divelab/Sys2Bench huggingface dataset:
Question: Avg cost of 3 sharpners and 6 erasers is Rs.72. The avg cost of 6 sharpners and 8 erasers is Rs.112. Find the total cost of 20 sharpners and 20 erasers?
Options:
A)190
B)160
C)130
D)200
E)180
Rationale: Avg cost of 3 sharpners and 6 erasers is Rs.72
(3 sharpner + 6 erasers) 9=72
therefore 1 sharpner cost is 72/9=8, so 3 sharpner cost is 3x8=24 and 6 erasers cost is 6x8=48
Again, avg cost of 6 sharpners and 8 erasers is Rs.112
(6 sharpner + 8 erasers) 14=112
therefore 1 sharpner cost is 112/14=8, so 6 sharpner cost is 6x8=48 and 8 erasers cost is 8x8=64
So 20 sharpner cost is (20/a)=160 and 20 erasers cost is (20x8)=160
ANSWER:B
Answer: B
Question: Sachin is younger than Rahul by 4 years. If their ages are in the respective ratio of 7:9, how old is Sachin?
Options:
A)24.9
B)24.6
C)24.2
D)24.8
E)24.5
Rationale: Let Rahul's age be x years.
Then, Sachin's age = (x - 7) years.
(x - 7)/x = 7/9
2x = 63 => x = 31.5
Hence, Sachin's age = (x - 7) = 24.5 years.
Answer: E
Answer: E
Question: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained?
Options:
A)9:1
B)8:1
C)9:8
D)2:1
E)1:1
Rationale: Milk = 3/5 * 20 = 12 liters, water = 8 liters
If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.
Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters
10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.
The ratio of milk and water in the new mixture = 16:4 = 4:1
If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 * 10 = 8 liters.
Amount of water removed = 2 liters.
Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.
The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
Answer:A
Answer: A
Question: Simplify
80âˆ’[5âˆ’(6+2(7âˆ’8âˆ’5Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯Â¯))]
Options:
A)23
B)25
C)89
D)30
E)32
Rationale: Explanation:
=80âˆ’[5âˆ’(6+2(7âˆ’8+5))]
(Please check due to overline, sign has been changed)
=80âˆ’[5âˆ’(6+2Ã—4))]
=80âˆ’[âˆ’9]=80+9=89
Option C
Answer: C
Question: In a game of 90 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60?
Options:
A)2.82
B)7.82
C)5.82
D)12.82
E)8.82
Rationale: In a game of 90 points,A give B 5 points and c 25 points means B=85,C=65
In 85 points B give 15 since 80-65=15
In 50 points B gives=50*15/85=8.82
ANSWER:E
Answer: E
Question: ABCD is a square where AB =âˆš6016. Let X be a point on AB and Y be a point on CD such
that AX = CY . Compute the area of trapezoid AXYD.
Options:
A)3008
B)2002
C)1008
D)2016
E)3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
6016/2= 3008 .
correct answer A
Answer: A
Question: 12 is what % of 80?
Options:
A)6
B)6.67
C)12
D)13
E)15
Rationale: We assume that 80 is 100%
assume 'x' is value we looking for
here,
80 = 100% and
x% = 12
therefore,
100/x = 80/12
100/x = 6.6667
x = 15
E
Answer: E
Question: 33
a3
+4b
___
88
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
Options:
A)12
B)10
C)13
D)24
E)34
Rationale: 3+3+b=8
b=2
3+a+4=8
a=1
ab=12
ans=A
Answer: A
Question: A train running at 1/4 of its own speed reached a place in 12 hours. How much time could be saved if the train would have run at its own speed?
Options:
A)9 hrs
B)10hrs
C)12hrs
D)15hrs
E)6hrs
Rationale: time taken if run its own speed = 1/4*12 = 3 hrs
Time saved = 12 - 3 = 9 hrs
Answer : A
Answer: A
Question: A collector collects stamps from foreign countries. In June, she gave 20 percent of her stamps to her friend. In July, she gave 35 percent of her remaining stamps to another friend. If these were the only changes in the number of stamps in the stamp collection during those two months, what percent of her collection at the beginning of June did she give to away in June and July?
