mathewhe/aqua_rat huggingface dataset:
Question: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars?
(A) m/(m + n)
(B) n/(m + n)
(C) mn/(m + n)
(D) mn/(m – n)
(E) mn/(n – m)
Rationale: “Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 1500 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 1500 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 1500 jars? ”
Since the number “1500 jars” appears over and over, let’s arbitrarily say 1500 jars = 1 lot, and we’ll use units of lots per hour to simplify our calculations.
P’s individual rate is (1 lot)/(m hours) = 1/m. The combined rate of P & Q is (1 lot)/(n hours) = 1/n. We know
(P’s rate alone) + (Q’s rate alone) = (P and Q’s combined rate)
(Q’s rate alone) = (P and Q’s combined rate) – (P’s rate alone)
(Q’s rate alone) = 1/n – 1/m = m/ (nm) – n/ (nm) = (m – n)/(nm)
We now know Q’s rate, and we want the amount of 1 lot, so we use the “art” equation.
1 = [(m – n)/ (nm)]*T
T = (mn)/(m – n)
Answer = D
Answer: (D) mn/(m – n)
Question: If 2x/|y| = -16 which of the following must be true?
(A) x = -y
(B) x = y
(C) x^2 =64 * y^2
(D) x^2 = y^2
(E) x^3 = y^3
Rationale: 2x/|y| = -16
2x= -16 |y|
Squaring both sides
4*x^2= (-16 |y|) ^2=256* y^2
x^2 = 64 * y^2
C is the answer
Answer: (C) x^2 =64 * y^2
Question: The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m.What is the area of the field?
(A) 32999
(B) 37500
(C) 37199
(D) 37512
(E) 37511
Rationale: Let length = x meters, then breadth = 0.6x
Given that perimeter = 800 meters
=> 2[ x + 0.6x] = 800
=> x = 250 m
Length = 250m and breadth = 0.6 * 250 = 150m
Area = 250 * 150 = 37500
Answer: B
Answer: (B) 37500
Question: Find the fourth proportion to 6,12,18
(A) 24
(B) 12
(C) 36
(D) 8
(E) 15
Rationale: Explanation:
6:12 :: 18:x
=> 6/12= 18/x
=> x = 18*12/6
=> x = 24
Answer:C
Answer: (C) 36
Question: A car takes 6 hours to cover a distance of 360 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 65
Rationale: Time = 6
Distance = 360
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 360/9 = 40 Kmph
Answer C.
Answer: (C) 40
Question: Two trains start simultaneously from opposite ends of a 160-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 160-km trip in 5 hours. Train Y, travelling at a constant rate, completes the 160-km trip in 3 hours. How many kilometers had Train X traveled when it met Train Y?
(A) 56
(B) 58
(C) 60
(D) 62
(E) 64
Rationale: If the two trains cover a total distance D, then Train X travels (3/8)*D while Train Y travels (5/8)*D. If the trains travel 160 km to the meeting point, then Train X travels (3/8)*160 = 60 km. The answer is C.
Answer: (C) 60
Question: Set S consists of integers {1,2,3,4}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 6?
(A) 1/3
(B) 1/6
(C) 2/3
(D) 2/5
(E) 3/7
Rationale: Number of ways you can choose 2 from 4 = 4C2 = 6
E = event of getting the 2 numbers is more than 6 = (3,4) = 1
probability = 1/6
Answer is B
Answer: (B) 1/6
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
(A) 2277
(B) 2987
(C) 2799
(D) 1277
(E) 9680
Rationale: A= P{1 + R/100}n
=> 8000{1 + 10/100}2 = Rs.9680
Answer: E
Answer: (E) 9680
Question: One hour after Yolanda started walking from X to Y, a distance of 65 miles, Bob started walking along the same road from Y to X. If Yolandaâs walking rate was 5 miles per hour and Bobâs was 7 miles per hour, how many miles had Bob walked when they met?
(A) 31
(B) 32
(C) 33
(D) 34
(E) 35
Rationale: Let t be the number of hours that Bob had walked when he met Yolanda. Then, when they met, Bob had walked 4t miles and Yolanda had walked 5(t + 1) miles. These distances must sum to 65 miles, so 7t + 5(t + 1) = 65, which may be solved for t as follows
7t + 5(t + 1) = 65
7t + 5t + 5 = 65
12t = 60
T = 5 (hours)
Therefore, Bob had walked 7t = 7(5) = 35 miles when they met. The best answer is E.
