mathewhe/aqua_rat huggingface dataset:
Question: The sum of three integers A, B and C is 240. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?
(A) 120
(B) 130
(C) 125
(D) 140
(E) 145
Rationale: A is one third of the sum of B and C..
or A=1/3(B+C)...
But A+B+C=240
so 1/3(B+C)+B+C=240
4(B+C)/3= 240
B+C =240*3/4 = 180
A=240-180=60
2)B is one fifth of the sum of A and C
or B=1/5(A+C)...
But A+B+C=240
so 1/5(A+C)+A+C=240
A+C=240*5/6=200
but A=60, so C=200-60=140
Answer :D
Answer: (D) 140
Question: Solve
(x-a)*(x-b)*(x-c)*...........(x-z)=?
(A) -1
(B) 0
(C) 1
(D) 2
(E) 3
Rationale: (x-a)*(x-b)*(x-c)*...........(x-z)
= (x-a)*(x-b)*(x-c)*...........(x-x)*(x-y)*(x-z)
since (x-x)=0 so, whole product is zero
(x-a)*(x-b)*(x-c)*...........(x-z )= 0
ANSWER:B
Answer: (B) 0
Question: The water from one outlet, flowing at a constant rate, can fill a swimming pool in 5 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 3 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
(A)  0.22
(B)  1.87
(C)  2.50
(D)  3.21
(E)  4.56
Rationale: Always remember RT=W i.e Rate*Time = Work
Also remember that rate can be added or subtracted. For e.g if A do a work in 2 day and B do a work in 2 day.
They both of them together will do a work in 1 day.
So now your question first determine both outlets rate.
1st outlet rate = 1/5 (R=W/T here W=1 work, T = 5hrs)
2nd outlet rate = 1/3 (R=W/T here W=1 work, T = 3hrs)
Both of them working together rate = 1st outlet rate + 2nd outlet rate = 1/5+1/3 = 8/15
again apply the formula RT=W
T = W/R = 1/8/15 = 15/8 =1.87
Answer is B.
Answer: (B)  1.87
Question: In a game of 100 points, A can give B 10 points and C 15 points. then how many points can B give C in a game of 70?
(A) 4.89
(B) 3.89
(C) 1.89
(D) 11.89
(E) 5.89
Rationale: In a game of 100 points,A give B 10 points and c 15 points means B=90,C=85
In 90 points B give 5 since 90-85=5
In 70 points B gives=70*5/90=3.89
ANSWER:B
Answer: (B) 3.89
Question: If it is true that x > -3 and x < 7, which of the following must be true?
(A) x > 3
(B) x < -7
(C) x < 3
(D) -3 < x < 7
(E) none of the above.
Rationale: the range is -3 < x < 7
A. x > 3 - no because x can be between -3 < x < 3
B. x < -7 - no because the values of x are always >-7
C. x < 3 - no because x can be between 3 < x < 7
D. -3 < x < 7 - true because x can be between -3 < x < 7
E. none of the above.
Answer: D
Answer: (D) -3 < x < 7
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different R arrangements of plays can be run, if the same play can’t be run more than once?
(A) 24
(B) 125
(C) 243
(D) 504
(E) 729
Rationale: Number of R ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Answer: (D) 504
Question: The area of a square is equal to five times the area of a rectangle of dimensions 27 cm * 16 cm. What is the perimeter of the square?
(A) 140
(B) 240
(C) 340
(D) 144
(E) 122
Rationale: Area of the square = s * s = 3(27 * 16)
=> s = 9 * 4 = 36 cm
Perimeter of the square = 4 * 36 = 144 cm.
Answer: D
Answer: (D) 144
Question: A present value of a machine is $900. Its value depletion rate is 10% per annum then find the machine value after 2 years?
(A) $900
(B) $810
(C) $915
(D) $715
(E) $729
Rationale: P= $900
R = 10%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=900*9/10 * 9/10
=$729
Answer is E
Answer: (E) $729
Question: How many 7 digit number are there having the digit 3 three times & the digit 0 four times ?
(A) 15
(B) 3^3 * 4^4
(C) 18
(D) 19
(E) 25
Rationale: The first digit on the left for 7 digit would always be fixed to 3 (as 0 as first digit will no longer makes it a 7 digit number).
So we are left with 6 places to be filled by number 3 two times and number 2 four time.
So possible arrangements at 6 place for repetitive numbers would be = 6! / 4!*2! = 15
ANSWER:A
Answer: (A) 15
Question: If 60% of a number is equal to one half of another number, what is the ratio of first number to the second number?
