mathewhe/aqua_rat huggingface dataset:
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 14% less than the price each head sold for the day before.what was the gross profit on this shipment?
(A) $100
(B) $115
(C) $125
(D) $130
(E) $135
Rationale: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 86% of the previous price: 86/100 * 1/2 = $(3/7)
Total revenue by selling 500 heads = 3/7 * 500 = 215
Total revenue after selling 1500 cabbage heads - 215+500 = $715
Money spent on the purchase: $600
Profit = 715-600 = $115
Ans: B
Answer: (B) $115
Question: Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum M in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is
(A) 90%
(B) 80%
(C) 70%
(D) 60%
(E) 40%
Rationale: The problem asks for the approximate chance that no more than 1/3 of the original investment is lost. We can apply the “1 – x” technique: what’s the chance that more than 1/3 of the original investment is lost? There are two outcomes we have to separately measure:
(a) All 3 investments become worthless.
(b) 2 of the 3 investments become worthless, while 1 doesn’t.
Outcome (a): The probability is (0.2)(0.2)(0.2) = 0.008, or a little less than 1%.
Outcome (b): Call the investments X, Y, and Z. The probability that X retains value, while Y and Z become worthless, is (0.8)(0.2)(0.2) = 0.032. Now, we have to do the same thing for the specific scenarios in which Y retains value (while X and Z don’t) and in which Z retains value (while X and Y don’t). Each of those scenarios results in the same math: 0.032. Thus, we can simply multiply 0.032 by 3 to get 0.096, or a little less than 10%.
The sum of these two probabilities is 0.008 + 0.096 = 0.104, or a little more than 10%. Finally, subtracting from 100% and rounding, we find that the probability we were looking for is approximately 90%.
The correct answer is A.
This problem illustrates the power of diversification in financial investments. All else being equal, it’s less risky to hold a third of your money in three uncorrelated (independent) but otherwise equivalent investments than to put all your eggs in one of the baskets. That said, be wary of historical correlations! Housing price changes in different US cities were not so correlated—and then they became highly correlated during the recent housing crisis (they all fell together), fatally undermining spreadsheet models that assumed that these price changes were independent.
Answer: (A) 90%
Question: 0.007 x 0.45=?
(A) 3.15e-05
(B) 0.000315
(C) 0.315
(D) 0.0315
(E) 0.00315
Rationale: 7 x 45 = 315
Sum of decimal places =5
Therefore, 0.007 x 0.45 = 0.00315
Answer is E.
Answer: (E) 0.00315
Question: Josiah had $42,895.39 in his savings account. He wanted to make a $10,000 deposit on a new car. The car was priced at $85,216.78. The interest rate that Josiah will be paying back, for having the vehicle financed, is 8.99%. What is the total amount that Josiah would have paid on the total cost (including financed amount (interest)) on the vehicle minus $10.000 deposit?
(A) 92,877.77
(B) 100,562.31
(C) 1.29
(D) 120,261.53
(E) 60,487.15
Rationale: A
Answer: (A) 92,877.77
Question: A, B and C can do a work in 6 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?
(A) 2 2/3
(B) 2 2/9
(C) 2 2/8
(D) 2 2/5
(E) 2 2/1
Rationale: Work done by all three of them in one day = 1/6 + 1/8 + 1/12 = 3/8.
The number of days required = 8/3 = 2 2/3 days.
Answer:A
Answer: (A) 2 2/3
Question: A line that passes through (–2, –4) and (3, k) has a slope = k. What is the value of k?
(A)  3/4
(B)  1
(C)  4/3
(D)  2
(E)  7/2
Rationale: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(3+2)
=> 5k = k+4
=> k =1
Ans B it is!
Answer: (B)  1
Question: The average age of 30students in a class is 5years. If teacher's age is also included then average increases 1year then find the teacher's age?
(A) 59
(B) 55
(C) 61
(D) 45
(E) 36
Rationale: Total age of 50 students = 30*5 = 150
Total age of 51 persons = 31*6 = 186
Age of teacher = 186-150 = 36years
Answer is E
Answer: (E) 36
Question: If x + (1/x) = 5, what is the value of R=x^2 + (1/x)^2?
