mathewhe/aqua_rat huggingface dataset:
Question: There are six different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
(A) 72
(B) 48
(C) 64
(D) 24
(E) 8
Rationale: Let's say that Models of Europe are represented by E1 and E2 respectively
Let's say that Models of South America are represented by S1 and S2
Let's say that Models of North America are represented by Na and N2
So we have to define the total ways of entries of E1 E2 S1 S2 N1 N2
We have to keep E1 E2 together and similarly N1 N2 together and similarly S1 S2 together so make three groups of two models from same region each
Arrangement of these three Group can be done in 3! ways
Arrangement of Models within Group can be done in 2!x2!x2! ways
i.e. Total Ways of Arranging the models so that they are grouped as per region together = (3!)*(2!x2!x2!) = 6*8 = 48
Answer: Option B
Answer: (B) 48
Question: Pat, Kate, and Mark charged a total of 117 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much time as Mark, how many more hours did Mark charge to the project than Kate?
(A) 18
(B) 36
(C) 72
(D) 90
(E) 65
Rationale: 65
all u do is do
2:1:6=>2x+x+6x=117=>x= 13
26:13:78
78-13=65
Answer E
Answer: (E) 65
Question: In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors S?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
Rationale: I like to put the numbers in prime factors so it is easier and faster to visualize.
14*n/60
If we write the factors of 14 --> 2, 7, and the factors of 60 --> 2, 2, 3, 5, we have
(2*7*n)/(2^2*3*5)
Simplifying
7*n/(2*3*5)
The only way the equation above has an integer value is if n has AT LEAST the factors 2, 3 and 5, so we can simplify again and we have the number 7.
The number could be 2*3*5, or 2*3*5*2, or 2*3*5*.....
However to be less than 200 we can not add any prime number.
2*3*5 = 120
If we added the next prime factor 7, we would have S=2*3*5*7 = 840
Thus, answer B
Answer: (B) 3
Question: Peter invests a sum of money and gets back an amount of $ 830 in 3 years . David invests an equal amount of money and gets an amount of $854 in 4 years. If both amounts were invested at the same rate (simple interest ) What was the sum of money invested ?
(A) 670
(B) 664
(C) 698
(D) 758
(E) 700
Rationale: Since both Peter and David invested the same amount of money at the same rate, they would earn same interest per year.
David invested for one year more than Peter and hence he got interest amount for one more year.
Interest earned per year = Amount received by David - Amount received by Peter = 854 - 830 = 24
Interest earned for 3 years = 24*3 = 72
Amount invested = 830 - 72 = 758
Answer: D
Answer: (D) 758
Question: What is the probability of getting sum 10 with the help of three dice?
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/10
Rationale: the following has 6 permutations.
(1, 3, 6),(1, 4, 5),(2, 3, 5)
Each of the following has 3 permutations.
(2, 2, 6),(2, 4, 4),(3, 3, 4)
the total possibility = 6*3 + 3*3 = 27
total no. of outcomes = 6*6*6 = 216
probability = 27/216 = 1/8 = 0.125
ANSWER:D
Answer: (D) 1/8
Question: A certain board game has a row of squares numbered 1 to 100. If a game piece is placed on a random square and then moved 7 consecutive spaces in a random direction, what is the probability T the piece ends no more than 7 spaces from the square numbered 49?
(A)  7%
(B)  8%
(C)  14%
(D)  15%
(E)  28%
Rationale: OA is E
required prob is 7 spaces any side of 49.
so total 14 spaces are required in 7 moves which can be achieved by max 7 move on any side
so total spaces = 28
probability T= 28%.E
Answer: (E)  28%
Question: 70% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 90 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
(A) (a) 15%
(B) (b) 5%
(C) (c) 10%
(D) (d) 20%
(E) (e) 25%
Rationale: so 30% employees don't have VCD devices.
25% employees don't have MO
10% employees don't have ACs
15% employees don't have WM
Summ of employees that don't have some device = 30%+25%+10%+15% = 80% < 100%
So definitely at least 20% employees have 4 devices.
ans: D
Answer: (D) (d) 20%
Question: I. 9a2 + 18a + 5 = 0,
II. 2b2 + 13b + 20 = 0 to solve both the equations to find the values of a and b?
(A) If a > b
(B) If a ≥ b
(C) If a < b
(D) If a ≤ b
(E) If a = b or the relationship between a and b cannot be established.
