divelab/Sys2Bench huggingface dataset:
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 11% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Options:
A)70 lbs
B)40 lbs
C)25 lbs
D)50 lbs
E)60 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 11% profit
A+B = 100 pounds
(.07A + .11B)/(A+B) = .10
.07A + .11B = .1A + .1B
.01B = .03A
1B = 3A
1/3 = A/B
So, for every 1 pounds of A, we have 3 pounds of B.
With 100 pounds total, we have 25 pounds of A and 75 pounds of B.
Option C
Answer: C
Question: When x is divided by y, the quotient is z with remainder v. Which of the following is equal to v?
Options:
A)yz – x
B)y/x−z
C)x – y – z
D)x – yz
E)zx – y
Rationale: (x/y)=z(+v)
(18/8)=2(+2)
x-yz
which is 18-(8*2)=2
Answer is D
Answer: D
Question: 84/12/0.8 = ?
Options:
A)8.17
B)7.14
C)6.23
D)4.35
E)8.75
Rationale: E
8.75
? = 84/(12*0.8) = 8.75
Answer: E
Question: A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many Y acres were used for corn?
Options:
A) 188
B) 258
C) 376
D) 470
E) 517
Rationale: consider 5x acres of land used for bean
consider 2x acres of land used for wheat
consider 4x acres of land used for corn
Total given is 1034 acres
11x =1034
x = 94
land used for corn Y= 4 * 94 = 376
correct option - C
Answer: C
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = f is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-f, -k), then what are the coordinates of the point P?
Options:
A)(-5f, -5k)
B)(-3f, -3k)
C)(2f, 2k)
D)(3f, 3k)
E)(5f, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-f, -k), so R is at a distance of 2f from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4f and coord (3f,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3f,3k).ans D
Answer: D
Question: There are 5 red balls, 7 blue balls, 6 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
Options:
A)10
B)23
C)43
D)40
E)24
Rationale: The worst case scenario would be if we pick 4 red balls, 6 blue balls, 5 (?) balls and 8 black balls. In this case we'll have 4+6+5+8=23balls and still won't have all the balls of one color. The next 24rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: E
Answer: E
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 8 less, he would have made a profit of 10%. The C.P. of the article was
Options:
A)1600
B)1500
C)1200
D)1388
E)1211
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 8
=> x = 1600
Answer: A) Rs 1600
Answer: A
Question: A students was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?
Options:
A)3
B)7
C)17
D)31
E)38
Rationale: adding all the numbers we get 137+x
GIVEN-(137+x)/12=12
137+x=12*12
x=144-137
x=7
ANSWER:B
Answer: B
Question: If the class marks in frequency distribution weights of students be 128, 137, 146, 155, 164, 173 and 182 kgs then the first class boundary is
Options:
A)123.8
B)123.7
C)123.5
D)223.5
E)1222.2
Rationale: Sol:
Rule for class boundary is = n1– (n2 – n1)/2.
So here n1 = 128, n2 = 137;
First class boundary = 128 – (137 – 128)/2 = 128 – 4.5 = 123.5
Hence option (C) is correct.
Answer: C
Question: A sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 70 extra yellow balls and making ratio of white balls to yellow balls 8/13. How many tennis balls did the retailer order originally.
Options:
A)180
B)130
C)140
D)160
E)224
Rationale: White:Yellow = x:(x+70) = 8:13 --> 13x = 8x + 560 --> x = 112.
The total # of balls originally x + x = 112 + 112 = 224.
Answer:E.
Answer: E
Question: There is 60% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
Options:
A)Rs. 2160
B)Rs. 3120
C)Rs. 3972
D)Rs. 6240
E)Rs. 5240
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = (100 * 60)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 10% p.a.
C.I. = [12000 * {(1 + 10/100)3 - 1}]
= 12000 * 331/1000 = Rs. 3972
ANSWER:C
Answer: C
Question: Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 1.5 screws and 4.5 nails?
