RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability L that the World Series will consist of fewer than 7 games?
A. 12.5%
B. 25%
C. 31.25%
D. 68.75%
Answer: D. 68.75%
Explanation: Your explanation is very close toManhattan GMAT's official answer - it's quite uncanny:
"There are many other ways this could happen. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for the two teams to split the first 6 games (3 wins for each).
There are then 2 possible outcomes to break the tie in Game 7. Thus, there are a total of 202 = 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is: (1/2)^7 = 1/128
40*1/128 = 40/128 = 31.25%
Thus the probability L=that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D."
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
A.12, 9
B.10, 5
C.12, 7
D.11, 6
Answer: C.12, 7
Explanation: x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER:C
Question: After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?
A.36
B.48
C.72
D.96
Answer: D.96
Explanation: Sequence of cities she can visit without any restrictions= 6*5*4= 120
Sequence of cities she can visit if she visits both Oslo and Stockholm on the same trip= 3*2 *1 *4 (after choosing Oslo and Stockholm, she is left with 4 cities to choose from)= 24
Sequence of cities to choose with restrictions= 120-24= 96
D is the answer
Question: A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, at what speed is the train travelling?
A.61 km/hr
B.56 km/hr
C.63 km/hr
D.60 km/hr
Answer: D.60 km/hr
Explanation: 21 telephone posts in 1 min
No of gaps b/w 21 posts = 20
adjacent post = 50 m
20*50 = 1000 m in 1 min
dist = 1000 m = 1 km
time = 1 min = 1/60 hr
speed = 1/(1/60) = 60 km/hr
ANSWER D
Question: At a constant Rate of flow, it takes 60 minutes to fill a swimming pool if a large hose is used and 90 minutes if a small hose is Used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
A.20
B.25
C.28
D.36
Answer: D.36
Explanation: time taken to fill the pool by Large Hose =30 minutes =L or 1/L=1/60 similarly 1/S=1/90
simultaneously it will take 1/L+1/S=1/60+1/90=5/180=36 minutes
Answer : D
Question: The sale price sarees listed for Rs.298 after successive discount is 12% and 15% is?
A.321
B.223
C.245
D.265
Answer: B.223
Explanation: Explanation:
298*(88/100)*(85/100) = 223
Answer: B
Question: A milk man has 15 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
A.20%
B.25%
C.33.33%
D.18%
Answer: A.20%
Explanation: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 20 liters of milk.
Therefore, profit percentage = 20 %. Answer: A
Question: 45% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
A.25%
B.35%
C.45%
D.55%
Answer: C.45%
Explanation: To maximize the percentage of companies offering both, let's assume that all 45% of companies which offer wireless internet also offer snacks.
The answer is C.
Question: How much interest will $10,000 earn in 9 months at an annual rate of 6%?
A.$250
B.$350
C.$450
D.$550
Answer: C.$450
Explanation: Soln:-
9 months = 3/4 of year;
6% = 6/100=3/50;
$10,000(principal)*3/50(interest rate)*3/4(time)=$450.
ANSWER:C
Question: A salad bowl of 4 ingredients is chosen from 3 types of lettuce and 4 types of tomatos. The salad must have at least 1 type of lettuce and at least 2 types of tomatos. How many ways can this salad be made?
A.106
B.30
C.16
D.18
Answer: B.30
Explanation: Solution: We have two possibilities 1L 3T or 2L 2T
(3C1)(4C3)+(3C2)(4C2)=30
B) 30
Question: Difference of two numbers is 1620. If 7.5% of the number is 12.5% of the other number , find the number ?
A.2660, 1000
B.3660, 2000
C.3000, 4160
D.2430, 4050
Answer: D.2430, 4050
Explanation: Let the numbers be x and y. Then, 7.5 % of x =12.5% of y
X = 125*y/75 = 5*y/3.
Now, x-y =1620
5*y/3 –y =1620
2*y/3= 1620
y =[ (1620*3)/2] =2430.
One number = 2430, Second number =5*y/3 =4050.
