divelab/Sys2Bench huggingface dataset:
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of (a + b)/2?
Options:
A)100
B)110
C)105
D)20
E)215
Rationale: Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
(A+B)/2 = 110 + 100 = 210/2=105
Ans : C
Answer: C
Question: SHOW TIMER STATISTICS
It takes 3 tons of copper ore and 5 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 60 tons of copper ore and 90 tons of iron ore?
Options:
A)18
B)18 3/4
C)20
D)30
E)50
Rationale: 3c + 5i = a
60c + 90i = ?
20(3c + 5i) = 60c + 100i = 20a, so the answer has to be less than 20 since we are dealing with 90i.
But, 18(3c + 5i) = 54c + 90i = 18a, here we get 54c < 60c. So answer must be 18 3/4 (B).
ANSWER:B
Answer: B
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 340 m in length?
Options:
A)18.9 sec
B)88.9 sec
C)22.9 sec
D)27.00 sec
E)72.0 sec
Rationale: D = 110 + 340 = 450 m
S = 60 * 5/18 = 50/3
T = 450 * 3/50 = 27.00 sec
Answer: D
Answer: D
Question: When an amount was distributed among 14 boys, each of them got $80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?
Options:
A)5050
B)5020
C)5040
D)5030
E)5075
Rationale: Let the total amount be Rs. X the,
x/14 - x/18 = 80 ==> 2x/126 = 80 ==> x/63 = 63 x 80 = 5040.
Hence the total amount is 5040.
Answer C.
Answer: C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is -.
Options:
A)1/2
B)1/10
C)1/3
D)1/8
E)1/5
Rationale: 10 books arranged ==>9!2!
req prob = 1/5
ANSWER E
Answer: E
Question: If selling price is doubled, the profit triples. Find the profit percent?
Options:
A)100%
B)110%
C)120%
D)140%
E)150%
Rationale: Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y - x) = (2y - x) y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
Profit % = x/x	x 100	% = 100%
A)
Answer: A
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)98
B)78
C)76
D)87
E)75
Rationale: Average = (76 + 65 + 82 + 67 + 85)/5
= 375/5 = 75.
Answer: E
Answer: E
Question: If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 24/r years. If Pat's parents invested $6,000 in a long-term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when Pat is ready for college?
Options:
A) $20000
B) $15000
C) $12000
D) $10000
E) $30000
Rationale: Since investment doubles in 24/r years, then for r=8 it'll double in 24/8=~3 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*6=$30,000 .
Answer: E.
Answer: E
Question: A man weighs 300 pounds and has enough food for his diet plan for 50 days. After 10 days he decides he is happy with the weight loss results and changes his diet plan so that the remaining food will now be enough for the same period of 50 days as before. How many pounds did he lose?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: 300 ---- 50
300 ---- 40
x ---- 50
x*50 = 300*40
x = 240
300
-------
60
Answer = E
Answer: E
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
Options:
A)12
B)9
C)8
D)6
E)4
Rationale: A's 1 hour's work = 1/4 ;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/3.
(A + B + C)'s 1 hour's work = ( 1/4 + 1/3 ) =7/12 .
B's 1 hour's work = ( 7/12 - 1/3) = 1/4.
Therefore A alone will take 4 hours to do the work.
E
Answer: E
Question: A man can row upstream at 22 kmph and downstream at 42 kmph, and then find the speed of the man in still water?
Options:
A)29
B)92
C)30
D)32
E)23
Rationale: US = 22
DS = 42
M = (42 + 22)/2 = 32
Answer:D
Answer: D
Question: A batsman's avg in 12 innings is 24.00. If his avg is to be double of the no of innings (15 innings), what should he score in the remaining three innings (avg)?
Options:
A)143
B)144
C)145
D)146
E)147
Rationale: let total runs done by a batsman in 12 innings be x
therefore,
x/12=24 that means x=12*24=288 runs
for 15 innings, avg was doubled i.e.. 48.00
therefore,
(x+y)/15=48 where y is the no of runs done in last 3 innings
y=432
therefore average is 432/3=144
ANSWER:B
Answer: B
Question: A train running at a speed of 60 kmph crosses a pole in 18 seconds.What is the length of the train?
