mathewhe/aqua_rat huggingface dataset:
Question: A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
(A) 87
(B) 37
(C) 80
(D) 36
(E) 13
Rationale: Given M + P + C = 80 * 3 = 240 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 240 = 80
Answer: C
Answer: (C) 80
Question: 12 welders work at a constant rate they complete an order in 3 days. If after the first day, 9 welders start to work on the other project, how many more days the remaining welders will need to complete the rest of the order?
(A) 5
(B) 2
(C) 8
(D) 4
(E) 6
Rationale: 1. We need to find out the time taken by 3 workers after day 1.
2. total no.of wokers * total time taken = time taken by 1 worker
3. Time taken by 1 worker = 12*3 = 36 days
4. But on day 1 twelve workers had already worked finishing 1/3 of the job. So 3 workers have to finish only 2/3 of the job.
5. Total time taken by 3 workers can be got from formula used at (2). i.e., 3* total time taken = 36. Total time taken by 3 workers to finish the complete job is 36/ 3 = 12 days.
6. Time taken by 6 workers to finish 2/3 of the job is 2/3 * 12 =8 days.
The answer is choice C
Answer: (C) 8
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
(A) 175.5
(B) 170
(C) 169.5
(D) 180
(E) 190
Rationale: Since first and second varieties are mixed in equal proportions.
average price = 126+135/2 = 130.50
o, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x - 153 = 22.50
x = 175.50
ANSWER A
Answer: (A) 175.5
Question: What approximate value should come in place of the question mark (?) in the following equation ?
5⁄7 of 1596 + 3015 = ? – 2150
(A) 7200
(B) 48000
(C) 5300
(D) 58000
(E) 6300
Rationale: ? ≈ 5 × 230 + 3000 + 2150
= 1150 + 3000 + 2150 = 6300
Answer E
Answer: (E) 6300
Question: A 12% stock yielding 8% is quoted at?
(A) 165
(B) 170
(C) 175
(D) 150
(E) 185
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.12, money invested = 100×12/8 = Rs.150
ie, market value of the stock = Rs.150
Answer is D.
Answer: (D) 150
Question: 3x + 2y = 19 , and x + 3y = 1. Find the value of 4x + 5y
(A) 10
(B) 18
(C) 11
(D) 20
(E) 5
Rationale: Add these two equations
4x + 5y = 20
Divide by 2 ( to Get 4x + 5y)
Answer will be D. 20
Answer: (D) 20
Question: In the coordinate plane, the points F (-1,1), G (1,4), and H (4,1) lie on a circle with center P. What are the coordinates of point P ?
(A) (0,0)
(B) (1,1)
(C) (1.5,1.5)
(D) (1,-2)
(E) (2.5, -2.5)
Rationale: I thought I need to find the 4th point that would lie on the circle
Hence my answer was D (1,-1)
But the the center of the circle will lie on (1.5,1.5)
D
Answer: (D) (1,-2)
Question: George's drawer has 10 loose black socks, 13 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that he had at least two matching pairs of socks in two different colors?
(A) 7
(B) 9
(C) 11
(D) 16
(E) 20
Rationale: The worst case scenario is choosing 13 blue socks. Then he would need 3 more socks to be sure of a matching pair of black socks or white socks.
The answer is D.
Answer: (D) 16
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 8 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
(A) 1/9
(B) 29/180
(C) 9/80
(D) 1/5
(E) 39/121
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 8*2 = 16 hours;
In 1 hour 15 journeymen can finish 1/16 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/16=9/80 of the job.
Answer: C
Answer: (C) 9/80
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 6 Gallons of water and 12 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
(A) 37.5
(B) 75
(C) 100
(D) 150
(E) 90
Rationale: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 12 gallons salt is added and 6 gallons of water is added.
So salt now becomes -> (0.2x + 12) and water --> (0.6x+6)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+12) = (0.6x+6)/2 => 0.4x+24=0.6x+6 ->0.2x=18
Solving, x = 90
Answer : E
Answer: (E) 90
Question: A group of students was interviewed for that if it was asked whether or not they speak French and / or English. Among those who speak French, 10 speak English well, while 40 of them do not speak English. If 75% of students do not speak French, how many students were surveyed?
