mathewhe/aqua_rat huggingface dataset:
Question: If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
(A) 700
(B) 720
(C) 740
(D) 760
(E) 780
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 120⋅x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
120x=85(x+2)+40
35x=210
x=6
So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720 hectares.
So answer is B.
Answer: (B) 720
Question: For a certain exam,a score of 60 was 2 standard deviations below mean and a score of 100 was 3 standard deviations above mean.What was the mean score for the exam?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82
Rationale: Mean-2SD=60
Mean+3SD=100
by solving above we get,
SD (absolute value)=8
Mean=76
Ans. B
Answer: (B) 76
Question: Three consecutive even numbers are such that thrice the first number exceeds double the third number by five. What is the third number?
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21
Rationale: Let the three numbers be x, x+2, and x+4.
3x = 2(x+4) + 5
x = 13 and then the third number is x+4 = 17.
The answer is C.
Answer: (C) 17
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(8)?
(A) 30/17
(B) 32/19
(C) 34/21
(D) 36/23
(E) 38/25
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
A(7) = 21/13
A(8) = 34/21
The answer is C.
Answer: (C) 34/21
Question: Present ages of Kiran and Syam are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Syam's present age in years?
(A) 20
(B) 24
(C) 25
(D) 28
(E) 30
Rationale: Ratio = 5:4
age of kiran = 5x
age of syam = 4x
after 3 yrs = 11:9
(5x+3):(4x:3) = 11:9
x=33-27 = 6
syam age= 4x=4*6=24
ANSWER B
Answer: (B) 24
Question: How many positive integers will divide evenly into 190?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 16
Rationale: The question is asking how many factors 190 has.
190 = 2*5*19
The number of factors is 2^3 = 8
The answer is C.
Answer: (C) 8
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
(A) 21:32
(B) 32:21
(C) 12:17
(D) 17:12
(E) None of these
Rationale: Explanation :
Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000*6 + 15000*6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000*4 : 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)
= (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3) : (30*2 : 50*2)
= 105:160
= 21:32. Answer : Option A
Answer: (A) 21:32
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 84. Find the third number?
(A) A)37
(B) B)85
(C) C)48
(D) D)43
(E) E)84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 84
6x = 84 => third number is 84.
Answer: Option E
Answer: (E) E)84
Question: After decreasing 40% in the price of an article costs Rs.1050. Find the actual cost of an article?
(A) 1200
(B) 1750
(C) 1050
(D) 1570
(E) 1005
Rationale: CP* (60/100) =1050
CP= 17.5 * 100 => CP
= 1750
Answer:B
Answer: (B) 1750
Question: If n is a natural number, then (6n2 + 6n) is always divisible by?
(A) 6 and 12 both
(B) 6 only
(C) 12 only
(D) 6 or 12
(E) None
Rationale: (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
A)
Answer: (A) 6 and 12 both
Question: A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
(A) 10
(B) 88
(C) 66
(D) 28
(E) 12
Rationale: A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: A
Answer: (A) 10
Question: By selling 20 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 80
(B) 60
(C) 50
(D) 30
(E) 10
Rationale: 80% --- 20
120% --- ?
80/120 * 20 = 30
Answer:D
Answer: (D) 30
Question: P is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2P is divided by 4 ?
(A) 3
(B) 2
(C) 1
(D) 0
(E) -1
Rationale: Let P = 4q + 3. Then 2P = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2P is divided by 4, the remainder is 2.
ANSWER:B
Answer: (B) 2
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 11 km/hr
(B) 50 km/hr
(C) 76 km/hr
(D) 88 km/hr
(E) 17 km/hr
Rationale: :
Speed of the train relative to man = (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: (B) 50 km/hr
Question: Of 30 applicants for a job, 13 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 14
(B) 13
(C) 9
(D) 6
(E) 5
Rationale: D. 6
30 - 3 = 27
27 - 13 - 18 = -6
Then 6 are in the intersection between 4 years experience and degree.
Answer D
Answer: (D) 6
Question: The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 21-inch flat-screen television than a square 19 -inch flat-screen television?
(A) 42
(B) 40
(C) 38
(D) 36
(E) 48
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 21-inch flat-screen television
The diagonal (hypotenuse) = 21
So, we can apply the Pythagorean Theorem to get x² + x² = 21²
Simplify: 2x² = 21²
Divide both sides by 2 to get: x² = 21²/2
Since the area of the square = x², we can see that the area of this square is 21²/2
square 19-inch flat-screen television
The diagonal (hypotenuse) = 19
So, we can apply the Pythagorean Theorem to get x² + x² = 19²
Simplify: 2x² = 19²
Divide both sides by 2 to get: x² = 19²/2
Since the area of the square = x², we can see that the area of this square is 19²/2
DIFFERENCE IN AREAS =21²/2-19²/2
= (21+19)(21-19)/2 =40
B
Answer: (B) 40
Question: If a 5 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?
