mathewhe/aqua_rat huggingface dataset:
Question: A set of numbers has the property that for any number t in the set,t+2 is in the set. If -3 is in the set, which of the following must also be in the set? I. 4 II. 6 III. 3
(A) III only
(B) II only
(C) I only
(D) I,III only
(E) I,II only
Rationale: question is asking for must be there elements.
According to the question if t is there t+2 must be there.
if -3 is the starting element the sequence is as follows.
S ={-3,-1,1,3,5....}
if -3 is not the starting element the sequence is as follows
S = {...-5,-3,-1,1,3,5...}
By observing the above two sequences we can say that 3 must be there in set S.
Answer : A
Answer: (A) III only
Question: From a pack of 52 cards, one card is drawn at random. Find the probability that the drawn card is a club or a jack?
(A) 17/52
(B) 8/13
(C) 4/13
(D) 1/13
(E) None of these
Rationale: EXPLANATION:
n(S) = 52
n(E) = 16
P(E) = n(E) / n(S) = 16/ 52
= 4/13
ANSWER IS C
Answer: (C) 4/13
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
(A) 15
(B) 20
(C) 24
(D) 30
(E) 35
Rationale: B = 1/8 â€“ 1/2 = 1/24 => 24 days
ANSWER C
Answer: (C) 24
Question: There is a train and car. The ratio btw the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480km in 8h. The speed of the bus is 3/4th of the speed of the train. How much distance will the car cover in 6h?
(A) 320 km
(B) 350 km
(C) 380 km
(D) 400 km
(E) 450 km
Rationale: Sol. Speed of bus = 480/8 = 60km/ h
Speed of train = (60*4)/3=80 km / h
Speed of train : Speed of car = 16 : 15
Speed of car =80/16 * 15 = 75 km/ h
Distance covered by car in 6 hr = 75 × 6 = 450 km
E
Answer: (E) 450 km
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
(A) XB < YD
(B) XB < YD
(C) AX > XB
(D) AX < CD
(E) AX > AB
Rationale: A------X--B
C--Y------D
AX < CD.
Answer: D.
Answer: (D) AX < CD
Question: Shopkeeper rise price by 35% and gives successive discount of 10% and 15%. What is overall % gain or loss?
(A) 5.275%
(B) 4.275%
(C) 3.275%
(D) 6.275%
(E) 7.275%
Rationale: Let d initial price be 100
35 % rise
now price = 135/100*100 = 135
10% discount
Then price = 135 * 90/100 = 121.5
15 % discount
Then price = 121.5 * 85/100 = 103.275
So Gain = 103.275 - 100 = 3.275
Gain % = Gain * 100 /CP
==> 3.275 * 100 /100 = 3.275%
ANSWER:C
Answer: (C) 3.275%
Question: A shopkeeper labeled the price of his articles so as to earn a profit of 50% on the cost price. He then sold the articles by offering a discount of 10% on the labeled price. What is the actual percent profit earned in the deal?
(A) 35%
(B) 20%
(C) 17%
(D) 18%
(E) None of these
Rationale: Explanation:
Let the CP of the article = Rs.100.
Then labeled price = Rs.150.
SP = Rs.150- 10% of 150 = Rs.150-15 = Rs.135.
Gain = Rs.135 â€“ Rs.100 = Rs.35
Therefore, gain/profit percent = 35%.
Answer: Option A
Answer: (A) 35%
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7 kmph
(B) 8 kmph
(C) 5 kmph
(D) 9 kmph
(E) 2 kmph
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer: B
Answer: (B) 8 kmph
Question: A man is walking at the rate of 7 km/hr crosses a bridge in 15 minutes. The length of the bridge is
(A) 1000 meters
(B) 1050 meters
(C) 1200 meters
(D) 1750 meters
(E) None of these
Rationale: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Speed=7âˆ—5/18=35/18m/sec
Time=15âˆ—60seconds=900seconds
Distance=Timeâˆ—Speed/Distance=35/18âˆ—900=1750meter
Option D
Answer: (D) 1750 meters
Question: For the past n days, the average (arithmetic mean) daily production at a company was 40 units. If today's production of 90 units raises the average to 45 units per day, what is the value of n ?