Rationale: I. 9a2 + 3a + 15a + 5 = 0
=>(3a + 5)(3a + 1) = 0 => a = -5/3, -1/3
II. 2b2 + 8b + 5b + 20 = 0
=>(2b + 5)(b + 4) = 0 => b = -5/2, -4
a is always more than b.
a > b.
ANSWER:A
Answer: (A) If a > b
Question: Griffin has a bag of marbles that contains 7 black marbles and 5 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?
(A) 1/22
(B) 2/33
(C) 3/44
(D) 4/55
(E) 5/66
Rationale: P(3 red marbles) = 5/12*4/11*3/10 = 1/22
The answer is A.
Answer: (A) 1/22
Question: If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $19,000 is invested at the same interest rate, what is the interest from the investment?
(A) $700
(B) $750
(C) $800
(D) $950
(E) $900
Rationale: -> 250/5,000=5% and 19,000*5%=950.
Thus, D is the answer.
Answer: (D) $950
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 20 miles per hour." What was their average speed in the whole journey?
(A) 13.3 miles/hour
(B) 12 miles/hour
(C) 11 miles/hour
(D) 13 miles/hour
(E) 14 miles/hour
Rationale: 2xy/x+y=13.3 miles/hour
ANSWER:A
Answer: (A) 13.3 miles/hour
Question: At a certain school 55% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?
(A) 1) 3/4
(B) 2)4/5
(C) 3)2/5
(D) 4)1/2
(E) 5)1/5
Rationale: This is the way to approach the question:
25% of the students join a band => 25% of the students either only join a band or both join a band and play sports
25% of the students play sports => 25% of the students either only play sports or both play sports and join a band
If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both
=20%/25% = 4/5
The answer is therefore (B)
Answer: (B) 2)4/5
Question: Find the value of y: y² + y − 2.
(A) -1 and 2
(B) -2 and -1
(C) -2 and 1
(D) 1 and 2
(E) 0 and 2
Rationale: That quadratic is factored as follows:y² + y − 2 = (y − 1)(y + 2).Now, it is easy to see that the first factor will be 0 when y = 1Now, it is easy to see that the second factor will be 0 when y = -2The solutions are:x	=	-2 and 1 C
Answer: (C) -2 and 1
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
(A) 91.2 kmph
(B) 61.9 kmph
(C) 45.9 kmph
(D) 61.2 kmph
(E) 71.2 kmph
Rationale: D = 100 + 155 = 255
T = 15
S = 255/15 * 18/5 = 61.2 kmph
ANSWER:D
Answer: (D) 61.2 kmph
Question: 2^2*3^3*2^3*3^2*2^2 =
(A) 3^5*2^5
(B) 2^9*3^4
(C) 2^4*3^9
(D) 5^8
(E) 6^10
Rationale: 2^2*3^3*2^3*3^2*2^2 =
A) 3^5*2^5
B) 2^9*3^4
C) 2^4*3^9
D) 2^7*3^5
E) 6^10
If the base is same, powers are added so that follows D) 2^7*3^5.
Hence the answer is D
Answer: (D) 5^8
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are
(A) 600
(B) 500
(C) 400
(D) 300
(E) None of these
Rationale: Explanation :
Given that the student got 125 marks and still he failed by 40 marks
=> The minimum pass mark = 125 + 40 = 165
Given that minimum pass mark = 33% of the total mark
=> Total Mark × (33/100) = 165
=> Total Mark = 16500/33 = 500
Answer : Option B
Answer: (B) 500
Question: If the mean of numbers 28, x, 42, 78, 82 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?
(A) 395
(B) 275
(C) 391
(D) 415
(E) 365
Rationale: The mean of numbers 28, x, 42, 78 and 104 is 62: 28+x+42+78+82+104=62*6 --> x=38;
So, the mean of 128, 255, 511, 1023 and x is (128+255+511+1023+38)/5=391.
Answer: C.
Answer: (C) 391
Question: A rotameter is a device that measures flow of liquid and gases. When measuring liquid phase flows, 2.5 inches represent 60 liters per minute of liquid. With gas measurements the rotameter moves 50% of the movement he moves with the liquid phase. How many liters of gas passed through the rotameter if it measured 4 inches?
