mathewhe/aqua_rat huggingface dataset:
Question: Martha has 5 dogs and 4 cats. She takes each animal separately for a daily walk. She can take the animals for a walk to the park or to the barber shop. How many different options for a walk with a single animal does Martha have?
(A) 8
(B) 9
(C) 10
(D) 18
(E) 20
Rationale: 5 dogs, 4 cats; park/barber shop
1 dog - 2 options - either park or barber shop, so, 5 dogs - 10 options and 4 dogs - 8 options.
Total = 18 options.
ANS:D
Answer: (D) 18
Question: A retailer sold an appliance for $70. If the retailer's gross profit on the appliance was 25 percent of the retailer's cost for the appliance, how many dollars was the retailer's gross profit?
(A) $14
(B) $16
(C) $20
(D) $24
(E) $25
Rationale: Gross Profit = Selling price - Cost = 70-x
70-x = 1/4x
x = 56
GP = 70-56 = 14
Answer: (A) $14
Question: If $1000 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years?
(A) 1000 (1.056)(3)
(B) 1000 (3+1.056)
(C) 1000 (1+3(0.056))
(D) 1000 (1+(0.056)^3)
(E) 1000 (1.056)^3
Rationale: 1000 * 1.056 * 1.056 * 1.056 = 1000 * 1.056^3.
ANSWER:E
Answer: (E) 1000 (1.056)^3
Question: What is the smallest integer a > 0 such that the inequality
1/n + 1
+
1/n + 2
+...+
1/2n + 1
< a - 2010-
1/3
is satisfied for all positive integers n?
(A) 2011
(B) 2012
(C) 2013
(D) 2014
(E) 2015
Rationale: Plugging in n = 1, we see that a > 2011. On the other hand, since there are n + 1
terms, and all of them are at most 1=(n + 1), the expression is at most 1, which means that
a = 2012 works.
correct answer B
Answer: (B) 2012
Question: What is the rate percent when the simple interest on Rs.1200 amount to Rs.160 in 4 Years?
(A) 3.3%
(B) 7%
(C) 9%
(D) 2%
(E) 4%
Rationale: 160 = (1200*4*R)/100
R = 3.3%
Answer: A
Answer: (A) 3.3%
Question: Convert the following unit:
2.1 hectares in ares
(A) 200 ares.
(B) 210 ares.
(C) 220 ares.
(D) 230 ares.
(E) 240 ares.
Rationale: 2.1 hectares in ares
1 hectare = 100 ares
Therefore, 2.1 hectares = 2.1 × 100 ares
= 210 ares.
ANSWER : OPTION B
Answer: (B) 210 ares.
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number W and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number W of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: (D) 88
Question: In a bag there are a certain number of black balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of black balls to white balls in the bag
(A) 1:2
(B) 2:1
(C) 1:1
(D) 4:1
(E) 1:4
Rationale: since the probability of drawing a white ball out of two picks is 1/2.
the ratio of the white ball to black balls should be 1:1
C
Answer: (C) 1:1
Question: A person crosses a 600m long street in 5minnutes. What is his speed in km per hour?
(A) 5.8km/hr
(B) 7.2km/hr
(C) 9km/hr
(D) 2.5km/hr
(E) 3km/hr
Rationale: Speed = 600/5*60 = 2m/sec
=2*18/5
=7.2km/hr
Answer is B
Answer: (B) 7.2km/hr
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 440. What is the sum of the last 8 of the even integers?
(A) 568
(B) 584
(C) 596
(D) 604
(E) 612
Rationale: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 440
The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =
440 + 8(16) = 440 + 128 = 568
The answer is A.
Answer: (A) 568
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 324 metres
(D) 100 metres
(E) 180 metres
Rationale: Speed=(60 x 5/18)/m/sec	=	50/3	m/sec.
Length of the train = (Speed x Time).
Length of the train =	50 x 6/3 m = 100 m.
ANSWER : OPTION D
Answer: (D) 100 metres
Question: What is the solution of the equations x - y = 0.5 and 1(x + y)-1 = 2 ?
(A) x = 0.5, y = 0
(B) x = 1, y = 0.1
(C) x = 2, y = 1.1
(D) x = 1.2, y = 0.3
(E) None
Rationale: Answer
x - y = 0.5 ...(i)
and 1(x + y)-1=2
⇒ 1/ (x + y) = 2
⇒ 2(x + y) =1
⇒ x + y = 1/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 0.5
and y = 0
Correct Option: A
Answer: (A) x = 0.5, y = 0
Question: In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 60 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
(A) A)0.9
(B) B)0.6
(C) C)0.45
(D) D)0.3
(E) E)0.25
Rationale: Percent of students who are 25 years old or older is 0.6*48+0.2*52=~39, so percent of people who are less than 25 years old is 100-39=61.