(A) 210
(B) 225
(C) 200
(D) 250
(E) 300
Rationale: Number of students who speak French are 40 + 10 = 50
Of total students, the percentage of students who do not speak French was 75% --> percentage of who do is 25%
50-------25%
x ------- 100%
x = 50*100/25 = 200 = number of all students
Answer is C
Answer: (C) 200
Question: Townville has 100 residents, and 40 of them are females. If half of Townville’s male residents are smokers, and 1/4 of the female residents are smokers, which of the following represents the total number of Townville’s residents who are NOT smokers?
(A) 54
(B) 58
(C) 62
(D) 60
(E) 64
Rationale: Number of people =100
Females = 40
men = 100-40=60
Half of the men are smoker60/2=30, that means the remaining men 60-30=30 are non smokers.
1/4 females are smoker. i.e 1/4*40 = 10.
40-10=30 females are non smokers
So, total number of non smokers in the town are 30+30 =60
Answer : D
Answer: (D) 60
Question: A cricket player whose bowling average was 21.5 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.5. What will be the number of wickets taken by him till the last match?
(A) 64
(B) 72
(C) 111
(D) 721
(E) 108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 21.5w + 52
Total wickets after last match = w + 5
(21.5w + 52) / (w + 5) = 21.5 - 0.5 = 21
w = 106
so total wickets aftr last match = w+5 = 111
ANSWER:C
Answer: (C) 111
Question: Three pieces of timber 54 m, 63 m and 81 m long have to be divided into planks of the same length, What is the greatest possible length of each plank ?
(A) 9 m
(B) 4 m
(C) 4 m
(D) 6 m
(E) None of these
Rationale: Answer
Greatest possible length of each plank = H.C.F of 54, 63, 81 = 9 m
Correct Option: A
Answer: (A) 9 m
Question: Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow?
(A) 4 mins
(B) 6 mins
(C) 5 mins
(D) 3 mins
(E) 7 mins
Rationale: Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by A = 3 liters.
Capacity of tank filled in 1 minute by B = 15 liters.
Therefore, capacity of the tank filled by both A and B in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.
ANSWER:C
Answer: (C) 5 mins
Question: Each month a retailer sells 100 identical items. On each item he makes a profit of $60 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?
(A) 191
(B) 213
(C) 221
(D) 223
(E) 226
Rationale: For this question, we'll need the following formula:
Sell Price = Cost + Profit
We're told that the profit on 1 item is $20 and that this represents 10% of the cost:
Sell Price = Cost + $60
Sell Price = $600 + $60
Thus, the Sell Price is $660 for each item. Selling all 100 items gives the retailer...
100($60) = $2,000 of profit
If the retailer offers a 5% discount on the sell price, then the equation changes...
5%(660) = $33 discount
$627 = $600 + $27
Now, the retailer makes a profit of just $27 per item sold.
To earn $2,000 in profit, the retailer must sell....
$27(X) = $2,000
X = 2,000/27
X = 222.222222 items
You'll notice that this is not among the answer choices.... 221 and 223 are.
Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.
Final Answer:
D
Answer: (D) 223
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor S of 2x and 3y?
(A) 1
(B) S=Cannot be determined
(C) S=2
(D) 5
(E) 6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: (B) S=Cannot be determined
Question: 0.0023*0.13/0.236=my age
0.022*0.12/0.220=my wife age
then what is difference b/w ages?
(A) 0.01073
(B) 0.02073
(C) 0.03076
(D) 0.04078
(E) 0.0578
Rationale: My age = 0.0023*0.13/0.236 = 0.000299/0.236 = 0.001266949
My wife age = 0.022*0.12/0.220 = 0.00264/0.220 = 0.012
difference b/w ages = 0.012 - 0.001266949 = 0.01073
ANSWER:A
Answer: (A) 0.01073
Question: The ratio of cats to dogs to birds to fish is 5:6:7:8. There are no other types of animals in the pet store.which of the followingcannotbe the total number of animals in the store?
(A) 52
(B) 78
(C) 104
(D) 130
(E) 223
Rationale: The parts add up to 5 + 6 + 7 + 8 = 26, so we know that any possible number of total answers must be a multiple of 26. All five answer choices are multiples of 26:
(A) 52= 26*2
(B) 78= 26*3
(C) 104= 26*4
(D) 130= 26*5
(E) 223 = not a multiple of 26
Answer: (E) 223
Question: Ashok has Rs.1000, He invests a part of it at 3% per annum and remainder at 8% per annum, He earns Rs.100 in 2 years. Find the sum invested at different rates of interest?