Options:
A)a. 4
B)b. 5/2
C)c. 2
D)d. 3/2
E)e. 20/11
Rationale: let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 1.5s and 4.5n= 1.5s+4.5*1.5s=8.25s..
ratio= 15s/8.25s=15/8.25=20/11
E
Answer: E
Question: A train 800 m long can cross a pole in 10 sec and then find the speed of the train?
Options:
A)280
B)282
C)284
D)286
E)288
Rationale: Length = Speed * time
Speed = L/T
S = 800/10
S = 80 M/Sec
Speed= 80*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 288 Kmph
Answer:E
Answer: E
Question: Given that there are 6 basketball players per team, how many ways can you select 3 basketball players from 3 teams if no more than one player can be selected from each team?
Options:
A) 15
B) 216
C) 60
D) 75
E) 90
Rationale: 3 teams can be selected from 3 teams in 3C3 ways = 1 ways
as the condition is that the 2 players should be from different teams
one player can be chosen from 1st team in 6 ways
similarly another player can be chosen from 2nd team in 5 ways
Total number of ways to choose the player = 6 * 6 * 6 = 216 ways
Correct Answer - B
Answer: B
Question: Look at this series: 75000,25000,5000... What number should come next?
Options:
A)1000
B)10
C)15
D)18
E)8
Rationale: 1000
This is a simple division series. Each number is divided by 5.
ANSWER A
Answer: A
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?
Options:
A)Rs. 4082.40
B)Rs. 1024.21
C)Rs. 2810.6
D)Rs. 3214
E)None of these
Rationale: Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
Answer IS A
Answer: A
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 10 mangoes. Find the gain percent?
Options:
A)7%
B)25%
C)21%
D)85%
E)24%
Rationale: SP = CP + g
150 SP = 150 CP + 10 SP
140 SP = 150 CP
140 --- 10 CP
100 --- ? => 7%
Answer:A
Answer: A
Question: a man buys postage stamps of denomination of 30ps. and 50 ps. for rs.10.00. he buys 22 stamps in all. find the no of 30ps. stamps bought by him.
Options:
A)5
B)6
C)17
D)8
E)9
Rationale: 50ps stamp = 17 (17*.50 = 8.50rs)
30ps stamp = 5 (5*.30 = 1.50rs)
ANSWER:A
Answer: A
Question: If the ratio of a to b is 5 to 3 and the ratio of b to c is 1 to 5, what is the ratio of a to c?
Options:
A)4/15
B)1/3
C)2/5
D)4/5
E)7/6
Rationale: a:b = 5:3 -- 1
b:c = 1:5
=>b:c = 3 :15 --2
From 1 and 2 , we get
a:c = 4:15
Answer B
Answer: B
Question: A, B AND C ARE EMPLOYED TO DO A PIECE OF WORK FOR RS. 529. A AND B TOGETHER ARE SUPPOSED TO DO 19/23 OF THE WORK AND B AND C TOGETHER 8/23 OF THE WORK. WHAT AMOUNT SHOULD A BE PAID?
Options:
A)RS. 315
B)RS. 345
C)RS. 355
D)RS. 375
E)NONE OF THESE
Rationale: WORK DONE BY A=(1-8/23)=15/23.
A:(B+C)=15/23:8/23=15:8
SO, A'S SHARE=RS. (15/23*529)=RS. 345.
CORRECT OPTION: B
Answer: B
Question: The sum of all the digits of the integers from 18 to 21 inclusive is 24 (1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24). What is the sum W of all the digits of the integers from 0 to 99 inclusive?
Options:
A)450
B)810
C)900
D)1000
E)1100
Rationale: We want the sum of the digits from 0 to 99, so I approximated:
0-9 ->45-> (9+0)*10/2
40-49 ->85(13+4)*10/2
90-99 ->135(18+9)*10/2
We can see at a glance that theweightgoes up as the numbers go up (meaning the difference between 85 and 45 is 40, while 135-85 is 50, this means that the second part of this sequence carries more weight for our result), so we know that the final answer has to be more than 850 (85*10) but close to it, and that's just W= 900:the answer is C.