(A) 100%
(B) 200%
(C) 300%
(D) 400%
(E) 500%
Rationale: The area A of the large cube is 5*5*6 = 150 square cm.
The area of the 125 small cubes is 125*6 = 750 = 5A, an increase of 400%.
The answer is D.
Answer: (D) 400%
Question: A train travels at an average of 40 miles per hour for 4 hours and then travels at a speed of 60miles per hour for 2hours. How far did the train travel in the entire 6 hours?
(A) 100miles
(B) 150miles
(C) 200miles
(D) 250miles
(E) 300miles
Rationale: Total distance traveled = (40*4)+(70*2) = 160+140 = 300 miles
Answer is E
Answer: (E) 300miles
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 20
(B) 40
(C) 80
(D) 100
(E) 200
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10
x - y = 20 .... (i)
and x + 20 = 2(y - 20)
x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
answer :D
Answer: (D) 100
Question: In an exam 80% of the boys and 40% of the girls passed. The number of girls who passed is 120, which is 2/3rd of the number of boys who failed. What is the total number of students who appeared for the exam?
(A) 1200
(B) 380
(C) 3800
(D) 2180
(E) 3180
Rationale: Let the Number of boys = x , Number of girls =y
40y/100 =120
y = 300
120= 2/3* 20x/100 = 2x/15
x = 900
Total = x+y = 300+900 =1200
ANSWER:A
Answer: (A) 1200
Question: In an examination, 35% candidates failed in one subject and 42% failed in another subject while 14% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
(A) 975
(B) 1020
(C) 1175
(D) 1225
(E) 1525
Rationale: Failed in 1st subject = 35*2500/100 = 875
Failed in 2nd subject = 42*2500/100 = 1050
Failed in both = 14*2500/100 = 350
Failed in 1st subject only = 875-350 = 525
Failed in 2nd subject only = 1050-350 = 700
Passed in either subject but not in both = 700+525 = 1225
Answer is D
Answer: (D) 1225
Question: A man incurs a loss of 5% be selling a watch for Rs. 1140. what price should the watch be sold to earn 5% profit.
(A) 1200
(B) 1260
(C) 1350
(D) 1250
(E) 1355
Rationale: (100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
= 95/1140 =105/x
= 1260
ANSWER B
Answer: (B) 1260
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?
(A) 7
(B) 5
(C) 8
(D) 4
(E) 2
Rationale: 28 * 2 = 56
21 * 3 = 63
-----------
7 years.Answer: A
Answer: (A) 7
Question: By using the numbers 1, 2, 3, 7 and 9 only once, how many five digit numbers can be made that are divisible by 25?
(A) 5
(B) 4
(C) Not possible
(D) 3
(E) 6
Rationale: A number to be divisible by 25 must end with 00, 25, 50, or 75.
So, not possible.
Answer: C.
Answer: (C) Not possible
Question: If 2log(4*5^2) = x, find x
(A) 5
(B) 6
(C) 7
(D) 4
(E) 8
Rationale: 2(log2^2*5^2)=x
2log(5*2)^2=x
2*2log(5*2)=x
4log10=x
log10 base 10=1
so
4*1=x
x=4
ANSWER:D
Answer: (D) 4
Question: A man swims downstream 72 km and upstream 45 km taking 5 hours each time; what is the speed of the current?
(A) 1.7
(B) 2.8
(C) 3.6
(D) 2.7
(E) 1.1
Rationale: 72 --- 5 DS = 14.4
? ---- 1
45 ---- 5 US = 9
? ---- 1 S = ?
S = (14.4 - 9)/2 = 2.7
Answer:D
Answer: (D) 2.7
Question: A and B together have $ 1210. If of A's amount is equal to of B's amount,What is the ratio between A and B?
(A) 2:3
(B) 3:2
(C) 4:5
(D) 5:3
(E) cannot be determined
Rationale: (4/15)a=(2/5)b
a=((2/15)*(15/4))b
a=(3/2)b
a/b=3/2
a:b=3:2
Option B
Answer: (B) 3:2
Question: A train travelling at a speed of 75 mph enters a tunnel 3 miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
(A) 2.5 min
(B) 3 min
(C) 3.2 min
(D) 3.5 min
(E) 3.8 min
Rationale: Total distance travel by train is 4 miles
and speed of the train is 75 miles per hour
so time is distance by speed = (4/75) hours
den we should change to minits then (4/75)*60 = 3.2
ANSWER:C
Answer: (C) 3.2 min
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
(A) 54
(B) 66
(C) 80
(D) 36
(E) 96
Rationale: A
54
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 54 miles
Answer: (A) 54
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter =5300	/26.50 m = 200 m.
