mathewhe/aqua_rat huggingface dataset:
Question: In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 14 kmph
(B) 11 kmph.
(C) 51 kmph.
(D) 61 kmph.
(E) 71 kmph.
Rationale: Speed in still water =1/2(14+8) kmph = 11 kmph.
Answer: B
Answer: (B) 11 kmph.
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?
(A) 12
(B) 14
(C) 15
(D) 19
(E) 10
Rationale: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15. Answer:C
Answer: (C) 15
Question: Divide 952 to A,B,C IN 37:18:13 RATIO.CALCULATE PART OF A.
(A) 518
(B) 428
(C) 552
(D) 526
(E) 624
Rationale: ADDITION OF RATIO NO. =68
PART OF A=952×37/68=518
ANSWER A
Answer: (A) 518
Question: If the sum of 5 consecutive integers is x, which of the following must be true?
I. x is an even number
II. x is an odd number
III. x is a multiple of 5
(A) I only
(B) II only
(C) III only
(D) I and III
(E) II and III
Rationale: I. If you start off with an even number, the sum (x) is even, and if you start off with an odd number the sum (x) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 5p + 10 = 5 (p+2) => divisible by 5. There this must be true in all cases.
Therefore C is the answer.
Answer: (C) III only
Question: 9. The least number which should be added to 28523 so that the sum is exactly divisible by 3, 5, 7 and 8 is
(A) 41
(B) 42
(C) 32
(D) 37
(E) 39
Rationale: LCM of 3, 5, 7 and 8 = 840
28523 ÷ 840 = 33 remainder = 803
Hence the least number which should be added = 840 - 803 = 37 Answer: Option D
Answer: (D) 37
Question: The contents of two vessels containing copper and tin in the ratio 2:3 and 5:7 are mixed in the ratio 3:5. The resulting mixture will have copper and tin in the ratio?
(A) 210:283
(B) 312:433
(C) 178:213
(D) 197:283
(E) 145:256
Rationale: The ratio of copper and tin the new vessel= (2/5*3/8 + 5/12*5/8) : (3/5*3/8 + 7/12*5/8)
= 197/480 : 283/480 = 197:283
Answer is D
Answer: (D) 197:283
Question: Suraj has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs thereby increasing his average by 5 runs. What is his average after the 13th innings?
(A) 48
(B) 64
(C) 36
(D) 72
(E) 27
Rationale: To improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings.
Thus, the average after the 13th innings
= 96 - 60 = 36.
ANSWER:C
Answer: (C) 36
Question: If a+b=−9, and a=30/b, what is the value of a^2+b^2?
(A) 31
(B) 21
(C) 41
(D) 61
(E) 51
Rationale: a^2 + b^2 should make you think of these formulas:
(a+b)(a+b) = a^2+b^2+2ab
We already know (a+b) = -9 and a*b = 30
(a+b)(a+b) = (-9)(-9) = a^2+b^2+2*(30)
a^2+b^2 = 81 - 60 = 21
Answer : B
Answer: (B) 21
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case.
(A) 627
(B) 528
(C) 626
(D) 657
(E) 673
Rationale: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
Answer:B
Answer: (B) 528
Question: The speed of a boat in upstream is 70 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph.
(B) 05 kmph.
(C) 18 kmph.
(D) 11 kmph.
(E) 12 kmph.
Rationale: Speed of the boat in still water = (70+80)/2 = 75 kmph. Speed of the stream = (80-70)/2
= 5 kmph.
Answer:B
Answer: (B) 05 kmph.
Question: To create paint with a certain shade of gray, one must combine 2.016 liters of black paint with every one liter of white paint. Approximately how many liters of white paint must be combined with 350 liters of black paint to create the certain shade of gray?
(A) 173.6
(B) 176.4
(C) 347.1
(D) 694.4
(E) 705.6
Rationale: Since the ratio of Black to White is 2.016 to 1 this implies that Amount of Black is going to be more than (approximately double) the amount of White. This implies Option C, D and E can not be correct.
Now between A and B:
Black:White = 2.016:1 Since the ratio is more than double, the amount of White Paint should be less than half of Black Paint. B is more than half so can not be the answer, A fits the criteria hence should be the correct answer
ANSWER:A
Answer: (A) 173.6
Question: The equation of line s is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line s?