Options:
A)32%
B)36%
C)40%
D)44%
E)48%
Rationale: Let x be the number of stamps in the original collection.
The percentage of the collection given away is:
0.2x + 0.35(0.8x) = 0.2x + 0.28x = 0.48x = 48%
The answer is E.
Answer: E
Question: How much pure alcohol should be added to 400ml of a 15% solution to make the strength of solution 32%?
Options:
A)100 ml
B)60 ml
C)120 ml
D)130 ml
E)150 ml
Rationale: 400ml has 15% alcohol i.e 60ml . This means we have 340ml of water or the liquid with which alcohol is mixed
Let V be the volume of alcohol added to make the strength 32%
then V/340+V = 32/100. solving this we get V as 160ml
so we need to add 160 -60 = 100 ml of alcohol
ANSWER:A
Answer: A
Question: The tailor has a 10 meter long piece of fabric for which to sew a ball room dress.
She has to cuts this fabric into strips of 200 centimeters each.
How long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ?
Options:
A)150
B)200
C)188
D)245
E)123
Rationale: The tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes. The answer is D
Answer: D
Question: Find the largest number of four digits which is exactly divisible by 26,18,12,15
Options:
A)9700
B)9710
C)9360
D)9130
E)9140
Rationale: Explanation:
LCM of 26-18-12-15 is 2340.
After dividing 9999 by 2340 we get 639 remainder.
So answer will be 9999-639 = 9360
Option C
Answer: C
Question: Set R has a mean of 15 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?
Options:
A){11,26}
B){18,19}
C){16,18}
D){16,16}
E){14,16}
Rationale: The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 15,the values (14,16) are closer than others.
Hence Answer : E
Answer: E
Question: Eggs are sold in packages of six or eleven only. If Doris bought 78 eggs exactly, what could be the number of large packs Doris bought?
Options:
A)6.
B)2.
C)3.
D)5.
E)4.
Rationale: No strategy involved. Simple question demanding fast calculation.
11x6 = 66=> 78-66=12 => 12/6 is an integer
Ans A. 6.
Good luck
Answer: A
Question: There 3 kinds of books in the library physics, chemistry and biology. Ratio of physics to chemistry is 3 to 2; ratio of chemistry to biology is 4 to 3, and the total of the books is more than 3000. Which one of following can be the total W of the book?
Options:
A)3003
B)3027
C)3024
D)3021
E)3018
Rationale: First, you have to find the common ratio for all 3 books. You have:
P:C:B
3:2 --> multiply by 2 (gives you row 3)
4:6
6:4:3
Hence:
P:C:B:T(Total)W
6:4:3:13 ----> This means, the Total Number must be a multiple of 13.
Answer A is correct since 299 is divisible by 13, hence is 2990 and so is 3003 (2990+13).
Answer: A
Question: The sum of squares of two numbers is 80 and the square of their difference is 36. The product of the two numbers is.
Options:
A)22
B)44
C)58
D)116
E)None
Rationale: Explanation :
Let the numbers be x and y . Then
x2+y2=80 and (x−y)2=36
(x−y)2=36⇒x2+y2−2xy=36
⇒2xy=(x2+y2)−36=80−36=44
⇒xy=22
Correct Option: A
Answer: A
Question: A salesperson receives a base salary of $900 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?
Options:
A)$1,500
B)$1,800
C)$2,100
D)$2,700
E)$2,800
Rationale: Ans : 900+ 7.5 % * 150 * (210-50) = $ 2700
Answer D
Answer: D
Question: If both 112 and 33 are factors of the number a * 43 * 62 * 1311, then what is the smallest possible value of a?