Answer: C
Question: A certain Sky Blue paint contains 10 percent blue pigment and 90 percent red pigment by weight. A certain green paint contains 70 percent blue pigment and 30 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?
Options:
A)1.5
B)2.5
C)3.5
D)4.5
E)5.5
Rationale: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each. Thus 5 grams a piece. Out of the 5 grams of the Dark Blue paint, 60% is red. Therefore, 5*.9 =4.5 Grams of red pigment
Answer: D
Question: How much water must be added to 10 gallons of 10% brine solution to decrease the concentration to 6%?
Options:
A)0—1.5 gal
B)1.5—3 gal
C)3—4.5 gal
D)4.5—6 gal
E)6+ gal
Rationale: Let amount of water that must be added in gallons to dilute concentration of brine solution = x
Amount of brine already present = 10/100 * 10 = 1 gallon
1/(10+x) *100 = 6
=>100 = 60 + 6x
=> x= 40/6 = 6.6
Answer E
Answer: E
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 Â½ hours after the first, and reaches Pune Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:2
B)1:3
C)10:27
D)5:4
E)10:40
Rationale: Explanation:
T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
ANSWER IS A
Answer: A
Question: Renu can do a piece of work in 5 days, but with the help of her friend Suma , she can do it in 4 days. In what time Suma can do it alone?
Options:
A)10
B)12
C)14
D)15
E)20
Rationale: Renuâ€™s one dayâ€™s work = 1/5
Sumaâ€™s one dayâ€™s work = 1/4 - 1/5 = 1/20
Suma can do it alone in 20 days.
ANSWER:E
Answer: E
Question: Set X consists of 15 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?
Options:
A)32
B)37
C)C.40
D)60
E)50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20, 20, 20, 20, 20, 40, 40, 40, 50, 60
This is possible. Hence it is the greatest such number.
Answer (D)
Answer: D
Question: In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last 5 days is ?
Options:
A)45
B)48
C)52
D)58
E)None
Rationale: Production during these 5 days = Total production in a month - production in first 25 days.
= 30 x 58 - 25 x 60
= 240
∴ Average for last 5 days = 240 / 5
= 48
Correct Option: B
Answer: B
Question: The music class consists of 4 girls and 5 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
Options:
A)80
B)158
C)161
D)165
E)172
Rationale: Reverse combinatorics approach is preferred method on this one
Note that at least 1 boy gives clue to using this method
All combinations - four girls = answer
All combinations is 9C3 = 84
All girls 4C3 = 4
So our answer is 84-4 = 80
Hence, answer is (A)
Answer: A
Question: How many digits are in the number 50^8 × 8^3 × 11^3?
Options:
A)22
B)20
C)19
D)18
E)17
Rationale: Whenever you are asked to find the number of digits, try to bring the number in multiples of 10. This way, we can wasily calculate the umber of 0's through the powers of 10
50^8 × 8^3 × 11^3 = (5^2*2)^8*2^9*11^3 = 5^16*2^17*11^3 = 2*11^3*10^16 = 2662*10^16
Hence we would have 16 trailing 0's and the three digits from 2662
Total digits = 4 + 16 = 20
Correct Option: B
Answer: B
Question: There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket?
Options:
A)60
B)90
C)120
D)150
E)180
Rationale: Required number of ways = 10C3 = 10!/3!7! = 10*9*8/3*2 = 120
Answer is C
Answer: C
Question: The mean of 30 values was 140. It was detected on rechecking that one value 145 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
Options:
A)151
B)140.33
C)152
D)148
E)None of the above
Rationale: Corrected mean = 140×30−135+145/30
= 4200−135+145/30
=4210/30=140.33
Answer B
Answer: B
Question: In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
Options:
A)400
B)625
C)1,250
D)2,500
E)1,000
Rationale: This is a rather straight forward ratio problem.
