mathewhe/aqua_rat huggingface dataset:
Question: The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas?
(A) 3:2
(B) 2:3
(C) 1:6
(D) 6:1
(E) None of these
Rationale: Explanation :
As a triangle has 3 sides and a regular hexagon has 6 sides , so the length of sides of triangle (let 2A) will be twice than that of Hexagon (let A)
A regular hexagon can be divided into 6 nos of equilateral triangles of side A.
As side of bigger triangle is double its area will be square of it i.e 4 times the smaller triangle.
Therefore Ar. of Trinagle : Ar. of Hexagon = 4X : 6X = 2:3
Answer : B
Answer: (B) 2:3
Question: If the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3, what is the ratio of apples to cucumbers?
(A) 4:9
(B) 4:3
(C) 3:7
(D) 2:5
(E) 1:6
Rationale: The ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9.
The ratio of apples to bananas to cucumbers is 4 to 3 to 9.
The answer is A.
Answer: (A) 4:9
Question: Ajay working in a Cellular company as a salesman. His monthly salary is Rs. 200. But he gets bonus as per given rule. If he sells simcards of Rs. X then his bonus will be [(x /100)2 +10]. In the first quarter of the year his average sale was Rs. 3000 per month. In the next 5 five month his average sale was Rs. 5000 per month and for next four month his average sale was Rs. 8000 per month. What is the average earning per month for the whole year?
(A) Rs. 3350
(B) Rs. 3610
(C) Rs. 3750
(D) Rs. 3560
(E) None of these
Rationale: Solution: Bonus for the first three month,
= [(3000 /100)2 +10] *3
= Rs. 2710.
Bonus for the next five month,
= [(5000 /100)2 +10] *5
= Rs. 12550.
Bonus for the next four month,
= [(8000 /100)2 +10] *4
= Rs. 25640.
Total earning as bonus for whole year,
= 2710 + 12550 +25640
= Rs. 40900.
His average bonus = 40900 /12 = Rs. 3410
Thus his average earning for whole year,
= 3410 + 200
= Rs 3610.
Answer: Option B
Answer: (B) Rs. 3610
Question: Every disk in a bag is either blue, yellow or green. The ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8. If the total number of disks in the bag is 126, how many more green disks than blue disks are in the bag?
(A) 25
(B) 28
(C) 30
(D) 35
(E) 40
Rationale: Let B:Y:G = 3x:7x:8x.
3x + 7x + 8x = 18x = 126 --> x= 7.
G - B = 8x - 3x = 5x = 35.
The answer is D.
Answer: (D) 35
Question: we have 6 weights one of 2 kg one of 3 kg one of 5 kg one of 1 kg one of 10 kg one of 50 kg by using only four weight how many weight you can weight
(A) 15
(B) 25
(C) 14
(D) 16
(E) 18
Rationale: select 6 weight out of 4, 6C4=15
ANSWER:A
Answer: (A) 15
Question: The unit digit in the product 3421*6721*4584*6784 is?
(A) 0
(B) 1
(C) 6
(D) 3
(E) 4
Rationale: Unit digit in the given product = unit digit in 1*1*4*4 = 6
Answer is C
Answer: (C) 6
Question: A boy has Rs. 640 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 110
(C) 140
(D) 130
(E) 120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 640
16x = 640
x = 40.
Hence, total number of notes = 3x = 120.
E
Answer: (E) 120
Question: P , Q, R enter into a partnership & their share are in the ratio 1/2 : 1/3 : 1/4 , after two months , P withdraws half of the capitals & after 10 months , a profit of Rs 378 is divided among them . What is Q's share?
(A) 114
(B) 120
(C) 134
(D) 144
(E) None of these
Rationale: Explanation :
The ratio of their initial investment = 1/2 : 1/3 : 1/4
= 6 : 4: 3
Let's take the initial investment of P, Q and R as 6x, 4x and 3x respectively
A:B:C = (6x * 2 + 3x * 10) : 4x*12 : 3x*12
= (12+30) : 4*12 : 3*12
=(4+10) : 4*4 : 12
= 14 : 16 : 12
= 7 : 8 : 6
B's share = 378 * (8/21) = 18 * 8 = 144. Answer : Option D
Answer: (D) 144
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
(A) 52 kmph
(B) 54 kmph
(C) 60 kmph
(D) 64 kmph
(E) 70 kmph
Rationale: Explanation:
S = 240/16 * 18/5 = 54 kmph
Option B
Answer: (B) 54 kmph
Question: The sum of 11 consecutive integers is 1111. What is the greatest integer in the set?