(A) 48
(B) 50
(C) 60
(D) 75
(E) 100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line s as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: (C) 60
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2017) = ?
(A) 2018
(B) 2088
(C) 270
(D) 1881
(E) 1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2017) = 2018
Ans: A
Answer: (A) 2018
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
(A) 25600.24
(B) 25600.29
(C) 25600.29
(D) 25600.29
(E) 25600.29
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer: A
Answer: (A) 25600.24
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/9 sec
(B) 80/7 sec
(C) 80/6 sec
(D) 89/7 sec
(E) 50/7 sec
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s
= (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer:B
Answer: (B) 80/7 sec
Question: What sum of money will produce Rs.70 as simple interest in 3 years at 3 1/2 percent?
(A) 263
(B) 500
(C) 367
(D) 368
(E) 666.7
Rationale: 70 = (P*3*7/2)/100
P = 666.7
Answer: E
Answer: (E) 666.7
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 34
(C) 35
(D) 46
(E) 50
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: (A) 20
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(A) 9000
(B) 9400
(C) 9600 is greatest number
(D) 9670
(E) 9800
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600. Answer: Option C
Answer: (C) 9600 is greatest number
Question: How many 4-digit positive integers are there in which all 4 digits are even?
(A) 625
(B) 600
(C) 500
(D) 400
(E) 256
Rationale: Positive integers - 2,4,6,8,0
Let the integers of a four digit positive number be ABCD
A can take four values (2,4,6,8)
B can take five values (0,2,4,6,8)
C can take five values (0,2,4,6,8)
D can take five values (0,2,4,6,8)
The total is 5*5*5*4
The answer according to me is 500
ANSWER:C
Answer: (C) 500
Question: The sum of two consecutive integers is 41. Find the numbers.
(A) 17, 18
(B) 7, 8
(C) 5, 6
(D) 20,21
(E) 8, 9
Rationale: n + (n + 1) = 41
2n + 1 = 41
2n = 40
n = 20
Answer: D
Answer: (D) 20,21
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 30 paise per sq. metre
(A) s255
(B) s780
(C) s880
(D) s480
(E) s980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*30
= 25500p
in Rs =25500/100=Rs255
ANSWER:A
Answer: (A) s255
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 45 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
(A) 22%
(B) 24%
(C) 25%
(D) 29%
(E) 28%
Rationale: Total sales =800
Comission = (20/100)*500+ (45/100)*300
=100 + 135
=235
%Comission =(235/800)*100=29.4~ 29%
Answer is D
Answer: (D) 29%
Question: A meeting has to be conducted with 5 employees.Find the number of ways in which the employees may be selected from among 8 employees,if 2 employees will not attend the meeting together.
(A) 1.35
(B) 2.91
(C) 3.12
(D) 4.126
(E) 5.36
Rationale: 8 employees, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two employees in it. That would mean selecting 5, from the remaining 6 which is 6C5 = 6
2. Meeting with one of the two employees. select 1 employees from two, and then select 4 from the remaining 6, which is 2C1 X 6C4 = 15.
So, answer is 30 + 6 = 36.
Answer : E
Answer: (E) 5.36
Question: 2.3.4.15.12
3.4.5.28.20
4.5.6.45.30
5.6.7.a .42
6.7.8.91.56
Value of a ?
(A) 65
(B) 66
(C) 67
(D) 68
(E) 69
Rationale: 2.3.4.15.12
3.4.5.28.20
4.5.6.45.30
5.6.7.a .42
6.7.8.91.56 so check each colounm u will find the increasing diff...in 'a' coloumn the diff is of 4..means 15...then 28 diff is of 13..then next term can b find out by adding 4 in 13..means add 17 to 28 u get 45 then same way keep on...
ANSWER:B
Answer: (B) 66
Question: Vijay bought 160 shirts at the rate of Rs. 235 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) Rs. 297
(B) Rs. 270
(C) Rs. 277.5
(D) Rs. 285
(E) None of these
Rationale: Total CP per shirt = 235 + 1400/160 + 1.75 + 320/160 = Rs. 247.5
SP = CP[(100 + profit%)/100]
= 247.5 * [(100 + 20)/100] = Rs. 297.