Answer D.
Question: Eesha bought 18 sharpeners for Rs.100. She paid 1 rupee more for each white sharpener than for each brown sharpener. What is the price of a white sharpener and how many white sharpener did she buy ?
A.s.6, 19
B.s.6, 10 white sharpener
C.s.6, 16
D.s.6, 11
Answer: B.s.6, 10 white sharpener
Explanation: Explanation: Just check the options. If she bought 10 white sharpeners at Rs.6 per piece, She has spent Rs.60 already. And with the remaining Rs.40, she bought 8 brown sharpeners at 40/8 = Rs.5 which is Rs.1 less than White sharpener.
Sol: B
Question: A cow and horse are bought for Rs.2,00,000. The cow is sold at a profit of 20% and the horse is sold a t a loss of 10%. The overall gain is Rs.4000, the Cost price of cow?
A.2 percent
B.3
C.4
D.5
Answer: A.2 percent
Explanation: Ans: Overall profit = 4000200000×100=2%4000200000×100 =2%
By applying alligation rule, we get
Answer:A
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.72
B.5.29
C.5.76
D.5.39
Answer: C.5.76
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2
=5.76
Answer:C
Question: For every integer n ≥ 3, the function g(n) is defined as the product of all the odd integers from 1 to n, inclusive. What is the value of g(101) – g(99)?
A.0
B.98
C.99
D.100
Answer: D.100
Explanation: g(101) = 1*3*5*7*9*...*99*101
g(99) = 1*3*5*7*9*...*99
g(101) - g(99) = 1*3*5*7*9*...*99*101 - 1*3*5*7*9*...*99 = 1*3*5*7*9*...*99*(101 - 1) = 1*3*5*7*9*...*99*100
hence:D
Question: Two cars are driving toward each other. The first car is traveling at a speed of 100 km/h, which is 25% faster than the second car's speed. If the distance between the cars is 720 km, how many hours will it take until the two cars meet?
A.3
B.3.5
C.4
D.4.5
Answer: C.4
Explanation: The speed of the first car is 100 km/h.
The speed of the second car is 100 / 1.25 = 80 km/h.
The two cars complete a total of 180 km each hour.
The time it takes the cars to meet is 720 / 180 = 4 hours.
The answer is C.
Question: The value of a machine depreciates at 25% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
A.$258375
B.$438375
C.$128375
D.$108375
Answer: D.$108375
Explanation: The value of the machine after two years = 0.75 * 0.75 * 1,50,000 = $84,375
SP such that a profit of $24,000 is made = 84,375 + 24,000 = $1,08,375
D
Question: What is the sum of the greatest common factor and the lowest common multiple of 36 and 56?
A.592
B.520
C.508
D.560
Answer: C.508
Explanation: Prime factorization of the given numbers
36= 2^2 * 3^2
56= 2^3 *7
Greatest common factor = 4
Lowest common multiple = 504
Sum = 4+ 504 = 508
Answer C
Question: How many words, with or without meaning, can be formed using all letters of the word BEAUTIFUL using each letter exactly once?
A.388,620
B.388,260
C.362,880
D.352,880
Answer: C.362,880
Explanation: The Word BEAUTIFUL has exactly 9 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 9 letters taken all at a time.
= P (9, 9) = 9!
= 9 x 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1
= 362,880
ANSWER:C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
A.12/428
B.12/420
C.12/455
D.12/429
Answer: C.12/455
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2C1)(4C2)/15C3
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer:C
Question: A firm is comprised of partners and associates in a ratio of 2:63. If 35 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm?
A.12
B.14
C.16
D.18
Answer: B.14
Explanation: The ratio 1:34 = 2:68 so the ratio changed from 2:63 to 2:68.
68-63 = 5 which is 1/7 of the increase in 35 associates.
The ratio changed from 14:441 to 14:476.
Thus the number of partners is 14.
The answer is B.
