divelab/Sys2Bench huggingface dataset:
Question: House owner decides to repaint the house. He want to make a particular wall in the hall, decorative and decides to put 7 coloured horizontal stripes in it. The seven colours he chose is Violet, Indigo, Blue, Green, Yellow, Orange, Red. As Blue, Violet and Indigo are very similiar shades he decides not to put them next to each other. How many different patterns do he have to choose from?
Options:
A)6! - (5!×3!)
B)7! - (5!×2!)
C)6! - (2!×4!)
D)7! - (5!×3!)
E)7! - (6!×3!)
Rationale: The answer is not direct. Problem require us to find the number of different arrangements of 7 coloured stripes. The constraints we have is that B, V and I should not come next to each other. We can find the answer by substracting the number of arrangments in which B, V and I come together from the total arrangements of 7 stripes. Arrangements in which B, V and I come together: we can consider B, V and I as a single object, but remembering that there can be 3! different such objects. For each BVI object we can arrange BVI, R, O, Y, G in 5! Ways. There four in total there is 5! × 3! Ways of arranging 7 stripes with B, V, I together. And total arrangement of 7 stripes is 7!. Therefore the answer we need is D. (7! -( 5!×3!))
Answer: D
Question: Four equal circles are described about the four corners of a square so that each touches two of the others. If a side of the square is 14 cm, then the area enclosed between the circumferences of the circles is :
Options:
A)24 cm2
B)42 cm2
C)154 cm2
D)196 cm2
E)None of these
Rationale: The shaded area gives the required region.
Area of the shaded region = Area of the square – area of four quadrants of the circles
= (14)2 - 4 × 1⁄4π(7)2
= 196 - 22⁄7 × 49 = 196 - 154 = 42 cm2
Answer B
Answer: B
Question: A number is to be multiplied by the fraction 4/5.But amit, by mistake multiplied it by 5/4 and obtained the number 81 more than the correct value.what was the original number?
Options:
A)200
B)240
C)180
D)120
E)100
Rationale: let the no. be x.
x*5/4 - x*4/5 =81. solving this we get 180
ANSWER:C
Answer: C
Question: The ratio of the adjacent angles of a parallelogram is 6 : 9. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
Options:
A)168°
B)228°
C)156°
D)224°
E)None of these
Rationale: The measures of the adjacent angles of a parallelogram add up to be 180°
Given
So, 6x + 9x = 180°
Or, 15x = 180°
Or, x = 12°
Hence the angles of the parallelogram are 72° and 108°
Further it is given
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Will be 72° + 84° = 156°
Answer : C
Answer: C
Question: What is x if x + 2y = 10 and y = 3?
Options:
A)2
B)4
C)5
D)8
E)9
Rationale: Substitute y by 3 in x + 2y = 10
x + 2(3) = 10
x + 6 = 10
If we substitute x by 4 in x + 6 = 10, we have 4 + 6 = 10. Hence
x = 4
correct answer B
Answer: B
Question: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 7 (B + G) is ?
Options:
A)more than 7
B)Less than 3
C)More than 3
D)Less than 1/3
E)none of these
Rationale: Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
7(B + G) = 7[(x/y) + (y/x)] = 7[(x2 + y2)/xy] > 7
ANSWER:A
Answer: A
Question: 10% of the inhabitants of village having died of cholera, a panic set in during which 25% of the remaining inhabitants left the village. The population is then reduced to 4050. Find the number of original inhabitants.
Options:
A)5000
B)6000
C)4000
D)8000
E)9000
Rationale: Let the total number of orginal inhabitants be x.
((75/100))*(90/100)*x)=4050 ==> (27/40)*x=4050
==> x=((4050*40)/27)=6000.
Answer B.
Answer: B
Question: The cost of a Washing machine was $400 in 1985. In 2014, the cost had increased to $800. What was the percent increase in the cost of Washing machine?
Options:
A)10
B)40
C)60
D)200
E)100
Rationale: Increase = 800 - 400 = 400
% increase = 400*100/400 = 100%
Answer: option E
Answer: E
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 3%. What is the cost price?
Options:
A)1000
B)2876
C)1077
D)2778
E)2711
Rationale: 90%
103%
--------
13% ---- 140
100% ---- ? => Rs.1077
Answer: C
Answer: C
Question: At a party, there were seven times as many females as males and twice times as many adults as children. Which of the following could NOT be the number of people at the party?
Options:
A)384
B)258
C)215
D)120
E)72
Rationale: Five times as many females as males --> F = 7M.