Answer: (E) 35
Question: The greatest possible length which can be used to measure exactly the length 3m ,6m 85cm, 8m 95 cm is?
(A) 25cm
(B) 101cm
(C) 5cm
(D) 42cm
(E) 35cm
Rationale: Required length = H.C.F of 300cm, 685cm, 895cm = 5cm
Answer is C
Answer: (C) 5cm
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 3 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 179:2
(B) 178:3
(C) 179:1
(D) 179:54
(E) 179:45
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 3 = 15/8 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 15/8 + 7/2 = 43/8 = 5.375 litres
As 7 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 5.375 : 1.625 = 179 : 54.
Answer:D
Answer: (D) 179:54
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
(A) 46
(B) 99
(C) 8826
(D) 266
(E) 232
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.Answer: A
Answer: (A) 46
Question: If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?
(A) 120
(B) 882
(C) 662
(D) 4112
(E) 2322
Rationale: The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2
Answer: A
Answer: (A) 120
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many W ways can the assembly line be arranged?
(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Rationale: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want W=6C!/2 -> 720/2 = 360
Answer: (C) 360
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) 36
(B) 50
(C) 88
(D) 66
(E) 22
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
Question: A sum of money doubles itself at a compound interest in 15 years . In how may years it will become 8 times ??
(A) 30 years
(B) 40 years
(C) 45 years
(D) 50 years
(E) 60 years
Rationale: If the sum doubles (x2) in 15 years, then it to become 2*2*2 = 8 times as large it should double three times, so three 15 years time period are needed, which is 3*15 = 45 years.
Answer: C
Answer: (C) 45 years
Question: In a school there are 20 balls for every 200 players. If the school has 600 players, how many balls are required?
(A) 34
(B) 45
(C) 60
(D) 36
(E) 14
Rationale: 20/200=x/600
x=60
Answer is C
Answer: (C) 60
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150m
(B) 180m
(C) 159m
(D) 250m
(E) 152m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A
Answer: (A) 150m
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) Rs.4
(B) Rs.5
(C) Rs.1
(D) Rs.3
(E) Rs.9
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer:D
Answer: (D) Rs.3
Question: The compound ratio of 1:4, 3:2 and 4:5?
(A) 1:9
(B) 1:7
(C) 1:2
(D) 3:10
(E) 1:4
Rationale: 1/4 * 3/2 * 4/5
= 3/10
=3:10
Answer: D
Answer: (D) 3:10
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
(A) 288
(B) 279
(C) 277
(D) 200
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12
= 200 m
Answer: D
Answer: (D) 200
Question: if v,w,x,y,z are non negative integer, each less than 11,then how many distinct combinations(w,v,x,y,z) satisfy v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: v(11^4)+w(11^3)+x(11^2)+y(11)+z=151001
151001/11 gives remainder 4.
v(11^4)+w(11^3)+x(11^2)+y(11) = 151001 - z
to make it divisible by 11, z should be 4..
as value of z cannot be any other number, we can form only on 1 distinct combination..
ANSWER:B
Answer: (B) 1
Question: If 9 is a factor of 2x, then which of the following may not be an integer?
(A) 6x/54 + 2x/3
(B) (4x-18)/9
(C) (2x+27)/9
(D) (81-4x^2)/81
(E) (2x-3)/3
Rationale: The questions provides that 2x is divisible by 9, so x is either a multiple of 9 or x = 9/2 = 4.5
If x = 4.5 then 6x/54 = (6*4.5)/ (6*9) = 1/2. Not an integer.
The answer is A.
Answer: (A) 6x/54 + 2x/3
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 7 2 ½ kmph
(B) 2 8 ½ kmph
(C) 8 2 ½ kmph
(D) 2 2 ½ kmph
(E) 2 1 ½ kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: D
Answer: (D) 2 2 ½ kmph
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 9% microphotonics; 14% home electronics; 10% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
(A) 108°
(B) 10°
(C) 18°
(D) 36°
(E) 52°
Rationale: 9% microphotonics;
14% home electronics;
10% food additives;
29% genetically modified microorganisms;
8% industrial lubricants;
100-(9+14+10+29+8)=30% basic astrophysics.
30% of 360° is 108°.
Answer: A.
Answer: (A) 108°
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 35 percent alcohol?