(A) 4:5
(B) 5:6
(C) 6:5
(D) 5:4
(E) 2:5
Rationale: Let 60% of A = 1/2 B. Then,
60A/100 = 1B/2 => 3A/5 = 1B/2
A/B = (1/2 * 5/3) = 5/6
A:B = 5:6.
Answer: B
Answer: (B) 5:6
Question: How much is 80% of 40 is greater than 4/5 of 30?
(A) 12
(B) 27
(C) 8
(D) 12
(E) 81
Rationale: (80/100) * 40 â€“ (4/5) * 30
32 - 24 = 8
Answer:C
Answer: (C) 8
Question: A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes Bil can make using this recipe?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.
Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.
Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.
answer is A
Answer: (A) 5
Question: If n is an even integer, which of the following must also be an even integer?
(A) n^2 + 1^2
(B) (n+1)^2
(C) n + 1
(D) 3n + 1
(E) n^2 + 1
Rationale: Answer: B
A: 2n = odd
B: -2n + 1 = even
C: -(n^2) = odd
D: 2n - 1 = odd
E: n^3 = odd
Answer: B
Answer: (B) (n+1)^2
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 6 years hence?
(A) 58
(B) 59
(C) 62
(D) 70
(E) 72
Rationale: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
5 years, their ages will be 46 and 26.
Sum of their ages = 46 + 26 = 72.
E)
Answer: (E) 72
Question: Nitin ranks 23th in a class of 60 students. What is rank from the last ?
(A) 33
(B) 38
(C) 32
(D) 28
(E) 19
Rationale: Explanation:
Number students behind the nitin in rank = (60 - 23) = 37
Nitin is 38nd from the last
Answer: B) 38
Answer: (B) 38
Question: Speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:
(A) 92 hours
(B) 24 hours
(C) 84 hours
(D) 48 hours
(E) None
Rationale: Sol.
Speed upstream = 3 kmph; Speed downstream = 9 kmph.
∴ total time taken = [210/3 + 210/9] hours = 84 hours.
Answer C
Answer: (C) 84 hours
Question: If ( log 5 5) (log 4 9) (log 3 2) is equal to
(A) 1
(B) 3/2
(C) 2
(D) 5
(E) 7
Rationale: Solution
Given expression	=log 9/log 4 ×log 2/log 3
‹=› log 3²/log 2²×log 2/log 3
= 2 log 3/ 2 log 2×log 2/log3
= 1.
Answer A
Answer: (A) 1
Question: John has taken four (4) tests that have an average of 84. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
(A) 87
(B) 93
(C) 92
(D) 94
(E) 97
Rationale: Traditional Method:
Total scored till now 84*4=328
Total score to avg 87 in 6 tests = 87*6=522
Total to be scored on 2 tests = 522-336=186
Avg on 2 tests = 186/2 = 93
Answer: B
Answer: (B) 93
Question: When positive integer V is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
(A) a. k + 1
(B) b. k -11
(C) c. 4k + 2
(D) d. (k-3)/3 +2
(E) e. V/3
Rationale: When positive integer V is divided by 6 the remainder is 3
So, V could equal 3, 9, 15, 21, etc
let's TEST V =3
a.3+ 1 = 4 (EVEN)
b.3-11 = -8 (EVEN)
c. 4(3) + 2 = 14 (EVEN)
d. (3-3)/3 +2 = 2 (EVEN)
At this point, we can already see the answer must be E.
Let's check E forfun
e.3/3 = 1 (ODD)
Great!
Answer: E
Answer: (E) e. V/3
Question: A right triangle ABC has to be constructed in the xy-plane so that the right angle is at A and AB is parallel to x axis. The coordinates of A, B and C are to satisfy the inequalities -1 ≤ x ≤ 7 and 1 ≤ y ≤ 7. The numbers of different triangles that can be constructed with these properties are?
(A) 63
(B) 336
(C) 567
(D) 3024
(E) 5040
Rationale: Choose the (x,y) coordinates for vertex A (right angle): 9C1*7C1;
Choose the x coordinate for vertex B (as y coordinate is fixed by A): 8C1, (9-1=8 as 1 horizontal dot is already occupied by A);
Choose the y coordinate for vertex C (as x coordinate is fixed by A): 6C1, (7-1=6 as 1 vertical dot is already occupied by A).
9C1*7C1*8C1*6C1=3024.
Answer: D.
Answer: (D) 3024
Question: At what rate percent on simple interest will Rs.1500 amount to Rs.2000 in 5 years?