(A) 30
(B) 18
(C) 10
(D) 9
(E) 7
Rationale: (average production for n days) * n = (total production for n days) --> 40n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 40n + 90 = 45 * (n+1) --> n=9
Answer: D.
Answer: (D) 9
Question: Ayesha’s father was 38 years of age when she was born while her mother was 33 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 9 years
(C) 6 years
(D) 8 years
(E) None
Rationale: EXPLANATION
Mother’s age when Ayesha’s brother was born = 33 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 33) years = 9 years.
Answer B
Answer: (B) 9 years
Question: There was a person who smoked a lot .One day he decided to quit his habbit,but he had 27 cigarettes with him.So he started smoking them one by one ,to finish them. He had the habit of smoking only 2/3rd of it and leaving the rest butt. Latter he found out that by joining 3 butts he can form 1 cigarette. So ,tell how many cigarettes in all he smoked.
(A) 30
(B) 40
(C) 50
(D) 60
(E) 45
Rationale: 27+9+3+1=40.
ANSWER:B
Answer: (B) 40
Question: Richard walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:30. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 40 meters. What is Richard's speed in meters per minute?
(A) 75
(B) 180
(C) 198
(D) 216
(E) 252
Rationale: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×30(per block dist)
Speed = 3000mts/40min =75m/min
A is the answer
Answer: (A) 75
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) 1.2
(D) 1.6
(E) 1.1
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: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 12 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
(A)  3
(B)  6
(C)  7.2
(D)  7.8
(E)  9
Rationale: Answer is A.
x/x+36=1/5
x=9
12-9=3
Answer: (A)  3
Question: What is the difference between the place value of 2 in the numeral 7669?
(A) 160
(B) 165
(C) 180
(D) 190
(E) 540
Rationale: Answer: Option 'E'
600 - 60 = 540
Answer: (E) 540
Question: A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. B alone
can do the whole work in
(A) 15 days
(B) 10 days
(C) 9 days
(D) 8 days
(E) None of these
Rationale: Explanation:
Ratio of times taken by A and B = 1:3
Means B will take 3 times which A will do in 1 Ɵme
If difference of time is 2 days, B takes 3 days
If difference of time is 10 days, B takes (3/2) * 10 =15 days
Answer: A
Answer: (A) 15 days
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 15000, then find the annual income of A?
(A) Rs. 424000
(B) Rs. 484000
(C) Rs. 502000
(D) Rs. 503000
(E) Rs. 504000
Rationale: B's monthly income = 15000 * 112/100 = Rs. 16800
B's monthly income = 2 parts ----> Rs. 16800
A's monthly income = 5 parts = 5/2 * 16800 = Rs. 42000
A's annual income = Rs. 42000 * 12 = Rs. 504000
E)
Answer: (E) Rs. 504000
Question: There are 7 non-collinear points. How many triangles can be drawn by joining these points?
(A) 35
(B) 10
(C) 8
(D) 7
(E) 6
Rationale: Solution:
A triangle is formed by joining any three non-collinear points in pairs.
There are 7 non-collinear points.
The number of triangles formed,
= 7C3
= [{7 *(7−1) *(7−2)} /3! ]
=(7 *6 *5)/(3 *2 *1) = 7 *5 = 35.
Answer: Option A
Answer: (A) 35
Question: Nine fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 72
(B) 75
(C) 81
(D) 84
(E) 88
Rationale: 9*8 = 72
The answer is A.
Answer: (A) 72
Question: In a kilometer race, A beats B by 48 meters or 6 seconds. What time does A take to complete the race?
(A) 22
(B) 119
(C) 110
(D) 109
(E) 12
Rationale: Time taken by B run 1000 meters = (1000 * 6)/48 = 125 sec.
Time taken by A = 125 - 6 = 119 sec.Answer:B
Answer: (B) 119
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
(A) 90 sec
(B) 87 sec
(C) 67 sec
(D) 28 sec
(E) 27 sec
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18
= (750 * 18) / (30 * 5)
= 90 sec
Answer:A
Answer: (A) 90 sec
Question: The radius of a wheel is 12.6 cm. What is the distance covered by the wheel in making 200 resolutions?