(A) Rs.5000, Rs.500
(B) Rs.600, Rs.400
(C) Rs.700, Rs.300
(D) Rs.300, Rs.700
(E) Rs.300, Rs.800
Rationale: (600÷100)×3×2=34
(400÷100)×8×2=64
Total=100
ANSWER:B
Answer: (B) Rs.600, Rs.400
Question: If q = 35! + 1, which of the following cannot be a prime factor of q?
I. 11
II. 19
III. 31
(A) I​ only
(B) III only
(C) II and III
(D) I and II
(E) I​, II, and III
Rationale: The numbers 11, 19, and 31 are all factors of 35!
Therefore they can not be factors of 35! + 1.
The answer is E.
Answer: (E) I​, II, and III
Question: what is the sum of all the 4 digit numbers that can be formed using all of the digits 2,3,5 and 7?
(A) 113323
(B) 113322
(C) 114322
(D) 113321
(E) 112322
Rationale: Actually there is the direct formula for this kind of problems.
1. Sum of all the numbers which can be formed by using the n digits without repetition is: (n-1)!*(sum of the digits)*(111…..n times).
2. Sum of all the numbers which can be formed by using the n digits (repetition being allowed) is: n^{n-1}*(sum of the digits)*(111…..n times).
so as per question:(4-1)!*(2+3+5+7)*1111=113322
ANSWER:B
Answer: (B) 113322
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 27 7/8
(B) 27 7/6
(C) 27 7/4
(D) 27 7/9
(E) 27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer: D
Answer: (D) 27 7/9
Question: If 25% of x is 30 less than 20% of 1000, then x is?
(A) 188
(B) 216
(C) 156
(D) 680
(E) 121
Rationale: 25% of x = x/4 ; 20% of 1000 = 20/100 * 1000 = 200
Given that, x/4 = 200 - 30 => x/4 = 170 => x = 680.
Answer: D
Answer: (D) 680
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum?
(A) 198
(B) 279
(C) 267
(D) 200
(E) 269
Rationale: P(11/10)4 - P(6/5)2
= 482
P = 200
Answer: D
Answer: (D) 200
Question: Rose and Anna are partners in a business. Rose runs the business and receives 12% of the profit for managing the business, the rest is divided in proportion of their capitals. Rose invested Rs.12000 and Anna invested Rs.20000. the rest is divided in proportion of their capitals. Out of a total profit of Rs.9000, how much did Rose receive?
(A) 5872
(B) 5839
(C) 5832
(D) 5838
(E) 5832
Rationale: ratio of their investments Rs.12000:20000=3:5
12% of the profit for managing the business =12/100*9000=1080
remaining profit=9000-1080=7920
share profit in ratio of investment 7920/5 =1584
Moses's ratio share=3*1584=4752
total money Moses collects=4752+1080=5832
Answer: C
Answer: (C) 5832
Question: Find the value of x from this equation? 7(x - 1) = 21
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 1. Divide both sides by 7:
2. Simplify both sides:
x - 1 = 3
3. Add 1 to both sides:
x - 1 + 1 = 3 + 1
4. Simplify both sides:
x = 4
B
Answer: (B) 4
Question: A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17thinnings?
(A) 11
(B) 7
(C) 76
(D) 37
(E) 9
Rationale: 16x + 85 = 17(x + 3)
x = 34 + 3 = 37
Answer: D
Answer: (D) 37
Question: Obra drove 150π meters along a circular track. If the area enclosed by the circular track on which she drove is 57,600π square meters, what percentage of the circular track did Obra drive?
(A) 6.67%
(B) 12.5%
(C) 18.75%
(D) 25%
(E) 31.25%
Rationale: area enclosed by the circular track on which she drove is 57,600π square meters
So, π(r^2) = 57,600π ---> (r^2)=57,600 ---> r=240
Circumference of the circular track = 2πr = 480π
Therefore, part of circumference covered = 150π/480π =31.25%
Hence, answer is E.
