mathewhe/aqua_rat huggingface dataset:
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 109%
(B) 160%
(C) 100%
(D) 600%
(E) 108%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: (C) 100%
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.567] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
(A) 0
(B) 1
(C) 27
(D) 0
(E) Cannot be determined
Rationale: K=[lCM of 80 and 45] * (any integer)
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
for value of k(60) * any integer unit value will be always zero .
D
Answer: (D) 0
Question: A shopkeeper sells 20% of his stock at 20% profit ans sells the remaining at a loss of 10%. He incurred an overall loss of Rs. 500. Find the total worth of the stock?
(A) 13500
(B) 12000
(C) 12500
(D) 15000
(E) 15500
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 6/5 = 6x/25
The SP of 80% of the stock = 4/5 * x * 0.9 = 24x/25
Total SP = 6x/25 + 18x/25 = 49x/50
Overall loss = x - 24x/50 = x/25
x/25 = 500 => x = 12500
Answer:C
Answer: (C) 12500
Question: A cab driver 5days income was $45, $50, $60, $65 , $90. Then his average income is?
(A) A)$58
(B) B)$42
(C) C)$65
(D) D)$48
(E) E)$62
Rationale: avg = sum of observations/number of observations
avg income=(45+50+60+65+90)/5 = 62
Answer is E
Answer: (E) E)$62
Question: What annual payment will discharge a debt of Rs. 1060 due in 2 years at the rate of 5% compound interest?
(A) 993.2
(B) 551.25
(C) 570.07
(D) 543.33
(E) 646.33
Rationale: Explanation:
Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1060
820x + 1060 * 441
x = 570.07
So, value of each installment = Rs. 570.07
Answer: Option C
Answer: (C) 570.07
Question: Two trains of length 210 m and 120 m are 160 m apart. They start moving towards each other on parallel tracks, at speeds 74 kmph and 92 kmph. After how much time will the trains meet?
(A) 35/10
(B) 31/10
(C) 31/10
(D) 36/10
(E) 37/10
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (74 + 92)*5/18 = 46.1 mps.
The time required = d/s = 160/46.1= 35/10 sec.
Answer:A
Answer: (A) 35/10
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 15 years old. At what age did the father get married ?
(A) 20years
(B) 21years
(C) 22years
(D) 23years
(E) 25years
Rationale: Explanation:
Ayush's present age = 15 years.
His mother's present age = (15 + 20) years = 35 years.
Ayush's father's present age = (35 + 5) years = 40 years.
Ayush's father's age at the time of Ayush's birth = (40 - 15) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
Answer: D) 23 year
Answer: (D) 23years
Question: On Tuesday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
(A) Tuesday
(B) Wednesday
(C) Thursday
(D) Friday
(E) Saturday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Tuesday, 3rd day is Friday. Next day, which he won't have a new combination for, is Saturday. (E)
Answer: (E) Saturday
Question: The present worth of Rs. 242 due in 2 years at 10% per annum compound interest is:
(A) Rs. 180
(B) Rs. 240
(C) Rs. 220
(D) Rs. 200
(E) Rs. 300
Rationale: Explanation:
Present worth of Rs. x due T years hence is given by
Present Worth (PW) = x/(1+R/100)^T
Present Worth (PW) = 242/(1+10/100)^2=242/(11/10)^2=Rs. 200
Answer : Option D
Answer: (D) Rs. 200
Question: A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/83 hours
(B) 15/13 hours
(C) 15/4 hours
(D) 30/19 hours
(E) 32/13 hours
Rationale: Speed downstream = 10 + 6 = 16 kmph.
Time required to cover 60 km downstream
= d/s = 60/16
= 15/4 hours.
Answer:C
Answer: (C) 15/4 hours
Question: A man jumps into a river from a overbridge ,at the same time a hat drops in the river which flows with the stream of the water. That man travels 10 minute upstream and returns back where he was asked to catch the hat. He catches hat at a distance of 1000 yard down at a second bridge . Find the speed of the river.
(A) 50
(B) 60
(C) 55
(D) 70
(E) 75
Rationale: Explanation :
Suppose x is the distance travelled by the man in 10 min upstream.