Options:
A)120 m
B)300 m
C)190 m
D)150 m
E)160 m
Rationale: 60 kmph=50/3 m/sec
50/3*18=300 m
ANSWER:B
Answer: B
Question: 1/3 of a certain journey is covered at the rate of 25km/hr,1/4 at the rate of 30 km/hr and the rest is 50 km/hr.the avg speed for the whole journey is :
Options:
A)30 km/hr
B)33 km/hr
C)33 1/3 km/hr
D)37 1/12 km/hr
E)37 km/hr
Rationale: let assume total distance will be 120km then
distance traveled at teh speed 25km/hr=1/3*120=40km the time=40/25=1.6hrs
distance traveled at the speed 30km/hr=1/4*120=30kmthe time is=30/30=1 hr
then remaining distance is 120-40-30=50km
the time taken to travel 50km=50/50=1hr
so total time is=1.6+1+1=3.6 hrs
so avg speed =120/3.6=33.33km/hr
ANSWER:C
Answer: C
Question: 5,7,13,20,33,53,86,?
Options:
A)135
B)139
C)130
D)120
E)138
Rationale: Each number is the sum of the previous two numbers, ie 53 + 86 = 139.
Answer : B
Answer: B
Question: In a partnership between Rose, Ben and Christine, Rose's capital is Rs.12000. If her share of a profit of Rs.6000 is Rs.3000 and Christine's share is Rs.1250, what is Ben's capital?
Options:
A)6200
B)5200
C)4500
D)6240
E)1223
Rationale: 3000 + 1250 = 330
6000 - 4250 = 1550
3000 ---- 12000
1550---- ? => 6200
ANSWER:A
Answer: A
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Bonus Transport Fuel	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount of bonus paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?
Options:
A)A)1%
B)B)1.5%
C)C)1.25%
D)D)3%
E)E)4%
Rationale: Required percentage
=(288 + 342 + 324 + 336 + 420)
=	[	17	x 100	]	%
1710
~= 1%.
Answer : A
Answer: A
Question: Find the average of the series : 80, 320, 100, 328 and 147?
Options:
A)174
B)195
C)190
D)185
E)171
Rationale: Average = (80 + 320 + 100 + 328 + 147)/5
= 975/5
= 195
Answer: B
Answer: B
Question: If 42 men do a work in 25 days, in how many days will 50 men do it?
Options:
A)23
B)22
C)19
D)20
E)21
Rationale: 42 * 25 = 50 * x
x = 21 days
Answer: E
Answer: E
Question: At what price must an article costing Rs.200 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 20% on the cost price?
Options:
A)62.5
B)62.0
C)266.67
D)62.1
E)62.2
Rationale: CP = 200
SP = 200*(120/100) = 240
MP*(90/100) = 240
MP = 266.67
Answer: C
Answer: C
Question: A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of man is :
Options:
A)12 kg
B)60 kg
C)72 kg
D)96 kg
E)None of these
Rationale: Solution
Volume of water displaced = (3 × 2 × 0.01) m3 = 0.06 m3.
∴ Mass of man = Volume of water displaced × Density of water
= (0.06 × 100)kg = 60 kg.
Answer B
Answer: B
Question: A man buys an item at Rs. 1300 and sells it at the loss of 20 percent. Then what is the selling price of that item
Options:
A)Rs. 660
B)Rs. 760
C)Rs. 860
D)Rs. 1040
E)None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 1300
= 80/100 * 1300
= 1040
Option D
Answer: D
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
Options:
A)38
B)42
C)28
D)25
E)12
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Answer: B
Question: A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variables costs averaging $11 per item. If the manufacturer’s selling price per item is $15, how many items the manufacturer produce and sell to earn an annual profit of $150,000?
Options:
A)2,858
B)8,667
C)21,429
D)35,000
E)70,000
Rationale: Let the items manufactured or sold bex
130000+11x = 15x-150000
4x = 280000
x = 70000
Ans:E
Answer: E
Question: Mrs. Rodger got a weekly raise of $185. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Options:
A)$204
B)$231
C)$156
D)$185
E)$200
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 185.
So after completing the 1st week she will get $ (x+185).
Similarly after completing the 2nd week she will get $ (x + 185) + $ 185.
= $ (x + 185 + 185)
= $ (x + 370)
So in this way end of every week her salary will increase by $ 185.
D
Answer: D
Question: Find the area of a parallelogram with base 26 cm and height 16 cm?
