mathewhe/aqua_rat huggingface dataset:
Question: Two persons start running simultaneously around a circular track of length 700 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 16 seconds
(B) 28 seconds
(C) 49 seconds
(D) 57 seconds
(E) 63 seconds
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 700 / (15 + 25)5/18 = 700* 18 / 40 * 5
= 63 seconds.
Answer:E
Answer: (E) 63 seconds
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) 12/489
(B) 12/452
(C) 12/455
(D) 12/429
(E) 12/292
Rationale: 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
Answer: (C) 12/455
Question: A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in?
(A) 7 years
(B) 10 years
(C) 15 years
(D) 20 years
(E) 25 years
Rationale: P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.
ANSWER:C
Answer: (C) 15 years
Question: A man buys a cycle for Rs.1400 and sells it at a loss of 18%. What is the selling price of the cycle?
(A) Rs.1148
(B) Rs.1160
(C) Rs.1190
(D) Rs.1202
(E) NONE
Rationale: Solution
S.P	= 82% of Rs.1400
= Rs.(82/100×1400)
Rs.1148.
Answer A
Answer: (A) Rs.1148
Question: The length of the longest rod that can fit in a cubical room of 4 m side is?
(A) 3:8
(B) 3:1
(C) 3:0
(D) 3:2
(E) 3:5
Rationale: 3:1
Answer:B
Answer: (B) 3:1
Question: The ratio of men to women in the Snyder community choir is 4 to 3. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?
(A) 27
(B) 25
(C) 31
(D) 32
(E) 34
Rationale: This question has a number of patterns in it that we can take advantage of. We can also TEST THE ANSWERS (but we can actually eliminate most of the answer choices rather quickly.
We're told that the ratio of the Men to Women in the Snyder choir is 4 to 3, so the number of men MUST be a multiple of 4 and the number of women MUST be a multiple of 3 The question asks how many WOMEN are in the SNYDER choir, so the answer MUST be a multiple of 3. We can eliminate Answers B,C, D and E (since they're NOT multiples of 3
Answer A
Answer: (A) 27
Question: Jadeja rented a power tool from a rental shop. The rent for the tool was $13 for the first hour and $8 for each additional hour. If Jadeja paid a total of $133, excluding sales tax, to rent the tool, for how many hours did she rent it?
(A) 14
(B) 19
(C) 16
(D) 13
(E) 12
Rationale: 13 + 8n = 133
n = 15
Total time = n+1 hrs = 15+1 hrs = 16 hrs
Answer : C
Answer: (C) 16
Question: Arjun started a business with Rs. 40,000 and is joined afterwards by Anoop with Rs.80, 000. After how many months did Anoop join if the profits at the end of the year are divided equally?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Suppose Anoop joined after 3 months.
Then, 40000 * 12 = 80000 * (12 – x)
=> x = 6.
ANSWER:D
Answer: (D) 6
Question: For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/11
(A) a) 12
(B) b) 6
(C) c) 10
(D) d) 14
(E) e) 32
Rationale: It seems that the accepted answer is wrong, according to WolframAlpha. The answer should be 26, which isn't even listed as a selectable answer.
D
Answer: (D) d) 14
Question: Each student is given a five-character identification code. The first three characters are selected from the numbers 0 to 9 inclusive, and the last two characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
(A) 652,000
(B) 665,000
(C) 676,000
(D) 683,000
(E) 694,000
Rationale: The number of possible codes is 10*10*10*26*26=26,000.
The answer is C.
Answer: (C) 676,000
Question: 1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?