(A) R=21
(B) R=22
(C) R=23
(D) 24
(E) 27
Rationale: Squaring on both sides,
x^2 + (1/x)^2 + 2(x)(1/x) = 5^2
x^2 + (1/x)^2 = 23
Answer: C
Answer: (C) R=23
Question: An error 5% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 4.05%
(B) 4.02%
(C) 4%
(D) 10.28%
(E) 2%
Rationale: Percentage error in calculated area
=(5+5+(5Ã—5)/100)%
=10.25%
ANSWER:D
Answer: (D) 10.28%
Question: Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21
(A) 1
(B) -1
(C) 2
(D) -2
(E) 3
Rationale: B
-1
19x + 19y + 17 = -19x + 19y - 21
38x = -38 => x = -1
Answer: (B) -1
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) Rs.250
(B) Rs.225
(C) Rs.275
(D) Rs.200
(E) Rs.100
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
ANSWER:A
Answer: (A) Rs.250
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $70,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
(A) $24,000
(B) $28,000
(C) $32,000
(D) $36,000
(E) $40,000
Rationale: The answer should be -> E. $40,000
Answer: (E) $40,000
Question: A train sets off at 2 p.m. at the speed of 50 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 65 kmph. At what time the trains will meet?
(A) 8.37 p.m
(B) 8.20 p.m
(C) 8.30 p.m
(D) 8.38 p.m
(E) 8.10 p.m
Rationale: D = 50 * 1 Â½ = 75 km
RS = 65 â€“ 50 = 15
T = 75/15 = 5 h
3.30 + 7 h = 8.30 p.m.
Answer: C
Answer: (C) 8.30 p.m
Question: What percent is 4 gm of 1 kg?
(A) 1.5 %
(B) 0.4 %
(C) 2.5 %
(D) 3.5 %
(E) 4 %
Rationale: 1 kg = 1000 gm
4/1000 × 100 = 400/1000
=2/5 = 0.4 %
B)
Answer: (B) 0.4 %
Question: A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” and “low” cards to earn 6 points if you must draw exactly 4 “low” cards?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Great question Ravih. This is a permutations problem (order matters) with repeating elements. Given thatlowcards are worth 1 pt andhigh cards2 pts, and you must draw 3 low cards, we know that you must also draw 1 high card. The formula for permutations problems with repeating elements isN!/A!B!...where N represents the number of elements in the group and A, B, etc. represent the number of times that repeating elements are repeated. Here there are 4 elements and thelowcard is repeated 3 times. As a result, the formula is:
5!/4! which represents (5*4*3*2*1)/(4*3*2*1) which simplifies to just 5, giving you answer E.
Answer: (E) 5
Question: Running at the same constant rate, 100 identical machines can produce a total of 500 coffee bar per minute. At this rate, how many bottles could 20 such machines produce in 2 minutes?
(A)  110
(B)  220
(C)  330
(D)  200
(E)  789
Rationale: Let's take the approach that uses the answer choices to eliminate wasted time.
500/100 = 5 coffee bar per minute per machine. 20 machines = 100 per minute. 2 minutes worth = 200 coffe bar.
Looking at the answers it is clear...we can only choose (D)
THE CORRECT ANSWER IS D.
Answer: (D)  200
Question: Two workers completed the painting of a building in 10 days. If they were to paint the building separately, how many days will it take each worker, if one of them can complete it in approximately 2 days earlier than the other.
(A) 9 and 11
(B) 19 and 21
(C) 8 and 10
(D) 10 and 15
(E) 10 and 12
Rationale: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two workers would complete a job in 10 days. This means that (individually) each of them would take MORE than 10 days to do the job.
Answers E, A and C are illogical, since the individual times must both be greater than 10 days.
so we can TEST the values for Answers B and D.
Using the values for Answers B and D...
Answer B: (19)(21)/(19+21) = 399/40 = 9.97 This is a match (complete it in approximately 2 days earlier than the other)
This IS a match
Final Answer:
B
Answer: (B) 19 and 21
Question: On Sunday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up L percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of L?
(A) 20%
(B) 30%
(C) 33 1⁄3%
(D) 40%
(E) 50%
Rationale: Let the original price be 100
discounted Price = 80
New Price = 20 +100 =120
L=(40/80)*100
Ans:E
Answer: (E) 50%
Question: A certain set of test scores has an average (arithmetic mean) of 70 and a standard deviation of 25. If m and n, two numbers in the set, are both within 2 standard deviations from the average, then which of the following could be the average of m and n?