(A) 158.210 m
(B) 704 m
(C) 153.256 m
(D) 158.256 m
(E) 204 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 200 resolutions.
= 200* 2 * 22/7 * 12.6 = 15825.6 cm
= 158.256 m
Answer:D
Answer: (D) 158.256 m
Question: Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 25
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
Answer: Option 'C'
Answer: (C) 15
Question: A retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price. If the retailer decreases the retail price by 20 percent this will have the same effect as increasing the wholesale price by what percent?
(A) 26
(B) 37.5
(C) 42
(D) 44
(E) 50
Rationale: Answer: D= 44.
Assume Rs. 100 to be the price at which the retailer buys from wholesaler.
80% increase makes Retail price = 180.
Now 20% decrease -> (1-20/100) * 180 = 144.
Now compared to the wholesale price of 100, 44% increase is what will have the same effect as increasing the wholesale price.
Answer: (D) 44
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the
child 5 years ago was 20 years. The present age of the husband is
(A) 40
(B) 35
(C) 45
(D) 55
(E) 65
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) years = 90 years.
Sum of the present ages of wife and child = (20 * 2 + 5 * 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years
Answer: Option A
Answer: (A) 40
Question: Average between two sets of numbers is closer to the set withmore numbers?
(A) 70
(B) 80
(C) 90
(D) 92
(E) 94
Rationale: If on a test three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group is not 85% but rather 3×90+2×805=4305=86.3×90+2×805=4305=86.
Here, 90 has a weight of 3 => it occurs 3 times.
Whereas 80 has a weight of 2 => it occurs 2 times.
So the average is closer to 90 than to 80 as we have just calculated.
B
Answer: (B) 80
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 220
(B) 230
(C) 245
(D) 355
(E) 345
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: Option C
Answer: (C) 245
Question: the difference between principal amount and simple interest is 100.the rate and time are 5% and 3 years respectively.calculate principal amount.
(A) 118
(B) 122.32
(C) 126.36
(D) 115.52
(E) 117.64
Rationale: let principal amount=x,simple interest=x-100.
x-100=x*5*3/100
100x-10000=15x
85x=10000
x=10000/85=117.64
answer E
Answer: (E) 117.64
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 5 years at 20% per annum is Rs.75 of money?
(A) 1489
(B) 6845
(C) 2598
(D) 1875
(E) 2600
Rationale: P = 75(100/20)5 => P = 1875
Answer: D
Answer: (D) 1875
Question: The sale price sarees listed for Rs.200 after successive discount is 20% and 10% is?
(A) 187
(B) 124
(C) 172
(D) 144
(E) 175
Rationale: 200*(80/100)*(90/100)
= 144
Answer:D
Answer: (D) 144
Question: A glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. If 65 cubic centimeters of the solution were poured into an empty container, how many grams of glucose would be in the container?
(A)  7.50
(B)  8.75
(C)  7.75
(D)  9.50
(E)  9.75
Rationale: We are given that a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution. Since we are dealing with a solution, we know that the grams of glucose is proportional to the number of cubic centimeters of solution. Thus, to determine how many grams of glucose would be in the container when we have 45 cubic centimeters of solution, we can set up a proportion.
We can say: “15 grams of glucose is to 100 cubic centimeters of solution as x grams of glucose is to 65 cubic centimeters of solution.” Let’s now set up the proportion and solve for x.
15/100 = x/65
When we cross multiply we obtain:
(15)(65) = 100x
975 = 100x
9.75 = x
There are 9.75 grams of glucose in the solution in the container.
The answer is E.
Answer: (E)  9.75
Question: At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
(A) 12
(B) 15
(C) 19
(D) 20
(E) 21
Rationale: Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26 4x = 20
x = 5.
Deepak's age = 3x = 15 years.
Ans-B
Answer: (B) 15
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
(A) 17/65
(B) 17/29
(C) 17/21
(D) P(EᴜP) =17/20
(E) 17/212
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20.Answer:D
Answer: (D) P(EᴜP) =17/20
Question: A person bought 129 glass bowls at a rate of Rs. 11 per bowl. He sold 118 of them at Rs. 15 and the remaining broke. What is the percentage gain for A?