Answer: B.
Answer: (B) B)0.6
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 12
(B) 16
(C) 18
(D) 19
(E) 11
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer: C
Answer: (C) 18
Question: Find the cost of fencing around a circular field of diameter 42 m at the rate of Rs.5 a meter?
(A) 655.9
(B) 659.75
(C) 650.57
(D) 655.9
(E) 600.3
Rationale: 2 * 22/7 * 14 = 131.95
131.95 * 5 = Rs.659.75
Answer: B
Answer: (B) 659.75
Question: An man deposited $10000 in his bank account with a compound interest rate of 20%. How many years it will take to get the amount increased by 50%?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 1 year: 100/4= $25: Total: 125
2nd year: 125/4 = $31: Total: 125+31= 156 >150
ANSWER:B - 2 years
Answer: (B) 2
Question: Susan weighs 15 pounds more than Anna does, and together they weigh a total of 145 pounds. Which of the following represents Anna’s weight in pounds?
(A) 60
(B) 65
(C) 63
(D) 64
(E) 61
Rationale: Total weight = 145
Anna's weight = 145-15 /2 = 65
Answer : B
Answer: (B) 65
Question: In expressing a length 81.479 km as nearly as possible with three significant digits, find the percentage error?
(A) 0.075%
(B) 0.156%
(C) 0.026%
(D) 0.048%
(E) 0.152%
Rationale: Error = 81.5-81.479 = 0.021
Required percentage = (0.021/81.479)*100 = 0.026%
Answer is C
Answer: (C) 0.026%
Question: What is the Mode of the following data set S- {1,2,6,9,6,6,10}
(A) 9
(B) 6
(C) 10
(D) 1
(E) 2
Rationale: Mode of a set is the data point that is repeated the most number of times. In the set given, 6 is repeated.
Answer: B
Answer: (B) 6
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 50 years now, the son's age five years back was:
(A) 19 years
(B) 14 years
(C) 33 years
(D) 38 years
(E) 20 years
Rationale: Let the son's present age be x years.
Then, (50 - x) = x
2x = 50 => x = 25
Son's age 5 years back = (25 - 5) = 20 years.
ANSWER:E
Answer: (E) 20 years
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 5 inches wide on each side, the total area would have been (M + 144) square inches. What is the perimeter of the photograph, in inches?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+10)(y+10)=M and so (2) xy + 10x + 10y + 100 = M+144
Let's subtract equation (1) from equation (2).
8x + 8y + 96 = 144
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.
Answer: (B) 12
Question: A family pays $800 per year for an insurance plan that pays 70 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.
(A) $1,000
(B) $1,200
(C) $1,400
(D) $1,800
(E) $2,200
Rationale: Upfront payment for insurance plan = 800$
Family needs to pay 30 % of first 1000 $ in expense = 300$
Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 300 = 1100 $
Total amount paid by insurance plan for first 1000 $ = 800 $
Total amount paid by family will equal amount paid by plan when medical expense = 1400 $
(Since insurance plan will pay 100% of amount that exceeds 1100$ )
Answer C
Answer: (C) $1,400
Question: Can you find the missing number in the sequence below
14 -20 34 -54 ? -144
(A) 55
(B) 99
(C) 77
(D) 66
(E) 88
Rationale: E
88
Explanation:
14 -20 34 -54 ? -144
The number is difference between right number and left number.
i.e
example
14-(-20) = 34
-20-(34) = -54
34-(-54) = 88 answer
-54-(88) = -143
Answer: (E) 88
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 180. The dividend from the stock is :
(A) 7.5 %
(B) 8 %
(C) 11.25 %
(D) None of these
(E) Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 180.
By investing Rs. 97, income = Rs. (180/1552x97)= Rs.11.25
âˆ´ Dividend = 11.25%.
Answer C
Answer: (C) 11.25 %
Question: Consider two statements
Statement 1 => If A is an integer and A=2p+1 where p is not an integer.
Statement 2 => If B is an integer and B=2q where q is not an integer
Which of the following correctly specifies the Even/Odd nature of A and B respectively
(A) 1) Odd,Even
(B) 2) Odd,Odd
(C) 3) Even,Odd
(D) 4) Even,Even
(E) 5) Cannot be determined
Rationale: answer will be E
A = integer
A = 2p+1 = integer here p can be any n/2 and n can be even or odd , matters alot 2 get cancelled out
if n were even A would odd
if n odd A would be even
ANSWER IS E
Answer: (E) 5) Cannot be determined
Question: A box contains 12 mangoes out of which 4 are spoilt. If four mangoes are chosen at random, find the probability that A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?