Three times as many adults as children --> (F + M) = 2C.
The number of people at the party = F + M + C = 2C + C = 3C.
The number of people at the party must be a multiple of 3. The only answer choice which is NOT a multiple of 3 is C.
Answer: C.
Answer: C
Question: Ratio of the earnings of A and B is 4:7. If the earnings of A increases by 50% and those of B decreased by 25%, the new ratio of their earnings becomes 8:7. What are A's earnings?
Options:
A)26,000
B)83,20
C)23,320
D)Data inadequate
E)39,309
Rationale: Answer: Option D
Explanation:
Let the original earnings of A and B be Rs. 4x and Rs. 7x.
New earnings of A = 150% 0f Rs. 4x = (150/100 * 4x) = Rs. 6x
New earnings of B = 75% of Rs. 7x = (75/100 * 7x) = Rs. 21x/4
6x:21x/4 = 8:7
This does not give x. So, the given data is inadequate.
Answer:D
Answer: D
Question: Village P’s population is 1150 greater than Village Q's population. If Village Q’s population were reduced by 200 people, then Village P’s population would be 4 times as large as Village Q's population. What is Village Q's current population?
Options:
A)600
B)625
C)650
D)675
E)700
Rationale: P = Q+1150.
P=4(Q-200).
4(Q-200)=Q+1150.
3Q=1950.
Q=650.
The answer is C.
Answer: C
Question: 22 + 23 + 24 + ... 61 + 62 + 63 = ?
Options:
A)1361
B)1362
C)1363
D)1364
E)1785
Rationale: Sum = 22 + 23 + 24 + ... 61 + 62 + 63
Sum of n consecutive positive integers starting from 1 is given as n(n+1)/2
Sum of first 63 positive integers = 63*64/2
Sum of first 21 positive integers = 21*22/2
Sum = 22 + 23 + 24 + ... 61 + 62 + 63 = 63*64/2 - 21*22/2 = 1376
Answer : E
Answer: E
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
Options:
A)18
B)76
C)24
D)20
E)12
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.Answer:C
Answer: C
Question: A and B invests Rs.6000 and Rs.12000 in a business. After 6 months, A withdraws half of his capital and B withdraws two-third of his capital. In what ratio should they share the profits at the end of the year?
Options:
A)27:32
B)25:32
C)32:27
D)27:29
E)27:31
Rationale: A : B
(6000*6)+(3000*6) : (12000*6)+(4000*6)
54000 : 96000
27 : 32
Answer: A
Answer: A
Question: On 5th Mar, 2012 Monday falls. What day of the week was it on 5th Mar, 2011?
Options:
A)Saturday
B)Sunday
C)Monday
D)Tuesday
E)Wednesday
Rationale: Explanation:
5th Mar 2012 – 5th Mar 2011 = 52 weeks 1 day. So Mar 5th 2011 is behind one day = Sunday
Answer: B
Answer: B
Question: A man saves 20% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 20%, he is only able to save Rs. 200 per month. What is his monthly salary?
Options:
A)5000
B)2999
C)2878
D)2990
E)2771
Rationale: Income = Rs. 100
Expenditure = Rs. 80
Savings = Rs. 20
Present Expenditure 80*(20/100) = Rs. 96
Present Savings = 100 – 96 =Rs. 4
100 ------ 4
? --------- 200 => 5000
Answer: A
Answer: A
Question: A dessert recipe calls for 50% melted chocolate and 50% raspberry puree to make a particular sauce. A chef accidentally makes 15 cups of the sauce with 30% melted chocolate and 70% raspberry puree instead. How many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50% of each?
Options:
A)1.5
B)2.14
C)3
D)4.5
E)5
Rationale: Yes, we assume that the mix is homogeneous. Otherwise, we will not be able to solve the question.
You have 15 cups of sauce with 30% chocolate. You also have unlimited amount of pure chocolate sauce. Now you need to mix these two in such a way that you get total 15 cups of sauce with 50% chocolate.
Using scale method:
w1/w2 = (100 - 50)/(50 - 30) = 5/2
w1 - Amount of 30% chocolate sauce
w2 - Amount of pure chocolate sauce
So for every 5/2 cups of 30% chocolate sauce, we need 2 cup of pure chocolate sauce. This will give us 7 cups of 50% chocolate sauce. But we need 15 cups of 50% chocolate sauce.
