mathewhe/aqua_rat huggingface dataset:
Question: When the price of a product was decreased by 20%, the number sold increased by 60%. What was the effect on the total revenue ?
(A) 28%
(B) 32%
(C) 35%
(D) 45%
(E) 52%
Rationale: Let the price of the product be $100 and let original sale be 100 pieces
Then , Total Revenue = 100*100 = $10000
New revenue = 80*160 = $ 12800
Increase in revenue = 2800*100/10000 = 28%
Answer is A
Answer: (A) 28%
Question: A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?
(A) 15 minutes
(B) 18 minutes
(C) 12 minutes
(D) 58 minutes
(E) 10 minutes
Rationale: Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes
ANSWER:A
Answer: (A) 15 minutes
Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was $90 per day. During the first 7 days, his average wages was $87 per day and the average wages during the last 7 days was $95 per day. What was his wage on the 8th day?
(A) $76
(B) $90
(C) $92
(D) $97
(E) $104
Rationale: Average daily wage of a worker for 15 consecutive working days = 90$
During the first 7 days , the daily average daily wage = 87$
During the last 7 days , the daily average daily wage = 95$
Wage on 8th day = 90*15 -( 87*7 + 95 *7)
= 1350 - (609 + 665)
=1350 - 1274
= 76
Answer A
Answer: (A) $76
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
(A) 1 hr 20 min
(B) 1 hr 11 min
(C) 1 hr 12 min
(D) 1 hr 30 min
(E) None of these
Rationale: Explanation :
New speed = 6/7 of usual speed.
New time = 7/6 of usual time
=> [7/6 of usual time] - (usual time) = 1/5 hr.
=> 1/6 of usual time = 1/5 hr
=> usual time = 6/5 hr = 1 hr 12 min.
Answer : C
Answer: (C) 1 hr 12 min
Question: U is a set containing 8 different positive odd numbers. V is a set containing 7 different numbers, all of which are members of U. Which of the following statements CANNOT be true?
(A) The range of V is even.
(B) The mean of U is even.
(C) The mean of V is even.
(D) The range of U is equal to the range of V.
(E) The median of V is equal to the mean of V.
Rationale: Given: U is a set containing 8 different positive odd numbers
Easily inferred: V is a set containing 7 differentoddnumbers
(A) The range of V is even. - Always even, since it is a difference of two odd numbers
(B) The mean of U is even. - can be. suppose 8 numbers consist of 4 pairs of (16n-1,16n+1) for different values of n. Adding these will give a multiple of 16, which when divided by 8 (to arrive at mean), will give an even number
(C) The mean of V is even. - Cannot be. Mean = (sum of 7 odd numbers)/7 = Odd number/odd number thus cannot be even.
(D) The range of U is equal to the range of V.
(E) The median of V is equal to the mean of V
Option C.
Answer: (C) The mean of V is even.
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 7 meters, and the interior of tank B has a height of 7 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 70%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: The radius of tank A is 7/(2*pi).
The capacity of tank A is 10*pi*49 / (4*pi^2) = 245 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 7*pi*100 / (4*pi^2) = 350 / (2*pi)
Tank A / Tank B = 245/350 = 7/10 = 70%
The answer is A.
Answer: (A) 70%
Question: A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 4 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
(A) 0.5< t < 0.75
(B) 1.75< t < 2.0
(C) 1 < t < 2
(D) 2.5 < t < 3.0
(E) 3 < t < 3.5
Rationale: D=2, and R=1
circumference thus is 2pi miles
we know that she walked 4mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 4mph
t = 2pi/4
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/4 = 44/28. This is greater than 1, but less than 2, therefore, 1<t<2. Answer choice C.
Answer: (C) 1 < t < 2
Question: How much interest can a person get on Rs. 8200 at 10.5% p.a. simple interest for a period of six years and six months?
(A) 5596.5
(B) 5596.55
(C) 5596.54
(D) 3587.51
(E) 3587.57
Rationale: I = (8200 * 6.5 * 10.5)/100
= (8200 * 13 * 21)/(100 * 2 * 2)
= Rs. 5596.5
Answer: A
Answer: (A) 5596.5
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/5 and that of B is 2/7. Find the probability that both of them are selected.
(A) 2/35
(B) 2/30
(C) 2/63
(D) 2/29
(E) 2/10
Rationale: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/5, P(B) = 2/7.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/5) Ã— (2/7) = 2/35
Answer: A) 2/35
Answer: (A) 2/35
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 337
(B) 299
(C) 375
(D) 662
(E) 201
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: (C) 375
Question: There is a 4 digit no. in which 3rd digit is twice of first one. Second digit is the sum of first and third. Fourth digit is twice of third. What is the no?