ANSWER:A
Answer: (A) Rs. 297
Question: When is |x-3| = 3-x?
(A) x<=3
(B) x=3
(C) x>3
(D) x=0
(E) x< 0
Rationale: When is |x-3| = 3-x?
Choice A: X=3, it is true but X cannot be always 3
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>3, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=3, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is A.
Answer: (A) x<=3
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is :
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Sol.
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60 ⇔ 47x/60 = 47/60 ⇔ x = 1.
∴ total distance = (3*1) km = 3km.
Answer C
Answer: (C) 3
Question: What least value should be replaced by * in 2631*4 so the number become divisible by 3
(A) 3
(B) 4
(C) 5
(D) 2
(E) 7
Rationale: Explanation:
Trick: Number is divisible by 3, if sum of all digits is divisible by 3, so (2+6+3+1+*+4) = 16+* should be divisible by 9,
16+2 will be divisible by 2,
so that least number is 2.
Answer: Option D
Answer: (D) 2
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 11,000, how many purple chips were selected?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 11,000 = 1*5^3*8*11
The factor of 8 must come from the purple point value, so there is 1 purple chip.
The answer is A.
Answer: (A) 1
Question: Which of the following CANNOT be the median T of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
(A) (w+x)/2 - 1
(B) (w+z)/2
(C) (x+y)/2
(D) (y+z)/2 -1
(E) (w+x+y+z)/4
Rationale: Using the properties of consecutive positive integers we could right away eliminate B,C and E.
(B) - The average of first and last terms is the median
(C) - For even number of integers, the median is the average of middle terms
(E) - The average is equal to median if the integers are consecutive
Remaining answer choices are A and D.
For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median T.
Answer (A)
Answer: (A) (w+x)/2 - 1
Question: 39! is divided by 41 then what is the remainder?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: (A) 1
Question: Rajeshâ€™s school bus is facing North when reaches his school. After starting from Rajeshâ€™s house, it turning twice and then left before reaching the school. What direction the bus facing when it left the bus stop in front of Rajeshâ€™s house?
(A) East
(B) North
(C) South
(D) West
(E) East-West
Rationale: West
ANSWER D
Answer: (D) West
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 277
(C) 2789
(D) 2669
(E) 2123
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400.Answer: A
Answer: (A) 2400
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 80/9
(B) 80/7
(C) 80/2
(D) 80/1
(E) 80/3
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
Answer: (B) 80/7
Question: In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate?
(A) Cannot be determined
(B) 43
(C) 3
(D) 6
(E) 10
Rationale: Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position.
Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points.
Answer: (A) Cannot be determined
Question: A trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?
(A) 118
(B) 88
(C) 90
(D) 42
(E) 22
Rationale: SP of 1m of cloth = 8925/85 = Rs. 125
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 125 - Rs. 7 = Rs. 118
Answer:A
Answer: (A) 118
Question: Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 20% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
(A) 17% less than N
(B) 25% less than N
(C) equal to N
(D) 20% greater than N
(E) 25% greater than
Rationale: Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 20% it becomes price2=P/N*1.20
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.20) i.e. N/1.20 i.e. .83*
Answer: (A) 17% less than N
Question: f, b, and c are positive integers. If f, b, and c are assembled into the six-digit number fbcfbc, which one of the following must be a factor of fbcfbc?
(A)  16
(B)  13
(C)  5
(D)  3
(E)  none of the above
Rationale: Plug in some values and check -
fbcfbc = 123123
Not divisible by 16 and 5
let fbcfbc = 125125
Not divisible by 3
Only option (B) and (E) is left in both the cases...
Check once more to marke (B) as correct answer
let fbcfbc = 135135
Again divisible by 13
So, mark answer as (B) 13
Answer: (B)  13
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.70 per glass on the first day, what was the price per glass on the second day?
(A) $0.15
(B) $0.20
(C) $0.30
(D) $0.40
(E) $0.46
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.7=3*x --> x=$0.46.
Answer: E.
Answer: (E) $0.46
Question: If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability E that N is divisible by 3?