(A) 176
(B) 192
(C) 202
(D) 218
(E) 284
Rationale: In case of liquid- 2.5 inches represents 60 lit/min.
In case of gas- 50% of 2.5 inches represents 60 lit/min
1.25 inches represents 60 lit /min
4 inches will represent 60*4/1.25= 192
B is the answer
Answer: (B) 192
Question: Mr. X is rewriting legislation to unevenly split $6,000,000 in funds to towns in his district. There are 5 counties in his district. What is the least amount of money he could spend to equally distribute the funds per county?
(A) $1,100,200
(B) $1,250,000
(C) $1,000,200
(D) $1,200,000
(E) none of the above
Rationale: This problem requires us to divide our main amount by 5.
Since the current amount is easily divisible by 5, as in anything that is either a multiple of 5 or 10 could be divided to an exact, whole number.
And by dividing our amount, we get the answer.
Correct option: D
Answer: (D) $1,200,000
Question: I flew my tiny seaplane to visit my mother. On the flight up, I flew at 110 mph. On the way home, I flew 90 mph. What was my average speed for the trip?
(A) 198 mph
(B) 110 mph
(C) 88 mph
(D) 100 mph
(E) 99 mph
Rationale: (110 mph +90 mph)/2= 100 mph
Correct answer is: D
Answer: (D) 100 mph
Question: Of the three-digit integers greater than 200, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A)  90
(B)  82
(C)  80
(D)  45
(E)  36
Rationale: Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)
[example numbers: 774,779,882,993 etc]
Case II.[ X=Z ]Y is not equal to XZ:XYXorZYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Z can be chosen in 1 way
After XZ are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)
[example numbers: 747,797,828,939 etc]
Case III.[ Y =Z ]X is not equal to YZ :XYYorXZZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 9 ways
After Y is chosen, Z can have 1 way
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)
[example numbers: 744,799,822,933 etc]
Therefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80
One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 200.
Answer:(E)
Answer: (E)  36
Question: The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic i
(A) 66
(B) 20
(C) 12
(D) 21
(E) 71
Rationale: Explanation:
Let the initial number of persons be x. Then,
16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20.
Answer: B
Answer: (B) 20
Question: If 4/(a + 5) = 7/(a - 4), then a = ?
(A) -15
(B) -19
(C) -17
(D) -18
(E) -13
Rationale: Multiply all terms of the given equation by (a + 5)(a - 4), simplify and solve
(a + 5)(a - 4)[ 4/(a + 5) ] = (a + 5)(a - 4) [ 7/(a - 4) ]
4 (a - 4) =7 (a + 5)
a = -17
correct answer C
Answer: (C) -17
Question: If the product of two numbers is 45276 and their H.C.F. is 22, find their L.C.M.
(A) 2574
(B) 2500
(C) 2100
(D) 2058
(E) None of these
Rationale: Explanation:
HCF * LCM = 45276, because we know
Product of two numbers = Product of HCF and LCM
LCM = 45276/22= 2058
Option D
Answer: (D) 2058
Question: Amit started walking positioning his back towards the sun. After some time, he turned left, then turned right and towards the left again. In which direction is he going now?
(A) North or South
(B) East or West
(C) North or West
(D) South or West
(E) none
Rationale: North or south
ANSWER:A
Answer: (A) North or South
Question: Twenty participants are participating in a competition. In how many ways can the first three prizes be won?
(A) 920
(B) 680
(C) 820
(D) 720
(E) 6840
Rationale: Out of 20 participants, the first three prizes can be won in,
20P3 = 20! / (20 - 3)!
= 20 x 19 x18
= 6840 ways
ANSWER:E
Answer: (E) 6840
Question: If the number of different positive factors of (2^y)(3^3) is the same as the number of different factors of (2^51), what is the value of y?