(A) 40
(B) 2900/129
(C) 2430/70
(D) 2791/11
(E) 2719/8
Rationale: CP=129*11=1419 and SP=118*15=1770
Gain %= 100*(1770-1419)/1419= 2900/129
ANSWER:B
Answer: (B) 2900/129
Question: 14, 28, 20, 40, 32, 64, ?
(A) 56
(B) 46
(C) 58
(D) 48
(E) 68
Rationale: This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer : A.
Answer: (A) 56
Question: If the sum of a number and its square is 182, what is the number?
(A) 13
(B) 26
(C) 39
(D) 45
(E) None
Rationale: Solution
Let the number be x.
Then, x + x2 = 182	‹=›x2 + x - 182 = 0
‹=›(x + 14) (x - 13) = 0.
‹=›x = 13.
Answer A
Answer: (A) 13
Question: Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively
(A) 19
(B) 17
(C) 13
(D) 15
(E) 18
Rationale: Explanation:
Trick is HCF of (400-9, 435-10, 541-14)
HCF of (391, 425, 527) = 17
Option B
Answer: (B) 17
Question: The population of a bacteria culture doubles every 1 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
(A) 9
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: This one's easy.
1000 * 2^t = 500,000
2^t = 500
Now gauging, since 2^8 = 256, then 2^9 = 512
So t = 9
But be careful, 't' is in time intervals of 1 minutes
So answer is 9*1 = 9 minutes
Answer (A)
Answer: (A) 9
Question: A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.40 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?
(A) 0.40x
(B) 1.20x
(C) 5.60x
(D) 1.60x
(E) 3.20x
Rationale: because we have a total of 4X
Also from Mar- Oct the rakes will be deducted by 1/8 X
so
In Apr they pay for the storage 0.4 * 4X * 7/8
In May they pay for the storage 0.4 * 4X * 6/8
In Jun they pay for the storage 0.4 * 4X * 5/8
In Jul they pay for the storage 0.4 * 4X * 4/8
In Aug they pay for the storage 0.4 * 4X * 3/8
In Sep they pay for the storage 0.4 * 4X * 2/8
In Oct they pay for the storage 0.4 * 4X * 1/8
total = 0.4 * 4X * 1/8 * [ 1+2+3+4+5+6+7]
= 0.4 * X/2 * (28)
= 5.6X
(C)
Answer: (C) 5.60x
Question: The function g(x)g(x) is defined as the greatest integer less than or equal to xx, while the function h(x)h(x) is defined as the least integer greater than or equal to xx. What is the product g(1.7)×h(2.3)×g(−1.7)×h(−2.3)?
(A) 6
(B) 9
(C) 12
(D) 16
(E) 24
Rationale: g(x) is round down to nearest integer unless its an integer already
h(x) is round up to nearest integer unless its an integer already
so we have
(1)(3)(-2)(-2) as our equation, negative x negative cancels so 3 x 2 x 2 = 6 x 2 = 12.
ANSWER:C
Answer: (C) 12
Question: Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 12 seconds. The length of the faster train is
(A) 80 m
(B) 270 m
(C) 120 m
(D) 180 m
(E) None
Rationale: Solution
Relative Speed	= (36 + 45) km/hr
= (81 x 5/18) m/sec
= (45/2) m/sec
Length of the train	= (45 / 2 x 12) m
= 270 m.
Answer B
Answer: (B) 270 m
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 7/9
Rationale: It has two vertices on sides, which do not make a diagonal but a side..
So remaining 3 vertices make diagonals... only the opposite vertex will make largest diagonal and other TWO smaller ones..
So prob =2/(2+1)=2/3
Answer:D
Answer: (D) 2/3
Question: P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?
(A) 10
(B) 15
(C) 18
(D) 20
(E) 22
Rationale: Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 = 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18
Option C
Answer: (C) 18
Question: For which of the following functions does f(−k)=−f(k) for all real number values of x?
(A) k^8
(B) −k^6
(C) k^5/k^7
(D) k^9
(E) k^4/k^2
Rationale: f(-k) = (-k)^9 = -k*k^8
-f(u) = -u^9
D
Answer: (D) k^9
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 60 ps per meter is?