Then
=> x/(v-u) = 10 where v is man's speed and u is river speed)
Total time taken to swim by the man upstream and down stream is equal to the time taken by the
hat to travel 1000 yards with the speed of river :
=> 1000/u = 10 + (x+1000) / (u+v)
=> now substitute x = 10(v-u) and simplify
we will get,
=> 100v = 2uv
=> 2u = 100
=> u = 50 yards per minute
Hence (A) is the correct answer.
Answer : A
Answer: (A) 50
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:7
(C) 2:1
(D) 2:3
(E) 2:2
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Answer: (A) 2:5
Question: How many three letter words are formed using the letters of the word TIME?
(A) 65
(B) 62
(C) 35
(D) 24
(E) 53
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24.
Answer:D
Answer: (D) 24
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.9
(B) 1.5
(C) 2.8
(D) 3.0
(E) 3.9
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: (B) 1.5
Question: Excluding stoppages, the speed of the bus is 54 kms /hr and with stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 20
Rationale: By including stoppages, bus will cover 9km less..(54km -45km = 9km)
Excluding stoppages, x = 54 kmph
Including stoppages, y = 45 kmph
Difference, z = 9km
Time taken to cover that 9km(bus stops per hour(60minutes))= z/x(60minutes)
= 9/54(60)
= 1/6(60)
= 10minutes.
ANSWER:B
Answer: (B) 10
Question: Of the five numbers in a sequence, the first term is 10,000, and each of the following terms is 70% of the previous term. What is the value range of the five numbers?
(A) 7,599
(B) 9,750
(C) 9,975
(D) 9,984
(E) 10,736
Rationale: 1st number= 10,000
2nd number = 70% of 10,000= 7000
3rd number= 70% of 7000= 4900
4th number = 70% of 4900= 3430
5th number= 70% of 3430= 2401
Range = 10,000-2401=7599
A is the answer
Answer: (A) 7,599
Question: There are 2 available positions and 50 candidates, one half of whom are democrats and another half are republicans. If it was decided that the positions would be filled at random, then what is the probability W that the both positions will be taken by members of just one party?
(A) 1/25
(B) 12/49
(C) 1/4
(D) 24/49
(E) 1/2
Rationale: W probability of one party having both spots:
(1/2) * (24/49) = 12/49
(1/2) or (25/50) because it does not matter which party or which person gets the first spot. (24/49) because after one person from a particular party is chosen, there are 24 members of the same party left out of 49 total candidates.
Since this result can happen for both parties, (12/49) + (12/49) = (24/49)
Answer: D
Answer: (D) 24/49
Question: The average of seven results is 156 and that of the first six is 169. The fifth result is?
(A) 120
(B) 160
(C) 89
(D) 78
(E) 148
Rationale: 7 * 156 â€“ 6 * 169 = 78
Answer: D
Answer: (D) 78
Question: A man complete a journey in 1010 hours. He travels first half of the journey at the rate of 2121 km/hr and second half at the rate of 2424 km/hr. Find the total journey in km.
(A) 121 km
(B) 242 km
(C) 224 km
(D) 112 km
(E) 110 km
Rationale: Solution 1
Average Speed =2Ã—21Ã—2421+24=22.4 km/hr=2Ã—21Ã—2421+24=22.4 km/hr
Total distance =22.4Ã—10=224 km
ANSWER IS C
Answer: (C) 224 km
Question: Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 150 miles per hour and the train's average speed when traveling from point B to point C was 100 miles per hour. What was the train's average speed, in miles per hour, when traveling from point A to point C?
(A) 22.5
(B) 21.43
(C) 25.5
(D) 26.5
(E) 27.5
Rationale: Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable d.
