mathewhe/aqua_rat huggingface dataset:
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
(A) 18 years
(B) 12 years
(C) 5 years
(D) 9 years
(E) 21 years
Rationale: Answer: Option A
Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
Answer: (A) 18 years
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 912 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
(A) 320
(B) 350
(C) 340
(D) 360
(E) 400
Rationale: You know that the answer is going to be three digits, and it's easy to figure out how many 1 and 2 digit numbers (9 and 90), so the real question is how many 3 digit number are there?
99+(912-9-90*2)/3=340
Answer : C
Answer: (C) 340
Question: The compound interest on $ 30,000 at 7% p.a is $. 4347.Find out the period (in years) ?
(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3
Rationale: Amount = 30,000 + 4347
= 34347 ......... Now by using compound interest formula we get, 30,000 * (107/100)^n = 34347 ====> n = 2 years Ans - C
Answer: (C) 2
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 50 hrs and a machine of type S does the same job in 20 hours. If the company used the same number of each type of machine to do the job in 5 hours, how many machines of type R were used?
(A) 18/7
(B) 16/7
(C) 15/7
(D) 22/7
(E) 20/7
Rationale: Rate of machine R =1/50
Rate of machine S =1/20
since same no of machines used for R and S to do the same work in 5 hrs
So collective rate needed to finish the work in 5 hrs= 1/5
Let the no of machine be x
So, x/50 +x/20 =1/5
(2x+5x)/100=1/5
7x=20
x=20/7
So no of machine R is 20/7
Answer E
Answer: (E) 20/7
Question: In 2 Kg mixture of copper and aluminium, 30% is copper. How much aluminium powder should be added to the mixture so that the proportion of copper becomes 20%
(A) 800 gm
(B) 600 gm
(C) 1200 gm
(D) 900 gm
(E) 1000 gm
Rationale: Mixture = 2 kg = 2000g.
Copper = 30% of 2000 = 600g.
To make copper 20% of mixture, we should need to mix 1000g of Aluminum.
As,
2000 + 1000 = 3000g mixture.
And 20% of 3000 = 600g.
ANSWER : B
Answer: (B) 600 gm
Question: In an election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 15000
(B) 15500
(C) 16800
(D) 17500
(E) 18000
Rationale: Let the number of votes enrolled be x. Then ,
Number of votes cast =75% of x. Valid votes = 98% of (75% of x).
75% of (98% of (75%of x)) =9261.
[(75/100)*(98/100)*(75/100)*x] =9261.
X = [(9261*100*100*100)/(75*98*75)] =16800.
ANSWER C
Answer: (C) 16800
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 1 and 100?
(A) 1250
(B) 1530
(C) 2120
(D) 2540
(E) 2550
Rationale: Average of the set: (largest+smallest)/2=(100+2)/2=51;
# of terms: (largest-smallest)/2+1=(100-2)/2+1=50
The sum = 51*50= 2550
Answer: E
Answer: (E) 2550
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 3.5 years
(B) 4years
(C) 4.5years
(D) 5years
(E) None of these
Rationale: Explanation:
Time = (100 x 81)/(450 x 4.5) years
= 4 years.
Answer: B
Answer: (B) 4years
Question: A certain company expects quarterly earnings of $0.80 per share of stock, half of which will be distributed as dividends to shareholders while the rest will be used for research and development. If earnings are greater than expected , shareholders will receive an additional $0.04 per share for each additional $0.10 of per share earnings. If quarterly earnings are $1.10 per share, what will be the dividend paid to a person who owns 500 shares of the company's stock?
(A) $260
(B) $96
(C) $26
(D) $120
(E) $240
Rationale: EPS Actual> EPS expected.
each gets and additional .12 per share.
Thus .52*500 --> $260
answer is A
Answer: (A) $260
Question: If the radius of a circle is decreased by 50%, find the percentage decrease in its area.