1. 40 fish tagged
2. 2 out of the 50 fish caught were tagged thus 2/50
2/50=40/x
thus, x=1000
Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?
You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.
E
Answer: E
Question: 11, 22, 14, 28, 20, 40, ?
Options:
A)21
B)25
C)31
D)31
E)32
Rationale: E
32
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: E
Question: A person took some amount with some interest for 2 years, but increase the interest for 1%, he paid Rs.120/- extra, then how much amount he took?
Options:
A)Rs.5500/-
B)Rs.6000/-
C)Rs.4000/-
D)Rs.7000/-
E)Rs.8000/-
Rationale: Explanation:
2 years = Rs.120/-
year = 120/2
Rate of Interest = 1%
100/1% × 120/2 = Rs.6000/-
P = Rs.6000/-
Answer: Option B
Answer: B
Question: The mantissa of log 3274 is 0.5150. The value of log(0.3274) is
Options:
A)1.5150
B)1.5150
C)2.515
D)None of these
E)Cannot be determined
Rationale: Solution
Since, 0.3274 gives characteristic 1. Therefore value of log (0.3274) = 1.5150. Answer A
Answer: A
Question: Find the area of a parallelogram with base 18 cm and height 16 cm?
Options:
A)423 cm2
B)122 cm2
C)420 cm2
D)251 cm2
E)288 cm2
Rationale: Area of a parallelogram
= base * height
= 18 * 16
= 288 cm2
Answer: E
Answer: E
Question: A,B, and C are on a trip by a car. A drives during the 1st hour at an average speed of 50km/hr. B drives during the next 2 hours at an average speed of 48km/hr. C drives for the next 3 hours at an average speed of 52km/hr. They reached their destination exactly after 6 hours. Their mean speed is?
Options:
A)45.5km/hr
B)50.3km/hr
C)56.9km/hr
D)62.5km/hr
E)38.9km/hr
Rationale: Total distance traveled = 50*1 + 48*2 + 52*3 = 302km
Total time taken = 6hrs
Mean speed = 302/6 = 50.3km/hr
Answer is B
Answer: B
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)170 sq.units
C)190 sq.units
D)940 sq.units
E)149 sq.units
Rationale: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer: Option A
Answer: A
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
Options:
A)18%
B)82%
C)72%
D)12%
E)11%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
Answer: D
Answer: D
Question: You roll P (P > 1) number of Q (Q > 1) sided dice at once. What is the probability that at least two of the P dice will land on difference numbers.
Options:
A)1 - P/(Q^P)
B)1 - Q/(P^Q)
C)1 - 1/(P^(Q-1))
D)1 - 1/(Q^(P-1))
E)1 - 1/(Q-1)^P
Rationale: This can be calculated by first finding the probability of all dice landing on the same number, and taking 1 - it:
The incorrect rolls are any Q-ples: 11...1, 22...2, ..., PP...P. This is makes Q possibilities. The P dice can roll Q*Q*...*Q (Q^P) number of ways. Thus the probability of landing on the same number is Q/(Q^P) = 1/(Q^(P-1)). Therefore, the probability of at least two of the P dice landing on different numbers is:
1 - 1/(Q^(P-1))
Answer: D.
Answer: D
Question: The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $76,875, how much profit did the business make?
Options:
A)$98,000
B)$106,000
C)$112,000
D)$118,000
E)$123,000
Rationale: Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = $76,875
P = $123,000
The answer is E.
Answer: E
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 $112 and $120 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?
Options:
A)600
B)784
C)1080
D)1200
E)1440
Rationale: $112 for 2 years = $56 per year.
Extra $8 yearned with the compound interest is the percent yearned on percent. So, $8 is yearned on $56, which means that the interest = 7%.
This on the other hand means that half of the savings = 56*7 = $392. Twice of that = $784.
Answer: B.
Answer: B
Question: Solution Y is 30 percent liquid A and 70 percent water. If 2 kilograms of water evaporate from 8 kilograms of solutions Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new liquid solution is liquid A?