(A) 10
(B) 14
(C) 17
(D) 19
(E) 21
Rationale: Given, mean = 70, SD = 25
Mean + 2(Standard Deviation) = 120
Mean - 2(Standard Deviation) = 20
m,n are both in this range i.e (20 to 120)
The least value that m,n take is 21 since m,n > 20
m=n=21
Average of 2 numbers is 21
Answer: E
Answer: (E) 21
Question: A money lender lends Rs.1200 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
(A) 2205
(B) 1978
(C) 2834
(D) 1323
(E) 2781
Rationale: A = 1200(21/20)2
= 1323
Answer: D
Answer: (D) 1323
Question: In a 60 liters of mixture of spirit and water, water is 7 %. In order to make water 19%, how much water should be added?
(A) 80/9 liters
(B) 70/9 liters
(C) 90/9 liters
(D) 60/9 liters
(E) 85/9 liters
Rationale: let the amount of spirit is x liters so according to the given condition
x = 60*0.93 = 55.8 and amount of water = 4.2
let the water added = y liters
so (4.2+y)/(60+y) = 19/100
on solving we will get y = 80/9 liters
ANSWER:A
Answer: (A) 80/9 liters
Question: A radio station has to choose five days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
(A) 9
(B) 15
(C) 21
(D) 35
(E) 56
Rationale: Behind the story, we are really being asked to evaluate 7C5. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C5, the third entry of the seventh row, is 21. Answer = C.
Answer: (C) 21
Question: 10 men and 15 women together can complete a work in 8 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
(A) 127 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 600 days
Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/8
15 women's 1 day work = (1/8 - 10/100) = 1/40
1 woman's 1 day work = 1/600
1 woman alone can complete the work in 600 days.
Answer:E
Answer: (E) 600 days
Question: The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?
(A) 12/35
(B) 1/35
(C) 35/8
(D) 7/32
(E) 7/33
Rationale: Let the numbers be a and b. Then,
a + b = 12 and ab = 35.
(a + b)/ab = 12/35
= (1/b + 1/a) = 12/35
Sum of reciprocals of given numbers = 12/35.
ANSWER:A
Answer: (A) 12/35
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:6
(B) 4:3
(C) 4:1
(D) 4:9
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer: B
Answer: (B) 4:3
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
(A) 4 hrs 46 min
(B) 4 hrs 24 min
(C) 4 hrs 34 min
(D) 3 hrs 34 min
(E) 4 hrs 14 min
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer: B
Answer: (B) 4 hrs 24 min
Question: Tina’s cat weighs 2.6 kilograms. Her dog weighs 8 times as much as her cat. How much does her dog weigh in kilograms?
(A) A)10.4kg
(B) B)20.8kg
(C) C)22kg
(D) D)48kg
(E) E)20kg
Rationale: 2.6*8=20.8kg.Answer is B.
Answer: (B) B)20.8kg
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 150. The amount of the bill is
(A) 1200
(B) 1764
(C) 1400
(D) 1354
(E) None of these
Rationale: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 150.
x Ã— 16 Ã— (9/12) Ã— (1/100) = 150 or x = 1250.
P.W. = Rs. 1250
Sum due = P.W. + T.D. = Rs.(1250
150) = Rs. 1400
Answer: C
Answer: (C) 1400
Question: Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.
(A) 56
(B) 24
(C) 16
(D) 8
(E) 7
Rationale: Solution: A triangle needs 3 points.
And polygon of 8 sides has 8 angular points.
Hence, number of triangle formed,
= 8C3 = (8*7*6)/(1*2*3)
= 56.
Answer: Option A
Answer: (A) 56
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 18, what is the total amount?
(A) 70
(B) 105
(C) 178
(D) 177
(E) 169
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 18
35 --- ? => 70
Answer: A
Answer: (A) 70
Question: (3136 + 6160) / 28
(A) 380
(B) 350
(C) 332
(D) 310
(E) None of these
Rationale: Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9296)/28 = 332
Option C
Answer: (C) 332
Question: Each Machine of type A has 4 steel parts and 2 chrome parts. Each machine of type B has 2 steel parts and 1 chrome parts. If a certain group of type A and type B machines has a total of 30 steel parts and 33 chrome parts, how many machines are in the group
(A) 12
(B) 13
(C) 14
(D) 16
(E) 19
Rationale: Look at the below representation of the problem:
Steel Chrome total
A 4 2 30 >>no. of type A machines=30/6=5
B 2 1 33 >>no. of type B machines=33/3=11
So the answer is 16 i.e D.