Speed A-B = 150
Speed B-C = 100
Average Speed = total distance/total rate
rate = distance/time
A====================B==========C
If A-B is twice the length of B-C then let A-B = 2d and let B-C = d
Average speed = 3d/(2d/150) + (d/100)
3d/(4d/300 + (3d/300)
3d/(7d/50)
150d/7d
Average speed = 21.43
ANSWER: B
Answer: (B) 21.43
Question: A father is now three times as old as his son. Six years back, he was four times as old as his son. The age of the son (in years) is
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: If father's age is F and son's age is S, then
F=3S
and
F-6 = 4*(S-6)
3S-6 =4S-24
S=18
F=54 years
ANSWER:C
Answer: (C) 18
Question: A fruit juice company earns $150 per 100 gallons of apple juice sold, $170 per 100 gallons of guava juice sold, $130 per 100 gallons of grape juice sold, $100 per 100 gallons of orange juice. If the company manages to sell 230 gallons of apple, 210 gallons of guava, 310 gallons of grape, 270 gallons of orange on a particular day. What is the average earning of the company per 100 gallon of the juice sold?
(A) 134.8
(B) 141.2
(C) 147.2
(D) 152.3
(E) 160.1
Rationale: Earning of the company from apple=150/100x230=345
Earning of the company from guava=170/100x210=357
Earning of the company from grape=130/100x310=403
Earning of the company from orange=100/100x270=270
Total earning of the company=345+357+403+270=1375
Total juice sold=1020
Average earning per 100 gallon of juice sold=(1375/1020)x100
=$134.8
Answer: A
Answer: (A) 134.8
Question: A biker covered half the distance between two towns in 2 hr 30 min. After that he increased his speed by 2 km/hr. He covered the second half of the distance in 2 hr 20 min. Find the distance between the two towns and the initial speed of the biker.
(A) 140
(B) 260
(C) 320
(D) 480
(E) 500
Rationale: Let x km/hr be the initial speed of the biker, then his speed during the second part of the trip is x + 2 km/hr. Half the distance between two cities equals 2*30/60⋅x km and 2*20/60⋅(x+2) km. From the equation: 2*30/60⋅x=2*20/60⋅(x+2) we get x=28 km/hr.
The intial speed of the biker is 28 km/h.
Half the distance between the two towns is
2h30min×28=2.5×28=70.
So the distance is 2×70=140 km
Answer: (A) 140
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 287
(B) 279
(C) 200
(D) 278
(E) 379
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
Answer:C
Answer: (C) 200
Question: If P = 775 × 778 × 781, what is the remainder when P is divided by 14?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: P 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A
Answer: (A) 6
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 7 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 45
(B) 65
(C) 75
(D) 79
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 7 = 75
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 75 + 4 = 79
D
Answer: (D) 79
Question: Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 1 hours, how many minutes did it take Cole to drive to work?
(A) 35
(B) 50
(C) 62
(D) 75
(E) 78
Rationale: First round distance travelled (say) = d
Speed = 75 k/h
Time taken, T2 = d/75 hr
Second round distance traveled = d (same distance)
Speed = 105 k/h
Time taken, T2 = d/105 hr
Total time taken = 1 hrs
Therefore , 1 = d/75 + d/105
LCM of 75 and 105 = 525
1= d/75 + d/105
=> 1 = 7d/525 + 5d/525
=> d = 525 / 12 Km
Therefore, T1= d/75
=> T1 = 525 / (12 x 75)
=> T1 = (7 x 60) / 12 -- in minutes
=> T1 = 35 minutes.
A
Answer: (A) 35
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 360 m and they cross each other in 24 sec, then the speed of each train is?
(A) 78
(B) 89
(C) 36
(D) 54
(E) 23
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (360 + 360)/24 => x =15
Speed of each train = 15 m/sec.
= 15 * 18/5 =54 km/hr.
Answer: Option D
Answer: (D) 54
Question: If Deepesh had walked 20 km/h faster he woulh have saved 1 hour in the distance of 60km. what is the usual speed of Deepesh?
(A) 100
(B) 299
(C) 208
(D) 273
(E) 222
Rationale: Explanation:
Let the original speed be x km/h, then
\inline \frac{600}{x}-\frac{600}{(X+20)}=1
\inline \Rightarrow 600\left ( \frac{x+20-x}{x(x+20)} \right )=1
\inline \Rightarrow \: \: x^{2}+120x-12000=0
\inline \Rightarrow \: \: (x-120)(x-100)=0
\inline \Rightarrow \: \: x=100 \: \: and\: \: x=120
\inline \therefore original speed = 100km/h
Answer: A
Answer: (A) 100
Question: In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points T is in the same quadrant as the fourth vertex of the square?