(A) 17/30
(B) 2/5
(C) 11/30
(D) 4/15
(E) 7/15
Rationale: The probability that the number is a multiple of 3 is 10/30. (Since 3*10 = 30).
Similarly the probability that the number is a multiple of 13 is 2/30. {Since 13*2 =
26).
Neither 3 nor 13 has common multiple from 1 to 30. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 3 or 13 is (10+2)/30 = 2/5.
ANSWER:B
Answer: (B) 2/5
Question: What is the sum of the different positive prime factors of 600?
(A) 5
(B) 7
(C) 10
(D) 17
(E) 24
Rationale: The prime factorization of 600
= 60 * 10
= 2^2*15 * 2*5
= 2^2*3*5 * 2*5
The sum of the different positive prime factors = 2+3+5 = 10
The answer is C.
Answer: (C) 10
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 18 minutes, how much time will she spend doing yoga? (rounded to minutes)
(A) 30 min.
(B) 41 min.
(C) 17 min.
(D) 23 min.
(E) 25 min.
Rationale: The ratio is 2:3 = gym:ride, so (18)(3/2) = 27 minutes at the gym, and 27 + 18 = 45 minutes exercise, so (2/3)(45) = 30 minutes yoga.
Answer: A
Answer: (A) 30 min.
Question: One boy forgot the last digit of a 7 digit telephone no. If he randomly dialthe final 3 digits after correctly dialing the 1st four, then what is the chance of dialing the correct no.?
(A) 1/500
(B) 2/455
(C) 1/1000
(D) 3/1000
(E) 4/1000
Rationale: it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C
Answer: (C) 1/1000
Question: A rectangular window is twice as long as it is wide. If its perimeter is 14 feet, then what are its dimensions in feet?
(A) 3/2 by 7/2
(B) 7/3 by 14/3
(C) 2 by 4
(D) 3 by 6
(E) 10/3 by 20/3
Rationale: Let x be the width of the window. Then the length is 2x.
x+2x+x+2x = 14
6x = 14
x = 14/6 = 7/3
The width is 7/3 and the length is 14/3.
The answer is B.
Answer: (B) 7/3 by 14/3
Question: A certain sum amounts to Rs.1525 in 3 years and Rs.1875 in 5 years. Find the rate % per annum?
(A) 6.76%
(B) 3.76%
(C) 5.26%
(D) 5.76%
(E) 4.76%
Rationale: 3 --- 1525
5 --- 1875
--------------
2 --- 350
N = 1 I = 75 R = ?
P = 1525 - 225 = 1300
75 = (1300*1*R)/100
R = 5.76%
ANSWER:D
Answer: (D) 5.76%
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 do
they meet?
(A) 10 am
(B) 11 am
(C) 12 pm
(D) 1 pm
(E) None of these
Rationale: Explanation:
Suppose they meet x hrs after 8 a.m.
then
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]
= 330
So, 60x+75(x-1) = 330
x=3.
So,they meet at (8+3). i.e 11a.m.
Answer: B
Answer: (B) 11 am
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 999
(B) 279
(C) 120
(D) 99
(E) 21
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6
= 120 m.
Answer: C
Answer: (C) 120
Question: In 2003 there are 28 days in February and 365 days in a year in 2004 there are 29 days in February and 366 days in the year. If the date march 11 2003 is Tuesday, then which one of the following would the date march 11 2004 would be?
(A) 21
(B) 2
(C) 8
(D) 7
(E) 11
Rationale: If 11-3-2003 is Tuesday, Then 11-3 - 2004 is Thursday
The number of odd days between the two dates are [3667]Rem[3667]Rem= 2.
Answer:B
Answer: (B) 2
Question: If a light flashes every 6 seconds, how many times will it flash in 1/3 of an hour?
(A) 101
(B) 201
(C) 301
(D) 401
(E) 501
Rationale: In 1/3 of an hour there are 20*60 = 1200 seconds
The number of 6-second intervals = 1200/6 = 200
After the first flash, there will be 200 more flashes for a total of 201.
The answer is B.
Answer: (B) 201
Question: If there are 11 containers and 562,156 apples, how many apples should be removed to equally distribute them across the containers?
(A) 5
(B) 0
(C) 1
(D) 8
(E) 3
Rationale: Given:
There are 11 containers
This means, the total number of apples should be divisible by 11
Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number.