(A) 8.33 %
(B) 3 6/7 %
(C) 2 6/7 %
(D) 5 %
(E) 6 %
Rationale: Explanation:
500 = (1500x5xR)/100
R = 8.33 %
Answer: Option A
Answer: (A) 8.33 %
Question: How many numbers from 2 to 7 are exactly divisible by 2?
(A) 3
(B) 4
(C) 5
(D) 8
(E) 9
Rationale: 2/2 = 1 and 7/2 = 3
3 - 1 = 2
2 + 1 = 3 Numbers
A)
Answer: (A) 3
Question: A and B started a business investing Rs. 90,000 and Rs 25,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
(A) 9:2
(B) 3:2
(C) 18:20
(D) 18:5
(E) 17:4
Rationale: A: B = 90000 : 25000
= 90 : 25
= 18 : 5
ANSWER:D
Answer: (D) 18:5
Question: How many integers between 500 and 1000 are there such that their unit digit is even?
(A) 250
(B) 150
(C) 500
(D) 100
(E) 200
Rationale: 500 numbers between - 500 and 1000
Out of which half would be even, half odd.
Number of even unit digit number = 250.
correct option is A
Answer: (A) 250
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
(A) 16
(B) 15
(C) 17
(D) 888
(E) 99
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
Answer: B
Answer: (B) 15
Question: What is the probability of getting a sum 9 from two throw of a dice?
(A) 1/6
(B) 1/8
(C) 1/9
(D) 1/12
(E) 1/13
Rationale: In two throws of die, n(S)=36
Let E =event of getting a sum 9
={(3,6), (4,5),(5,4),(6,3)}
P(E)=4/36=1/9
ANSWER C 1/9
Answer: (C) 1/9
Question: The length of a rectangular garden is three times its width. If the area of the rectangular garden is 507 square meters, then what is the width of the rectangular garden?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Let x be the width of the garden.
3x^2 = 507
x^2 = 169
x = 13
The answer is D.
Answer: (D) 13
Question: The goalkeeper of a Hockey team is 31 years old and the captain is 4 years older and the team size is 11. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 28.5 years
(B) 24 years
(C) 25 years
(D) none of the above
(E) Cannot be determined
Rationale: Explanation :
Let the average age of the whole team by x years.
=> 11x - (31 + 35) = 9(x -1)
=> 11x - 9x = 57
=> 2x = 57
=> x = 28.5.
So, average age of the team is 28.5 years.
Answer : A
Answer: (A) 28.5 years
Question: The difference between compound interest and simple interest on a sum for 3 years at 10% p.a. is Rs.124 Find the sum.
(A) Rs.5000
(B) Rs.4000
(C) Rs.6000
(D) Rs.8000
(E) Rs.7000
Rationale: For 3 years, we know
C.I-S.I= p(R/100)^3+3(R/100)^2
so, putting all values we have,
124=p((10/100)^3+3(10/100)^2)= 4000
ANSWER:B
Answer: (B) Rs.4000
Question: Points X, Y, and Z lie, in that order, on a straight railroad track. The distance from point X to point Y is twice the distance from point Y to point Z. A train traveled from point X to point Z without stopping. The train's average speed when traveling from point X to point Y was 100 miles per hour and the train's average speed when traveling from point Y to point Z was 75 miles per hour. What was the train's average speed, in miles per hour, when traveling from point X to point Z?
(A) 90
(B) 85
(C) 85.5
(D) 70
(E) 90
Rationale: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable D.
Speed X-Y = 100
Speed Y-Z = 75
Average Speed = total distance/total rate
rate = distance/time
X====================Y==========Z
If X-Y is twice the length of Y-Z then let X-Y = 2d and let Y-Z= d
Average speed = 3d/(2d/100) + (d/75)
3d/(6d/300) + (4d/300)
3d/(10d/300)
900d/10d
Average speed = 90
ANSWER: A
Answer: (A) 90
Question: The mass of 1 cubic meter of a substance is 700 kilograms under certain conditions. What is the volume, in cubic centimeters, of 1 gram of this substance under these conditions? (1 kilogram = 1,000 grams and 1 cubic meter = 1,000,000 cubic centimeters)
(A) 0.8
(B) 1.42
(C) 8.0
(D) 12.5
(E) 80.0
Rationale: Density is mass divided by volume. So density of the given substance will be mass/volume=700kg/1m^3=700 kg/m^3 or 1g/1.42cm^3=0.7 g/cm^3.
Next, ask yourself if 700,000 g is equivalent to 1,000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters? --> 1 g - 1,000,000/700,000 = 10/8 = 1.42 cubic centimeters.
