MU-NLPC/Calc-aqua_rat huggingface dataset:
Rodrick mixes a martini that has a volume of 'n' ounces having 36% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add? Choose one:
A) n/6	B) n/3	C) 4n/9	D) 5n/6	E) 8n/5

Solution: total V G   1 ounce 0.36 0.6   n ounce 0.36n 0.6n -------------initial expression   lets say g ounces of gin is added to this mixture   n+g 0.36n 0.6n+g --------------final expression   given that after adding g ounces of gin , V should become 25% of the total volume.   =>Volume of V/total volume = 25/100   => 0.36n /n+g = 1/4   => 1.44n = n+g   => g = 4n/9   Answer is C.   Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:   0.36n=0.25(n+g) --> g=4n/9   Answer: 4n/9.
Answer: C
The difference between the compounded interest and simple interest on a certain sum at 10% per annum for 2 years is Rs.631. Find the sum.	Choose the correct choice from the following options:
A) Rs. 52255	B) Rs. 50000	C) Rs. 63200	D) Rs. 63100	E) None

Solution: Let the sum be Rs. X .Then, C.I.. = x( 1 + 10/100 )2 - x = 21x/100 S.I. = [ (x*10*2)/100] = x/5 (C.I.) – (S.I.) = [ (21x)/100 – (x/5) ] = x/100 => x/100 = 631 => x= 63100 Hence, the sum is Rs. 63100   Answer Rs. 63100
Answer: D
A waiter's salary consists of his salary and tips. During one week his tips were 3/4 of his salary. What fraction of his income came from tips ? Choose the correct option.
A) 3/7 B) 5/4 C) 5/8 D) 5/9 E) 6/9

Solution: Income = salary (s) +tips = s + s*3/4 = s*7/4   Tips = s*3/4   fraction of his income came from tips = (s*3/4)/(s*7/4)= 3/7   3/7NSWER:3/7
Answer: A
A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^14, respectively, what is the value of A?  Answers.
A) -24(5^12)  B) -23(5^12)  C) -24(5^6)  D) 23(5^12)  E) 24(5^12)

Solution: Ans : A   Assume that the numbers appear as shown below on the number line   A-----B-----C-----D-----E-----F-----G-----H   (5^12) (5^13)   As the values for G and H are given , we can calculate the difference between any two terms of the series .   Common Difference ,d = (5^13) - (5^12)   = (5^12) *[ 5-1 ]   = (5^12)*(4)   Also F + d = G as the terms are in equidistant and in increasing order.   So F + (5^12)*(4) = (5^12).   That is , F = (5^12) - (5^12)*(4)   = (5^12)[ 1-4]   = (5^12) (-3)   Similarly , E = F - d   = (5^12)[-3-4]   = (5^12)*(-7)   You can see a -4 getting added to the non-exponent part of the values . That is , according to the pattern , D SHOULD BE (5^12)*(-7-4)= (5^12)*(-11)   Following this pattern , -24(5^12) = (5^12)*(-24)
Answer: A
10 people meet and shake hands. The maximum number of handshakes possible if there is to be no “cycle” of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, ……, ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ……, {ak-1, ak}, {ak, a1} shake hands).	Choose one:
A) 7  B) 6  C) 9  D) 8  E) 10

Solution: The question is not written in proper manner but we can work in 3 methods   1) If these are random handshakes, then total methods = 10*9/2*1= 
10*9/2*1 = 45
45   2) If these are cyclic handshakes, then total methods= 10   3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9   ANSWER:9
Answer: C
When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 5/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
Options:
A) 10/9 n  B) 4/3 n  C) 9/2 n  D) 9/4 n  E) 7/3n

Solution: C is the answer.   To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.   Given   - tank was already 1/3 full.   - When n ltr added, it became 5/9   So 1/3 + n = 5/9   n = 5/9 - 3/9   n = 2/9   capacity of the tank is full fraction . i.e. 1 i.e. 9/9   so the question is 9/9 is how much times n   = 9/9= 
9/9 = 1
1= xn   so x = 9/2   and total = 9/2n
Answer: C
The price of a DVD Player is marked at $ 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it? Options.
A) $ 8721
B) $ 6383
C) $ 8739
D) $ 8766
E) $ 7739