Options:
A)121
B)3267
C)363
D)33
E)None of the above
Rationale: Explanatory Answer
Step 1: Prime factorize the given expression
a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311
Step 2: Find factors missing after excluding 'a' to make the number divisible by both 112 and 33
112 is a factor of the given number.
If we do not include 'a', 11 is not a prime factor of the given number.
If 112 is a factor of the number, 112 should have been in 'a'
33 is a factor of the given number.
If we do not include 'a', the number has only 32 in it.
Therefore, if 33 has to be a factor of the given number 'a' has to contain 31 in it.
Therefore, 'a' should be at least 112 * 3 = 363 if the given number has 112 and 33 as its factors.
The smallest value that "a" can take is 363.
Choice C is the correct answer.
Answer: C
Question: Of the students at a certain high school, 90 percent took a course in algebra or geometry and 10 percent took courses in both. If the percent of students who took a course in algebra was 3 times the percent of students who took a course in geometry, what percent of the students took a course in algebra but not geometry?
Options:
A)35%
B)45%
C)55%
D)65%
E)70%
Rationale: You can also just use the formula
n(A or B) = n(A) + n(B) - n(A and B)
90 = 3X + X - 10
X = 25
3X = 75
This is the number of people who took algebra including those who took both. To get the number of people who took only algebra, 75 - 10 = 65%
Answer (D)
Answer: D
Question: If a certain sample of data has a mean of 25.0 and a standard deviation of 3.0, which of the following values is more than 2.5 standard deviations from the mean?
Options:
A)12.0
B)13.5
C)17.5
D)23.5
E)26.5
Rationale: The standard deviation is 3. 2.5 standard deviations, which is just 2.5 x 3.0 is 7.5. The only answer more than 7.5 away from the mean is C.
Answer: C
Question: At the time of marriage, a man was 7 years elder to his wife. 10 years after their marriage, his age is 4/3 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
Options:
A)36 years
B)30 years
C)26 years
D)24 years
E)11 years
Rationale: let wifes age= x
husband age = x+7
now after 10 years of mrg x+10 wifes age
x+7+10 husbands age
4/3(x+10)=x+7+10
after solving x=11
ANSWER:E
Answer: E
Question: 45 x ? = 60% of 900
Options:
A)16.2
B)12
C)5
D)500
E)None
Rationale: Answer
Let 45 x A = (60 x 900)/100
∴ A = (60 x 9)/45 = 12
Correct Option: B
Answer: B
Question: A 500 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
A)2 min 48 sec
B)4 min 48 sec
C)4 min 38 sec
D)4 min 18 sec
E)4 min 8 sec
Rationale: S = 500/40 = 12.5 mps
S = 3600/12.5 = 288 sec = 4 min 48 sec
ANSWER:B
Answer: B
Question: If an amount of Rs 42,460 is distributed equally
amongst 22 persons, how much amount would each
person get?
Options:
A)Rs 1905
B)Rs 2000
C)Rs 1930
D)Rs 765
E)None
Rationale: Required amount =42460/22 = Rs 1930
Answer C
Answer: C
Question: What is the average of four tenths and two thousandths
Options:
A)0.2022
B)0.3325
C)0.201
D)0.2012
E)0.2114
Rationale: Explanation:
Four tenths = 0.4
two thousandths = 0.002
The average is (0.4 + 0.002)/2 = 0.201
Answer: C
Answer: C
Question: If x^2 - 1 = 0 and x < 0, which of the following must be equal to 0 ?
Options:
A) x^2 - 9x
B) x^2 - 9x + 20
C) x^2 - 2x + 3
D) x^2 + 2x + 1
E) x^2 + 5x + 6
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= -1 in the equation x^2 +2x+1 = 1-2+1 = 0
D is also the answer
Answer: D
Question: A factory has 500 workers, 18 percent of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20 percent?
Options:
A) 3
B) 10
C) 20
D) 30
E) 35
Rationale: Currently the factory has 0.18*500=90 women.