Answer: (E) 31.25%
Question: There are four different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
(A) 72
(B) 48
(C) 64
(D) 24
(E) 8
Rationale: Since we have 2 continental pairs (EU, SA, NA), these 2 pairs have 2*1 = 2 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2= 4). So we have 2*4 = 8.
Please correct me if im wrong.
Answer E.
Answer: (E) 8
Question: If the numerator of a fraction E is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
(A) 16 1⁄6%
(B) 25%
(C) 33 1⁄3%
(D) 50%
(E) 66 2⁄3%
Rationale: This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction E is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D
Answer: (D) 50%
Question: If X boxes of mango juice cost 112 cents, how much will Y boxes cost in dollars?
(A) 2Y*1.12/x
(B) 3Y*1.12/x
(C) Y*12/x
(D) Y*0.12/x
(E) Y*1.12/x
Rationale: X boxes of mango juice cost 112 cents or 1.12 dollars.
cost of mango juice = 1.12/x
Cost of Y mango juices = Y*1.12/x
Hence Answer : E
Answer: (E) Y*1.12/x
Question: Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 13 km/hr and 23 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 28 sec
(B) 30 sec
(C) 17 sec
(D) 23 sec
(E) 27 sec
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 300 / (13 + 23)5/18 = 300* 18 / 36 * 5 = 30 seconds.
Answer : B
Answer: (B) 30 sec
Question: You are given three coins: one has heads on both faces, the second has tails on both faces,
and the third has a head on one face and a tail on the other. You choose a coin at random and
toss it, and it comes up heads. The probability that the other face is tails is
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 4/3
Rationale: the three coins are HH LL HT
total possiblity are 6
1st head probablity are 2/6,
2 nd head probablity are 0,
third head probablity are 1/6,
The total head probablity is 2/6+0+1/6=1/2,
Then tail probablity is 1-1/2=1/2
ANSWER:C
Answer: (C) 1/2
Question: One hour after Yolanda started walking from X to Y, a distance of 31 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 1 miles per hour and Bobâs was 2 miles per hour, how many miles had Bob walked when they met?
(A) 19
(B) 20
(C) 22
(D) 21
(E) 19.5
Rationale: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked (t + 1) miles. These distances must sum to 31 miles, so 2t + (t + 1) = 31, which may be solved for t as follows
2t + (t + 1) = 31
2t + t + 1 = 31
3t = 30
T = 10 (hours)
Therefore, Bob had walked 2t = 2(10) = 20 miles when they met. The best answer is B.
Answer: (B) 20
Question: In a graduating class of 236 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 117
(E) 31
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 236 = 27
Greatest - Smallest is 144-27 = 117
So answer must be D. 117
Answer: (D) 117
Question: if a number cube is rolled once and a coin is tossed once. what is the probability that coin will show tails and composite number on on the cube
(A) 1/6
(B) 2/6
(C) 3/6
(D) 4/6
(E) 5/6
Rationale: 1/2 * 2/6 = 1/6
ANSWER:A
Answer: (A) 1/6
Question: A corporation four time of its annual bonus to 35 of its employees. What percent of the employees’ new bonus is the increase?
(A) 5%
(B) 12%
(C) 25%
(D) 75%
(E) 63%
Rationale: Let the annual bonus be X.
A corporation triples its annual bonus.
So new bonus = 4X.
Increase = 4X-X =3X
The increase is what percent of the employees’ new bonus
= (3X/4X)*100
= 75%
Hence D.
Answer: (D) 75%
Question: What should be next in the given series?
2, 7, 10, 22, 18, 37, 26
(A) 22
(B) 37
(C) 29
(D) 271
(E) 52
Rationale: Explanation:
This question contains two series’ running simultaneously:
=> The numbers in odd places are increasing by 8
2 + 8 = 10
10 + 8 = 18
18 + 8 = 26
=> The numbers in even places are increasing by 15
7 + 15 = 22
22 + 15 = 37
37 + 15 = 52
Therefore, Next number will be 37+15= 52
ANSWER: E
Answer: (E) 52
Question: A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. In how many hours B can complete the work ?
(A) 10 hours
(B) 12 hours
(C) 16 hours
(D) 18 hours
(E) 20 hours
Rationale: Explanation:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)–(1/2) = 1/12
=> B alone can complete the work in 12 hour
Option B
Answer: (B) 12 hours
Question: A trailer carries 3, 4 and 6 crates on a trip. Each crate weighs no less than 100 kg. What is the maximum weight of the crates on a single trip?