Solution: $ 8721   $ 8721   $ 8721ctual price = 95% of 90% of 85% of $ 12000   = 95/100 * 90/100 * 85/100 * 12000= 
95/100 * 90/100 * 85/100 * 12000 = 8_721
$ 8721.
Answer: A
Three runners T, B and C run a race, with runner T finishing 12m ahead of runner B and 18m ahead of runner C, while runner B finishes 8m ahead of runner C. Each runner travels entire distance at a constant speed. What was the length of the race?	Select the correct option.
A) 36m  B) 48m  C) 60m  D) 72m  E) 84m

Solution: Let distance of race be x mtrs. Then when T finishes x m , B has run (x- 12)mtrs and C has run x-18 mtrs. so at this point B is 6 m ahead of C. Now to finish race b needs to run another 12 m, so he runs another 12 m. when B finishes race he is 8 m ahead of C. so last 12 m B has run, C has run 10 m.   as speeds are constant, we have equation,   x-12/ x-18 = 12/10 > x = 48.   Answer 48m
Answer: B
Due to a reduction of 25/4% in the price of sugar, a man is able to buy 1 kg more for Rs. 120. Find the original rate of sugar.	Choose the correct choice from the following:
A) 7 B) 8 C) 8.5 D) 9 E) 9.5

Solution: Rate reduced by 6.25%,   So amount Rs 120 reduced by= (6.25/100) * 120= 
(6.25/100) * 120 = 7.5
7.5   So in Rs 7.5 extra sugar obtained is 1 kg   i.e. new rate is Rs. 7.5 per kg   Thus original rate= [7.5 / (100 – 6.25)]/100   = 7.5 / 0.9375 = Rs. 8   ANSWER :OPTION 8
Answer: B
A train is 360 meter long is running at a speed of 30 km/hour. In what time will it pass a bridge of 140 meter length?  Choose the most appropriate option:
A) 87
B) 69
C) 60
D) 72
E) 21

Solution: Speed = 30 Km/hr = 30*(5/18) m/sec = 25/3 m/sec   Total distance = 360+140= 
360+140 = 500
500 meter   Time= Distance/speed   = 500 * (3/25)= 
500 * (3/25) = 60
60 seconds   Answer: 60
Answer: C
A sum of Rs. 14,000 amounts to Rs. 22,400 in 12 years at the rate of simple interest. What is the rate of interest?  Choose the correct choice from the following answers
A) 7% B) 6% C) 5% D) 4% E) 3%

Solution: Explanation :   Simple Interest for 12 years (SI) = (22400 - 14000) = Rs.8400   R = ?   T = 12 years   P = Rs. 14000   R=100×SI/PT=100×8400/14000×12   =5%   Answer : Option 5%
Answer: C
The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Pick:
A) 277 cm B) 800 cm C) 626 cm D) 245 cm E) 152 cm

Solution: Area of the square = s * s = 5(125 * 64)   => s = 25 * 8= 
25 * 8 = 200
200 cm   Perimeter of the square= 4 * 200= 
4 * 200 = 800
800 cm.   Answer: 800 cm
Answer: B
What is the remainder of E=3^19 when divided by 10?  Select:	A) 0	B) 1	C) 5	D) 7	E) 9

Solution: I looked for patterns:   ^2 - units digit 9   ^3 - units digit 7   ^4 - units digit 1   ^5 - units digit 3   hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9   and we can then see:   ^16 - units digit 1, or   ^18 - units digit 9   and ^19 - units digit 7   therefore, E=when divided by 10, the remainder must be 7.7
Answer: D
If a young child was 19 months old one year ago, how old was the child, in months, x months ago?	Choose the correct answer:
A) x − 31	B) x − 12	C) 19 − x	D) 24 − x	E) 31 − x