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m.
answer : C
Answer: (C) 60
Question: Seats for Maths, Physics and Biology are in the ratio of 5 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
(A) 2 : 3 : 4
(B) 6 : 7 : 8
(C) 6 : 8 : 9
(D) Cannot be determined
(E) None of these
Rationale: Reqd ratio 5 × 140⁄100 : 7 × 150⁄100 : 8 × 175⁄100
= 5 × 140 : 7 × 150 : 8 × 175 = 2 : 3 : 4
Answer A
Answer: (A) 2 : 3 : 4
Question: Laxmi goes 6 km towards South-East from her office.Then she goes 15 km turning to West. After this she goes 6 km towards North-West and in the end she goes 11 km towards East. How far is she from her office ?
(A) 10 km
(B) 11 km
(C) 4 km
(D) 6 km
(E) 8 km
Rationale: Explanation:
From the above fig we can observe that distance between Laxmi and her office is 15-11 = 4 kms.
ANSWER IS C
Answer: (C) 4 km
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 24 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 288
(B) 540
(C) 877
(D) 278
(E) 178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 24 + 21 = 45
T = 12
D = 45 * 12 = 540
Answer: B
Answer: (B) 540
Question: A can do a piece of work in 3 hours; B and C together can do it in 2 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
(A) 6hours
(B) 3hours
(C) 2hours
(D) 5hours
(E) 4hours
Rationale: A's 1 hour work = 1/3;
(B + C)'s 1 hour work = 1/2;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/3 + 1/2) = 5/6
B's 1 hour work = (5/6 - 1/2) = 1/3
B alone will take 3 hours to do the work.
Answer:B
Answer: (B) 3hours
Question: The average age of 15 students of a class is 16 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?
(A) 22years
(B) 24years
(C) 26years
(D) 28years
(E) 30years
Rationale: Age of the 15th student
=[15 * 16 - (14 * 5 + 16 * 9)]
= (240 - 214) = 26 years.
Answer:C
Answer: (C) 26years
Question: Tomy's age 14 years hence will be thrice his age four years ago. Find Tomy's present age?
(A) 12 years
(B) 13 years
(C) 15 years
(D) 17 years
(E) 18 years
Rationale: Let MTomy's present age be 'x' years.
x+ 14 = 3(x- 4)
=> 2x = 26 => x = 13 years.
B
Answer: (B) 13 years
Question: A test has 100 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.
Let C be the number of correct answers and let I be the number of incorrect answers.
To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.
For every correct question above 40, the test taker has 4 incorrect answers.
Then, the I = 4*(C - 40).
Also, I + C <= 100. Thus 5C <= 260 and so C <= 52.
Then 40 <= C <= 52 and C can have 13 possible values.
The answer is E.
Answer: (E) 13
Question: If a,b,c,d,e are five consecutive odd integers,then what is their average?
(A) a+4
(B) abcde/5
(C) 5(a+b+c+d+e)
(D) a+8
(E) a+6
Rationale: b=a+2,c=a+4,d=a+6 and e=a+8
Required average = (a+a+2+a+4+a+6+a+8)/5=a+4
Answer is A
Answer: (A) a+4
Question: A worker earns $24 on the first day and spends $18 on the second day. The worker earns $24 on the third day and spends $18 on the fourth day. If this pattern continues, on which day will the worker first reach a net total of $72?
(A) 9
(B) 12
(C) 17
(D) 21
(E) 24
Rationale: Every two days, the net total is $6.
After 16 days, the worker will have $48.
On day 17, the worker will receive $24 for a net total of $72.
The answer is C.
Answer: (C) 17
Question: 34.	The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 6 feet, and the diagonal of the rectangular plate was 10 ft. What is height of the of the cylinder?
(A) 7
(B) 10
(C) 8
(D) 12
(E) 15
Rationale: Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 8. Correct answer C.
Answer: (C) 8
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) Rs.21.60
(B) Rs.21.69
(C) Rs.21.87
(D) Rs.21.68
(E) Rs.21.19
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 =Rs.21.60
Answer:A
Answer: (A) Rs.21.60
Question: The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
(A) 14 years
(B) 17 years
(C) 18 years
(D) 12 years
(E) 11 years
Rationale: 9 * 2
= 181
Answer:C
Answer: (C) 18 years
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 180. The amount of the bill is
(A) 1200
(B) 1764
(C) 1680
(D) 1354
(E) None of these
Rationale: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 180.
x Ã— 16 Ã— (9/12) Ã— (1/100) = 180 or x = 1500.
P.W. = Rs. 1500.