(A) 1/3
(B) ¼
(C) 9/25
(D) 5/16
(E) 0
Rationale: Prime digits are: 2, 3, 5, 7
Total number of 2 digit #s with both digits prime are: 4*4 = 16
out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.
=> prob = 5/16.
Ans D. Took me 3:20 mins.
Answer: (D) 5/16
Question: In a certain school, the ratio of boys to girls is 5 to 17. If there are 72 more girls than boys, how many boys are there?
(A) 27
(B) 36
(C) 45
(D) 72
(E) 108
Rationale: The ratio of b to G is 5:13 and the other data point is G are more than boys by 72...
Looking at the ratio we can say that the 12(17-5) extra parts caused this diff of 72. so 1 part corresponds to 72/8=9 and so
5 parts correspond to 12*9 = 108.
E
Answer: (E) 108
Question: A certain collage has total of 450 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
(A) 130
(B) 80
(C) 75
(D) 60
(E) 50
Rationale: Answer is A.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 450 seniors.
So e + f = 150. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 130.
A
Answer: (A) 130
Question: Calculate the average mark scored by Adam if he had the following scores in an examination: 85, 67, 52, 69, 56, 62, and 59 marks (out in 100) in Spanish Language, Mathematics, Biology, Physics, French Language,Fine art and Chemistry respectively?
(A) 64.3
(B) 62.1
(C) 65.2
(D) 57.4
(E) 67.1
Rationale: Explanation:
Average mark = 85+67+52+69+56+62+59/7=64.3
Answer: Option A
Answer: (A) 64.3
Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
(A) 99
(B) 98
(C) 97
(D) 96 answer
(E) 95
Rationale: The square roots of all numbers from answer choices are between 9 and 10, so the product of primes of the number we are looking should be less then 9, so this number should have only 2-s, only 3-s, only 5-s, or only 2-s and 3-s as its primes. Only 96 satisfies this.
Answer: D.
Answer: (D) 96 answer
Question: Find the surface area of a10cm x 4cm x 3cm brick
(A) 84
(B) 124
(C) 164
(D) 180
(E) 120
Rationale: Explanation:
surface area = [2(10 x 4 + 4 x 3 + 10 x 3)]cm2 = 164 cm2
Answer: C
Answer: (C) 164
Question: Which of the following is closest to the difference between sum E of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
(A) 2.82
(B) 2.72
(C) 1.82
(D) 1.72
(E) 0.82
Rationale: Sum E of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Answer: (D) 1.72
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 123. What is that number?
(A) 12
(B) 29
(C) 27
(D) 18
(E) 99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 123
6x + 15 = 123
6x = 108
x = 18
ANSWER:D
Answer: (D) 18
Question: The timing of a college is from 12 p.m to 4.10 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
(A) 52 minutes
(B) 45 minutes
(C) 46 minutes
(D) 48 minutes
(E) 44 minutes
Rationale: Explanation:
Total time a student spends in college = 4 hours 10 minutes = 250 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (250 â€“ 20)/5
= 46 minutes
ANSWER C
Answer: (C) 46 minutes
Question: If 15 toys cost Rs. 545, what do 37 toys cost ?
(A) Rs. 1344
(B) Rs. 1349
(C) Rs. 1346
(D) Rs. 1341
(E) Rs. 1343
Rationale: Explanation:
Let the required cost be Rs. x.
More toys, More cost (Direct proportion)
Therefore 15 : 37 :: 545 : x
(15 * x) = (37 * 545)
x = (37*545)/15
= 1344.33
Hence, the cost of 37 toys is Rs. 1344.33
ANSWER: A
Answer: (A) Rs. 1344
Question: If it takes 10 kids 6 hours to wear out their teacher, how long would it take 15 kids?
(A) 5 hours
(B) 4 hours
(C) 3 hours
(D) 2 hours
(E) 1 hour
Rationale: 10 * 6 = 15 * x
x = 4
Answer: B
Answer: (B) 4 hours
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.59 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
(A) $1.63
(B) $1.40
(C) $1.68
(D) $1.72
(E) $1.76
Rationale: Average price = (550*1.59)+(270*1.38)/550+270=1.40 (Approx)
Answer B
Answer: (B) $1.40