Options:
A)297 cm2
B)384 cm2
C)672 cm2
D)416 cm2
E)286 cm2
Rationale: Area of a parallelogram
= base * height
= 26 * 16
= 416 cm2
Answer: D
Answer: D
Question: In a survey about potential presidential candidates A and B, 33% of the public like A and 51% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
Options:
A)28%
B)32%
C)37%
D)22%
E)67%
Rationale: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
33% + 51% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 21% and 2x = 42%
100% = 21% + 42% + Neither
Neither = 37%
The answer is C.
Answer: C
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 40% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
Options:
A)1/2 m
B)1/3 m
C)1/4 m
D)1/5 m
E)1/6 m
Rationale: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/6.
Answer: E.
Answer: E
Question: Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 35% and its breadth is decreased by 21%?
Options:
A)4.65% increase
B)5.65% increase
C)6.65% increase
D)6.65% decrease
E)7.65% increase
Rationale: let L and B be 100 each
100 * 100 = 10000
L increase by 35% = 135
B decrease by 21% = 79
135 * 79 = 10665
6.65% increase
ANSWER:C
Answer: C
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Options:
A)25 hrs
B)28 hrs
C)20 hrs
D)35 hrs
E)40 hrs
Rationale: Explanation:
1/x + 1/(x + 10) = 1/12
x = 20
ANSWER IS C
Answer: C
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 60% of the required amount. What is the net difference in the expenditure on that product?
Options:
A)A)12.5%
B)B)13%
C)C)13.15%
D)D)14%
E)E)15%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.6 x 1.25 = 0.755
Decrease in price = (0.125/1) × 100 = 12.5%
A)
Answer: A
Question: Daniel went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 5%, then what was the cost of the tax free items?
Options:
A)A)18.7
B)B)20
C)C)21.3
D)D)21.5
E)E)22
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 5%
∴ (25−30/100−x)5/100 = 30/100
⇒ 5(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 6
⇒ x = 25 − 0.3 − 6
= 18.7
A
Answer: A
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 2 fantasy books, there are 5 reference books. If the proportion of history to fantasy books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
Options:
A)16
B)21
C)27
D)35
E)36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7. After the change, H:F = 4:7 = 8:14
For every 2 fantasy books, there are 5 reference books:
F:R = 2:5 = 14:35
H:F:R = 8:14:35
There are fewer than 60 fantasy books, so there are 14, 28, 42, or 56 fantasy books.
The number of history books could be 8, 16, 24, or 32.
The answer is A.
Answer: A
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 31 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
Options:
A)2:5
B)5:14
C)3:5
D)5:13
E)14:5
Rationale: Answer = D) 5:14
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:26 = 5:13
D
Answer: D
Question: Express a speed of 56 kmph in meters per second?
Options:
A)10.56 mps
B)17.56 mps
C)97.56 mps
D)15.56 mps
E)18.56 mps
Rationale: 56 * 5/18
= 15.56 mps
Answer: D
Answer: D
Question: A, B and C started a business A's investment is 2 times of B's investment is 5 times of C's investment. Find the profit of B in the total profit of Rs. 32000.
Options:
A)Rs. 25600
B)Rs. 8500
C)Rs. 10000
D)Rs. 8000
E)None of these
Rationale: Explanation:
A = 2B and B = 5C
=> A : B = 2:1 and B : C = 5 : 1
=> A : B : C = 10 : 5 : 1
Ratio of capitals of A, B and C = 10 : 5 : 1
B's share = Rs.[(5/16) × 32000] = Rs. 10000
Answer: Option C
Answer: C
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 80 revolutions. How many revolutions does the second wheel make in covering d feet?
Options:
A)80y/x
B)80x/y
C)80-x
D)80-y
E)80x-y
Rationale: A wheel covers 2πr distance in one revolution. where r= diameter/2
First wheel covers d feet in 80 rev. => d= 80* 2π * (x/2)
Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)
comparing both equations:-
=> p= (80∗2π∗x/2)/(2π∗y/2)
=> 80x/y
Answer :- B
Answer: B
Question: On the number line, if x is halfway between -8 and 4, and if y is halfway between -4 and 6, what number is halfway between x and y?
Options:
A)-1.5
B)-0.5
C)0.5
D)1.5
E)2.5
Rationale: x= -2 and y = 1.