Solution: The child's age today is 19 months + 12 months = 31 months   x months ago, the child's age was (31 - x) months old.   The answer is 31 − x.
Answer: E
Jerry went to a shop and bought things worth Rs. 25, out of which 30 $ went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  Select the correct option:
A) 19  B) 19.7  C) 21.3  D) 21.5  E) 21.7

Solution: Total cost of the items he purchased = Rs.25   Given that out of this Rs.25, 30 $ is given as tax   => Total tax incurred = 30 $ = Rs.30/100   Let the cost of the tax free items = x   Given that tax rate = 6%   ∴ (25−30/100−x)6/100 = 30/100   ⇒ 6(25 −0.3 −x) = 30   ⇒ (25 − 0.3 − x) = 5   ⇒ x = 25 − 0.3 − 5 = 19.7   19.7)
Answer: B
In what time will a train 140 m long cross an electric pole, it its speed be 108 km/hr? Choose the correct choice from the following answers
A) 2.5
B) 4.7
C) 2.9
D) 2.3
E) 2.1

Solution: Speed = 108 * 5/18= 
108 * 5/18 = 30
30 m/sec   Time taken= 140/30   = 4.7 sec.   Answer: 4.7
Answer: B
The average of 50 numbers id 62. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
Answers:
A) 22.3
B) 33.2
C) 22.2
D) 51.3
E) 62.5

Solution: 62.5xplanation:   Total of 50 numbers = (50×62)=3100   Total of 48 numbers =(3100-(45+55)]=3000   Required average = 3000/48= 
3000/48 = 125/2 = around 62.5
62.5   Answer:62.5
Answer: E
In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by	Choose one
A) 2	B) 8	C) 1	D) 1/8	E) 1/64

Solution: Say r=2 => V1 = 1/16   when r=1; V2 = 1/4   V2 = 2*V1.   2nswer=2=2
Answer: A
The average age of three boys is 40 years and their ages are in proportion 2:6:8. What is the age in years of the youngest boy?
Choose the correct choice from the following answers
A) 8  B) 9  C) 7  D) 6  E) 5

Solution: 2x + 6x + 8x = 40   x =2.5   2x = 5   Answer:5
Answer: E
Frank is 15 years younger then John. In 3 years John will be twice as old as Frank. How old will Frank be in four years? Pick one
A) 8	B) 10	C) 12	D) 14	E) 16

Solution: Frank is 15 years younger then John --> F+15=J;   In 5 years John will be twice as old as Frank (in 3 year John will be J+3 years old and Frank will be F+3 years old) --> J+3=2*(F+3) --> (F+15)+3=2*(F+3) --> F=12;   In 4 years Frank will be 12+4= 
12+4 = 16
16 years old.   Answer: 16.
Answer: E
Abhijit started a business investing 60000. Anuja joined him after six months with an amount of 110000 and Sunil joined them with 1.2 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?
Choose the correct choice
A) 15 :18 :32
B) 24 :32 :26
C) 36 : 55 :48
D) 26 :12 :24
E) 15: 25 :35

Solution: Ratio of their investments   = 60 × 36 : 110 × 30 : 120 × 24 = 36 : 55 : 48   Answer 36 : 55 :48
Answer: C
When a train moves at an average speed of 100 kmph it reaches its destination on time. When its average speed becomes 80 kmph, then it reaches its destination 20 minutes late. Find the length of journey rounded to two decimal places. Choose the correct option: A) 99.33 km B) 133.33 km C) 125.33 km D) 156.66 km E) None

Solution: Sol.   Difference between timings = 20 min = 1/3 hr.   Let the length of journey be x km.   Then, x/80 - x/100 = 1/3   â‡” 5x - 4x = 133.33   â‡” x = 133.33 km.   Answer 133.33 km
Answer: B
The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be? Pick one: A) 22678 B) 26699 C) 26788 D) 19000 E) 26711

Solution: Money paid in cash = Rs. 1000   Balance payment = (20000 - 1000) = Rs. 19000   Answer: 19000
Answer: D
There are 10 flavors of ice cream, 3 types of nuts and 5 types of fruit at an ice cream store. If a person can choose 2 ice cream flavors as base, 2 types of nuts and 2 types of fruit. How many different variations are possible if repetition is allowed ?  Choose the correct choice from the following answers:	A) 150	B) 250	C) 22500	D) 225	E) 225000