(A) 1224
(B) 1324
(C) 1444
(D) 1524
(E) 1354
Rationale: Let the 4-digit no. be "abcd"
c = 2*a
b=a+c
d = 2*c => d=4a
abcd => (a)(a+c)(2a)(4a)
Possible values of a ll be 1 nd 2... Bcozzz a>2 implies d>10....Digits should ranges between 0 nd 9...
If a=1, then c=2,d=4, b=3... The no. is 1324
If a=2, then c=4,d=8, b=6... The no. is 2648
Ans : 1324 (or) 2648
ANSWER:B
Answer: (B) 1324
Question: Find the circumference and area of radius 11 cm.
(A) 124 cm²
(B) 144 cm²
(C) 380 cm²
(D) 284 cm²
(E) 394 cm²
Rationale: Area of circle = πr²
= 22/7 ×11 ×11 cm²
= 154 cm²
ANSWER:C
Answer: (C) 380 cm²
Question: A student gets 55% in one subject, 65% in the other. To get an overall of 55% how much should get in third subject.
(A) 75%
(B) 25%
(C) 45%
(D) 55%
(E) 65%
Rationale: Let the 3rd subject % = x
55+65+x = 3*55
120+x =165
x = 165-120=45
Answer :C
Answer: (C) 45%
Question: A train 385 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) 5
(B) 21
(C) 7
(D) 8
(E) 9
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 = [385 * 3/55] sec = 21 sec
Answer: Option B
Answer: (B) 21
Question: What is the probability that the sum of two dice will yield a 8, and then when both are thrown again, their sum will again yield a 8? assume that each die has 7 sides with faces numbered 1 to 7.
(A) 1/144
(B) 1/36
(C) 1/12
(D) 1/6
(E) 1/49
Rationale: Solution -
Rolling dices is an independent event.
The combinations to get 8 are (1,7), (7,1), (2,6), (6,2), (3,5), (5,3), (4,,4) and total combinations of both dices is 49.
The probability of getting 8 in first attempt is 7/49=1/7.
Probability of getting 8 again in second attempt = (1/7)*(1/7) = 1/49. ANS E
Answer: (E) 1/49
Question: In a kilometer race, A beats B by 20 meters or 10 seconds. What time does A take to complete the race?
(A) 290 sec
(B) 190 sec
(C) 199 sec
(D) 192 sec
(E) 490 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/20 = 500 sec.
Time taken by A = 500 - 10 = 490 sec.
Answer: E
Answer: (E) 490 sec
Question: A tap can fill a tank in 6 hours. After half the tank is filled then 3 more similar taps are opened. What will be total time taken to fill the tank completely.
(A) 2 hours 30 mins
(B) 2 hours 45 mins
(C) 3 hours 30 mins
(D) 3 hours 45 mins
(E) None of these
Rationale: Explanation:
Half tank will be filled in 3 hours
Lets calculate remaining half,
Part filled by the four taps in 1 hour = 4*(1/6) = 2/3
Remaining part after 1/2 filled = 1-1/2 = 1/2
2/3:1/2::1:X
=>X=(1/2∗1∗32)
=>X=3/4hrs=45 mins
Total time = 3 hours + 45 mins = 3 hours 45 mins
Option D
Answer: (D) 3 hours 45 mins
Question: On a map, 1 centimeter represents 19 kilometers. Two cities 627 kilometers apart would be separated on the map by how many centimeters?
(A) 15
(B) 27
(C) 49
(D) 33
(E) 280
Rationale: X=627/19= 33
Answer: D
Answer: (D) 33
Question: x = y - (10/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
(A) decrease
(B) stay the same
(C) increase four fold
(D) double
(E) increases to more than double
Rationale: Alternate approach
Plug in some values of y > 0
Let y = 10
So, x = y - (10/y)
Or, x = 10 - (10/10) =9
Let y = 20
So, x = y - (10/y)
Or, x = 20 - (10/20) =>19.5
So, x increases from 9 to 19.5
Hence the number increases 2.1 times, thus the correct answer will be (E)
Answer: (E) increases to more than double
Question: If pq = p^6 + q^2 – 2pq, for what value of q is pq equal to p^6 for all values of p?