Sum due = P.W. + T.D. = Rs.(1500
180) = Rs. 1680.
Answer: C
Answer: (C) 1680
Question: On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $20,000, in how many years, the total value of the investment plus interest will increase to $30,000?
(A) 15
(B) 16
(C) 18
(D) 20
(E) 24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 5,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 5,000.00 took to double 10,000.00.
Again, 10,000.00 took to double 20,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 20,000.00 takes the same (72/x) no of years to double 30,000.00.
72/x = 6 years.
So altogather:
5,000 - 10,000 = 6 years
10,000 - 20,000 = 6 years
20,000 - 30,000 = 3 years
Answer A 15 years.
Answer: (A) 15
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 9/10, what is the probability that Taylor makes exactly one basket in three tries?
(A) 3^5/10^3
(B) 3^4/10^3
(C) 3^3/10^3
(D) 3^2/10^3
(E) 3^4/10^4
Rationale: Probability of basket = 1/10
Probability of no basket = 9/10
Required probability= 3* (1*9*9/1000)
= 3^5/10^3
A is the answer
Answer: (A) 3^5/10^3
Question: there is a equilateral triangle whose area is A.another triangle is formed by joining the mid points.this process is continued.find the sum of these areas.
(A) A/3
(B) 2A/3
(C) A
(D) 4A/3
(E) 5A/3
Rationale: Area of equilateral triangle =(root(3)/4)*a^2=A(given)
side of triangle=a
now side is a/2
then total area A+A/4 +A/16-------
A/1-(1/4)=A*4/3 is total area
ANSWER:D
Answer: (D) 4A/3
Question: If 2x + y = 7 and x + 2y = 5, then (2x + 2y)/3 =
(A)  3
(B)  4/3
(C)  17/5
(D)  18/5
(E)  4
Rationale: 2*(x+2y = 5) equals 2x+4y=10
2x+4y=10
- 2x + y= 7
= 3y=3
Therefore Y = 1
Plug and solve...
2x + 1 = 7
2x=6
x=3
(2*3+2*1)/3= (6+3)/3
=9/3
=3
A
Answer: (A)  3
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
(A) 5
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Solution
Let the number be x.	Then, 3(2x+9) = 75
‹=› 2x+9 = 25
‹=›2x = 16
Answer B
Answer: (B) 8
Question: The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is the amountby which he might have fallen short.
(A) 30
(B) 40
(C) 50
(D) 60
(E) 80
Rationale: Let the price of gift pack be 'aa'
Then number of packs bought =a+1=a+1
Hence total cost is a(a+1)a(a+1)
It is given that 380<a(a+1)380<a(a+1)
If a=19a=19, the total cost =19×20=380=19×20=380
Dexter would not have fallen short, If:
a=20a=20, a(a+1)=420a(a+1)=420
So he would have fallen short by Rs 40.
This is the minimum amount by which he may have fallen short.
B)
Answer: (B) 40
Question: The ratio of the volumes of two cubes is 512 : 729. What is the ratio of their total surface areas?
(A) 1:22
(B) 81:12
(C) 41:46
(D) 41:19
(E) 84:12
Rationale: Ratio of the sides = ³√512 : ³√729
= 8 : 9
Ratio of surface areas = 82:92
= 41:46
Answer: C
Answer: (C) 41:46
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability P that the game will end after the fourth throw?
(A) 1/16
(B) 3/32
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty P is 1/16 + 1/16 = 1/8.C
Answer: (C) 1/8
Question: The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)
(A) 12, 14, 18
(B) 14, 20, 36
(C) 16, 12, 14
(D) 16, 28, 36
(E) None
Rationale: Sol.
Let thier present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 ⇔ 20x = 80 ⇔ x = 4.
∴ Their present ages are 16 years, 28 years and 36 years respectively.
Answer D
Answer: (D) 16, 28, 36
Question: Set X consists of 10 integers and has median of 10 and a range of 10. What is the value of the greatest possible integer that can be present in the set?
(A) 32
(B) 37
(C) C.40
(D) 20
(E) 50
Rationale: Note that both median and range do not restrict too many numbers in the set. Range is only concerned with the smallest and greatest. Median only cares about the middle.
Quick check of each option starting from the largest:
(E) 50
Range of 20 means the smallest integer will be 30. So 20 cannot lie in between and hence cannot be the median.
(D) 43
Range of 20 means the smallest integer will be 23. So 20 cannot lie in between and hence cannot be the median.
(C) 40
Range of 20 means the smallest integer will be 20. 20 can lie in between such as:
20, 20, 20, 20, 20, 20, 20, 20, 20, 20
This is possible. Hence it is the greatest such number.
Answer (D)
Answer: (D) 20