(A) 100
(B) 625
(C) 600
(D) 7500
(E) 375
Rationale: Max No. of crates=6.
Max Weight=100Kg
Max. weight carried = 6*100=100Kg=A.
Answer: (A) 100
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
(A) 20
(B) 24
(C) 18
(D) 15
(E) 17
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
ANSWER C
Answer: (C) 18
Question: Which of the following numbers is the biggest => [-6/7 , -7/8 , -9/10 , -12/13 , -34/35]
(A) -6/7
(B) -7/8
(C) -9/10
(D) -12/13
(E) -34/35
Rationale: Another way to solve this question :
[-6/7 , -7/8 , -9/10 , -12/13 , -34/35] can be written as
-1+1/7, -1+1/8, -1 + 1/10, -1+1/13, -1+1/35
Now, in order to make the number larger, we need to add something larger to -1.
In first option, we can see 1/7 is the largest of all the other given
Hence, A
Answer: (A) -6/7
Question: The sum of the heights of two high-rises is x feet. If the second high rise is 37 feet taller than the first, how tall will the first high rise be ?
(A) (x+z)/2 + 37
(B) 2x−(37+z)
(C) (x−37)/2 + z
(D) (x - 37 )/2
(E) (2x−37)/z
Rationale: I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:
h1 + h2 = x
and h12= h21+ 37 =>
h1 + h1+ 37 = x => 2h1 = x-37 =? h1 = (x-37)/2
, CORRECT ANSWER D
Answer: (D) (x - 37 )/2
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 42.5%. What would have been the percentage of profit earned if no discount had been offered?
(A) 28.5
(B) 27.675
(C) 30
(D) 50
(E) None of these
Rationale: Giving no discount to customer implies selling the product on printed price. Suppose the cost price of the article is 100.
Then printed price = 100Ã—(100+42.5)/(100âˆ’5)=150
Hence, required % Profit = 150 â€“ 100 = 50%
Answer D
Answer: (D) 50
Question: There are 10 books on a shelf: 5 English books, 4 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
(A) 31/90
(B) 3/10
(C) 1/3
(D) 38/45
(E) 28/90
Rationale: Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
Favourable Outcomes
Case-1: One book is English (out of 5 English books) and one book is Spanish (out of 4 Spanish books) i.e. 5C1*4C1
Case-2: One book is Spanish (out of 4 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 4C1*2C1
Case-3: One book is English (out of 8 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 8C1*2C1
Total favourable Outcomes = 5C1*4C1+4C1*2C1+5C1*2C1 = 20+8+10 = 38
Total Possible Outcomes = 10C2 = 45
i.e. Probability = 38/45
D
Answer: (D) 38/45
Question: 3 people gave you 5 dollars. How many dollars do you have in all
(A) 15
(B) 17
(C) 0
(D) 67
(E) 100
Rationale: If 3 people give you 5 dollars you will have 15
3x5=15 A
Answer: (A) 15
Question: In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 200 more than the correct answer. Find the number.
(A) 125
(B) 280
(C) 384
(D) 400
(E) 500
Rationale: Explanation:
Let the number be x.
5*x/6 = 5*x/16 + 200
25*x/48 = 200
x = 384
ANSWER: C
Answer: (C) 384
Question: The Red Hotel has booked 1/4 of its rooms. The Blue Hotel has Has three times the capacity of the red hotel but has only booked 1/8 of its rooms. If all the bookings from the Red Hotel switched to the Blue Hotel, What fraction of the Blue Hotel's rooms would be booked?
(A) 2/8
(B) 3/4
(C) 7/16
(D) 5/24
(E) 1/5
Rationale: We will pretend that the Red Hotel has a total of 8 rooms. This means that the Blue Hotel would have 24 rooms. From this, we can deduce that there is 2 bookings at the Red Hotel and 3 bookings at the Blue Hotel. If the two bookings from the Red Hotel moved to the blue hotel that would mean a total of 5 bookings at the Blue Hotel. This would make 5 of the 24 rooms would be filled. (Answer: D)
Answer: (D) 5/24