562156 => (5+2+5) - (6+1+6) = 12-13 = -1 which is not divisible by 11
The closest divisible number to -1(or 1) is 0, thus we remove 1 apple
So By removing 1 apple we make the total 562155 => (5+2+5)-(6+1+5) = 0 which is divisible by 11
ANSWER: C
Answer: (C) 1
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 1899
(C) 7861
(D) 1229
(E) 2991
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) 1000
Question: There are 780 male and female participants in a meeting. Half the female participants and one-quarterof the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 130
(B) 100
(C) 125
(D) 175
(E) 225
Rationale: Let m be the number of male participants and f be the number of female articipants in the meeting. Thetotal number of participants is given as 780.
Hence, we have m+f= 780
Now, we have that half the female participants and one-quarter of the male participants are Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
d = 780/3 = 260
Solving the three equations yields the solution
f = 260,m= 520, and d= 260.
The number of female democratic participants equals half the female participants equals
260/2 = 130.
ANSWER:A
Answer: (A) 130
Question: A shopkeeper sold an book offering a discount of 5% and earned a profit of 14%. What would have been the percentage of profit earned if no discount was offered?
(A) 140
(B) 120
(C) 130
(D) 110
(E) 150
Rationale: Let C.P. be $100.
Then, S.P. = $114
Let marked price be $x. Then, 95/100 x = 114
x = 114/95 = $120
Now, S.P. = $120, C.P. = $100
Profit % = 20%.
B
Answer: (B) 120
Question: Divide Rs. 1600 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) Rs.800
(B) Rs.400
(C) Rs.600
(D) Rs.500
(E) Rs.900
Rationale: A+B+C = 1600
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1600 => 400
ANSWER:B
Answer: (B) Rs.400
Question: The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 3 years ago?
(A) 152460
(B) 214560
(C) 152381
(D) 210000
(E) 200000
Rationale: population 2 years ago = 176400/(1 + 5/100)^3
Answer is C
Answer: (C) 152381
Question: David purchased a house for Rs.75000 and a site for Rs.15000 respectively, if he sold the house for Rs.83000 and the site for Rs.10000, then find the resultant percentage of gain?
(A) 30 %
(B) 330/3 %
(C) 31/3 %
(D) 3.33 %
(E) None
Rationale: Sol.
Total CP = 90000 & total SP = 93000 ⇒ gain = SP/CP = 93000/90000 = 1.0333 = 3.33%.
Answer D
Answer: (D) 3.33 %
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 227
(B) 268
(C) 375
(D) 998
(E) 121
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: (C) 375
Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 132. What is the number of frogs in the pond ?
(A) 148
(B) 134
(C) 156
(D) 144
(E) None
Rationale: Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 132.
So, total number of Ducks and Frogs in the Pond,
= 2* 132 = 262.
Therefore,
Number of Frogs, = (262*39)/76 = 134.
Answer: Option B
Answer: (B) 134
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 4t seconds, then what is the length of the platform?
(A) 0.5L
(B) L
(C) 1.5L
(D) 2L
(E) 3L
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 4t
(L+P) / (L/t) = 4t
P = 3L
The answer is E.
Answer: (E) 3L
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 42,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
(A) Rs. 1000
(B) Rs. 4000
(C) Rs. 3500
(D) Rs. 3000
(E) None of these
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 42,000 = Rs. 14,000
Salary of A = Rs. (15000 – 14000) = Rs. 1000
ANSWER: A
Answer: (A) Rs. 1000
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many metres does the wheel move in two hour?
(A) 240 metre
(B) 12 metre
(C) 120 metre
(D) 1200 metre
(E) 2200 metre
Rationale: Expl : Number of times wheel moves in 2 hour = 10 * 120 = 1200
:. Distance moves = (1200 *20) cm = 24000 cm
In metres = 240 metre
Answer: A
Answer: (A) 240 metre
Question: The simple interest on Rs.500 at 6% per annum from May 3rd to July 15th in the same year is
(A) Rs. 8
(B) Rs. 6
(C) Rs. 4
(D) Rs. 9
(E) Rs.10
Rationale: Explanation :
Time from May 3rd to July 15th = 28 days of May + 30 days of June and 15 days of July
= 73 days= 73/365 years = 15 years
Simple interest = PRT/100=500×6×15/100=6
Answer : Option B
Answer: (B) Rs. 6
Question: 8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution. What is the percentage of alcohol in the new solution?