After 50 additional workers are hired, there will be total of 550 workers and we need 0.2*550=110 of them to be women, so we need 110-90=20 more women.
Answer: C.
Answer: C
Question: An airplane flies along the four sides of a square field at the speeds of 200, 400, 600 and 800 km/h. The average speed of the plane around the field in km/h is
Options:
A)384
B)400
C)500
D)284
E)None of these
Rationale: Explanation :
Let each side of the square field be x km.
So, average speed of the plane
= 4x/((x/800)+(x/600)+(x/400)+(x/200))
= (4*2400)/(3+4+6+12) = 9600/25
= 384
Answer : A
Answer: A
Question: If N = 2^0.1 and N^b = 16, b must equal
Options:
A)3/80
B)3/5
C)40
D)5/3
E)80/3
Rationale: 10/100 = 1/10
N = 2 ^ 1/10
N^b = 2^4
(2^1/10)^b = 2^4
b = 40
Answer: C
Answer: C
Question: A can run 4 times as fast as B and gives B a start of 63 m. How long should the race course be so that A and B might reach in the same time?
Options:
A)70 m
B)60 m
C)80 m
D)65 m
E)84 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 63m he gains 63*(4/3)
I.e 84m
ANSWER:E
Answer: E
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Options:
A)3377
B)2678
C)5460
D)1976
E)1671
Rationale: 5000 * 104/100 * 105/100 => 5460
Answer: C
Answer: C
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 9 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
Options:
A)29
B)48
C)55
D)67
E)86
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 9.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 10, 29, 48, 67, 86,...
The answer is C.
Answer: C
Question: In how many ways can the letters of the word ED456 be rearranged such that the numbers always appear together?
Options:
A)25
B)16
C)36
D)9
E)29
Rationale: ED456
456 will come together as a group which can be arranged in 3!=6ways.
456,E,D can be arranged in 3!=6 ways.
total possible arrangements = 6*6=36 ways
ANSWER:C
Answer: C
Question: A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?
Options:
A)28
B)29
C)31
D)35
E)37
Rationale: Explanation:
Clearly, we have :
A = B - 3 ...(i)
D + 5 = E ...(ii)
A+C = 2E ...(iii)
B + D = A+C = 2E ...(iv)
A+B + C + D + E=150 ...(v)
From (iii), (iv) and (v), we get: 5E = 150 or E = 30.
Putting E = 30 in (ii), we get: D = 25.
Putting E = 30 and D = 25 in (iv), we get: B = 35.
Putting B = 35 in (i), we get: A = 32.
Putting A = 32 and E = 30 in (iii), we get: C = 28.
Answer: A
Answer: A
Question: Two employees X and Y are paid a total of Rs. 330 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
Options:
A)s.150
B)s.200
C)s.250
D)s.350
E)s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 330
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 330
â‡’ y[12/10 + 1] = 330
â‡’ 22y/10 = 330
â‡’ 22y = 3300
â‡’ y = 3300/22 = 300/2 = Rs.150
A)
Answer: A
Question: A certain car increased its average speed by 4 miles per hour in each successive 5-minute interval after the first interval. If in the first 5-minute interval its average speed was 20 miles per hour, how many miles did the car travel in the third 5-minute interval?
Options:
A)1.0
B)1.5
C)2.0
D)2.5
E)3.0
Rationale: In the third time interval the average speed of the car was 20+4+5=29 miles per hour;
In 5 minutes (1/12 hour) at that speed car would travel 29*1/12=2.5 miles.
Answer: D.
Answer: D
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 24 kmph and 48 kmph. After how much time will the trains meet?
Options:
A)20/8 sec
B)20/4 sec
C)20/7 sec
D)22/7 sec
E)5 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (24 + 48)*5/18 = 4*5 = 20 mps.
The time required = d/s = 100/20 = 5 sec.Answer:E
Answer: E
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)868
B)869
C)865
D)860
E)861
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Answer: D
Answer: D
Question: Find the lowest common multiple of 24, 36 and 40.