Options:
A)30%
B)33 1/3%
C)37 1/2%
D)40%
E)50%
Rationale: Answer:C
Took time to solve this one, the statement2 kilograms of solution Y are added to the remaining 6 kilograms of liquidwas confusing to me. After thinking more deeply, it was clear to me that new 2 kg of solution Y will also be 30% liquid A and 70% water, and then I was able to get the answer. That was a bit tricky and nice question.=C
Answer: C
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel six times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
Options:
A)4
B)6
C)8
D)7
E)12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/6 and W = 6S
Then we have 1/(6*S) + 1/S = 1/6 <=> 7/(6*S) = 1/6 <=> S = 7
ANS: D
Answer: D
Question: 150 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?
Options:
A)1~10
B)10~20
C)20~30
D)45~55
E)55~65
Rationale: 150 = 2*3*5^2
There are factors in each range except for 55~65
The answer is E.
Answer: E
Question: Which of the following inequalities is equivalent to –2 < x < 4 ?
Options:
A)| x – 2 | < 4
B)| x – 1 | < 3
C)| x + 1 | < 3
D)| x + 2 | < 4
E)None of the above
Rationale: Soln:-
(A) | x – 2 | < 4 => -2<x<6: out
(B) | x – 1 | < 3 => –2 < x < 4: yeah
(C) | x + 1 | < 3 => -4<x<2: out
(D) | x + 2 | < 4 => -6<x<2: out
(E) None of the above: out
Ans: B
Answer: B
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
Options:
A)2 : 5
B)2 : 8
C)2 : 1
D)2 : 0
E)2 : 2
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
Answer: A
Answer: A
Question: 3,5,11,29,83,245,?
Options:
A)731
B)728
C)715
D)705
E)645
Rationale: We have to find the differences between the given numbers and then by applying
that number with 3 we can get the result
5-3=2
See here the result is 2,then multiply it with 3
11-5=6
29-11=18
83-29=54
245-83=162
731-245=486
ANSWER:A
Answer: A
Question: As part of a game, seven people each must secretly choose an integer between 1 and 7, inclusive. What is the approximate likelihood that all seven people will choose different numbers?
Options:
A)1%
B)12%
C)16%
D)20%
E)25%
Rationale: Ans:a)
1st person has option no's- (1,2,3,4,5,6,7) - there fore probability of getting a no =7c1/7c1 = 1
2nd person has option no's any six ,
he has to choose a no from six no's - there fore probability of getting a no = 6c1/7c1 = 6/7
3rd person has option no's any five,
he has to choose a no from five no's -there fore probability of getting a no = 5c1/7c1 =5/7
4th person has 4 options - there fore probability of getting a no= 4c1/7c1 =4/7
5th person has 3 options - there fore probability of getting a no= 3c1/7c1 = 3/7
6th person has 2 options - there fore probability of getting a no= 2c1/7c1 = 2/7
7th person has only one option - there fore probability of getting a no= 1c1/7c1 = 1/7
=1*6/7*5/7*4/7*3/7*2/7*1/7 = 1%
Answer: A
Question: When positive integer N is divided by positive integer P, the quotient is 20, with a remainder of 7. When N is divided by (P + 2), the quotient is 15 and the remainder is 2. What is the value of N?
Options:
A)107
B)331
C)511
D)691
E)871
Rationale: N/P=10 7/P= 20P+7
N/(P+2)=15 2/(P+2)=15P+30+2
solving these two equations
we get P=5 N= 107 answer is A.
Answer: A
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations T of soloists can appear in the liner notes?
Options:
A)5!
B)10!/(5!5!)
C)10!/5!
D)10!
E)10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations T of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: B
Question: The average of first 18 natural numbers is?
Options:
A)9.6
B)9.5
C)9.9
D)9.4
E)9.1
Rationale: Sum of 18 natural no. = 342/2 = 171
Average = 171/18 = 9.5
Answer:B
Answer: B