(A) 25 %
(B) 50 %
(C) 75 %
(D) 95 %
(E) None of them
Rationale: Let original radius = R. New radius =(50/100) R = (R/2)
Original area=22/7( R )2= and new area=  ((R/2))2= ( ( R )2)/4
Decrease in area =((3(22/7) (R )2 )/4 X (1/(22/7)( R)2) X 100) % = 75%
Answer is C.
Answer: (C) 75 %
Question: I sold a book at a profit of 10%. Had I sold it for $90 more, 15% would have been gained. Find the cost price?
(A) $1800
(B) $2500
(C) $3000
(D) $3120
(E) $1540
Rationale: 115% of cost - 110% of cost = $90
5% of cost = $90
cost = 90*100/5 = $1800
Answer is A
Answer: (A) $1800
Question: A, B, C and D enter into partnership. A subscribes 1/3 of the capital B 1/4, C 1/5 and D the rest. How much share did A get in a profit of Rs.2460?
(A) 12211
(B) 22777
(C) 29777
(D) 14000
(E) 21689
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer:D
Answer: (D) 14000
Question: Mr. Evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children. If Mr. Evans has 2 children and 6 grandchildren, then approximately what percentage of Mr. Evans estate will each grandchild receive?
(A) 20%
(B) 17%
(C) 5.5%
(D) 3.3%
(E) 2.8%
Rationale: 33.33/6=5.5
Answer : C
Answer: (C) 5.5%
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
(A) 3
(B) 87
(C) 42
(D) 767
(E) 27
Rationale: Explanation:
required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154 = 42 sq cm.
Answer: C) 42
Answer: (C) 42
Question: If 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 176
(B) 253
(C) 342
(D) 458
(E) 560
Rationale: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.
The number of ways to select 2 lines from 23 lines is 23C2 = 253
The answer is B.
Answer: (B) 253
Question: Farmer Charlie has a chicken farm. On a certain day, Charlie calculates in how many days he will run out of chicken-food. He notices that if he would sell 75 of his chickens, he could feed the remaining chickens twenty days longer with the chicken-food he has, and that if he would buy 100 extra chickens, he would run out of chicken-food fifteen days earlier.
One chicken lays two eggs in three days. How many eggs do three chickens lay in nine days?
(A) 11
(B) 17
(C) 18
(D) 20
(E) 23
Rationale: C
18
1 chicken lays 2 eggs in 3 days, so 3 chickens lay 3×2=6 eggs in 3 days. In 9 days, these 3 chickens lay 3 times as much eggs as in 3 days. Conclusion: three chickens lay 3×6=18 eggs in nine days.
Answer: (C) 18
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
(A) 1hour
(B) 2hour
(C) 3hour
(D) 4hour
(E) 5hour
Rationale: Let the duration of the flight be x hours
Then 600/x - 600/x (1/2) = 200
= 600/x - 1200/2x+1 =200
=x(2x+1) =3
=2xsquare + x -3 = 0
=(2x+3)(x-1) = 0
= x= 1 hr ( neglecting the -ve value of x)
Answer: Option A
Answer: (A) 1hour
Question: Two numbers are in the ratio 3 : 4. If their L.C.M. is 72. what is sum of the numbers?
(A) 42
(B) 56
(C) 76
(D) 84
(E) 85
Rationale: Explanation:
Let the numbers be 3x and 4x
LCM of 3x and 4x = 12x (Since LCM of 3 and 4 is 12. Hence LCM of 3x and 4x is 12x)
Given that LCM of 3x and 4x is 72
=> 12x = 72
=> x = 72/12 = 6
Sum of the numbers
= 3x + 4x
= 7x
= 7 x 6 = 42
Answer: Option A
Answer: (A) 42
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 14 minutes more to walk to work than to ride his bike to work, then x equals?