So we need to mix 5*15/7 = 12.5 cups of 40% chocolate sauce with 1*15/7 = 2.14 cups of pure chocolate sauce.
Answer (B)
Answer: B
Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Options:
A)45m
B)50m
C)54m
D)72m
E)70m
Rationale: Explanation:
2 kmph =	(	2 x5/18)m/sec =	5/9m/sec.
4 kmph =(4x5/18)m/sec =10/9m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then,	(x/y-5/9)=9and(x/y -	10/9)=10.
9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.
ANSWER IS B
Answer: B
Question: A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.
Options:
A)9
B)10
C)7
D)12
E)13
Rationale: 213ab may be written as
213ab = 21300 + 10a + b
When 213ab is divide by 100, the reminder is 10a + b. The only way for the remainder to be less that 10 is that a = 0. Hence the sum of the digits is
2 + 1 + 3 + 0 + b = 13
Solve for b
b = 7
correct answer C
Answer: C
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?
Options:
A)Rs 10
B)Rs 12
C)Rs 14
D)Rs 16
E)Rs 18
Rationale: Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14.
ANSWER C 14
Answer: C
Question: For all integers x>1. <x>=2x+(2x-1)+(2x-2)+......2+1. What is the value of <4>*<2>?
Options:
A) 60
B) 116
C) 360
D) 263
E) 478
Rationale: Since <x>=2x+(2x-1)+(2x-2)+......2+1=1+2+..+(2x-2)+(2x-1)+2x then<x> is basically the sum of all integers from 1 to 2x, inclusive.
Hence <4> is the sum of all integers from 1 to 2*4=8 and <2> is the sum of all integers from 1 to 2*2=4 --> <4>=36 and <2>=10 --> <3>*<2>=36*10=360.
Answer: C.
Answer: C
Question: If a function f is defined by f(x)= -1/x for all non zero numbers x. If f(a) = -1/2 and f(ab) = 1/12 then b= ?
Options:
A)-1/6
B)1/6
C)6
D)-6
E)3
Rationale: f(a) = -1/2 = -1/a, and thus a = 2
f(ab) = 1/12, and thus ab = -12
2b = -12
b = -6
The answer is 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 $50,000, how much profit did the business make?
Options:
A)$80,000
B)$100,000
C)$120,000
D)$150,000
E)$200,000
Rationale: Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 50000
P = $80,000
The answer is A.
Answer: A
Question: Using only the digits from 0 to 6 , how many 5 digit codes can be constructed, if the first digit can not be 4 and no digits is used more than once ?
Options:
A)1080
B)2160
C)777
D)720
E)620
Rationale: code can be contain zero,(ex 0122---, 0731---)
sw, we can consider 0 at first place.
so it should be 6*6*5*4*3= 2160
ANSWER:B
Answer: B
Question: A, Band C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
Options:
A)7 days
B)8 days
C)9 days
D)10 days
E)11 days
Rationale: (A+B)'s 1 day's work = 1/11+1/20 = 31/220
(A+C)'s 1 day's work = 1/11+1/55 = 6/55
work done in 2 day's = 31/220+6/55 = 55/220 = 1/4
1/4th work done in 2 days
work done= 4*2 = 8 days
ANSWER:B
Answer: B
Question: L is a positive integer and 225 and 216 are both divisors of L. If L=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?
Options:
A)4
B)5
C)6
D)8
E)7
Rationale: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
L would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(D) (answer) ...
Answer: D
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
Options:
A)123600 m
B)141600 m
C)153600 m
D)161600 m
E)165600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: C
Question: If a and b are each greater than x and y, which of the following must be true?
I. ab > xy
II. |a| + |b| > |x| + |y|
III.a + b > x + y
Options:
A)I only
B)II only
C)I and II
D)I and III
E)I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: B.
Answer: B
Question: If a boat goes 5 km upstream in 50 minutes and the speed of the stream is 3 kmph, then the speed of
the boat in still water is
Options:
A)9 kmph
B)13 kmph
C)14 kmph
D)15 kmph
E)None of these
Rationale: Explanation:
Rate upstream = (5/50)*60 kmh = 6 kmph.
Speed of stream = 3 kmph.
Let speed in still water is x km/hr
Then, speed upstream = (x ï¿½3) km/hr.
x-3 = 6 or x = 9 kmph
Answer: A
Answer: A
Question: The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?
Options:
A)a
B)b
C)a + b
D)ab - a
E)a + b^2
Rationale: ab+a is odd
a and b are integers
If a were even "ab+a" would be even despite any value of b.