Question: Find the odd man out. 18, 16, 12, 24, 21, 34, 46
A.16
B.46
C.24
D.21
Answer: D.21
Explanation: Explanation :
21 is the only odd number in the given series
Answer : Option D
Question: A train 120 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
A.443 m
B.354 m
C.450 m
D.380 m
Answer: D.380 m
Explanation: D
350
D = 72 * 5/18 = 25 = 500 â€“ 120 = 380
Question: If p ≠ 1 and if qp/(q - p) = 1, what is the value of q in terms of p?
A.(p+1)/p
B.(p - 1)/p
C.p/(p + 1)
D.p/(1-p)
Answer: D.p/(1-p)
Explanation: This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator.
Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one.
Final Answer:
D
Question: The probability of rain showers in Barcelona on any given day is 0.4. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
A.0.144
B.0.072
C.0.432
D.0.72
Answer: C.0.432
Explanation: P(Rain) = 0.4 = 2/5
So, P(no rain) = 0.6 = 3/5
Let R represent Rain, and let N represent no rain
So, P(Rain exactly once) = P(R-N-N OR N-R-N OR N-N-R)
= P(R-N-N) + P(N-R-N) + P(N-N-R)
= (2/5)(3/5)(3/5) + (3/5)(2/5)(3/5) + (3/5)(3/5)(2/5)
= 18/125 + 18/125 + 18/125
= 54/125
NO DECIMAL CONVERSION NEEDED
Notice that 62.5/125 = 1/2 = 0.5, so 54/125 = a little less than 0.5
Answer:C
Question: Which one of the given numbers is divisible by 11?
A.4823718
B.8423718
C.8432718
D.4872318
Answer: D.4872318
Explanation: Explanation:
4872318 = (4+7+3+8) – (8+2+1) = 11
So, the given number is divisible by 11
Answer:D
Question: If the cost price of 18 articles is same as the selling price of 25 articles. Find the gain or loss percentage?
A.30% Gain
B.28% Loss
C.40% Gain
D.40% Loss
Answer: B.28% Loss
Explanation: Explanation:
18 cp = 25 sp
Cost price CP = 25
Selling price SP = 18
Formula = (SP-CP)/CP * 100 = (18 - 25)/25 * 100 = 28 % Loss
Answer: Option B
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
A.17327
B.15008
C.13272
D.15000
Answer: D.15000
Explanation: Explanation:
The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000 = Rs.10000 Share of A in the total profit = 3/5 * 25000 = Rs.15000
Answer: D
Question: What least no. must be subtracted from 10154 so that remaining no.is divisible by 30?
A.10
B.12
C.14
D.8
Answer: C.14
Explanation: Explanation:
On dividing 10154 by 30 we get the remainder 14, so 14 should be subtracted
Option C
Question: The sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?
A.5 years
B.7 years
C.9 years
D.6 years
Answer: D.6 years
Explanation: 100 ---- 300 --- 3
900 --- 3
----
6 years
Answer: D
Question: A tank 3 m long, 2 m wide and 1.5 m deep is dug in a field 20 m long and 14 m wide. If the earth dug out is evenly spread out over the field, the level of the field will raise by nearly?
A.1390
B.2987
C.2889
D.2689
Answer: A.1390
Explanation: 2(25 * 15 + 15 * 8 + 25 * 8)
2(375 + 120 + 200)
=> 1390
Answer: A
Question: Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems.
Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly,
still he got less than 72% problems right. How many more questions he would have to answer more to get
passed
A.5
B.14
C.7
D.8
Answer: B.14
Explanation: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 72% = 72% of total quations
= 72 % of 75 = 45.
He would have to answer 54 - 40 = 14
Answer: Option B
Question: The area of a square field is 7201 sq m. How long will a lady take to cross the field diagonally at the rate of 1.2 km/hr?