(A) 11
(B) 12
(C) 13
(D) 48
(E) 51
Rationale: Number of factors of N=a^x∗b^y where 'a' and 'b' are prime factors of N is
(X+1) (y+1)
So 4 (y+1)=52
y=12
ANSWER:B
Answer: (B) 12
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 278
(C) 100
(D) 202
(E) 270
Rationale: Profit on first article = 10% of 1000 = 100.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: C
Answer: (C) 100
Question: The speed of three cars in the ratio 5 : 4 : 6. The ratio between the time taken by them to travel the same distance is
(A) 5 : 4 : 6
(B) 6 : 4 : 5
(C) 12 : 15 : 10
(D) 10 : 12 : 15
(E) None
Rationale: Sol.
Ratio of time taken = 1 / 5 : 1/4 : 1/6 = 12 : 15 : 10.
Answer C
Answer: (C) 12 : 15 : 10
Question: A and B starts a business with Rs.8000 each, and after 9 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 4:3
(B) 18:5
(C) 14:10
(D) 18:14
(E) 14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 9 months and then withdraws Rs.4000. So, the investment of B for remaining 9 months is Rs.4000 only.
A : B
8000*18 : (8000*9) + (4000*9)
14400 : 108000
A:B = 4:3
Answer: A
Answer: (A) 4:3
Question: The first ticket is purchased at $2,40 and then the following purchases of ten tickets costs $2,20/ticket. What is the total number of tickets purchased if $90,40 is paid?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Rationale: a is the number of ten packs of tickets.
90,40 = 2,40 + 10 * 2,20 *a
a = 4
The total number of tickets --> 4*10+1 = 41
Answer: D
Answer: (D) 41
Question: In a certain population, there are 2 times as many people aged twenty-one or under as there are people over twenty-one. The ratio of those twenty-one or under to the total population is
(A)  1 to 2
(B)  1 to 3
(C)  1 to 4
(D)  2 to 3
(E)  3 to 4
Rationale: Consider the ratio of the under population of 21 to over the 21 as 2:1
therefore 2x:1X
Now the ratio of the under to the whole population becomes 2x/2x+1x
= 2/3
Answer is D
Answer: (D)  2 to 3
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 5/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) 7/16
(B) 7/15
(C) 10/21
(D) 17/35
(E) 5/14
Rationale: Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 5/6*6=$5;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$5=$20;
Fraction of total revenue from large cups: 20/(36+20)=5/14.
Answer: E
Answer: (E) 5/14
Question: Set A of 8 positive integers may have the same element and have 39. And set B of 8 positive integers must have different elements and have 39. When m and n are the greatest possible differences between 39 and other elements’ sums in set A and set B, respectively, m-n=?
(A) 20
(B) 23
(C) 21
(D) 25
(E) 26
Rationale: This is maximum-minimum. Hence, 39-(1+1+1+1+1+1+1)=32 and 39-(1+2+3+4+5+6+7)=11. So, 32-11=21. The correct answer is C.
Answer: (C) 21
Question: The line P represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1
(A) y = 2x^2+5x+1
(B) y = x^2+5x+2
(C) y = 3x^2+5x+2
(D) y = 3x^2+7x+2
(E) y = x^2+7x+1
Rationale: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.
So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line P which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.C
Answer: (C) y = 3x^2+5x+2
Question: Find large no. from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 20 as remainder
(A) 1235
(B) 1456
(C) 1634
(D) 1678
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 20
5x = 1345
x = 269
Large number = 269+1365 = 1634
C
Answer: (C) 1634
Question: What quantity of water should taken out to concentrate 21 liters of 40% acidic liquid to 60% acidic liquid?
(A) 5liters
(B) 10liters
(C) 7liters
(D) 8liters
(E) 6liters
Rationale: Required answer is = 21(60-40)/60 = 7 liters
Answer is C
Answer: (C) 7liters
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 30% but the selling price
remains constant, approximately what percentage of the selling price is the profit
(A) 69%
(B) 89%
(C) 99%
(D) 100%
(E) None of above
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 130% of Rs. 100 = Rs. 130
New S.P. = Rs. 420.
Profit = Rs. (420 - 130) = Rs. 290
Required percentage = (290/420) * 100
= 69%(approx)
Answer: A
Answer: (A) 69%
Question: There is 60% increase in an amount in 6yrs at SI. What will be the CI of Rs. 12,000 after 3 years at the same rate?
(A) 2354
(B) 2450
(C) 2540
(D) 2650
(E) 3972
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 12000 x 1 + 10 3 - 1
100
= Rs. 12000 x 331
1000
= 3972.