(A) 100
(B) 102
(C) 104
(D) 106
(E) 108
Rationale: Let x be the first integer in the set, then x+10 is the largest integer.
The sum is: x+(x+1)+(x+2)+...+(x+10)
= 11x + 10*11/2
= 11(x+5)
Then x+5=101
x=96
The largest integer in the set is 96+10=106
The answer is D.
Answer: (D) 106
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother two years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 7 years
(E) 8 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 2) years = 40 years.
Required difference = (40 - 36) years = 4 years.
Answer: Option B
Answer: (B) 4 years
Question: A motorcycle importer is planning on increasing the price of a certain model by $1000. At this new price 10 fewer motorcycles will be sold per month, but the total revenues will increase by $26,000 to $594,000. What is the number of motorcycles the manufacturer will sell at this new price?
(A) 61
(B) 65
(C) 75
(D) 45
(E) 40
Rationale: Responding to a pm: To solve this question, I will make an equation in x and then make educated guesses. Here's how:
Assuming x motorcycles were sold every month initially.
(568000/x + 1000)(x-10) = 594000
(568/x + 1)(x-10) = 594
Now 568 = 8*71
Assuming x = 71 (We have all integers so it is obvious that 568/x should be an integer.
We get 9*66 = 594 (matches)
So he will sell 71 - 10 = 61 bikes this month
Answer (A)
Answer: (A) 61
Question: Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 40 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?
(A)  16
(B)  18
(C)  20
(D)  24
(E)  30
Rationale: Time taken = Total Distance / Relative Speed
Total Distance = 40 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 40 / 10 = 4 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 4 = 24 kms... Answer - D
Answer: (D)  24
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 17. What could be the ratio of Cats to dogs in the pet store?
(A) 1:3
(B) 1:4
(C) 1:5
(D) 2:5
(E) 68:85
Rationale: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 17 --> x(a - b) = 17. Since 17 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*17.
The above implies that either x = 1 and (a - b )= 17 or x = 17 anda - b = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 17.
For the original question only option which fits is E, 4:5. Cats = 17*4 = 68 and dogs = 17*5 = 85.
Answer: E.
Answer: (E) 68:85
Question: 15 litres of mixture contains 25% alcohol and the rest water. If 3litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 20.83%
(B) 23%
(C) 18.3%
(D) 19.75%
(E) 21.23%
Rationale: Alcohol in the 15litres of mix. = 25% of 15litres = (25*15/100) = 3.75litres
water in it = 15-3.75 = 11.25litres
new quantity of mix. = 15+3 = 18 litres
Quantity of alcohol in it = 3.75litres
Percentage of alcohol in new mix. = 3.75*100/18 = 20.83%
Answer is A
Answer: (A) 20.83%
Question: In 15 year’s time the combined age of my four brothers will be 107. What will it be in six year’s time?
(A) 65
(B) 87
(C) 71
(D) 60
(E) 66
Rationale: C
71
Combined age in 15 years = 107.
4 × 15 = 60, therefore combined age now is 107 – 60 = 47.
In 6 years time, therefore, combined age will be
47 + 24 (4 × 6) = 71.
Answer: (C) 71
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 16299
(B) 1640
(C) 277
(D) 298
(E) 279
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer:B
Answer: (B) 1640
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
(A) 2800
(B) 3000
(C) 3200
(D) 3400
(E) 3500
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
B
Answer: (B) 3000
Question: ((1^m)/(5^m))((1^17)/(4^17)) = 1/(2(10)^33)
What is m?
(A) 17
(B) 18
(C) 34
(D) 35
(E) 33
Rationale: ((1^m)/(5^m))((1^17)/(4^17)) = 1/(2(10)^33)
((1/5)^m ) * ((1/2)^34) = 1/ (2 * (2*5)^33))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^m= (1/5)^33
((1/5)^m ) * ((1/2)^34) = 1/[(2^34)*(5^33)]
So, m=33
Answer E
Answer: (E) 33
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
(A) 45%
(B) 23%
(C) 20%
(D) 60%
(E) 56%
Rationale: C
C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
Answer: (C) 20%
Question: The average age of 12 students is 20 years. If the age of one more student is included, the average decreases by 1, what is the age of the new student?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: Average age of 12 students is 20 years means sum of 12 students age is 240
If the age of one more student is included, the average decreases by 1, means 13 students age is 13*19 =247
Difference between 12 and 13 students is 7.