(A) 4
(B) 7
(C) 10
(D) 15
(E) 21
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 840(which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=840 ----> 40x=840-> x = 21.
option E
Answer: (E) 21
Question: In how many E ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 30
Rationale: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning E= 24 - 6 = 18
Answer: C
Answer: (C) 18
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts seven hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 3
(B) 4.5
(C) 4
(D) d) 5.5
(E) e) 14
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 7+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(7+T) = 40*T
T = 21 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*21/60 = 14 hrs
Time taken by A = 7+T = 7+21 = 28 hrs
Time taken by K = 14 hrs
So K starts 28-14 = 14 hrs after A. (ANSWER E)
Answer: (E) e) 14
Question: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?
(A) 6 2/3%
(B) 6 2/8%
(C) 7 2/3%
(D) 6 5/3%
(E) 4 2/3%
Rationale: 4/9 P = (P*R*R)/100
R = 20/3 = 6 2/3%
Answer:A
Answer: (A) 6 2/3%
Question: If Rs.450 amount to Rs.540 in 4 years, what will it amount to in 6 years at the same rate % per annum?
(A) 338
(B) 277
(C) 585
(D) 676
(E) 181
Rationale: 90 = (450*4*R)/100
R = 5%
I = (450*6*5)/100 = 135
450 + 135 = 585
Answer:C
Answer: (C) 585
Question: In an exam, Amar scored 49 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
(A) 344
(B) 826
(C) 207
(D) 269
(E) 208
Rationale: Average mark scored by all the three boys =
[49/100 (800) + 36/100 (800) + 44/100 (800)] / 3
= 344
Answer: A
Answer: (A) 344
Question: X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year?
(A) 3:1
(B) 2:1
(C) 2:5
(D) 2:3
(E) 6:1
Rationale: Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 45000 * 12: 30000 * 9
= 45 * 12: 30 * 9
= 3*12: 2 * 9
= 2:1
Answer is B
Answer: (B) 2:1
Question: With both inlets open, a water tank will be filled with water in 36 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
(A) 9,000
(B) 4,500
(C) 1,750
(D) 1,000
(E) 2,000
Rationale: The work Done by Inlet A and B together in 1 min = 1/36
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/36)- (1/120) =1/51
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/51)- (1/120) = 50 Cubic meter
i.e.4500 Cubic Meter
Answer: option B
Answer: (B) 4,500
Question: What is the greatest of 3 consecutive integers whose sum is 27 ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 11
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 27;
=> 3n = 27;
=> n = 9
The greatest of the three numbers is therefore 9 + 2 = 11 Answer: E
Answer: (E) 11
Question: The difference between the simple and the compound interest compounded every six months at the rate of 10% p.a. at the end of two years is 124.05. What is the sum?
(A) 10,000
(B) 6,000
(C) 12,000
(D) 8,000
(E) None of these
Rationale: Let the sum be x.
Then, [x(1+5/100)4−x]−[x×10×2/100]=124.05
Solving the above eqns, we get x = 8,000.
Answer D
Answer: (D) 8,000
Question: Maria sold 10kg of apples in her first hour at the market, but only 2kg of apples in the second hour. On average, how many kg of apples did she sell in two hours at the market?
(A) 6 kg
(B) 5 kg
(C) 12 kg
(D) 24 kg
(E) 20 kg
Rationale: (10 kg + 2kg)/2 = 6 kg
Correct answer is: A
Answer: (A) 6 kg
Question: If 3 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King, one of them will be Queen and one of them will be Jack?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen and 1 jack in each suit
(A) 96/5525
(B) 48/5525
(C) 16/5525
(D) 8/16575
(E) 1/2197
Rationale: Let K,Q and J represent King, Queen and Jack respectively.
One possible combination is KQJ and this can be arranged in 3! ways.
Probability of KQJ = (4/52)*(4/51)*(4/50)
Total probability = 3! * (4/52)*(4/51)*(4/50) . No need for final calculation. Reduce this to simpler form and you only have 1 option with 16 in the numerator. C is the correct answer.