E
Answer: (E) 3972
Question: A wolf eats 6 Kg of meat in 2 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?
(A) 11.25
(B) 9.25
(C) 8.5
(D) 7.5
(E) 6.25
Rationale: 3/2*6+3/4*3=11.25kg
A
Answer: (A) 11.25
Question: A man goes into a barbershop and gets a $15 haircut. He pays the barber with a $20 bill, but the barber doesn't have change because it is an especially slow day. The barber goes to the flower shop next to his own and trades the $20 bill for a $10 dollar bill and two $5 bills. Then he gives the man his $5 in change.
Later the lady from the flower shop confronts the barber and tells him that the $20 bill he gave her was counterfeit. The barber agrees and he gives the lady a different $20 bill.
Later that day he tries to figure out how much money he lost. What did he lose?
(A) $5
(B) $10
(C) $12
(D) $15
(E) $20
Rationale: He lost $5. The lady from the flower shop gave him $20 in change, but eventually got $20 back. She broke even. The man who got the haircut gave the barber nothing (except counterfeit money) but got $5 back from the barber. So the barber lost only $5, and gave a free haircut.
Answer: (A) $5
Question: Mr. loyd wants to fence his Square shaped land of 60Sqft each side.If a pole is laid every 12ft how many poles do he need?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: If each side is 120 feet..then total perimeter is 60*4=240
poles every 12 feet hence no of poles= 240/12=20
ANSWER:A
Answer: (A) 20
Question: A train crosses a platform 100 m long in 60 seconds at a speed of 45 kmph.The time taken by the train to cross an electric pole is
(A) 8 sec
(B) 52 sec
(C) 1 minute
(D) 2 minute
(E) data inadequate
Rationale: let the length of the train be x m.
and that of platform is 100m.
:., Total distance covered = (x+100)m
Speed of the train= 45 km/hr. = 45*5/18 m/s = 12.5 m/s
Since it crosses the platform in 60 sec.
So, (x+100)/12.5=60
or, x=60*12.5-100=650m
It will cross an electric pole in 650m/12.5m/s=52sec.
ANSWER:B
Answer: (B) 52 sec
Question: It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 140 pages?
(A) 12
(B) 18
(C) 20
(D) 42
(E) 30
Rationale: If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)(b+3)=0
b=10
Thus it takes A 15 minutes to print 50 pages and 15*140/50=42 minutes to print 140 pages (ANSWER D)
Answer: (D) 42
Question: A cricketer scored 142 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
(A) 57.75%
(B) 54.54 %
(C) 63%
(D) 70%
(E) None of these
Rationale: Explanation :
Number of runs made by running = 142 - (12 x 4 + 2 x 6)
= 142 - (60)
= 82
Now, we need to calculate 82 is what percent of 142.
=> 82/142 * 100 = 57.75 %
Answer : A
Answer: (A) 57.75%
Question: The average earning of amechanic for the first 4days of a week is Rs.25 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?
(A) s. 10
(B) s. 24
(C) s. 30
(D) s. 40
(E) s. 50
Rationale: Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x 25+ 4 x 22 -20
= Rs. 168
âˆ´ Average earning = 168/ 7
= Rs. 24
B
Answer: (B) s. 24
Question: A man performs 1/2 of the total journey by rail, 1/3 by bus and the remaining 2km on foot. His total journey is
(A) 16km
(B) 10km
(C) 12km
(D) 24km
(E) 25km
Rationale: Explanation:
Let the journey be x km
Then, 1x/2 + 1x/3 +2 =x
5x +12 =6x
X = 12km
Answer: Option C
Answer: (C) 12km
Question: An electric wire runs for 1 km b/w some no: of poles. If one pole is removed the distance b/w each pole increases by 1 2/6 (mixed fraction). How many poles were there initially?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: let there be x no. of poles
distance b/w them= 1/(x-1)
now when one pole is removed
distance bw each pole=1/(x-2)
now according to the question
1/(x-2) =8/6 (1/x-1)
on solving you will get x=5
ANSWER:B
Answer: (B) 5
Question: For any integer n greater than 1, n* denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between 6* + 2 and 6* + 6, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.
Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.
Answer: A.
Answer: (A) None