Answer is B
Answer: (B) 1.42
Question: An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 9 candidates for the 4 consultant slots. If 2 out of 9 consultants refuse to be on the same team, how many different teams are possible?
(A) 540
(B) 630
(C) 740
(D) 820
(E) 980
Rationale: Answer= Total number combinations - Total number of combinations with constraints
Total number of combinations = 2C1*3C1*9C4= 756
Total number of combinations with constraints = 2C1*3C1*7C2=126
Answer=756-126=630
ANSWER: B
Answer: (B) 630
Question: Baker Raj is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
(A) 330
(B) 300
(C) 252
(D) 225
(E) 210
Rationale: Baker Raj is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.
To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.
Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210.
Answer: (E) 210
Question: If the number 5 * 2 is divisible by 6, then * = ?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 1
Rationale: 6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.
Then, (5 + x + 2) must be divisible by 3. So, x = 2.
ANSWER A
Answer: (A) 2
Question: Three partners A, B, C in a business invested money such that 3(Aâ€™s capital) = 6(Bâ€™s capital) = 9(Câ€™s capital) then, The ratio of their capitals is
(A) 63 : 45 : 34
(B) 6 : 3 : 2
(C) 36 : 54 : 28
(D) 63 : 45 : 35
(E) None of these
Rationale: Explanation:
Let3(Aâ€™s capital) = 6(Bâ€™s capital) = 9(Câ€™s capital) = Rs.x
Then, Aâ€™s capital = Rs x/3, Bâ€™s capital = Rs. x/6 and Câ€™s capital = Rs. x/9.
A : B : C = x/3 : x/6 : x/9
6 : 3 : 2
Answer: Option B
Answer: (B) 6 : 3 : 2
Question: What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?
(A) Rs. 9000.30
(B) Rs. 9720
(C) Rs. 10123.20
(D) Rs. 10483.20
(E) None of these
Rationale: Explanation:
Amount
= Rs.[25000 x (1 + 12/100)3]=Rs. 35123.20
C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
ANSWER IS C
Answer: (C) Rs. 10123.20
Question: if log 7 = 0.845098, the number of digits in 7128 is
(A) 100
(B) 120
(C) 109
(D) 280
(E) 110
Rationale: Explanation:
log(7128) = 128log(7) = 128 × 0.845098 ≈ 108.17
ie, its characteristic = 108
Hence, number of digits in 2128 = 108+1 = 109
Answer: Option D
Answer: (D) 280
Question: 1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $140
(B) $125
(C) $145
(D) $135
(E) $155
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
ANSWER : OPTION C =$145
Answer: (C) $145
Question: A box contain Red, Blue and Green colored balls. The number of Red balls is 80 and the number of Blue balls is 60.
The number of Green balls subtracted from the number of Red balls is the same as the number of Green balls added with the number of Blue balls. Then the number of Green balls is?
(A) 80
(B) 70
(C) 60
(D) 85
(E) 140
Rationale: Answer
Let the number of Green balls be x.
Then, x - 60= 80 - x
â‡’ 2x = 80+ 60= 140
â‡’ 2x = 140
âˆ´ x = 70
Correct Option: B
Answer: (B) 70
Question: On the x y plane, there are 8 points of which 4 are collinear. How many straight lines can be formed by joining any 2 points from the 8 points ?
(A) 28
(B) 22
(C) 20
(D) 23
(E) 56
Rationale: Each line is defined by two points.
4 points are collinear => 1 line passes through those.
Now each of those points form 5 line => 4 lines with the "out" points and 1 line is the common one
but this is counted (the common) so we just add 4(point)*4(lines)=16 to the sum.
Finally the 4 points "out" of the common line form 4C2 = 6 different lines
1+16+6=23 totals	ANS:D
Answer: (D) 23
Question: three men invested sum. and their ratio is 5:7:6. profit is 9000.then b's share
(A) 2000
(B) 2100
(C) 2200
(D) 2300
(E) 3500
Rationale: b's share =7/18*9000=3500
ANSWER:E
Answer: (E) 3500
Question: The average runs of ten batsmen is 25. If three players whose marks are 3,8 and 4 are removed , then find the approximate average runs of the remaining players.
(A) 28
(B) 34
(C) 55
(D) 29
(E) 52
Rationale: Exp. Total runs of 10 players = 25*10 = 250,
Total runs after the removal of 3 players = 250 –(3 + 8 + 4)
= 250 – 15 = 235
Approximate average runs = 235/(10-3) = 235/ 7 = 34
Answer: B
Answer: (B) 34
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) 338
(B) 237
(C) 197
(D) 285
(E) 171
Rationale: Explanation:
Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Answer: (D) 285
Question: James and David work at a grocery shop with 6 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that James and David will both be chosen?