(A)  7/2
(B)  300/13
(C)  20/3
(D)  8
(E)  39/4
Rationale: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 35% of (100+x)
OR
20+x=(100+x)7/20
400+20x=700+7x
13x=300
x=300/13
Ans:B
Answer: (B)  300/13
Question: 3,5,8,13,22,__
(A) 37
(B) 38
(C) 39
(D) 40
(E) 41
Rationale: 5=3*2-1
8=5*2-2
13=8*2-3
22=13*2-4
39=22*2-5
ANSWER:C
Answer: (C) 39
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 3/8
(B) 3/2
(C) 3/6
(D) 3/1
(E) 3/7
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: B
Answer: (B) 3/2
Question: The size of a television screen is given as the length of the screen's diagonal. If the screens were flat, then the area of a square 19-inch screen would be how many square inches greater than the area of a square 17-inch screen?
(A) 36
(B) 4
(C) 16
(D) 38
(E) 40
Rationale: Pythogoras will help here!
let the sides be x and diagonal be d
Then d ^2 = 2x^2
and
Area = x^2
Now plug in the given diagonal values to find x values
and then subtract the areas
Ans will be 19^2/2 - 17^2 /2 = 72 /2 = 36
Ans A.
Answer: (A) 36
Question: The banker's gain of a certain sum due 3 years hence at 10% per annum is Rs. 36. What is the present worth ?
(A) Rs. 400
(B) Rs. 300
(C) Rs. 500
(D) Rs. 350
(E) None of these
Rationale: Explanation :
T = 3 years
R = 10%
TD = (BG ×100)/TR = (36×100)/(3×10) = 12 × 10 = Rs. 120
TD = (PW × TR)/100
⇒ 120 = (PW ×3×10)/100
⇒ 1200 = PW × 3
PW = 1200/3 = Rs. 400 Answer : Option A
Answer: (A) Rs. 400
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/459
(B) 12/452
(C) 12/455
(D) 22/452
(E) 12/453
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2C1)(4C2)/15C3
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
Answer:C
Answer: (C) 12/455
Question: The cost price of a Rs. 100 stock at 4 discount, when brokerage is 1/5% is
(A) 96.0
(B) 96.5
(C) 96.2
(D) 96.8
(E) 96.6
Rationale: Cost Price = 100−4+1/5=96.2
Answer is C.
Answer: (C) 96.2
Question: If I, J and K are digits and 9IJK is a 4-digit number that is divisible by 5, which of the following is a possible product of I, J and K?
(A) 23
(B) 48
(C) 72
(D) 25
(E) 94
Rationale: Key to this question is to remember the fact that a number divisible by 5 must end with 5 OR 0 (i.e K).
If K had to be 0, product should also be 0 regardless of I and J.
The product is a multiple of 5. Only one answer choice meets the requirement.
Ans D.
Answer: (D) 25
Question: If 2/3 of A=75% of B=0.6 of C, then A:B:C is
(A) 2:3:3
(B) 3:4:5
(C) 4:5:6
(D) 9:8:10
(E) None
Rationale: Solution: According to the question,
Or, (2A/3) = (75B/100) = (C*6/10);
Above relation gives;
A*2/3 = B*3/4;
→	A/B = 9/8;
And,
B*3/4 = C*3/5;
→	B/C = 8:10;
Thus,
A:B:C = 9:8:10.
Answer: Option D
Answer: (D) 9:8:10
Question: The average number of shirts with Salman, Ambani and Dalmiya is 54, if all of them reached a shopping mall in Delhi and purchased 8 shirts each of them then average number of shirt each of them now has
(A) 66
(B) 63
(C) 62
(D) can't be determined
(E) None of these
Rationale: Answer
Required average
= Old average + New average
= 54 + 8 = 62
Correct Option: C
Answer: (C) 62
Question: The product of Diana's age, in years, and a third of Rashid's age, in years, is 32. If Diana is 4 years older than Rashid is, then how old is Rashid ?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 15
Rationale: Let D be Diana's age, in years, and Rashid's age be R
D*R/3 = 32
D = R+4
Now (R+4)R / 3 = 32 = > R^2+4R-96 => R = 8 or -12.
ANS option B.
Answer: (B) 8
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.75
(B) 4
(C) 2
(D) 8
(E) 7
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
ANSWER A
Answer: (A) 3.75
Question: Jack and Christina are standing 240 feet apart on a level surface. Their dog, Lindy, is standing next to Christina. At the same time, they all begin moving toward each other. Jack walks in a straight line toward Christina at a constant speed of 3 feet per second and Christina walks in a straight line toward Jack at a constant speed of 3 feet per second. Lindy runs at a constant speed of 10 feet per second from Christina to Jack, back to Christina, back to Jack, and so forth. What is the total distance, in feet, that Lindy has traveled when the three meet at one place?