A.6 min
B.5 min
C.5.5 min
D.4 min
Answer: A.6 min
Explanation: Area of a square field = 7201 sq m
Let the side of square = a
a^2 = 7201
=> a = 84.86
Diagonal = (2)^(1/2) * a
= 1.414 * 84.86
=120
Speed of lady = 1.2 km / hour
= 1200 m / hour
= 20 m / min
Time taken by lady to cross the field diagonally = 120/20 = 6 min
Answer A
Question: A bowl was filled with 10 ounces of milk, and 0.002 ounce of the milk evaporated each day during a 50-day period. What percent of the original amount of milk evaporated during this period?
A.A)0.001%
B.B)0.01%
C.C)1%
D.D)10%
Answer: C.C)1%
Explanation: Total amount of milk evaporated each day during a 50-day period = .002 * 50
=.002 * 100/2
= .2/2
= .1
percent of the original amount of milk evaporated during this period = (.1/10) * 100%
= 1 %
Answer C
Question: The area of a square is equal to five times the area of a rectangle of dimensions 20 cm * 16 cm. What is the perimeter of the square?
A.289 cm
B.160 cm
C.829 cm
D.288 cm
Answer: B.160 cm
Explanation: Area of the square = s * s
= 5(20* 16)
=> s = 40
= 40 cm
Perimeter of the square
= 4 * 40
= 160 cm.
Answer: B
Question: If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?
A.- 11
B.- 1
C.0
D.1
Answer: B.- 1
Explanation: Let us say that n = 0 then 6^0 = 1 which is a divisor of any number.
Now the question is asking the value of 0^6 - 6^0 = -1
ANSWER:B
Question: Find the lowest positive integer that can be divided by each of the following integers: 8,9,10,11,12,13,
A.51480
B.6000
C.34872
D.2348
Answer: A.51480
Explanation: To get the least positive integer that can be divided by each of these numbers 8,9,10,11,12,13, you calculate the lowest common denominator of all the numbers. Express each number as a product of their prime factors and multiply the set of prime numbers from each set with the highest exponent value.
LCM=2^3*3^2*5*11*13
The answer is A)
Question: What is the value of 16^2 + 17^2 + 18^2 + 19^2 + 20^2 + 21^2 + 22^2 + 23^2 + 24^2 ?
A.3298
B.3660
C.3670
D.3328
Answer: B.3660
Explanation: This is what I did, all the nos are close to 20, and squared, so 20^2 plus there are 9 numbers, so (20)^2 x 9 =3600,
now squaring the last digits of each no individually comes up to (16+9+4+1+0+1+4+9+16) = 60.
when you add the 2 up it gives you a (3600+60) =3660,
Answer is B
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.17 1/9
B.17 1/3
C.17 1/7
D.17 1/9
Answer: C.17 1/7
Explanation: 1/20 + 1/30 - 1/40 = 7/120
120/7 = 17 1/7
Answer: C
Question: A rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing. If the poles of the fence are kept 4 metres apart, how many poles will be needed ?
A.55
B.70
C.57
D.58
Answer: B.70
Explanation: Solution
Perimeter of the plot = 2(90 + 50) = 280 m.
∴ Number of poles = [280/4] =70m Answer B
Question: The length of a rectangle is halved, whileits breadth is tripled. Wat is the % change in area?
A.40%
B.45%
C.50%
D.65%
Answer: C.50%
Explanation: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Question: 45 litres of mixture is created by mixing Liquid A and Liquid B in the ratio 3:2. How much more Liquid B must be added to make the ratio 9:11?
A.9 Litres
B.10 Litres
C.12 Litres
D.15 Lt
Answer: D.15 Lt
Explanation: In current ratio A = (3/5) * 45 = 27
B is 18
Suppose "b" amount of b is added
new ratio = 27/(b+18) = 9/11
=> b+18 = 33
=> b = 15
So, answer will be D
Question: A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.45
B.60
C.75
D.90
Answer: C.75
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 400
16x = 400
x = 25.
Hence, total number of notes = 3x = 75.
Answer: Option C
Question: A number is trebled and 10 is subtracted. If the resultant is divided by 5, it becomes 35. What is that number?
A.73.5
B.185/3
C.155/3
D.None of these
Answer: B.185/3
Explanation: Solution
Let the number be x.