ANSWER:B
Answer: (B) 7
Question: Sahil purchased a machine at Rs 13000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
(A) Rs. 22000
(B) Rs. 24500
(C) Rs. 26500
(D) Rs. 28500
(E) None of these
Rationale: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 13000 + 5000 + 1000 = 19000
150% of 19000 = 150/100 * 19000 = 28500
Option D
Answer: (D) Rs. 28500
Question: A container contains 30 liters of milk. From this container 5 liter of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
(A) 17.26liter
(B) 17.39 liter
(C) 17.36 liter
(D) 17.32 liter
(E) 57.36 liter
Rationale: Explanation:
No explanation is available for this question!
ANSWER:C
Answer: (C) 17.36 liter
Question: Factor: 5x2 – 15x – 20
(A) (a) 5(x-4)(x+1)
(B) (b) -2(x-4)(x+5)
(C) (c) -5(x+4)(x-1)
(D) (d) 5(x+4)(x+1)
(E) (e) 5(x-4)(x-1)
Rationale: 5x2 – 15x – 20.
= 5(x2 – 3x – 4).
= 5(x2 – 4x + x – 4).
= 5{x(x - 4) +1(x - 4)}.
= 5(x-4)(x+1).
the answer is (A)
Answer: (A) (a) 5(x-4)(x+1)
Question: A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.
(A) 7/9
(B) 7/15
(C) 3/5
(D) 4/3
(E) 8/5
Rationale: let S be the sample space
Then n(S)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)/(2*1)=45
Let E=event of getting both balls of same colour
Then n(E)=no of ways(2 balls out of six) or(2 balls out of 4)
=(6c2+4c2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=n(E)/n(S)=21/45=7/15
Ans: B
Answer: (B) 7/15
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 111.12
(B) 111.16
(C) 111.15
(D) 111.19
(E) 111.18
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer: A
Answer: (A) 111.12
Question: The perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 28 cm2
(B) 27 cm2
(C) 29 cm2
(D) 25 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 20/2
= 25 cm2
Answer: D
Answer: (D) 25 cm2
Question: An advertising agency finds that, of its 210 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
(A) 56
(B) 70
(C) 90
(D) 110
(E) 120
Rationale: Total=210
Television=115
Radio=110
Magazine=130
All the three =210-115-110-130+85+75+95=110
ANSWER D
Answer: (D) 110
Question: How many multiples of 2 are there between 1 and 52, exclusive?
(A) 21
(B) 22
(C) 25
(D) 26
(E) 28
Rationale: 25
multiples of 2 between 1 and 52 exclusive.
from 2 * 1 upto 2*25, (1,2,3,4,...,25). Hence, 25 multiples !
correct option is C
Answer: (C) 25
Question: A day-trader plans to invest a total of $23,600 into 15 separate investments. If each investment requires a minimum deposit of $1,400, then which of the following is the maximum amount that she could put into any one investment?
(A) $2,800
(B) $4,000
(C) $3,500
(D) $3,800
(E) $3,900
Rationale: We can also just keep track of the HUNDREDS DIGITS(since the hundreds digit is different for each answer choice).
Total of 14 minimized investments = (14)(1400) = $???600
The 15th investment + $???600 = $23,600
So, the HUNDREDS DIGITS of the 15th investment must be 0
Answer: B
Answer: (B) $4,000
Question: The value of x + x(xx) when x = 4 is:
(A) A)36
(B) B)16
(C) C)18
(D) D)68
(E) E)10
Rationale: x + x(xx)
Put the value of x = 2 in the above expression we get,
4 + 4(44)
= 4 + 4(4 × 4)
= 4 + 4(16)
= 4 + 64
= 68
D
Answer: (D) D)68
Question: Jim is able to sell a hand-carved statue for $660 which was a 20% profit over his cost. How much did the statue originally cost him?