(A) 0
(B) -1
(C) -2
(D) 1
(E) 2
Rationale: p6 + q2 â€“ 2pq = p6
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
A
Answer: (A) 0
Question: A 250 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 250
(B) 245
(C) 240
(D) 235
(E) 230
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 250)/9 = 500/9 => x = 250.
Answer: Option A
Answer: (A) 250
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) 288
(B) 269
(C) 245
(D) 888
(E) 121
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: C
Answer: (C) 245
Question: The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
(A) 2/3
(B) 3/2
(C) 4/5
(D) 5/8
(E) 4/2
Rationale: Let the earnings of P and Q be 9x and 10x respectively.
New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2
Answer:B
Answer: (B) 3/2
Question: The average of first ten prime numbers which are odd is?
(A) 22.2
(B) 22.1
(C) 15.3
(D) 15.8
(E) 14.6
Rationale: Explanation:
Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer:D
Answer: (D) 15.8
Question: Consider 6 points, two of which are A and B, such that each pair of points is connected by a
line segment and no three points are collinear. Compute the number of distinct paths from A
to B such that no point is visited more than once.
(A) 61
(B) 62
(C) 63
(D) 64
(E) 65
Rationale: We consider cases based on the length of the path. Note that there is 1 path of
length 1, 4 paths of length 2, 4 *3 = 12 paths of length 3, 4* 3 *2 = 12 paths of length 4,
4 * 3 * 2 * 1 = 24 paths of length 5, and no paths of length 6 or greater. Therefore, there are a
total of 1 + 4 + 12 + 24 + 24 = 65 distinct paths.
correct answer E
Answer: (E) 65
Question: If it takes a tub 6 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?
(A) 48 seconds
(B) 1 minute, 12 seconds
(C) 1 minute, 50 seconds
(D) 2 minutes, 24 seconds
(E) 4 minutes, 12 seconds
Rationale: If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained.
If it takes 6 minutes to drain 5/7 th of tub it takes 6*(7/5) minutes to drain the entire tub and 6*(7/5)*(2/7) min to drain 2/7 th of the tub which is 2.4 minutes or 12/5 minutes or 2 minute 24 seconds
So answer is D
Answer: (D) 2 minutes, 24 seconds
Question: A qualified worker digs a well in 6 hours. He invites 2 apprentices, both capable of working 3/4 as fast and 2 trainees both working 1/5 as fast as he. If the five-person team digs the same well, how much time does the team need to finish the job?
(A) 1:24
(B) 1:34
(C) 1:44
(D) 1:54
(E) 2:14
Rationale: and answer is correct as you have calculated : 100/64 hrs that is 1.82 hrs - 1 hr and 54 minutes, so 1:54, hence, D.
Answer: (D) 1:54
Question: Find the compound interest and the amount on Rs.6000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) s.1261.75
(B) s.1440.75
(C) s.1185.75
(D) s.1346.75
(E) s.945.75
Rationale: A = 6000(21/20)3
= 6945.75
= 6000
---------
945.75
ANSWER:E
Answer: (E) s.945.75
Question: how many internal diagonals does a octagon (eight sided polygon) have?
(A) 90
(B) 85
(C) 70
(D) 35
(E) 20
Rationale: Number of diagonals in any polygon can be found using this formula: n(n-3)/2
Here n = 8
No. of diagonals = 8(8 - 3)/2
= 20
Ans E
Answer: (E) 20
Question: x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) + (10x + z) could be equal to
(A) 33
(B) 36
(C) 44
(D) 63
(E) 95
Rationale: 1) firstly we are not given that all are different integers..
2) since each is a positive single digit integer and x=a/4... a can take only 4 and 8 as value, and x can take 1 and 2..
3) same as 2) for b and z.
so in (10a + b) + (10x + z) ..
10a+b can be
44,48,84,88..
10x+z can be
11,12,21,22..
ans E
Answer: (E) 95
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 10 sec. What is the length of the fast train?
(A) 55 7/6 m
(B) 55 7/4 m
(C) 55 7/2 m
(D) 55 7/9 m
(E) 55 5/9 m
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 10 = 500/9 = 55 5/9 m.Answer:E
Answer: (E) 55 5/9 m
Question: When 15% is lost in grinding wheat, a country can export 30 lakh tons of wheat. On the other hand, if 10% is lost in grinding, it can export 40 lakh tons of wheat. The production of wheat in the country is
(A) 20 lakh tons
(B) 80 lakh tons
(C) 200 lakh tons
(D) 800 lakh tons
(E) None
Rationale: Sol.