The answer is B.
Answer: B
Question: Approximately how many cubic feet of water are needed to fill a circular swimming pool that is 80 feet across and 10 feet deep?
Options:
A)10000
B)50000
C)80000
D)85000
E)90000
Rationale: Answer Should be B.
V= \pir^2h= \pi*40^2*10= approximately 50000
Answer: B
Question: In a town 65% people watched the news on television , 40% read a newspaper and 25% read a newspaper and watched the news on television also. What percent of the people neither watched the news on television nor read a news paper ?
Options:
A)15
B)20
C)25
D)30
E)35
Rationale: n(a+b) = n(a) + n(b) - n(a*b), here + and * represents OR and AND
so n(a+b) = 65+40-25 = 80
so 20 % people neither watched TV nor read newspaper
ANSWER:B
Answer: B
Question: In 2010, Arman’s birthday was on a Thursday. What day of the week was it 65 days after his birthday?
Options:
A)Thursday
B)Friday
C)Saturday
D)Sunday
E)Monday
Rationale: Day of week after 65 days after Arman's birthday = 7*9 + 2
Saturday as the period will have 9 weeks and 2 days .
The 2 days in the end will be Friday and Saturday .
Answer C
Answer: C
Question: Find the number of different prime factors of 2400
Options:
A)4
B)2
C)3
D)5
E)6
Rationale: Explanation:
L.C.M of 2400 = 3 x 2 x 2 x 2 x 2 x 2 x 5 x 5
3, 2, 5
Number of different prime factors is 3.
Answer: Option C
Answer: C
Question: A tap can fill a tank in 4 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?
Options:
A)1 hr 20 min
B)4 hr
C)3 hr
D)2 hr 40 min
E)2 hr 50 min
Rationale: Explanation:
1 tap can fill the tank in 4 hours.
Therefore
1 tap can fill half tank in 2 hours.
3 taps can fill the tank in 4/3 hour.
Therefore
3 taps can fill half tank in 4/6 hour =40 minutes.
Total time taken=2 hour 40 minutes
Answer: Option D
Answer: D
Question: At a certain conference, 80% of the attendees registered at least
two weeks in advance and paid their conference fee in full. If
10% of the attendees who paid their conference fee in full did
not register at least two weeks in advance, what percent of
conference attendees registered at least two weeks in
advance?
Options:
A) 18.0%
B) 62.0%
C) 79.2%
D) 88.89%
E) 82.0%
Rationale: I do not think that Venn will be helpful here. A table will make more sense. But here is my approach.
80% regestered at least 2 weeks and paid full fee.
10% paid full fee and did not registered at least 2 weeks in advance. Then 90% paid full fee and registered at least 2 weeks before.
90% *X=80% where X is the number of people who registerd 2 weeks in advance and paid full fee. (ANSWER D)
Answer: D
Question: If -1<x<0, what is the median M of these six numbers listed below
1/x^3,1/x^2, 1/x,x, x^2,x^3
Options:
A)1/x
B)x^2
C)x^2(x+1)/2
D)M=x(x^2+1)/2
E)x^2/2x
Rationale: My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows:
-8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that.
median will be between -0.5 and -0.125.
So, (x^3+x)/2 (D).
Answer: D
Question: a little girl went to the farm to buy fruits. she bought a bag of apples and grabbed a bag of oranges which was 5 times as heavy as the apples. She brought home a total of 12 pounds of fruits. How many pounds was the oranges?
Options:
A)5
B)7
C)8
D)10
E)12
Rationale: pounds of apples = x
pounds of oranges = 5x
x + 5x = 12
6x = 12
x = 12/6 = 2
oranges = 5x = 5 * 2 = 10
ANSWER: D
Answer: D
Question: The smallest 3 digit prime number is
Options:
A)A)109
B)B)103
C)C)101
D)D)113
E)E)None
Rationale: The smallest 3-digit number is 100, which is divisible by 2.
100 is not a prime number.
101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.
101 is a prime number.
Hence 101 is the smallest 3-digit prime number.
C)
Answer: C
Question: A shopkeeper fixes the marked price of an item 30% above its cost price. The percentage of discount allowed to gain 6% is
Options:
A)18.45%
B)18.46%
C)18.47%
D)18.48%
E)None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 130
Required gain = 6%,
So Selling price = Rs 106
Discount = 130 - 106 = 24
Discount% = (24/130)*100 = 18.46%
Option B
Answer: B
Question: Jack can row at 7 kmph and still water. He takes 7/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 3 kmph?