(A) $496.30
(B) $512.40
(C) $550
(D) $574.90
(E) $588.20
Rationale: Cost Price = 660/120 * 100 = 550
Answer : C
Answer: (C) $550
Question: In what ratio should a variety of rice costing Rs. 5.5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
(A) 5/6
(B) 5/9
(C) 5/1
(D) 5/8
(E) 7/6
Rationale: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (8.75 - 7.50) / (7.50 - 5.5) =5/8
Answer: D
Answer: (D) 5/8
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 299
(B) 240
(C) 277
(D) 255
(E) 143
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
Answer: (B) 240
Question: If 20% of A is the same as 30% of B, then A : B is :
(A) 5:4
(B) 5:3
(C) 4:3
(D) 3:2
(E) 1:3
Rationale: Expl : 20% of A I= 30 % of B =20A/100 = 30B/100 = 3/2 = 3:2
Answer:D
Answer: (D) 3:2
Question: A certain university will select 1 of 8 candidates eligible to fill a position in the mathematics department and 2 of 12 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 340
(B) 380
(C) 472
(D) 528
(E) 630
Rationale: 1C8*2C12 = 8*66 = 528
the answer is (D)
Answer: (D) 528
Question: At Peter's firm's annual revenue grows twice as fast as its costs. In 2007 it operated at a $1000 loss, it broke even in 2008, and in 2009 its revenues were 44% higher than in 2007. If the firm's revenues and costs grew at a constant rate over this period, what was its profit in 2009?
(A) 700
(B) 1000
(C) 1300
(D) 1600
(E) 2000
Rationale: At Peter's firm's annual revenue grows twice as fast as its costs.First solve for how much revenue is increasing each year:
R2008= R2007*(1+x)
R2009= R2007*(1+x)^2=1.44*R2007
(1+x)^2 = 1.44
1+x=1.2
x=0.2 aka revenue increases 20% each year and cost increases 10% annually
Next solve for R2007and C2007:
R2007= C2007- 1000
1.2*R2007- 1.1*C2007= 0
1.2*[C2007- 1000] - 1.1*C2007= 0
0.1*C2007= 1,200
C2007= 12,000
R2007= 11,000
Finally find 2009 profits:
Profit2009= 1.44*11,000 - 1.21*12,000
Profit2009= 15,840 - 14,520
Profit2009= 1320
Answer: C
Answer: (C) 1300
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 60 cm^2
(B) 30 cm^2
(C) 20 cm^2
(D) 40 cm^2
(E) 50 cm^2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
ANSWER B
Answer: (B) 30 cm^2
Question: The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
(A) 20
(B) 30
(C) 48
(D) 58
(E) 68
Rationale: Explanation:
Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8 =5*3/5 : 8*3/5 =3: 24/5
A : B : C = 2 : 3 :	24/5=10:15:24
B =	98* 15/49 =30.
Answer IS B
Answer: (B) 30
Question: In a simultaneous throw of 2 dice what is the probability of getting a total of 5?
(A) 1/4
(B) 1/9
(C) 2/11
(D) 3/13
(E) 1/5
Rationale: n(S) = 6*6 = 36
E = {(1,4),(2,3),(3,2),(4,1)}
Probability = 4/36 = 1/9
Answer is B
Answer: (B) 1/9
Question: In What proportion must flour at $0.8 per pound be mixed with flour at $0.9 per pound so that the mixture costs $0.835 per pound?
(A) 1:3
(B) 1:2
(C) 1:1
(D) 2:1
(E) 3:1
Rationale: Using weighted average method:
Let x be the proportion in which the $0.8 per pound flour is mixed with $0.9 per pound flour.
Thus 0.8*x + 0.9*(1-x) = 0.835
0.9 – 0.1x = 0.835
x = 0.65
Thus ratio of both flours is 2:1
D
Answer: (D) 2:1
Question: A man took some money for borrowed, for 3 years the total will be Rs.6500 and 5 years it will be Rs.7500/-. Then how much amount he borrowed?
(A) s.5000/-
(B) s.5500/-
(C) s.5770/-
(D) s.5800/-
(E) s.5820/-
Rationale: 3 years --------> Rs.6500/-
5 years --------> Rs.7500/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.6500/- - Rs.1500/- = Rs.5000/-
P = Rs.5000/-
A
Answer: (A) s.5000/-
Question: The cost of an item was reduced from its usual selling price of $23.99 to $20.99. Which of the following is closest to the percent decrease in the price of the item?
(A) 12%
(B) 21%
(C) 24%
(D) 25%
(E) 42%
Rationale: The price decreased by 23.99 - 20.99 = $3.
$3 is a bit more than 12% of original price of $24.
Answer: A.
Answer: (A) 12%
Question: Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 81, then which of the following can be a value of 2y + 3g?