Solution: Ice cream flavors: 10x10 = 100   Nuts: 3x3 = 9   Fruit: 5x5 = 25   Total = 22500   Answer: 22500
Answer: C
What no. should be subtracted from x^3+4x^2−7x+12x^3+4x^2−7x+12, if it is to be perfectly divisible by x+3x+3?  Choose the most appropriate option:
A) 38	B) 42	C) 45	D) 46	E) 48

Solution: According to remainder theorem when dfracf(x)x+adfracf(x)x+a, then the remainder is f(−a)f(−a).   In this case, as x+3x+3 divides x3+4x2−7x+12–kx3+4x2−7x+12–k perfectly (kk being the number to be subtracted), the remainder is 0 when the value of xx is substituted by -3.   i.e., (−3)3+4(−3)2−7(−3)+12−k=0(−3)3+4(−3)2−7(−3)+12−k=0   or −27+36+21+12=k−27+36+21+12=k   or k=k= 42   42
Answer: B
A number of 9 digits has the following properties: The number comprising the leftmost two digits is divisible by 2, that comprising the leftmost three digits is divisible by 3, the leftmost four by 4, the leftmost five by 5, and so on for the nine digits of the number i.e. the number formed from the first n digits is divisible by n, 2  Choose the correct choice from the following options:  A) 381654729  B) 381654728  C) 381655729  D) 381754729  E) 361654729

Solution: 381654729   because 38 is divided by 2   381 is divided by 3   3816 is divided by 4   38165 is divided by 5   381654 is divided by 6   3816547 is divided by 7   38165472 is divided by 8   381654729 is divided by 9   381654729NSWER:381654729
Answer: A
A room is a square of side 50 feet. A second room is of area
100 square yards. A third room is of area 200 square feet.
Which of these can seat maximum people? (Hint:1 yard=3
feet)  Choose the correct choice from the following choices.
A) 200 sq feet B) 300 sq feet C) 400 sq feet D) 500 sq feet E) 600 sq feet

Solution: first room because area 50*50= 
50*50 = 2_500
2500 sq feet   second room area 100 sq yard in feet 300 sq feet   third room area 200 sq feet   200 sq feetNSWER:200 sq feet
Answer: A
What is the price of a banana?
(a) 14 banana and 35 oranges cost Rs. 84
(b) with a 50% discount on banana, Rs. 12 can buy 4 bananas and 5 oranges Answers.
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 14X1+35X2=84   4XO.5+5X2=12   So price of banana =1 and orange=2   1NSWER:1
Answer: A
The diference of two numbers is 20% of the larger number, if the smaller number is 20, then the larger number is :	Choose the correct choice from the following.
A) 33 B) 25 C) 76 D) 28 E) 19

Solution: Explanation:   Let the large number be x.   Then x - 20 = 20x/100 <=> x - x/5 = 20 => x = 25.   Answer: 25) 25
Answer: B
In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 78% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?	Choose the correct option.
A) 69.	B) 73.	C) 53	D) 91	E) 108

Solution: Total students = 420   Boys = 312, Girls = 108   Total playing soccer = 250   78%of 250 = 195 are boys who play soccer.   Girls who play soccer = 55.   Total girls who do not play soccer = 108 - 55= 
108 - 55 = 53
53.   53orrect option: 53
Answer: C
If an item that originally sold for w dollars was marked up by u percent and then discounted by v percent, which of the following expressions represents the final price of the item?  Choose the most appropriate option
A) (10,000w + 100w(u – v) – uvw)/10,000
B) (10,000w + 100w(v – u) – uvw)/10,000
C) (100w(u – v) – uvw)/10000
D) (100w(v – u) – uvw)/10000
E) 10000 /(u – v)