(A) 340
(B) 360
(C) 380
(D) 400
(E) 420
Rationale: The relative speed of Jack and Christina is 3 + 3 = 6 feet per second.
The distance between them is 210 feet, hence they will meet in (time) = (distance)/(relative speed) = 240/6 = 40 seconds.
For all this time Lindy was running back and forth, so it covered (distance) = (speed)*(time) = 10*40 = 400 feet.
Answer: D.
Answer: (D) 400
Question: Find the area of a parallelogram with base 24 cm and height 16 cm?
(A) 198 cm2
(B) 384 cm2
(C) 279 cm2
(D) 128 cm2
(E) 297 cm2
Rationale: Area of a parallelogram
= base * height
= 24 * 16 = 384 cm2
Answer:B
Answer: (B) 384 cm2
Question: There are six cards in which it has two king cards. all cards are turned down and two cards are opened what is the possibility to get at least one king.
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 6/5
Rationale: POSSIBILITY TO GET AT LEAST ONE KING IS : 2C1*4C1/6C2 + 2C2/6C2 = 8/15+1/15=3/5
ANSWER:C
Answer: (C) 3/5
Question: In a camp,there is a meal for 120 men or 200 children.If 120 children have taken the meal,how many men will be catered to with the remaining meal ?
(A) 20
(B) 30
(C) 40
(D) 48
(E) 60
Rationale: Solution
There is a metal for 200 children. 120 children have taken the meal.
Remaining meal is to be catered to 80 children.
Now, 200 children = 120 men
80 children =( 120/200x80)men= 48 men. Answer D
Answer: (D) 48
Question: For an international Mathematics Olympiad, country D will send six delegates in total — two will be supervisors and four will be contestants. There are 210 ways in which the six delegates can be chosen and there are seven candidates competing for the four contestants’ places available. How many candidates are competing for the two supervisors’ slots available?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Option A wrong as 2 supervisor need to be selected.
Going by statement: 4 contestant chosen from 7 -- 7C4 == 35
and total ways =210
Consider 2 supervisor will be chosen from : X people.
So as per question: 35*X= 210
X= 6
So by using options,
Option A already decided wrong.
Option B 2C2 will be 1 not 6.
Option C 3C2 will be 3 not 6
Option D 4C2 will be 6 correct answer
Option E 5C2 will be 10 not 6.
ANS:D
Answer: (D) 4
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
(A) 87
(B) 16
(C) 18
(D) 13
(E) 19
Rationale: d2 = 122 + 42 + 32
= 13
Answer:D
Answer: (D) 13
Question: A train 100 m long pass a telegraph pole in 5 seconds. Find the speed of the train
(A) 66 km/hr
(B) 68.4 km/hr
(C) 72 km/hr
(D) 79.2 km/hr
(E) None
Rationale: Sol.
Speed = [100/5] m/sec = [20 * 18/5] km/hr = 72 km/hr.
Answer C
Answer: (C) 72 km/hr
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 8/3%
(B) 33 1/7%
(C) 33 1/3%
(D) 33 7/3%
(E) 33 1/8%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: A person's present age is two-fifth of the age of his mother. After
8 years, he will be one-half of the age of his mother. What is the present age of the mother?
(A) 40
(B) 60
(C) 70
(D) 30
(E) 35
Rationale: Let present age = x
age of mother = 5x/2
after 8 yrs the person will be one-half of the age of his mother
(x+8) = 1/2(5x/2 + 8)
x =16
present age of mother=
5x/2 = 5*16/2 = 40
ANSWER A
Answer: (A) 40
Question: Bill has a collection of new and used trading cards that he stores in two albums. His first album contains 200 cards, 60% of which are used. If 90% of the cards in his second album are used, and 65% of all of his cards are used, what is the total number of trading cards in Billâ€™s collection?
(A) 290
(B) 260
(C) 240
(D) 156
(E) 254
Rationale: (60/100)*200 + (90/100)*B = (65/100)*(200+B)
B = 40
Total cards = 200+B = 240
Answer: C
Answer: (C) 240
Question: A phone manufacturer has 4 different types of phones namely: x1, x2, x3, and x4. if x2 costs 12% less than x1 and x3 costs 15% lesser than x2, and x4 costs 5% less than x3. what percent of x1's cost is x4?