Let the production be x lakh tons.
Then, 15% of x - 10% of x = (40 - 30) lakh tons
⇔ 5% of x = 10 lakh tons
⇔ x = (10 x 100 / 5) = 200 lakh tons.
Answer C
Answer: (C) 200 lakh tons
Question: There are 27 different three-digit integers that can be formed using only the digits 1, 2 and 4. If all 27 of the integers were listed, what would their sum be?
(A) 6693
(B) 6793
(C) 6893
(D) 6993
(E) 7093
Rationale: There must be nine 1's in the hundreds place, nine 1's in the tens place, and nine 1's in the units place. This is also true for the 2's and 4's. Then the sum is:
9(111+222+444)=9*(777)=6993.
The answer is D.
Answer: (D) 6993
Question: What is the probability of rolling tow six-sided dice, and getting a different number on each die?
(A) 1/12
(B) 5/6
(C) 4/9
(D) 5/9
(E) 7/18
Rationale: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6 x 5 = 30 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 = 36).
30/36 = 5/6
Answer:B.
Answer: (B) 5/6
Question: 0, 5, 15, 30, 50, 75, 105, 140, ?What number should replace the question mark?
(A) 180
(B) 185
(C) 190
(D) 175
(E) 170
Rationale: A 180add 5,10,15,20,25.
Answer: (A) 180
Question: In May Mrs Lee's earnings were 60 percent of the Lee family's total income. In June Mrs Lee earned 40 percent more than in May. If the rest of the family's income was the same both months, then, in June, Mrs Lee's earnings were approximately what percent of the Lee family's total income ?
(A) 64%
(B) 68%
(C) 72%
(D) 76%
(E) 80%
Rationale: Let in May Lee family's total income =100
in May Mrs Lee's income =60
in May rest of the family's income = 40
In june Mrs Lees income = 60*140/100 = 84
In june Total income = 84+ 40 = 124
% of Mrs Lee's income = 84/124 =67.74
(B)
Answer: (B) 68%
Question: Find the odd man out: 111, 133, 143, 155, 188, 200.
(A) 111
(B) 143
(C) 200
(D) All of these.
(E) tortilla chips
Rationale: In each of the numbers the product of the first and the third digit is the middle one except 143.
1*1=1
1*3=3
1*5=5
1*8=8
2*0=0
ANSWER: B
Answer: (B) 143
Question: A construction company wants to number new houses using digit plates only. If the company puts an order for 1212 plates, how many houses are to be given numbers? (The numbers of houses are consecutive and the number of the first house is 1).
(A) 260
(B) 440
(C) 556
(D) 792
(E) 1200
Rationale: Run the numbers for houses. For the first 9 houses we need 9 signs.
For the next 90 we need 2 signs each or 180.
For the next 900 houses we need 3 signs each.
If we assume 300 homes, we will need 189 signs for the first 99 homes and then 603 signs for the 201 homes. So, we will use 792 signs for the first 300 homes and will have 420 signs remaining, which is enough for 42034203 or another 140 homes.
The total number of homes is 440
Answer: B
Answer: (B) 440
Question: If 20% of a = b, then b% of 20 is the same as
(A) 2% of a
(B) 3% of a
(C) 4% of a
(D) 5% of a
(E) 7% of a
Rationale: 20% of a = b
=> b = 20/100a
b% of 20 = (b/100)20 = [(20/100a)/100]20
= (20 × 20 × a)/(100 × 100)
= 4a/100 = 4% of a
C)
Answer: (C) 4% of a
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is
(A) 60 gallons
(B) 80 gallons
(C) 120 gallons
(D) 160 gallons
(E) None
Rationale: Solution
Work done by the waste pipe in 1 minute
=1/15-(1/20+1/24)
= (1/15-11/20)
= - 1/40	[ - ve sigh means emptying]
Volume of 1/40 part	= 3 gallons.
Volume of Whole	= (3×40)
=120 gallons.
Answer C
Answer: (C) 120 gallons
Question: The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $5.20 and the price of commodity Y was $7.30. In which year will the price of commodity X be 90 cents more than the price of commodity Y?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
(E) 2014
Rationale: The price of commodity X increases 25 cents each year relative to commodity Y.
The price difference is $2.10 and commodity X needs to be 90 cents more than commodity Y.
$3.00 / 25 cents = 12 years
The answer is 2001 + 12 years = 2013.
The answer is D.