Options:
A)360
B)420
C)510
D)320
E)280
Rationale: LCM=2*2*2*3*3*5=360.
Answer is A
Answer: A
Question: The measurement of a rectangular box with lid is 25cmx4cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
Options:
A)11.12
B)10.11
C)72
D)10.66
E)9.2
Rationale: d=4, r=2;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*2*2*2= 10.66πcm3 ANSWER:D
Answer: D
Question: Length of a rectangular plot is 10 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)55 m
B)60 m
C)80 m
D)82 m
E)84 m
Rationale: Let breadth = x metres.
Then, length = (x + 10) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 10) + x] = 200
2x + 10 = 100
2x = 90
x = 45.
Hence, length = x + 10= 55 m
A
Answer: A
Question: The concentration of spirit in three different vessels A, B and C are 30%, 50% and 25% respectively. If 4 litres from vessel A, 5 litres from vessel B and 6 litres from vessel C are mixed, find the concentration of spirit in the resultant solution.
Options:
A)32.54%
B)33%
C)34.67%
D)35%
E)36.62%
Rationale: Quantity of spirit in new solution=(4*30/100)+(5*50/100)+(6*25/100)=1.2+2.5+1.5=5.2 liters
So % concentration of spirit=100*5.2/(4+5+6)=34.67%
ANSWER:C
Answer: C
Question: The side of a rhombus is 24 m and length of one of its diagonals is 18 m. The area of the rhombus is?
Options:
A)410.47
B)403.47
C)420.47
D)400.47
E)300.47
Rationale: area of the rhombus = 1/2 * p * √4(a)2 - (p)2
a= 24 ; p = 18
A=1/2 * 18 *√4(24)2 - (18)2
=1/2 * 18 *√2304 - 324
=1/2 * 18 *√1980
A =400.47
Answer : D
Answer: D
Question: If the C.I. on a sum for 2 years at 12 1/2 % per annum is Rs. 510, the S.I. on the same sum at the same rate for the same period of time is?
Options:
A)298
B)278
C)299
D)480
E)276
Rationale: Let the sum be Rs. P. Then,
[P(1 + 25/(2 * 100))2 - P] = 510
P[(9/8)2 - 1] = 510.
Sum = Rs. 1920
So, S.I. = (1920 * 25 * 2) / (2 * 100) = Rs. 480
Answer: D
Answer: D
Question: If the number a60,858,61b is evenly divisible by 88, what are the values of a and b?
Options:
A)b = 6, a = 6
B)b = 2, a = 3
C)b = 2, a = 1
D)b = 4, a = 6
E)b = 4, a = 3
Rationale: a60,858,61b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
61b/8 => 616/8 = 77 => b = 6
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a6085861-6 => a608585-5 => a60858-0 => a6085-8 => a607-7 => a60-0 => a6-0 => a6 => 66/11 = 6.
So a = 6.
Answer: A
Answer: A
Question: From a pack of cards, two cards are drawn one after the other, with replacement. What is the probability that the first card is a club and the second card is a king or queen?
Options:
A)2/13
B)3/13
C)1/26
D)1/52
E)3/52
Rationale: P(club) = 1/4
P(king or queen) = 2/13
P(club then a king/queen) = 1/4 * 2/13 = 1/26
The answer is C.
Answer: C
Question: Select the non termination decimal among the following.
Options:
A)22/3
B)3/4
C)4/5
D)7/8
E)9/10
Rationale: A. Non terminating decimal means that 22/3 = 7.33333 and so on.
Answer: A
Question: Two pipes A and B can fill a cistern in 9 and 18 minutes respectively, and a third pipe C can empty it in 24 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)6 min
B)7 min
C)8 min
D)10 min
E)17 min
Rationale: 1/9 + 1/18 - 1/24
= 1/8
8/1= 8
Answer:C
Answer: C
Question: How many liters of water must be evaporated from 50 liters of a 8-percent sugar solution to get a 10-percent solution?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: 8% of a 50 liter solution is 4L which is 10% of the solution at the end.