(A) 11
(B) 99
(C) 32
(D) 44
(E) 66
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer: C
Answer: (C) 32
Question: 5 tables and 10 chairs were sold for 20000.15%gain for table,10%loss on chair.overall profit rs 750.the cp of table is
(A) 840
(B) 1940
(C) 2040
(D) 2140
(E) 3240
Rationale: let cost of table is X and chair is Y.
sold price is 20000 and profit is 750 .
so cost for both is 19250.
then
first eq is 5X+10Y=19250
second eq is 5*(115/100)X + 10* (90/100)Y =20000
solve both eqations , then get X=2140
ANSWER:D
Answer: (D) 2140
Question: The H.C.F. of two numbers is 30 and the other two factors of their L.C.M. are 10 and 15. The larger of the two numbers is:
(A) 350
(B) 250
(C) 450
(D) 500
(E) 620
Rationale: Explanation:
Clearly, the numbers are (30 x 10) and (30 x 15).
{\color{Blue} \therefore } Larger number = (30 x 15) = 450.
Answer: C) 450
Answer: (C) 450
Question: On average, the boys in the class have 12 erasers and the girls have 26 erasers. If the overall class average is 18 erasers, what is the ratio of boys to girls in the class?
(A) 2/1
(B) 3/2
(C) 4/3
(D) 5/4
(E) 6/5
Rationale: (26G + 12B) / (G+B) = 18
26G + 12B = 18(G+B)
8G=6B
B/G = 4/3
The answer is C.
Answer: (C) 4/3
Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 15
(B) 20
(C) 18
(D) 24
(E) 22
Rationale: son age is x then father age x+24
2(x+2)=(x+24+2)
2x+4=x+26
x=22 yrs
ANSWER E
Answer: (E) 22
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 21. The quotient obtained by him was 35. The correct quotient is?
(A) 20
(B) 24
(C) 28
(D) 29
(E) 30
Rationale: Number = (35 * 12) = 420
Correct quotient = 420/21 = 20
A)
Answer: (A) 20
Question: Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 6 and the product of the given number and the sum of its digits is equal to 136.
(A) 82
(B) 93
(C) 39
(D) 28
(E) 17
Rationale: Using the elimination method the option that fits this description is 17
7-1 = 3 (unit's digit that exceeds its ten's digit by 3)
17*8 = 136 (the product of the given number and the sum of its digits is equal to 175)
answer :E
Answer: (E) 17
Question: For what range of values of 'x' will the inequality 15x - 2/x > 1?
(A) x > 0.4
(B) x < 1/3
(C) -1/3 < x < 0.4, x > 15/2
(D) -1/3 < x and x< 0, x > 2/5
(E) x < -1/3 and x > 2/5
Rationale: In Case 1 where x > 0, I agree. I calculated x > (-1/3) and x > 2/5, and because x > 0, it must be x > 2/5.
In Case 2 where x < 0, I don't understand why you say that the range must be x > -1/3 and x < 0, since the values that satisfy the inequality 15x^2 - x - 2 < 0show that x < -1/3 and x < 2/5.
I have the same doubt. Shouldn't the answer be D?
____________
The answer IS D.
Answer: (D) -1/3 < x and x< 0, x > 2/5
Question: Selling 1 kilogram of mangoes for Rs. 500, a shop keeper gains 5%. During an seasonal time, the shopkeeper allows a discount of 5% on the marked price. His gain/loss percent during the sale is?
(A) 0.1%
(B) 2%
(C) 0.2%
(D) 5%
(E) 10%
Rationale: Explanation:
Marked price = Rs. 500
C.P. = 100/105 * 500 = Rs. 476.19
Sale price = 95% of Rs. 500 = Rs. 475
Required LOSS % = .119/476.19 * 100 = 0.2%.
Answer: C
Answer: (C) 0.2%
Question: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
(A) 2999
(B) 2669
(C) 2600
(D) 1500
(E) 1267
Rationale: (5/100) A = (15/100) B
A = 3B
A + B = 2000
4B = 2000 => B = 500
A = 1500
Answer: D
Answer: (D) 1500
Question: Eight fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 52
(B) 56
(C) 60
(D) 64
(E) 72
Rationale: 8*7 = 56
The answer is B.
Answer: (B) 56
Question: A group of 36 students are visiting an amusement park. The tickets are $6 for an individual or $30 for a group up to 10 people. What is the minimum amount the group has to pay?