Answer: (D) 2013
Question: An investment yields an interest payment of $216 each month. If the simple annual interest rate is 9%, what is the amount of the investment?
(A) $28,300
(B) $30,400
(C) $28,800
(D) $32,500
(E) $35,100
Rationale: Let the principal amount = P
Simple annual interest = 9%
Simple monthly interest = (9/12) = (3/4)%
(3/4)*(P/100) = 216
=>P = (216 *4 * 10^2 )/3
= 72*4*10^2
= 288 * 10^2= 28800
Answer C
Answer: (C) $28,800
Question: A group of 5 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 4 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x?
(A) x/70
(B) x/35
(C) 3x/70
(D) 3x/10
(E) 4x/45
Rationale: cost of boat per day = x
cost per person =x/5
if three more persons afre there, cost =x/9
difference = x/5-x/9
=4x/45
Ans E
Answer: (E) 4x/45
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 82%
(B) 52%
(C) 12%
(D) 19%
(E) 22%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Answer: (C) 12%
Question: A river 8m deep and 25 m wide is flowing at the rate of 8 kmph the amount of water that runs into the sea per minute is?
(A) 26666
(B) 26166
(C) 29666
(D) 22666
(E) 26699
Rationale: Rate of water flow-8kmph--8000/60--133.33 m/min
depth of river--8m
width of river--25m
vol of water per min--133.33 *8*25---26666
Answer A
Answer: (A) 26666
Question: In January of 2016, there were 100 cats and 125 dogs in a town. In January of 2017, there were 115 cats and 150 dogs. By approximately what percent did the ratio of cats to dog decrease from the 2016 to 2017.
(A) 12.9%
(B) 11.0%
(C) 15%
(D) 18%
(E) 5%
Rationale: 2016: cats/dogs = 100/125 =660/750
2017: cats/dogs = 115/150 =575/750
ASIDE: It's useful to write both ratios with the same denominator. This allows us to IGNORE the denominator and focus solely on the numerators.
So, our ratio went from 660/750 to 575/750
Ignoring the denominators, we went from 660 to 575
The percent change = 100(difference in values)/(original value)
= (100)(660-575)/660
= (100)(85)/660)
≈ 12.878...
Answer: A
Answer: (A) 12.9%
Question: In a party every person shakes hands with every other person. If there were a total of 171 handshakes in the party then what is the number of persons present in the party ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 171
n(n-1)/2 = 171 âˆ´ n = 19
Answer : Option E
Answer: (E) 19
Question: A goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds. What is the length of the goods train?
(A) 230 m
(B) 270m
(C) 643m
(D) 832m
(E) 290m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 230/26	= 20
x + 230 = 520
x = 290.
Answer:E
Answer: (E) 290m
Question: In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (12, 2), (12,-7)?
(A) 64
(B) 68
(C) 72
(D) 76
(E) 80
Rationale: By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (10 + 9) × 8 = 76.
The answer is D.
Answer: (D) 76
Question: Find the H.C.M of the fractions 1/3, 3/5 and 7/12
(A) 1/30
(B) 1/60
(C) 1/15
(D) 1/20
(E) 1/34
Rationale: Explanation:
H.CF = H.C.F of numarator/L.C.M of denominator
H.C.F = H.C.F of 1, 3, 7 / L.C.M of 3, 5, 12
H.C.F = 1/60
Answer: Option B
Answer: (B) 1/60
Question: A school has 4 section of Chemistry in Class X having 70, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.
(A) 50.9
(B) 52.9
(C) 51.9
(D) 53.25
(E) None of the above
Rationale: Required average marks
= 70Ã—50+35Ã—60+45Ã—55+42Ã—45/70+35+45+42
= 3500+2100+2475+1890/192
= 9965â„192 = 51.90
Answer C
Answer: (C) 51.9
Question: A, B and C can do a work in 90, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
(A) 15
(B) 66
(C) 77
(D) 88
(E) 11
Rationale: One days's work of A, B and C = 1/90 + 1/30 + 1/45
= (1 + 3 + 2)/90 = 1/15
A, B and C together can do the work in 15 days.
Answer:A
Answer: (A) 15
Question: If shares of two persons in profits are Rs.800 and Rs.600 then ratio of their capitals is
(A) 3:4
(B) 2:3
(C) 4:3
(D) 1:3
(E) 1:5
Rationale: total profit =1000
ratio=800/600
=4:3
ANSWER:C
Answer: (C) 4:3