of pure gold must be added to create an alloy that is 90 percent gold?
Choose the correct choice.
A) 6	B) 9	C) 12	D) 24	E) 48

Solution: In 24 ounces, gold is 24 * (70/100)= 
24 * (70/100) = 84/5 = around 16.8
16.8 ounces. Now we add x ounces of pure gold to make it 90% gold.   So 16.8 + x= (24 + x)* 90/100 => x =48.   Answer is 48.
Answer: E
Find b and c so that the parabola with equation y = 4x2 - bx - c has a vertex at (2 , 4)?	Choose the correct choice
A) -10 B) -20 C) -30 D) -40 E) -50

Solution: h = b / 8 = 2 : formula for x coordinate of vertex   b = 16 : solve for b   y = 4 for x = 2 : the vertex point is a solution to the equation of the parabola   4(2)2 - 16(2) - c = 4   c = -20 : solve for c   correct answer -20
Answer: B