Solution: Assume w=100, u=10, v=10. So final price is 99. Now put these value each option. Only option (10,000w + 100w(u – v) – uvw)/10,000 will give right answer.
Answer: A
A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x?
Choose one
A) 1/4
B) 1/3
C) 1/2
D) 1
E) 3

Solution: 1/2oncentration of salt in pure solution = 0   1/2oncentration of salt in salt solution = 60%   1/2oncentration of salt in the mixed solution = 20%   The pure solution and the salt solution is mixed in the ratio of --> (60 - 20)/(20 - 0) = 2/1   1/x --  (60 - 20)/(20 - 0)= 
--  (60 - 20)/(20 - 0) = 2
2/1   1/x= 2/1   x = 1/2   Answer: 1/2
Answer: C
How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Choose the correct option:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: B   4   By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.   Required number of number = 4.
Answer: B
In a bag, there are 5 green, 6 black and 7 red pens. One pen is picked up randomly. What is the probability that it is neither red nor green? Answers.
A) 5/18	B) 7/18	C) 1/3	D) 1/2	E) 1/5

Solution: Explanation :   Neither red nor green means the pen drawn is black.   Total number of outcomes = (5+6+7)= 
(5+6+7) = 18
18.   Number of Favourable outcomes= 6 = Number of black pens.   Hence, Probability of the event = 6/18 = 1/3.   Answer : 1/3
Answer: C
The ratio of earnings of A and B is 4:5. If the earnings of A increase by 20% and the earnings of B decrease by 20%, the new ratio of their earnings becomes 6:5. What are A's earnings?
Choose the correct choice from the following answers
A) 375099  B) 37500  C) 27899  D) 28778  E) 19911

Solution: Explanation:   Let length = x meters, then breadth = 0.6x   Given that perimeter = 800 meters   => 2[ x + 0.6x] = 800   => x = 250 m   Length = 250m and breadth = 0.6 * 250= 
0.6 * 250 = 150
150m   Area= 250 * 150= 
250 * 150 = 37_500
37500 \fn_jvn {\color{37500lue}m^{2}}   Answer: 37500
Answer: B
Magnabulk Corp sells boxes holding z magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?	Choose the correct choice from the following options:
A) 100m/(bz)	B) 100bz/m	C) bz/(100m)	D) m/(bz)	E) bz/m

Solution: We're given some facts to work with:   1) Magnabulk Corp sells boxes holding Z magnets each.   2) The boxes are shipped in crates, each holding B boxes.   3) Magnabulk charges M DOLLARS for each crate   We're asked for the price charged per magnet, in CENTS....   IF....   Z = 2   B = 3   M = 12   (2 magnets per crate)(3 crates) = 6 magnets   $12 for 6 magnets = $2 per magnet = 200 cents per magnet   So we're looking for an answer that equals 200 when Z=2, B=3 and M=12. There's only one answer that matches...   100m/(bz)nswer is 100m/(bz)
Answer: A
In a 100m race, Sam beats John by 5 seconds. On the contrary, if Sam allowed John to start 35m ahead of Sam, then Sam and John reach the finishing point at the same time. How long does Sam take to run the 100m race?
Choose the correct option:
A) 13 seconds
B) 25 seconds
C) 29 seconds
D) 21 seconds
E) 6.25 seconds

Solution: Their difference is 5 second but this difference is 0 if john allows Sam to start the race from 35m ahead . that means Jhon was 35m away from finishing line when they started together . so He will cover 35 m in 5 seconds . so his speed =35/5= 
35/5 = 7
7 metre / second . so time taken=100/5= 
100/5 = 20
20 seconds . so Sam took= 13 seconds .   correct answer = 13 seconds
Answer: A
The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec. respectively .If they all change simultaneously at 8:20:00 hours, then at what time they again change simultaneously .  Options.
A) 8:27:12
B) 8:25:12
C) 8:26:12
D) 8:24:12
E) None of them

Solution: Interval of change = (L.C.M of 48,72,108)sec.=432sec.   So, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec   Hence , next simultaneous change will take place at 8:27:12 hrs.   8:27:12nswer is 8:27:12.
Answer: A
The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?  Choose the correct choice from the following answers.
A) 7 years	B) 9 years	C) 6 years	D) 4 years	E) 5 years