(A) 52
(B) -55
(C) 141
(D) 142
(E) 160
Rationale: 800score Official Solution:
First note that g can either be 9 or -9. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 9 and then g = -9. If g = 9, then x = 8/5. If g = -9, then x = -2. Since all of our solutions are whole numbers, we can dismiss 8/5. We use g = -9 and x = -2 to determine the value of y: y = 2(-9) + 4 = -14. Finally, we substitute the values for y and g into the last expression to determine its value : 2(-14) + 3(-9) = -28 - 27 = -55;the correct answer is (B).
Answer: (B) -55
Question: A certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water. If between 8 and 15 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
(A) 3
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: If sides are 7, vol=7^3=343
80%= 274.4, 85%=291.55
so vol above water, between 68.6 and 51.45 -->too big
If side are 4, vol = 64
80%=51.2, 85%=54.4
vol above water between 12.8 and 9.6
So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
80%= 100, .85%=106.25
vol above water between 18.75-25
(Sides are 4 cubic centimeters)
B
Answer: (B) 4
Question: How many three digit numbers contain the digit 5 at least once?
(A) 52
(B) 128
(C) 252
(D) 648
(E) 900
Rationale: The question is basically asking how many numbers between 100-999 contain at least one digit as 5.
Let ABC be a 3 digit number A can be filled with 9 digits, B can be filled with 10 digits and C can be filled with 10 digits. (because hundredth digit can only be between 1-9= 9 digits)
Therefore total number of ways we can form 3 digit number=9*10*10=900 ways (100-999)
Number of ways we can form a 3 digit number without the digit 5= 8*9*9= 648 ways
ANSWER:D
Answer: (D) 648
Question: A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. 5
II. 1
III. -5
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: The question is which of the following must be in the set, not could be in the set.
If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.
Answer: C.
Answer: (C) I and II only
Question: There are two decks of 10 cards each. The cards in each deck are labeled with integers from 11 to 22 inclusive. If we pick a card from each deck at random, what is the probability that the product of the numbers on the picked cards is a multiple of 6?
(A) 0.23
(B) 0.36
(C) 0.4
(D) 0.42
(E) 0.46
Rationale: If 6 is a multiple, we need 2 and 3 as a factor of the number. If we factor the numbers 11 through 20 we have:
11 = 11
12 = 2*2*3
13 = 13
14 = 7*2
15 = 5*3
16 = 2*2*2
17 = 17
18 = 3*2*3
19 = 19
20 = 5*2*2
Combos that have a 2 and a 3 as factors (first + second card):
12 + anything - 19 of these possibilities (we count 12 + 12 only once)
14 + 15 - 2 of these possibilities
15 + 16 - 2 of these possibilities
15 + 20 - 2 of these possibilities
18 + anything (except 12, since that is counted in our first option) - 17 of these possibilities
Total possibilities that will be a multiple of 6: 42
Total possibilites: 10*10=100
Probability = 42/100 = 0.36
Answer:B
Answer: (B) 0.36
Question: A certain number successively divided by 2, 5 and 7 leaves remainders 1, 2 and 3 respectively. When the same number is divided by 70, what is the remainder?
(A) 33
(B) 34
(C) 35
(D) 36
(E) 37
Rationale: 2) 105 (52 5) 52 (10 7) 10 (1
104 50 7
-------- -------- - -----
1 2 3
=> 65
105/70 = 35 (Remainder)
ANSWER:C
Answer: (C) 35
Question: John can finish a job in 30 days. If he worked for 15 days alone before he was joined by Kennedy to complete the job in 3 days, how many days will it take both of them to complete the entire job?
(A) 4
(B) 3
(C) 5
(D) 6.5
(E) 6
Rationale: Explanation:
John and Kennedy complete half work in 3 days
=> they can complete whole work in 6 days
Answer: Option E
Answer: (E) 6
Question: SUMO,INC recently conducted a survey and found that 200,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of SUMO,INC customers live in urban areas ?
(A) 200,000
(B) 216,000
(C) 360,000
(D) 480,000
(E) 600,000
Rationale: Let's say that we have a starting value of X...
100% of X = X
100% MORE than X = X + X = 2X
200% MORE than X = X + 2X = 3X
300% MORE than X = X + 3X = 4X
Etc.
Here, we're told that 200,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...
3(200,000) = 600,000
Final Answer:E
Answer: (E) 600,000