(A) $520.
(B) $320.
(C) $220.
(D) $420.
(E) $120.
Rationale: There are 2 options to buy tickets for 36 students.
• Option 1: 3 group tickets + 6 single tickets.
The cost for option 1 is $30 × 3 + $6 × 6 = $126.
• Option 2: 4 group tickets
The cost for option 2 is $30 × 4 = $120.
The option 2 is cheaper. Therefore, the minimum amount the group has to pay is $120.
correct answer E
Answer: (E) $120.
Question: If points X and Y are two distinct points in the coordinate plane, which of the following can have more than one possible value?
(A) The circumference of a circle with diameter XY.
(B) The area of a square with diagonal XY.
(C) The perimeter of a right isosceles triangle with a leg XY.
(D) The area of a circle with chord XY.
(E) The area of an equilateral triangle with base XY.
Rationale: All other options will have distinct values.
ANSWER:C
Answer: (C) The perimeter of a right isosceles triangle with a leg XY.
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $252 per week. How much does she earn in dollars per hour?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $252 per week
36x =252
x =7
Correct Option :E
Answer: (E) 7
Question: Two trains 140 m and 150 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9 sec
(B) 13.8 sec
(C) 53.8 sec
(D) 10.44 sec
(E) 10.4 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 150 = 290 m.
Required time = 290 * 9/250 = 10.44 sec.
Answer: D:
Answer: (D) 10.44 sec
Question: The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
(A) 504
(B) 536
(C) 544
(D) 548
(E) 586
Rationale: Required number = (L.C.M. of 12, 15, 20, 54) + 8
= 540 + 8
= 548.
Answer: Option D
Answer: (D) 548
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 4 days. B can do the work alone in?
(A) 19
(B) 12
(C) 11
(D) 24
(E) 114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/4
6/x = 1/4 => x = 24
So, B takes 12 hours to finish the work.
Answer: D
Answer: (D) 24
Question: What is the ratio of y to x if (x + 3y) / ( x - y) = 5/4?
(A) -15/4
(B) -5/3
(C) 1/17
(D) 3/5
(E) 15/1
Rationale: Solving for y/x gives, 1/17 (C)
Answer: (C) 1/17
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 1.15 km respectively. The time taken by the slower train to cross the faster train in seconds is?
(A) 65 sec
(B) 54 sec
(C) 48 sec
(D) 33 sec
(E) 12 sec
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.10 + 1.15 = 2.25 km = 2250 m.
Required time = 2250 * 3/125
= 54 sec.
Answer:B
Answer: (B) 54 sec
Question: The distance from the x-axis to point P is half the distance from the y-axis to point P. If the coordinates of P are (x,-5), how many units is P from the y-axis?
(A) 2.5
(B) 5
(C) 7.5
(D) 10
(E) 12
Rationale: The x-axis is 5 units from the point P.
Thus the y-axis is 10 units from the point P.
The answer is D.
Answer: (D) 10
Question: Evaluate:60 - 12*3*2 =?
(A) 42
(B) 52
(C) 62
(D) 72
(E) 82
Rationale: According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
60 - 12*3*2 = 60 - 8 = 52
correct answer B
Answer: (B) 52
Question: Jackson purchased a refrigerator and a mobile phone for $15000 and $8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
(A) profit of Rs. 200
(B) profit of Rs. 100
(C) loss of Rs. 100
(D) loss of Rs. 200
(E) None of these
Rationale: A
profit of Rs. 200
Let the SP of the refrigerator and the mobile phone be $ r and $ m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = $200
As this is positive, an overall profit of $200 was made.
Answer: (A) profit of Rs. 200
Question: 81 men working 8 hours per day dig 30 m deep. How many extra men should be put to dig to a depth of 50 m working 6 hours per day?