The solution at the end must be 40 L.
We need to evaporate 10 liters.
The answer is B.
Answer: B
Question: The salary of a worker is first increased by 20% and afterwards reduced by 20%. What is the net change in the worker's salary?
Options:
A)4% decrease
B)8% decrease
C)4% increase
D)8% increase
E)no change
Rationale: Let x be the original salary.
The final salary is 0.8(1.2x) = 0.96x
The answer is A.
Answer: A
Question: A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 36 years and that of the grandchildren is 6 years. What is the average age of the family?
Options:
A)28 4â„7 years
B)31 5â„7 years
C)32 years
D)27 1â„2 years
E)None of these
Rationale: Required average = (67Ã—2+36Ã—2+6Ã—3/2+2+3)
=224/7
= 32 years
Answer C
Answer: C
Question: How many digits to the right of the decimal point are there in the product of .32655 * 65.01?
Options:
A)8
B)5
C)4
D)6
E)7
Rationale: Product of is .32655 * 65.01 is 21.2290155.
Therefore number of digits to right of decimal point is 7
Answer is E.
Answer: E
Question: Laura has a deck of standard playing cards with 18 of the 54 cards designated as aheart.If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
Options:
A)1/4
B)1/3
C)5/26
D)12/42
E)13/42
Rationale: No replacement there, 10 cards are dealt and we are asked to find the probability that 10th card is a heart.
If there is no replacement then how is the (P) that the 10th card is 18/54 ??
there are many cases here to be considered here if there is no replacement such as:
H- Denotes heart X-may be any diamond, spade or club.
1. HXXXXXXXXH
2. HHXXXXXXXH
3. HHHXXXXXXH
.
.
.
.
.
9. HHHHHHHHHH
10. XXXXXXXXXH
All cases from 1 to 10 will have different probabilities for heart to be at the 10th place and it will take hell lot of time to calculate all of them.
For according to me the above solution by Ian is only valid if cards are replaced (Every card has a 18/54 = 1/3 chance of being a heart; it doesn't matter if it's the top card in the deck or the tenth card in the deck.)If that's the case that brings back me to my original question ----how do we determine that the cards are replaced or not?? based on the question given ....
B
Answer: B
Question: A man who goes to work long before sunrise every morning gets dressed in the dark. In his sock drawer he has 6 black and 8 blue socks. What is the probability that his first pick was a black sock, but his second pick was a blue sock?
Options:
A)24/91
B)24/90
C)24/97
D)24/95
E)24/93
Rationale: This is a case of without replacement. We have to multiply two probabilities. 1. Probability of picking up a black sock, and probability of picking a blue sock, given that first sock is black.
6C114C1×8C113C1=24/91
Answer:a
Answer: A
Question: If y exceeds x by 20%, then x is less than y by?
Options:
A)16 2/8%
B)16 8/3%
C)16 2/3%
D)76 2/3%
E)17 2/3%
Rationale: X=100	y=120
120------20
100-------? => 16 2/3%
Answer:C
Answer: C
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?
Options:
A)82 days
B)26 days
C)32 days
D)34 days
E)25 days
Rationale: 1600 ---- 28 days
1600 ---- 24
1200 ---- ?
1600*24 = 1200*x
x = 32 days
Answer:C
Answer: C
Question: A positive integer is divisible by 3 if and only if the sum of its digits is divisible by 3. If the six-digit integer is divisible by 3, and n is of the form 4k2,k21, where k represents a digit that occurs twice, how many values could n have?
Options:
A)2
B)3
C)6
D)5
E)4
Rationale: 4k2k21
Taking sum of the numericals = 4 + 2 + 2 + 1 = 9
We require the values of K such that they are also divisible by 3
402021
432321
462621
492921
Answer = 4 = E
Answer: E