Then, (3x - 10)/5 ‹=› 35
‹=› 3x - 10 = 175
‹=› 3x= 185
x= 185/3.
Answer B
Question: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 70 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?
A.60 %
B.65 %
C.70%
D.75%
Answer: A.60 %
Explanation: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 70 - {Both correctly} + 5
{Both correctly} = 60.
Answer: A.
Question: In a certain alphabet, 16 letters contain a dot and a straight line. 30 letters contain a straight line but do not contain a dot. If that alphabet has 50 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
A.4
B.8
C.12
D.16
Answer: A.4
Explanation: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).
First we find the total # of letters with lines: 16 +30 = 46;
Next, we find the total # of letters without line: 50 - 46 = 4;
Finally, we find the # of letters that contain a dot but do not contain a straight line: 4 - 0 = 4.
Answer: A
Question: One computer can upload 100 megabytes worth of data in 2 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 10 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
A. 6.6
B. 7
C. 9
D. 11
Answer: A. 6.6
Explanation: Since the first computer can upload 100 megabytes worth of data in 2 seconds then in 2*10=20 seconds it can upload 10*100=1000 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-1000=300 megabytes worth of data. The second computer can upload 100 megabytes of data in 6.6 seconds.
Answer: A.
Question: A six-sided die is rolled once. What is the probability that the number rolled is greater than 3?
A.2 / 3
B.1 / 2
C.3 / 3
D.4 / 5
Answer: B.1 / 2
Explanation: Only 4, 5 & 6 so, 3 / 6 = 1/2
correct answer B
Question: Before 2 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
A.36
B.42
C.54
D.60
Answer: A.36
Explanation: A - 2 = 4(B - 2) --> A - 4B = -6.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 14 --> A = 3(18) = 50
A - B = 50 - 14 = 36
Answer: A
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
A.180degree
B.160degree
C.120degree
D.150degree
Answer: A.180degree
Explanation: We know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6×360/12=180°
Answers is A.
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 44 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
A.40
B.42
C.44
D.46
Answer: B.42
Explanation: Annie earned 40x + 4(2x) = 48x
Let H be the number of hours that Harry worked.
Harry earned 30x + 1.5x(H-30) = 48x
(1.5x)(H) = 63x
H = 42 hours
The answer is B.
Question: In a certain store, the profit is 100% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A.30%
B.70%
C.37.5%
D.250%
Answer: C.37.5%
Explanation: Let C.P. = Rs. 100. Then, profit = Rs. 100, S.P. = Rs. 200
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 200
Profit = 200 - 125 = Rs. 75
Required percentage = 75/200 * 100 = 37.5%
ANSWER:C
Question: Mrs. Angel. invested $24,000; part at 5%, and part at 8%. The total interest on the investment was $1,680. How much did she invest at each rate?
A.x=$13,000, y =$26,000
B.x=$8,000, y =$16,000
C.x=$14,000, y =$28,000
D.x=$15,000, y =$30,000
Answer: B.x=$8,000, y =$16,000
Explanation: I approached this question like a mixture problem.
I don't like the wordingpartat 5% andpartat 8% because we have variables x and y in the answer choices and I have no idea which one is x or y.
Anyway here's how I did it.
0.05(x) + 0.08(y) = 0.07(x+y)
0.01(y) = 0.02(x)
y = 2x
Note: 0.07(x+y) because $1,680 is 7% of 24,000
In which answer choice is y = 2(x)
Answer B
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.500, what is the reduced price for kg?
A.25
B.60
C.70
D.80
Answer: A.25
Explanation: A
500*(25/100) = 125 ---- 5
? ---- 1 => Rs.25
Question: The Simple interest and the true discount and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is :
A.Rs. 1800
B.Rs. 1450
C.Rs. 1360
D.Rs. 6800
Answer: C.Rs. 1360
Explanation: Solution
Sum =S.I xT.D./ ( S.I ) - ( T.D. ) = 85x80/85 - 80 = Rs. 1360.
Answer C