Hope its clear .
Answer: (D) 16
Question: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 5 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 5 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 5 jars?
(A) m+n
(B) 5n/25-mn
(C) m-n
(D) m
(E) n
Rationale: working rate p = 5/m ; working rate pq =( 1/p +1/q)* n =5 or mn/5 +n/q =5 0r n/q = 5-mn/5 = 25-mn/5
q = 5n/25-mn
B
Answer: (B) 5n/25-mn
Question: A can do a certain job in 18 days. B is 60% more efficient than A. How many days does B alone take to do the same job?
(A) 11 1/4 days
(B) 8 days
(C) 5 days
(D) 9 days
(E) None of them
Rationale: Ratio of times taken by A and B = 160 : 100 = 8 : 5.
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 18 : x = 8x = 5 x 18 =x = 11 1/4 days.
Answer is A.
Answer: (A) 11 1/4 days
Question: If the digits 31 in the decimal 0.00031 repeat indefinitely, what is the value of (10^5-10^3)(0.00031)?
(A) 31
(B) 0.31
(C) 0.0031
(D) 0.00031
(E) 3.1e-05
Rationale: 99*0.31=30.69 approx. 31
Answer : A
Answer: (A) 31
Question: 1.5, 2.5, 4.5, 7.5, 11.5, (....)
(A) 16.5
(B) 15.5
(C) 14.5
(D) 17.5
(E) 17
Rationale: Explanation:
1, 2, 3, 4, 5, etc.
Hence 5=16.5
Answer : A
Answer: (A) 16.5
Question: Source: Knewton
A cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. What is the maximum distance, in miles, that the cyclist could travel in 5 hours?
(A)  42
(B)  56
(C)  70
(D)  98
(E)  140
Rationale: We are told that:generallya cyclist's speed varies, depending on the terrain, between 6.0 miles per hour and 14.0 miles per hour, inclusive. Is it possible the cyclist to travel with maximum speed for some time? Why not, if there is right terrain for that. So, if there is long enough terrain for the maximum speed of 14 mph then the maximum distance, in miles, that the cyclist could travel in 5 hours would be 5*14=70 miles.
Answer: C.
Answer: (C)  70
Question: What is the probability of flipping a fair coin six times and the coin landing on heads on at least two flips?
(A) 11/16
(B) 23/32
(C) 29/32
(D) 51/64
(E) 57/64
Rationale: The number of possible outcomes is 2^6=64.
0 heads: There is 1 way to have all tails.
1 head: There are 6 ways to have one head.
P(0 or 1 head)=7/64
P(at least 2 heads)=1 - 7/64 = 57/64
The answer is E.
Answer: (E) 57/64
Question: What number should replace the question mark?
100, 93, 79, 58, ?
(A) 30
(B) 26
(C) 37
(D) 33
(E) 17
Rationale: A
30
The sequence progresses –7, –14, –21, –28.
Answer: (A) 30
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
(A) 30%
(B) 50%
(C) 40%
(D) 55%
(E) 60%
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50%
B
Answer: (B) 50%
Question: With what number must 0.987 be multiplied in order to obtain the number 987?
(A) 100
(B) 1,000
(C) 10,000
(D) 100,000
(E) None of these
Rationale: Explanation: The decimal must be moved three places to the right. To do this, we must multiply by a number with three zeroes. The correct answer is 1000.The decimal must be moved three places to the right. To do this, we must multiply by a number with four zeroes. The correct answer is 1000.
Answer : (B)
Answer: (B) 1,000
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 327
(B) 280
(C) 277
(D) 216
(E) 287
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: B
Answer: (B) 280
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 245. What was Simran share in the profit?
(A) s 950.10
(B) s 10,000
(C) s 125.00
(D) s 105.00
(E) s 140.00
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.245 x	3/7	= Rs. 105.