Answer: (C) 16/5525
Question: Tough and Tricky questions: Combinations.
Nine students - 4 boys and 5 girls - are to sit side by side for a makeup exam. How many ways could they arrange themselves given that no two boys and no two girls can sit next to one another?
(A) 12
(B) 36
(C) 72
(D) 240
(E) 5760
Rationale: 4!*5!*2 = 24*120*2 = 5760 ways.
Ans. E) 5760
Answer: (E) 5760
Question: The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time will they meet?
(A) 10.30 a.m
(B) 11 a.m
(C) 10 a.m
(D) 12 noon
(E) None of these
Rationale: Explanation:
Assume that they meet x hours after 8 a.m.
Then,train1,starting from A , travelling towards B, travels x hours till the trains meet
⇒Distance travelled by train1 in x hours = Speed ×Time = 60x
Then, train2, starting from B , travelling towards A, travels (x-1) hours till the trains meet
⇒Distance travelled by train2 in (x-1) hours = Speed ×Time = 75(x-1)
Total distance travelled = Distance travelled by train1 + Distance travelled by train2
=> 330 = 60x + 75(x-1)
=> 12x + 15(x-1) = 66
=> 12x + 15x - 15 = 66
=> 27x = 66 + 15 = 81
=> 3x = 9
=> x = 3
Hence the trains meet 3 hours after 8 a.m., i.e. at 11 a.m.
Answer: Option B
Answer: (B) 11 a.m
Question: If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectangles can be formed in the chess board?
(A) 1136
(B) 1268
(C) 1244
(D) 1296
(E) 1308
Rationale: Here m = 9, n = 9
Hence, number of rectangles that can be formed
= mC2 × nC2
= 9C2 × 9C2 = (9C2)^2
= 36^2
=1296
Ans-D
Answer: (D) 1296
Question: Jessica can text 125 words per minute, while Maurice can text 10 words per minute. An abridged English translation of Tolstoy’s War and Peace contains 410,400 words. Working together, how many days will it take Jessica and Maurice to text the entire abridged translation of War and Peace?
(A) 0.3
(B) 2.1
(C) 3
(D) 9
(E) 11.3
Rationale: Since the answer choices are reasonably spaced out, we can approximate and save time
Combined words per day = 135*60*24 which should be 194400
410400/194400 will be 2.1,
So, Answer should be B.
Answer: (B) 2.1
Question: A certain manufacturer of cake, muffin, and bread mixes has 100 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 18 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) 1/10
(B) 3/10
(C) 1/2
(D) 7/25
(E) 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 100
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-18-2CMB = 100
B-CB-MB-2CMB = 28
hence the probability = 28/100 = 7/25.
D
Answer: (D) 7/25
Question: The cash difference between the selling prices of an article at a profit of 6% and 8% is Rs 3. The ratio of two selling prices is
(A) 51:52
(B) 52:53
(C) 53:54
(D) 54:55
(E) None of these
Rationale: Explanation:
Let the Cost price of article is Rs. x
Required ratio = (106% of x) / (108% of x)
=106/108
=53/54 = 53:54.
Answer: C
Answer: (C) 53:54
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
(A) 22
(B) 20
(C) 99
(D) 88
(E) 76
Rationale: P = (P*5*R)/100
R = 20%
Answer: B
Answer: (B) 20
Question: Which of the following points is symmetric with y=x at (1,2)?
(A) (-2,-1)
(B) (-2,1)
(C) (2,1)
(D) (-1,-2)
(E) (-1,2)
Rationale: We can think of line y = x as a mirror. Any point (x,y) becomes (y,x) when it isreflectedover the mirror. Reverse the coordinate and keep the same sign. These two points will be symmetric to the line y = x.
(1,2) would become (2,1).
Answer (C).
Answer: (C) (2,1)
Question: A machine puts c caps on bottles in m minutes. How many seconds will it take to put caps on b bottles?