(A) A)99
(B) B)77
(C) C)66
(D) D)55
(E) E)88
Rationale: (81 * 8)/30
= (x * 6)/50
=> x =180
180 – 81
= 99
Answer:A
Answer: (A) A)99
Question: There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family
(A) 1
(B) 2
(C) 3 women
(D) 4
(E) 5
Rationale: Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12 and number of women = 15-12 = 3
ANSWER:C
Answer: (C) 3 women
Question: An exam consists of 2 true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above 70% is a passing grade, what is the probability that Brian passes?
(A) 1/16
(B) 37/256
(C) 1/2
(D) 219/256
(E) 15/16
Rationale: If you have 8 T or F and Brian is going to guess then each question he has a 50% chance of getting correct.
If a passing score is 70% it means Brian needs to get 6/8=75%, 7/8=87.5%, or 8/8=100% to pass. Each is a possibility. If Brian gets a 5/8(=62.5%) or below he fails.
So first figure out the number of ways that Brian can get 6 out of 8, 7 out of 8, and 8 out of 8 questions correct.
Which is 8 choose 6, equals is 28, 8 choose 7, equals 8, and 8 choose 8, equals 1. This sums to 37.
The number of possible questions outcomes -the sum of 8 choose 8, 7 choose 8, 6 choose 8….2 choose 8, 1 choose 8, and 0 choose 8 is 256, so the chance of him passing is 1/16.
A
Answer: (A) 1/16
Question: A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different colors c patterns can be floor be parqueted?
(A)  104
(B)  213
(C)  3^5
(D)  705
(E)  726
Rationale: Total number of squares we need to fill = 6
Number of colors we have = 3
Therefore, total number of patterns c= 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
Answer: (E)  726
Question: How many integers between 1 and 1,050 are divisible by 10, 25, and 35?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 3
Rationale: Prime factorization of given numbers
10=2*5
25=5^2
35=5*7
LCM of the given numbers
=2*5^2*7
=50*7
=350
Therefore , number of integers = 1050/350
=3
Answer:option E
Answer: (E) 3
Question: Akhil borrowed a certain sum of money at the rate of 6%, 9% and 14% for a period of first two years, next three years and beyond the period of five years respectively. If at the end of nine years, he paid Rs. 8550 as interest, then find the sum of money he had borrowed.
(A) Rs. 9,002
(B) Rs. 9,019
(C) Rs. 9,199
(D) Rs. 9,000
(E) Rs. 9,192
Rationale: Explanation:
Let Rs.P be the money borrowed by Akhil.
I) R = 6%, T = 2 years
Simple Interest of 2 years = PRT/100
= P * 6 * 2/100 = 12P/100
II) R = 9%, T = 3 years
Simple Interest of 3 years = P * 9 * 3/100 = 27P/100
III) R = 14%, T = 4 years
Simple Interest of 3 years= P * 14 * 4/100 = 56P/100
Therefore, total Simple Interest of 9 years
= 12P/100 + 27P/100 + 56P/100
= 95P/100
The total interest paid after nine years = Rs.8550
95P/100 = 8550
Therefore, 95P = 855,000
P = 855,000/95 = Rs. 9,000
Amount of money borrowed by Akhil = Rs. 9,000
ANSWER: D
Answer: (D) Rs. 9,000
Question: Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $126 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts were the same, what was the amount of Julie's initial savings?
(A) 600
(B) 720
(C) 1080
(D) 1200
(E) 1440
Rationale: We need to find the amount off Julie's Initial savings...Let that be 2x
So x goes in simple interest and x goes in compund interest for a period of 2 years...
In case of Simple interest, The interest paid out is same for each year..Hence if $120 was interest for 2 years that means interest per year will be 60 $
So we have S.I,120 = x∗2∗R100x∗2∗R100
or 6000 =x*R
For CI, in 126 $, 6$ represents nothing but interest earned on interest of 1st year.