(A) (-5, -3)
(B) (-5, 3)
(C) (5, -3)
(D) (3, -5)
(E) (3, 5)
Rationale: The question:In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points T is in the same quadrant as the fourth vertex of the square?
I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means
Vertex #1 = (c, d) is in QII (that is, negative x and positive y)
Vertex #2 = (c, -d) is in QIII (that is, both xy negative)
Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)
That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.
Answer: (E) (3, 5)
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.740 in 2 years?
(A) 221
(B) 287
(C) 400
(D) 288
(E) 671
Rationale: Explanation:
740 = P(21/20)2
P = 671
Answer:E
Answer: (E) 671
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) 356
(B) 200
(C) 127
(D) 279
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
Answer: B
Answer: (B) 200
Question: A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 54 inches and the width of the wall is 68 inches, what is the length of the wall, in inches?
(A)  25.7
(B)  72.7
(C)  70.7
(D)  85.7
(E)  56.7
Rationale: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 54^2=2916.Area of rectangle is double of that 2 *2916=5832.Now A=lw and we need find w so A/l=w ; 5832/68= 85.7 Answer!
Answer is D
Answer: (D)  85.7
Question: The proportion of X’s and Y’s ages is 4:5. If the difference between the current age of X and the age of Y 0.5 decades hence is 3, then what is the sum of current ages of X and Y?
(A) 83 years
(B) 39 years
(C) 72 years
(D) 48 years
(E) 93 years
Rationale: D
72 years
We simplified the most of steps because lack of font prolem.
X = 32 years
and, Y = (5/4) x 32 = 40 years
Therefore X + Y = 40 + 32 = 72 years.
Answer: (D) 48 years
Question: What is the area of a square with perimeter 8P ?
(A)  16p^2
(B)  4P^2
(C)  P^2/4
(D)  P/16
(E)  P^2/16
Rationale: Each side is 2p
A = (2p)^2 = 4(p^2)
Answer B
Answer: (B)  4P^2
Question: Insert the missing number
121, 112, ..., 97, 91, 86
(A) 102
(B) 108
(C) 99
(D) 104
(E) 106
Rationale: first and second number difference is starting from 9, and further decresed by 1 by each iteration.
121, 112, ..., 97, 91, 86....
Difference between two numbers Will be as 9, 8, 7, 6, 5,...
ANSWER:D
Answer: (D) 104
Question: Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
(A) 2/5
(B) 3/5
(C) 3/10
(D) 3/11
(E) 4/5
Rationale: Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
Answer: (C) 3/10
Question: How many seconds will a 700 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 22
(B) 42
(C) 99
(D) 77
(E) 12
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 700 * 3/50 = 42 sec.
Answer: B
Answer: (B) 42
Question: A positive whole number has factors of 3 and 4. The number MUST be divisible by:
I. 12 II. 24 III. 48
(A) I
(B) I & III
(C) II
(D) II & III
(E) III
Rationale: 12 , 24 is not divisible by 48.But 48 is divisible by 3,4,12,24.
So answer is III
Answer : E
Answer: (E) III
Question: If 500 gm of salt solution has 30% salt in it, how much salt must be added to make the concentration of salt 50% in the solution?
(A) 200 gm
(B) 280 gm
(C) 202 gm
(D) 700 gm
(E) 206 gm
Rationale: Explanation:
Amount of water in solution = 100 % - 30 % = 70 % of total
Amount of water = 70 % x 500 = 350 gm
Amount of water remains same for both the solutions. Therefore, let amount of new solution be x gm.
x = 350 x (100/ 50)
x = 700
Salt added = (700 – 500) = 200 gm
Alternate solution:
Quantity of sugar to be added :
= [Solution (Required % value – Present % value)] / (100 – Required % value)
= [500 (50 – 30)] / 100 – 50
= (500 x 20) / 50
= 200 gm
ANSWER: A
Answer: (A) 200 gm
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 5
(B) 7
(C) 3
(D) 1/2
(E) 4
Rationale: Explanation:
M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: C
Answer: (C) 3
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.29
(B) 5.2
(C) 5.76
(D) 5.12
(E) 5.93
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Answer: (C) 5.76
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 7:4:5 and 5:3:8 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
(A) 41:81:37
(B) 33:91:81
(C) 16:7: 12
(D) 12:70: 16
(E) 12:7: 16
Rationale: Let the weight of the two alloys be w each
Required ratio =
(7w/16 +5w/16): ( 4w/16 +3w/16 ): (5w/16+6w/16)
= 12w/16 : 7w/16 : 11w/16
= 12:7: 16
ANSWER:E
Answer: (E) 12:7: 16
Question: Pipe A can fill a tank in 2 hours. Due to a leak at the bottom, it takes 3 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?