(A) 60bm/c
(B) bm/60c
(C) bc/60m
(D) 60b/cm
(E) b/60cm
Rationale: A machine puts c caps on bottles in m minutes.
So, the machine puts 1 cap in m/c minutes
To put caps on b bottles, the machine will take bm/c minutes
In order to calculate the no. of hours taken , multiply the product by 60.
So, our answer is bm60/c
Answer : A
Answer: (A) 60bm/c
Question: Oak trees line both sides of a street for a length of 6/8 of a kilometer. If there is 12 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
(A) a)	59
(B) b)	23
(C) c)	24
(D) d)	44
(E) e)	46
Rationale: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.
6/8 of 1 km = 750 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*12 = 750
Solve for x and we get x = 59, answer is A
Answer: (A) a)	59
Question: A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?
(A) 2 days
(B) 8 days
(C) 6 days
(D) 8 days
(E) 9 days
Rationale: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: B
Answer: (B) 8 days
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers T are there between 6* + 2 and 6* + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes T in this range.
Answer: A.
Answer: (A) None
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-half of the males and three-fourths of the females in the class?
(A) 218
(B) 226
(C) 234
(D) 242
(E) 250
Rationale: 1/2*2/5 + 3/4*3/5 = 4/20 + 9/20 = 13/20
The number of degrees is 13/20 * 360 = 234 degrees
The answer is C.
Answer: (C) 234
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 1/9%
(C) 33 1/3%
(D) 33 8/3%
(E) 33 2/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3%
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7, 8, 9}(repetition of digits is not allowed)?
(A) 840
(B) 697
(C) 278
(D) 279
(E) 274
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is
7Pâ‚„ =7* 6 * 5 * 4
= 840.
Answer: A
Answer: (A) 840
Question: (1^2+2^2+3^2+.....+12^2)=?
(A) 330
(B) 345
(C) 365
(D) 385
(E) 650
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=12
=(1/6x12x13x25)
=650
Answer is E.
Answer: (E) 650
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 286 m
(B) 278 m
(C) 278 m
(D) 150 m
(E) 276 m
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150 m
Question: Two friends want to buy a snack. They combine their money and find they have $3.10, consisting of quarters, dimes, and nickels. If they have 28 coins and the number of quarters is half the number of nickels, how many quarters do they have?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the number of quarters. Then 2x is the number of nickels.
(1) 25x + 10x + 10D = 310. Then 7x + 2D = 62
(2) 3x + D = 28. Then 6x + 2D = 56
Let's subtract equation (2) from equation (1).
x = 6
The answer is D.
Answer: (D) 6
Question: Given a collection of points P in the plane a 1-set is a point in P that can be separated from the rest by a line; i.e the pint lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P) . The maximum value of n1(P) over all configurations P of 4 points in the plane is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: maximum no of 1-sets will be the no of points itself...as in even a simple configuration we can separate one point from others to make it 1-set
ANSWER:A
Answer: (A) 1
Question: John received a 10% raise each month for three consecutive months. What was his salary after the three raises if his starting salary was $1,000 per month?
(A) $1,248
(B) $1,300
(C) $1,331
(D) $1,410
(E) $1,463
Rationale: 1,000 + 100 (10%) = 1,100
1,100 + 110 (10%) = 1,210
1,210 + 121 (10%) = 1,331
Answer: C
Answer: (C) $1,331
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
(A) 32.5
(B) 32.4
(C) 32.1
(D) 32.9
(E) 32.3
Rationale: 36/7 r = 6.3 = 32.4
Answer:B
Answer: (B) 32.4
Question: In a survey about potential presidential candidates A and B, 39% of the public like A and 57% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
(A) 28%
(B) 35%
(C) 43%
(D) 22%
(E) 61%
Rationale: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
39% + 57% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 24% and 2x = 48%
100% = 24% + 48% + Neither
Neither = 28%
The answer is A.
Answer: (A) 28%