In the First year, Interest amount is same for S.I and C.I
So we have
x(1+R100)2−x=126x(1+R100)2−x=126
or x(1 + R^2/10000+ 2R/100)-x=126
x+xR^2/10000+2xR/100)-x=126
x+R*6000/10000+12000/100-x=126
0.6R+120=126
0.6R=6 or R=10
So x=600...2x=1200 is the Initial savings. Answer is D
Answer: (D) 1200
Question: A company that ships boxes to a total of 14 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of the colors in a pair does not matter)
(A) 7
(B) 8
(C) 5
(D) 9
(E) 6
Rationale: Back-solving is the best way to solve this problem.
You basically need 14 combinations (including single colors)
If we start from option 1->
1=> 4C2 + 4 = 10 (Not enough)
2=> 5C2 + 5 = 15 (Enough)
Since the minimum number is asked. It should be 5.
Answer - C
Answer: (C) 5
Question: The population of a town is 286900. If it increase at the rate of 5% per annum. What will be its population for 3years hence?
(A) 200000
(B) 215600
(C) 194582
(D) 332122
(E) 215460
Rationale: population after 3years = 286900*(1+ 5/100)^3 = 332122
Answer is D
Answer: (D) 332122
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1400, then what is the income of P1?
(A) s.800
(B) s.2400
(C) s.4000
(D) s.3500
(E) s.4200
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 1400 …(i) and 4x – 2y = 1400 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1400 -> x = 700
P1’s income = Rs 5*700 = Rs.3500
ANSWER:D
Answer: (D) s.3500
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7020 km and comes back to the starting point. The total time taken by him is:
(A) 914.2 hours
(B) 900 hours
(C) 915 hours
(D) 891.4 hours
(E) 915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7020/18 + 7020/14 = 390 + 501.4 = 891.4 hours
Answer: Option D
Answer: (D) 891.4 hours
Question: Miles breeds Beagles and sells the puppies. He has nine customers that each want the same amount of puppies. Miles currently has 138 puppies. How many puppies would he have to keep to accommodate their requests?
(A) 1
(B) 4
(C) 5
(D) 8
(E) 3
Rationale: We add the sum of the digits together to get twelve and subtract to get a number that can be divided by 9. 12 - 9 = 3. This means Miles will have to keep three puppies(option D).
Answer: (D) 8
Question: Convert 100miles into yards?
(A) 25630 yards
(B) 35200 yards
(C) 39520 yards
(D) 42560 yards
(E) 176000 yards
Rationale: 1 mile = 1760 yards
100 miles = 100*1760 = 176000 yards
Answer is E
Answer: (E) 176000 yards
Question: How much time does a train 150 metres long running at 54 km/hr take to pass a pole?
(A) 7.9s
(B) 2.5s
(C) 7.5s
(D) 7.6s
(E) 10s
Rationale: Explanation:
54 km/hr = 54 * 5/18 = 15 m/s
Speed = distance/time; v = d/t
15 = 150/t
t = 10s
ANSWER: E
Answer: (E) 10s
Question: Mike and Fritz ran a 30-mile Marathon. Mike ran 10 miles at 10 miles per hour and then ran at 5 miles per hour for the remaining 20 miles.Fritz ran the first one-third (by time) of the run at 10 miles per hour and the remaining two-thirds of the run at 5 miles per hour. How much time in hours did Fritz take to complete the Marathon?
(A) 3
(B) 3.5
(C) 4
(D) 4.5
(E) 5
Rationale: Let total time= t
F travelled at rate 10 mph for t/3 time and 5 mph for 2t/3 time
d= s1t1+s2t2
30= 10*t/3 + 5*2t/3
30= 20t/3
t= 4.5
D is the answer
Answer: (D) 4.5
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability Q that the number of men is equal to that of women?
(A) Q=18/35
(B) Q=16/35
(C) 14/35
(D) 13/35
(E) 12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: (A) Q=18/35
Question: The average of 20 numbers is calculated as 30. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
(A) 40
(B) 26
(C) 60
(D) 97
(E) 12
Rationale: 20 * 30 + 36 – 26
= 160/10
= 60
Answer: 60
Answer is C
Answer: (C) 60