(A) 89.1%
(B) 77.8%
(C) 60.7%
(D) 80.4%
(E) 71.06%
Rationale: Let the cost of x1 be $100
x2 costs 12% less than x1=$100-$12--88(cost of x2)
x3 costs 15% lesser than x2--$88-13.2--74.8(cost of x3)
x4 costs 5% less than x3--74.8-3.74--71.06(cost of x4)
therefore --71.06*100/100
Answer is E
Answer: (E) 71.06%
Question: If two 2-digit positive integers have their respective tens digits exchanged, the difference between the pair of integers changes by 4. What is the greatest possible difference between the original pair of integers?
(A) 76
(B) 80
(C) 82
(D) 90
(E) 94
Rationale: For maximizing most of 2 digit integer questions, you will have numbers closes to 90s and 10s.
Start with 10 and 99 you see that the differences are 89 (=99-10) and 71 (=90-19) giving you a change of 89-71=18, a lot more than 4.
Next check with 15 and 99, you get 84 (=99-15) and 76 (=95-19), you get 84-76=8. Thus the difference has been decreasing.
Finally check with 99 and 17, you get 82 (=99-17) and 78 (=97-19), giving you 82-78 = 4 . This is the answer.
Thus, the maximum difference is 99-17=82. C is the correct answer.
Answer: (C) 82
Question: find cp when sp =Rs 40.60 : gain=16%
(A) Rs 55
(B) Rs 36
(C) Rs 47
(D) Rs 30
(E) Rs 35
Rationale: cp=Rs{(100/116)*40.60}=Rs 35
Answer is E.
Answer: (E) Rs 35
Question: An error 2% in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square?
(A) 3.07
(B) 2.3
(C) 3.2
(D) 4.04
(E) 5.92
Rationale: D
4.04
Percentage error in calculated area
=(2+2+(2×2/100))%=4.04
Answer: (D) 4.04
Question: Find the day of the week on 16th july, 1776.
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
(E) Wednesd21
Rationale: Explanation:
Split the year 1775 + 16th july 1776
Till 1600 years no odd days.
1601 to 1700 = 5 odd days
1701 to 1775 = 75 + 18 = 93 = 2 odd days. (75 years has 93 odd days (∵∵ 18 leap + 57 non leap years)
upto 15th july 1776 = 31 + 29 + 31 + 30 + 31 + 30 + 15 = 197 = 1 odd day.
Total odd days = 5 + 2 + 1 = 8 = 1 odd day.
So one day after Monday. That is Tuesday.
Answer: C
Answer: (C) Tuesday
Question: A train 125 m long passes a man, running at 12 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 37 km/hr
(B) 50 km/hr
(C) 36 km/hr
(D) 57 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 12 = 45 => x = 57 km/hr.
Answer:D
Answer: (D) 57 km/hr
Question: Rs.2600 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%?
(A) 1600
(B) 1700
(C) 1800
(D) 1900
(E) 2000
Rationale: (x*5*1)/100 + [(2600 - x)*6*1]/100 = 140
X = 1600
ANSWER:A
Answer: (A) 1600
Question: The value of (.02)2 + (0.52)2 + (0.035)2/ (0.002)2 + (0.052)2 + (0.0035)2
(A) 100
(B) 1000
(C) .001
(D) .0001
(E) .01
Rationale: (.02)2 + (0.52)2 + (0.035)2 / (0.002)2 + (0.052)2 + (0.0035)2
= a2+b2+c2 / ( a /10) 2+ ( b/10) 2 + ( c/10) 2
where a= .02, b= .52, c= .035
= 100(a2+b2+c2) / a2+b2+c2 = 100
ANSWER:A
Answer: (A) 100
Question: There are 2 sections A and B in a class, consisting of 30and 20 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, Find the average of the whole class?
(A) 35kg
(B) 37kg
(C) 42kg
(D) 38kg
(E) 29.78kg
Rationale: Total weight of 36+44 students = 30*40 + 20*35 = 1900
Average weight of the class is = 1900/50 = 38 kg
Answer is D
Answer: (D) 38kg
Question: In Arun's opinion, his weight is greater than 61 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 64 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
(A) 86.5 kg
(B) 62.5 kg
(C) 46.5 kg
(D) 26.5 kg
(E) 16.5 kg
Rationale: Let Arun's weight be X kg.
According to Arun, 61 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 64.
The values satisfying all the above conditions are 62 and 63.
Required average = (62 + 63) / 2 = 62.5 kg
Answer: B
Answer: (B) 62.5 kg