(A) 21.2%
(B) 21.6%
(C) 22.0%
(D) 22.4%
(E) 22.8%
Rationale: The total amount of alcohol is 0.25(8) + 0.12(2) = 2.24 liters.
The percentage is 2.24 / 10 = 22.4 / 100 which is 22.4%
The answer is D.
Answer: (D) 22.4%
Question: 19.19/2000 is equal to:
(A) 1.01252633
(B) 0.01262533
(C) 0.12526333
(D) 0.012793333
(E) 0.12725333
Rationale: 19.19/2000 = 2525/200000
= 0.012793333
ANSWER:D
Answer: (D) 0.012793333
Question: If 2x+3y=34 and ((x + y)/y)=13/8,then find the value of 5y+7x.
(A) 75
(B) 65
(C) 85
(D) 95
(E) None of them
Rationale: The given equations are:
2x+3y=34 …(i) and, ((x + y) /y)=13/8 => 8x+8y=13y => 8x-5y=0 …(ii)
Multiplying (i) by 5,(ii) by 3 and adding, we get : 34x=170 or x=5.
Putting x=5 in (i), we get: y=8.
Therefore, 5y+7x=((5*8)+(7*5))=40+35=75
Answer is A.
Answer: (A) 75
Question: A dish of Babette’s mango surprise consists entirely of mangoes, slivered almonds, agave nectar, and assorted other fruits. If a serving of the dish contains 6 oz. of mango, 5 oz. of slivered almonds, and 2 oz. of agave nectar, and the ratio of mangoes to sunflower seeds is trippled, what is the ratio of mangoes to the rest of the ingredients in the new serving of the dish?
(A) 1: 3
(B) 12 : 27
(C) 4: 8
(D) 2 : 16
(E) The answer cannot be determined from the information given.
Rationale: This answer really has too many words for such a simple question. The answer is E.
Answer: (E) The answer cannot be determined from the information given.
Question: In a class of students, the ratio of girls to boys is 2:5. If 4 more girls joined the class, the ratio would be 1:2. How many students are in the class?
(A) 42
(B) 49
(C) 50
(D) 54
(E) 56
Rationale: Let x be the number of students in the class.
(2/7)*x=(1/3)(x+4)-4
6x=7x+28-84
x=56
The answer is E.
Answer: (E) 56
Question: Find the value of “n” where 348 + 31996 + 33943 + 33n.
(A) 1963
(B) 1964
(C) 1960
(D) 1991
(E) 1992
Rationale: 3^48 + 3^1996 + 3^3943+3^3n
(3^16 )^3 + 3^1996 + 3^3943 + (3^n)^3
its expansion of (a+b)^3=a^3+3a^2b+3ab^2+b^3
=> 3*(3^16)^2*3^n=3^1996
=> 3^(33+n)=3^1996
=> n = 1963
ANSWER:A
Answer: (A) 1963
Question: Two trains run in opposite directions on a circular track. Train A travels at a rate of 4π miles per hour and Train B runs at a rate of 6π miles per hour. If the track has a radius of 6 miles and the trains both start from Point R at the same time, how long, in hours, after the trains depart will they again meet at Point R?
(A) 3
(B) 6
(C) 9
(D) 18
(E) 22
Rationale: I don't agree with your solutions, first. And second the answer choices don't seem to contain the right answer.
My solution is as follows, and I ask anyone to correct me if I am wrong.
Solution 1
Let the distance covered by train A be X, thus that covered by the train B will be 12*3.14-X
dA = X dB = 12*3.14 - X
Times taken by A and B are
tA= X/4*3.14 , tB = (12*3.14 - X)/6*3.14 (ii)
Since they have been traveling for the same period of time, then
X/4*3.14 = (12*3.14 - X)/6*3.14
X/2 =(12*3.14 -X)/3
3X = 2(12*3.14 -X)
5X = 24*3.14
X = 24*3.14/5
Plugging that in either equation of (ii) yields t = 6/5
Solution 2
We add the speed of A and B: totalSpeed R= 4*3.14 + 6*3.14 = 10*3.14
Total distance covered = 12*3.14
t ime = distance / speed = 12*3.14/10*3.14 = 6/5.
tA =( X/4*3.14) =(24*3.14/5)/4*3.14 = 6/5=B
Answer: (B) 6
Question: what should be multiplied to 2880 to make it a perfect square?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Step 1== 288*10
Step 2== 144*2*2*5
Step 3== 12*12*2*2*5 if perfect square===12*12*2*2*5*5
So answer is 5 we have to multiply it by 5 to make it as a perfect square.
ANSWER:D
Answer: (D) 5