Solution: 28 * 2= 
28 * 2 = 56
56   20 * 3= 
20 * 3 = 60
60   -----------   4 years   Answer: 4 years
Answer: D
If in a certain sequence of consecutive multiples of 50, the median is 525, and the greatest term is 950, how many terms that are smaller than 525 are there in the sequence?
Choose the correct choice:
A) 6
B) 9
C) 8
D) 12
E) 13

Solution: Since the median is 525 we know there must be a even number of integers because 50 is not a multiple of 525.   So the list around 525 must go.500 (525) 550 600 650 700 750 800 850 900 950   Since we know there are 9 numbers greater than 525 then there must be 9 numbers less then 525.   answer:9
Answer: B
If the average marks of three batches of 49, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is  Choose the correct choice from the following
A) 54.87	B) 54.68	C) 54.6	D) 54.58	E) None of these

Solution: Explanation:   =(49*50+60*55+45*60)/(49+60+45)=54.87   54.87nswer: Option 54.87
Answer: A
1/4 of all the juniors and 2/3 of all the seniors are going on a trip. If there are 2/3 as many juniors as seniors, what fraction of the students are not going on the trip? Choose the correct choice from the following answers.
A) 4/9
B) 1/2
C) 2/3
D) 1/3
E) 5/6

Solution: J be the number of Juniors and S be the number of Seniors.   there are 2/3 as many juniors as seniors   23∗S=J   J/S=23   Going on Trip = J4+23∗S   Fraction = (J4+23S)/(J+S)   = (2/3*1/4 + 2/3 )/ (2/3 +1 )   = 1/2   Fraction not on trip = 1/2   ANSWER:1/2
Answer: B
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?  Options:  A) 1/455  B) 1/478  C) 1/428  D) 1/459  E) 1/429

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.   Probability that all the three marbles picked at random are blue   = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)   = 1/455   1/455nswer:1/455
Answer: A
An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent J of the gasoline in the tank is brand Z? Choices:  A) 50%  B) 40%  C) 37.5%  D) 331⁄3%  E) 25%

Solution: Work with fraction of brand Z in the tank.   1st step: brand Z is 1   2nd step: brand Z is 1/2   3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4   4th step: brand Z is (1/2)*(3/4) J= 3/8 = 37.5%   Answer (37.5%)
Answer: C
For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 4| + |-b| + |b – a| + |ab| = Select.
A) a-b+4	B) ab-b+4	C) ab + 2b + 4	D) 2ab+b+2	E) ab+2b+2

Solution: Observation-1: |a – b| = b – a   which is possible only when signs of a and b are Same   Since Given a > 0   so we figure out that a and b are both positive   Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a   Now you may choose the values of a and b based on above observations   e.g. b = 4 and a=1 and check the value of given functions and options   |a + 4| + |-b| + |b – a| + |ab| = |1 + 4| + |-4| + |4 – 1| + |1*4| = 16   ab + 2b + 4= 1*4+8+4= 
1*4+8+4 = 16
16   all other options are not equal to 16   Answer : ab + 2b + 4
Answer: C
The cost of 10 grams of gold was $75 in 2001. In 2015, the price had increased to $400. What was the percent increase in the cost of the 10 grams of gold?
Choose the most appropriate option:	A) 255%	B) 433.3%	C) 325%	D) 125.5%	E) 300.98%

Solution: Increase = 400-75= 
400-75 = 325
325   % increase= 325*100/75 = 433.3%   Answer: option 433.3%
Answer: B
Solve for x and check: 25x = 675 Options:
A) 675	B) 725	C) 895	D) 1025	E) None of these

Solution: Solution : Dividing each side by 25, we obtain   (25x/675)=(675/25)= 
(675/25) = 27
27   Check :   25x=675   (25*27)= 
(25*27) = 675
675   675=675   675NSWER : 675
Answer: A
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?  Choices.
A) 276  B) 289  C) 220  D) 400  E) 278

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer: 400
Answer: D