(A) 1/20
(B) 1/22
(C) 1/23
(D) 1/25
(E) 1/15
Rationale: Probability that James and David will both be chosen out of 6 workers
= (2/6)*(1/5)
= 1/15
Answer E
Answer: (E) 1/15
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
(A) 240
(B) 88
(C) 77
(D) 266
(E) 121
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240.
Answer: A
Answer: (A) 240
Question: You collect pens. Suppose you start out with 7. Mike gives you another 22 pens. Since her father makes pens, Cindy decides to double your pens. Since you're nice, you give Sharon 19 pens. How many pens do you have at the end?
(A) 39
(B) 40
(C) 41
(D) 42
(E) 43
Rationale: Solution
Start with 7 pens.
Mike gives you 22 pens: 7 + 22 = 29 pens.
Cindy doubles the number of pens you have: 29 × 2 = 58 pens.
Sharon takes 19 pens from you: 58 - 19 = 39 pens.
So you have 39 at the end.
Correct answer: A
Answer: (A) 39
Question: A drum contains 4 red balls, 3 blue balls and 2 white balls. Three balls are removed (no replacement) what is the probability that there will be one of each?
(A) 22
(B) 21
(C) 24
(D) 25
(E) 28
Rationale: 4*3*2 / 9*8*7.
There is a 4/9 chance of taking a red ball first; if you do, ther'es a 3/8 chance of taking a blue ball next, and if you get that far, there's a 2/7 chance of getting a white ball third.
Or you might get white first, blue second and red third: 2/9, followed by 3/8 and then 4/7. No matter what order it might occur, the multiplication will always be (4*3*2)/(9*8*7).
Since 4*2 = 8 and 3 is a factor of 9, you can cancel out the entire top row to leave 1 / (3*1*7) ie. 1 chance in 21.
answer B
Answer: (B) 21
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $204
(B) $231
(C) $156
(D) $145
(E) $200
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Answer: (D) $145
Question: Sivagami is 2 years elder than Meena. After 6 years the total of their ages will be 7 times of their current age. Then age of Sivagami is :
(A) 19 years
(B) 17 years
(C) 15 years
(D) data inadequate
(E) 16 years
Rationale: Explanation:
Let Meena’s age = A.
Then Sivagami’s age = A + 2
After 6 years the total of their ages will be 7 times of what?
Not clear.
So the given data are inadequate. Answer: D
Answer: (D) data inadequate
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 6
(B) 8
(C) 10
(D) 14
(E) 15
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 25%?
(A) 37.5%
(B) 37.6%
(C) 38.5%
(D) 17.1%
(E) 37.2%
Rationale: Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 75
Gain % = 11/64 * 100 = 17.1%.
Answer: D
Answer: (D) 17.1%
Question: In a bucket there are 3 green balls and 2 yellow balls. What is the probability of drawing at least one green ball when drawing two consecutive balls randomly?
(A) 16/20
(B) 9/10
(C) 2/5
(D) 3/5
(E) ½
Rationale: P(at least one green) = 1 - P(no green, so 2 yellow) = 1- 2/5*1/4 = 9/10.
Answer: B.
Answer: (B) 9/10
Question: The points A(0, 0), B(0, 4a - 5) and C(2a + 3, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?
(A) 114
(B) 116
(C) 118
(D) 119
(E) 120
Rationale: 1/2bh=1/2(2a+3)(2a+6)
Now 4a-5=2a+6
2a=11
Therefore,
A(0,0); B(0,17); C(14,17)
1/2*14*17=119
Answer: D
Answer: (D) 119
Question: A cicketer bas a certain average for 10 innings, In the eleventh inning, he scorod 108 runs, thereby increasing his average by 6 runs. His new average is?
(A) 11 runs
(B) 27 runs
(C) 48 runs
(D) 28 runs
(E) 29 runs
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 6 => 11x + 66 = 10x + 108 => x = 42.
New average = (x + 6) = 48 runs.
Answer: C
Answer: (C) 48 runs
Question: The average of five numbers id 27. If one number is excluded,the average becomes 25. The excluded number is
(A) 25
(B) 27
(C) 30
(D) 35
(E) 34
Rationale: given x/5=27 so x=135 and y/4=25 so y=100. excluded no is x-y=135-100=35.
ANSWER:D
Answer: (D) 35