(A) 287
(B) 369
(C) 150
(D) 279
(E) 361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 0.60
= Rs.150
Answer:C
Answer: (C) 150
Question: During a trip on an expressway, Ron drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5%
(B) 50%
(C) x/12%
(D) 60/x%
(E) 500/x%
Rationale: so Ron drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E
Answer: (E) 500/x%
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 4:3. The ratio of economy cars to sport utility vehicles is 6:5. What is the ratio of luxury cars to sport utility vehicles?
(A) 9:10
(B) 8:9
(C) 3:2
(D) 2:3
(E) 1:2
Rationale: The ratio of economy to luxury cars is 4:3 --> E:L = 4:3 = 24:18.
The ratio of economy cars to sport utility vehicles is 6:5 --> E:S = 6:5 = 24:20.
Thus, L:S = 18:20 = 9:10.
Answer: A.
Answer: (A) 9:10
Question: Simplify 586645 * 9999
(A) 5865863355
(B) 5665863355
(C) 4865863355
(D) 4665863355
(E) 4556834553
Rationale: Explanation:
Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
586645 * (10000 - 1) = 5866450000 - 586645 = 5865863355
Answer: Option A
Answer: (A) 5865863355
Question: The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is :
(A) 8%
(B) 1%
(C) 20%
(D) 80%
(E) None
Rationale: Explanation:
Let the business value changes from x to y.
Then, 4% of x = 5% of y or 4/100×x=5/100×y
or y = 4/5x
Change in business = (x−4/5x)=1/5x
Percentage slump in business
= (1/5x×1/x×100)%
Correct Option: C
Answer: (C) 20%
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 8 sec
(B) 6 sec
(C) 3 sec
(D) 9 sec
(E) 5 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
=[55/3] m/sec.
Time taken to pass the man
= [110 * 3/55] sec
= 6 sec
Answer:B
Answer: (B) 6 sec
Question: What is the ratio of 5/7 to the product 3*(7/3)?
(A) 3:7
(B) 1:3
(C) 5:49
(D) 1:7
(E) 3:49
Rationale: 3/7 / 21/3 = 5/49...
IMO option C.
Answer: (C) 5:49
Question: Look at this series: 1000, 200, 40, ... What number should come next?
(A) 8
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: 1000/5=200
200/5=40
40/5=8
ANSWER:A
Answer: (A) 8
Question: A person walking at 10 Kmph reaches his office 10 minutes late. If he walks at 15 Kmph, he reaches there 10 minutes earlier. How far is the office from his house?
(A) 5km
(B) 15km
(C) 8km
(D) 10km
(E) 20km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 10*15/5 * 20/60
= 30 * 20/60
= 10 km
Answer is D
Answer: (D) 10km
Question: How many zeroes are there at the end of the number N, if N = 100! + 200! ?
(A) 73
(B) 49
(C) 20
(D) 48
(E) 24
Rationale: The number of zeroes at the end of 100! will be less than the number of zeroes at the end of 200!
Hence it would be sufficient to calculate the number of zeroes at the end of 100!
Number of zeroes = [100/5] + [100/25] + [100/125] = 20 + 4 + 0 = 24
Correct Option: E
Answer: (E) 24
Question: Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?
(A) 33
(B) 77
(C) 33
(D) 80
(E) 12
Rationale: We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300
D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.
Answer:D
Answer: (D) 80
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is:
(A) 700
(B) 780
(C) 760
(D) 750
(E) 459
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: Option D
Answer: (D) 750
Question: The volume of a cube is 1728 cc. Find its surface.
(A) 864
(B) 277
(C) 299
(D) 268
(E) 191
Rationale: a3 = 1728 => a = 12
6a2 = 6 * 12 * 12 = 864
Answer: A
Answer: (A) 864
Question: A is twice as good workman as B, and together they complete a work in 3 days. In how many days can the work be complete by B alone?
(A) 35 days
(B) 65 days
(C) 9 days
(D) 75 days
(E) 95 days
Rationale: B=3A
9 days
C
Answer: (C) 9 days