B can't be odd, so "b" must be even.
Ans : B
Answer: B
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)1987 sq m
B)7867 sq m
C)1897 sq m
D)4783 sq m
E)4312 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:E
Answer: E
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE
Options:
A)110
B)112
C)114
D)118
E)120
Rationale: Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114.
C
Answer: C
Question: What is the difference between the C.I. on Rs. 8000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
Options:
A)s.3.26
B)s.2.08
C)s.2.02
D)s.2.83
E)s.2.42
Rationale: C.I. when interest is compounded yearly
= [8000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 8000 * 26/25 * 51/50 = Rs. 8486.4
C.I. when interest is compounded half-yearly
= [8000 * (1 + 2/100)2]
= (8000 * 51/50 * 51/50 * 51/50)
= Rs. 8489.66 Difference
= (8489.66 - 8486.4
= Rs.3.26.
Answer: A
Answer: A
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum V of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
Options:
A)6x
B)V=4x
C)V=5x/3
D)3x/2
E)3x/5
Rationale: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)
But what about C,D,E? Any ideas why these could be wrong?
Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.
Answer: B.
Answer: B
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Options:
A)6
B)7
C)8
D)5
E)3
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min. Answer: A
Answer: A
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?
Options:
A)9/10
B)6/10
C)2/10
D)3/10
E)5/10
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20
Let E = event of getting a multiple of 4 or 15
=multiples od 4 are {4, 8, 12, 16, 20}
And multiples of 15 means multiples of 3 and 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}.
= the common multiple is only (15).
=> E = n(E)= 6
Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10.
Answer is D
Answer: D
Question: There are 2 couples. If they will sit 4 chairs in a row such that each couple sits side by side, how many possible cases are there?
Options:
A)120
B)8
C)1,200
D)2,460
E)3,840
Rationale: Tie the couples. Then we have 2 persons that have to be arranged in 2 places. 2! ways.
Now the couples can change position with each other. 2! ways.
2! * (2!)^2 = 2 *4 = 8
Answer is B.
Answer: B
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
Options:
A)10 min
B)20 min
C)30 min
D)40 min
E)60 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: D
Question: A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
Options:
A)2.5 km/hr
B)12.5 km/hr
C)1 2.6 km/hr
D)22.5 km/hr
E)22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=7.5
3x = 15
x = 5
i.e., speed upstream = 5 km/hr
Rate of stream = 1/2(2x−x)=x/2=5/2=2.5 km/hr
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 Q 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 Q 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: What is the place value of 0 in the numeral 2074?
Options:
A)0
B)1
C)2
D)5
E)6
Rationale: Note : The place value of zero (0) is always 0. It may hold any place in a number,
its value is always 0.
A
Answer: A
Question: A boat running downstream cover a distance of 24km in 6 hr while covering the same distance upstream it takes 8 hr then the speed of the boat still in the water
Options:
A)4.5km/hr
B)9.5km/hr
C)3.5km/hr
D)25.6km/hr
E)12.3km/hr
Rationale: rate down stream=(24/6)= 4kmph
rate upstream=(24/8)= 3kmph
speed still water =1/2(4+3)kmph=3.5km/hr
Answer(C)
Answer: C
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 12, how many more dollars, in terms of x, will it cost per person?
Options:
A) x/6
B) x/16
C) x/40
D) 3x/40
E) 3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 12 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is C.
Answer: C
Question: A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500?
Options:
A)1991
B)2991
C)3991
D)4521
E)5991
Rationale: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009.
Required sale = Rs. [ (4500 x 6) - 24009 ]
= Rs. (27000 - 24009)
= Rs. 2991
Answer: Option B
Answer: B
Question: On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $5, the second $500, and the third $5000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. What is the probability that a contestant will win more than $5000?
Options:
A)1/9
B)4/6
C)3/6
D)1/2
E)1/6
Rationale: Let's call the boxes that contain $5, $500, and $5000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $5000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $5000, not more than $5000. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $5000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer: E
Answer: E
Question: Working simultaneously and independently at an identical constant rate, 30 machines of a certain type can produce a total of x units of product P in 3 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 10 days?
Options:
A)41
B)44
C)45
D)47
E)50
Rationale: The rate of 30 machines is rate=job/time=x/3 units per day --> the rate of 1 machine 1/30*(x/3)=x/90 units per day;
Now, again as {time}*{combined rate}={job done}
then 10*(m*x/90)=5x --> m=45.
Answer: C.
Answer: C