Options:
A)12 km
B)20 km
C)18 km
D)14 km
E)10 km
Rationale: Let the distance between A and B be x km.
Total time = x/(7 + 3) + x/(7 - 3) = 7/2
=> x/10 + x/4 = 7/2 => (5x + 2x)/20 = 7/2 => x = 10 km.
ANSWER:E
Answer: E
Question: To ‘yield’ is to surrender, submit, and obey someone unconditionally. 'Resist’ which means defy, oppose and refusing to accept is the opposite word.
Options:
A)22
B)278
C)277
D)99
E)72
Rationale: Answer:A
Answer: A
Question: At a recent small town election for mayor a total of 979 votes were cast for the four candidates, the winner exceeding his opponents by 53, 79 and 105 votes, respectively. How many votes were cast for the candidate in fourth place?
Options:
A)134
B)178
C)199
D)166
E)194
Rationale: The number of votes the winning candidate received was
979 + 53 + 79 + 105	/4= 304.
The second received 304 – 53 = 251
The fourth place received 304 – 105 = 199.
C
Answer: C
Question: The sum of the squares of three numbers is 125, while the sum of their products taken two at a time is 50. Their sum is:
Options:
A)15
B)30
C)40
D)50
E)None of these
Rationale: x^+y^2+z^2=125
xy+yz+zx=50
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=125+(2*50)
(x+y+z)^2=225
so x+y+z=15
ANSWER:A
Answer: A
Question: A sandwich of 6 ingredients is made from 4 types of meat and 8 types of cheese. The sandwich must have at least 1 type of meat and at least 2 types of cheese. How many ways can this plate be made?
Options:
A)896
B)196
C)890
D)300
E)292
Rationale: Solution: We have four possibilities 4M 2C , 3M 3C, 2M 4C, 1M 5C
(4C4)(8C2)+(4C3)(8C3)+(4C2)(8C4)+(4C1)(8C5)=896
A) 896
Answer: A
Question: What is the average of 12, 13, 14, 510, 520, 530, 1,115, 1,120, and 1,125,2140 , 2345?
Options:
A) 419
B) 551
C) 601
D) 620
E) 858.54
Rationale: Add 12, 13, 14, 510, 520, 530, 1,115, 1,120, and 1,125, 2140, 2345
Grouping numbers together may quicken the addition
sum = 9444
4959/11 =858.54
.E
Answer: E
Question: There are 10 books on a shelf: 5 English books, 5 Spanish books and 2 Portuguese books. What is the probability of choosing 2 books in different languages?
Options:
A)1
B)0
C)1/3
D)31/45
E)28/90
Rationale: Probability = Favourable outcome / Total Outcome = 1- (Unfavourable outcome / Total Outcome)
METHOD-1
Favourable Outcomes
Case-1: One book is English (out of 5 English books) and one book is Spanish (out of 5 Spanish books) i.e. 5C1*5C1
Case-2: One book is Spanish (out of 5 Spanish books) and one book is Portuguese (out of 2 Portuguese books) i.e. 5C1*2C1
Case-3: One book is English (out of 5 English books) and one book is Portuguese (out of 2 Portuguese books) i.e. 5C1*2C1
Total favourable Outcomes = 5C1*5C1+5C1*2C1+5C1*2C1 = 25+10+10 = 45
Total Possible Outcomes = 10C2 = 45
i.e. Probability = 45/45 =1
A
Answer: A
Question: Susan, John, Peter, Jack, Daisy, Tim, Matt and Kim need to be seated in 8 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Options:
A)22360
B)21120
C)21800
D)21060
E)20160
Rationale: Total # of arrangement of 8 people is 8!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 8!/2=20160.
Answer: E.
Answer: E
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?
Options:
A)9
B)12
C)10
D)13
E)14
Rationale: Explanation :
Let the required number of days be x
More persons, less days (indirect proportion)
More hours, less days (indirect proportion)
⇒ 39 × 5 × 12 = 30 × 6 × x
⇒ 39 × 5 × 2 = 30 × x
⇒ 39 = 3 × x
⇒ x = 13. Answer : Option D
Answer: D