ANSWER :D
Answer: (D) s 105.00
Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 10 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
(A)  2.8%
(B)  3.6%
(C)  4.4%
(D)  5%
(E)  6.0%
Rationale: Let amount spent by Jill = 100
Clothing=50, Food=20, others=30
Tax on clothing= 2
Tax on others=3
Percentage= 5/100 =5%
Answer: D
Answer: (D)  5%
Question: A number Y is chosen at random from the numbers 1, -3, -1, 0, 1, 2, 3. What is the probability that |X|<3?
(A) 2/5
(B) 3/5
(C) 3/7
(D) 4/9
(E) 4/11
Rationale: |X||X| can take 7 values.
To get |X|<2|X|<2 ( i.e., −2<x<+2−2<x
⇒ P(|X|<2)= Favourable CasesTotal CasesP(|X|<2)= Favourable CasesTotal Cases
= 3/7
C
Answer: (C) 3/7
Question: The average (arithmetic man) of three integers a, b, and c is exactly poland the median. If a < b < c and a = 0, what is the value of c/b?
(A) 2
(B) 3
(C) 8
(D) 5
(E) Cannot be determined from the information given.
Rationale: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=3b --> since a=0, then (0+b+c)/3=3b --> c=8b --> c/b=8.
Answer: C.
Answer: (C) 8
Question: A car traveled 80% of the way from Town X to Town Y at an average speed of 80 mph. The car traveled at an average speed of v mph for the remaining part of the trip. The average speed for the entire trip was 50 mph. What is v in mph?
(A) 25
(B) 35
(C) 45
(D) 55
(E) 20
Rationale: Assume total distance = 100miles
Time taken for 80 miles = 80/80 = 1 hour
Time taken for the rest of the 20 miles = 20/v hours.
Average speed = 50
Therefore the total time needed = 2 hours.
2 = 1 + 20/v
Hence v = 20 mph
Answer : E
Answer: (E) 20
Question: A wears black shoes 25% of the time while B wears black shoes 68% of the time. 20% of the time A and B wear black shoes on the same day. Over a period of 100 days, how many days will they both not have black shoes?
(A) 27%
(B) 12%
(C) 45%
(D) 17%
(E) 80%
Rationale: A and B both wear black shoes 20% of the time: 0.20x100=20 days
.68x100=68-20=48 days A is wearing black shoes when B is not
.25x100=25-20=5 days B is wearing black shoes when A is not
48+5+20=73/100 either A or B is wearing black shoes
1-73/100 = 27% either A or B is NOT wearing black shoes
Answer is A
Answer: (A) 27%
Question: A reduction of 25% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) Rs.42
(B) Rs.46
(C) Rs.40
(D) Rs.41
(E) Rs.34
Rationale: 800*(25/100) = 200 ---- 5
? ---- 1 => Rs.40
Answer: C
Answer: (C) Rs.40
Question: If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs. 370 will be:
(A) Rs. 300
(B) Rs. 200
(C) Rs. 100
(D) Rs. 350
(E) None of these
Rationale: Z share = Z,
Y = 1.2Z
X = 1.25Ã—1.2Z,
X+Y+Z =740
(1.25Ã— 1.2+1.2+1)Z=37
3.7Z=370, Z=100
Answer: . C
Answer: (C) Rs. 100
Question: An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 18 as commission, the cloth sold through him on that day is worth
(A) 333
(B) 500
(C) 887
(D) 720
(E) 132
Rationale: Explanation:
Let the total sale be Rs. x.
Then, 2.5%. of x = 18 <=> (25/10 * 1/100 * x) = 18 <=> x = 720.
Answer: D
Answer: (D) 720
Question: A circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter. What fraction of the big plate's surface is not covered by the small plate?
(A) 11/36
(B) 23/10
(C) 5/14
(D) 22/11
(E) 3/4
Rationale: The questions asks us to find the surface which is not covered by the plate i.e., area of the surface not covered.
Where as circumference is the length along the edge of the circle,
2*pi*r implies the length of the curve
pi*r^2 implies area enclosed by that curve..hence Area of the circle is considered for this problem
Area of the big plate=pi* r^2, where r=6
=>pi*36
Area of the small plate=pi*25
Surface not covered by the plate=pi*36-pi*25=Pi*11
fraction of big plate's surface is not covered by small plate= Pi*11/total area of the big plate
=>Pi*11/Pi*36
Answer A
Answer: (A) 11/36