(A) 10
(B) 9
(C) 7
(D) 6
(E) 5
Rationale: Let the leak can empty the full tank in x hours 1/2 - 1/x = 1/3
=> 1/x = 1/2 - 1/3 = (3 - 2)/6 = 1/6
=> x = 6.
Answer: D
Answer: (D) 6
Question: The perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters. What is the length of the yard if the area of the yard is 9 meters squared?
(A) 8
(B) 1
(C) 3
(D) 4
(E) 6
Rationale: Perimeter of rectangular yard = 2(l + b) = 12 --> l + b = 6
Area = l * b = 9
b = 6 - l
l(6 - l) = 9
6l - l^2 = 9
l^2 - 6l + 9 = 0
Upon simplifying we get l = 3.
Answer: B
Answer: (B) 1
Question: If 5a + 7b = k, where a and b are positive integers, what is the largest possible value of k for which exactly one pair of integers (a, b) makes the equation true?
(A) 35
(B) 48
(C) 69
(D) 70
(E) 74
Rationale: We 'll start putting the values of with a = 10 and b = 1.
Keep decreasing the value of a by 1 and increasing the value of b by 1.
At a = 10 and b = 1, 5a + 7b = 57
At a = 9 and b = 2, 5a + 7b = 59
At a = 8 and b = 3, 5a + 7b = 61
We see a pattern, for every decrease in a and every decrease in b, the result is increasing by 2.
So,
At a = 4 and b = 7, 5a + 7b = 69.
ANSWER:C
Answer: (C) 69
Question: Each day a man meets his wife at the train station after work, and then she drives him home. She always arrives exactly on time to pick him up. One day he catches an earlier train and arrives at the station an hour early. He immediately begins walking home along the same route the wife drives. Eventually his wife sees him on her way to the station and drives him the rest of the way home. When they arrive home the man notices that they arrived 16 minutes earlier than usual. How much time did the man spend walking?
(A) 45 minutes
(B) 50 minutes
(C) 40 minutes
(D) 55 minutes
(E) 52 minutes
Rationale: As they arrived 16 minutes earlier than usual, they saved 16 minutes on round trip from home to station (home-station-home) --> 8 minutes in each direction (home-station) --> wife meets husband 8 minutes earlier the usual meeting time --> husband arrived an hour earlier the usual meeting time, so he must have spent waking the rest of the time before their meeting, which is hour-8 minutes=52 minutes.
Answer: E
Answer: (E) 52 minutes
Question: Two perpendicular line segments divide a large rectangle
into 4 small rectangles. The areas of 3 of these 4 small
rectangles are shown. What is the area of the other small
rectangle?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Label the 4 small rectangles R1, R2, R3, and R4 so that the areas of R1, R2,
and R3 are 8, 6, and 9 respectively and R4 is the rectangle whose area we want to find.
Denote the area of R4 by x. Then 8 · 9 = 6 · x. (Note that R1 and R2 have the same
base and so do R3 and R4. Also, R1 and R4 have the same height and so do R2 and
R3.)
correct answer A
Answer: (A) 12
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31750. What percentage of profit did he make?
(A) 42.7
(B) 27
(C) 40
(D) 26
(E) 11
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31750
Profit(%) = (31750 - 22250)/22250 * 100 = 42.7%.Answer:A
Answer: (A) 42.7
Question: A certain list consists of 21 different numbers. If n is in the list and n is 5 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
(A) 1/20
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 5*x
Hence, a1+a2+..+a20+n = 25x
So, the fraction asked = 5x/25x = 1/5
Answer C
Answer: (C) 1/5