mathewhe/aqua_rat huggingface dataset:
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many Q different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
(A) 5
(B) 6
(C) 9
(D) 12
(E) 18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible Q is 2*6=12.
Answer: D.
Answer: (D) 12
Question: John and Peter are among the eight players a basketball coach can choose from to field a five-player team. If all five players are chosen at random, what is the probability of choosing a team that includes John and Peter?
(A) 2/5
(B) 2/7
(C) 2/9
(D) 5/14
(E) 8/21
Rationale: The total possible ways of selecting a 5-member team is 8C5 = 56
The possible ways which include John and Peter is 6C3 = 20
The probability of choosing both John and Peter is 20/56 = 5/14
The answer is D.
Answer: (D) 5/14
Question: Randy can rebuild an automobile engine in b hours. Alvin can rebuild the same engine in a hours. If Randy and Alvin work together at their respective rates to rebuild the engine, which of the following represents the portion of the job that Randy will not have to complete?
(A) ab/(a+b)
(B) (a-b)/(a+b)
(C) b/(b+a)
(D) a/(a+b)
(E) b/(a-b)
Rationale: Randy can do the job in a hrs, Alvin can do the job in b hrs.
When they work together, you need to find the fraction of work that Randy doesn't need to do i.e. the fraction that will be done by Alvin.
Ratio of Randy's speed:Alvin's speed = b:a (since time taken by them is in the ratio a:b)
So Randy does a/(a+b) of the work and Alvin does b/(a+b) of the work.
Answer (C).
Answer: (C) b/(b+a)
Question: A train ride from Two P to Town Q costs $6.35 more than does a bus ride from Town P to Town Q. Together, the cost of one train ride and one bus ride is $9.85. What is the cost of a bus ride from Town P to Town Q?
(A) $1.75
(B) $2.50
(C) $4.10
(D) $4.70
(E) $8.20
Rationale: Let x be the cost of a bus ride.
x + (x+635) = 985
2x = 350
x = $1.75
The answer is A.
Answer: (A) $1.75
Question: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.
When everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.
So they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.
Finally, they woke up the 7th thief and this time the diamonds were divided equally.
How many diamonds did they steal in total?
(A) 300
(B) 301
(C) 302
(D) 303
(E) None
Rationale: They stole 301 diamonds in total.
We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60.
60 + 1 = 61, not a multiple of 7
60 x 2 + 1 = 121, not a multiple of 7
60 x 3 + 1 = 181, not a multiple of 7
60 x 4 + 1 = 241, not a multiple of 7
60 x 5 + 1 = 301, a multiple of 7
Answer B
Answer: (B) 301
Question: How many seconds will a 500 m long train take to cros a man walking with a speed of 3 kmph in the direction of the moving train if the speed of the train is 63 kmph
(A) 25
(B) 30
(C) 40
(D) 45
(E) 50
Rationale: time=distance(here length of the train)/relative speed (63-3)
thus time=500/60*5/18=500*18/ 60*5
=30 seconds
ANSWER:B
Answer: (B) 30
Question: If there are Six periods in each working day of a school, In how many ways can one arrange 5 subjects such that each subject is allowed at least one period?
(A) 2388
(B) 3600
(C) 2791
(D) 1817
(E) 1911
Rationale: To arrange 6 periods with 5 subjects, then one subject can be arranged in two slots.
5 Subjects can be arranged in 6 periods in 6P56P5 ways and now we have 1 period which we can fill with any of the 5 subjects in 5 ways. so 6P5×5=6P5×5=3600
Alternate method:
Assume the subjects are X1, X2, A, B , C, D,. Here X is the subject which repeats. So arranging 6 objects in 6 places will be equal to 6! = 720 (here no need to divide this number with 2! as even though the subject is same, but not identical)
But this repeated subect can be any of the five. So total arrangements are 720 x 5 = 3600
Answer:	B
Answer: (B) 3600
Question: If 5√5 x 5^3 + 5^-3/2 = 5 ^(a + 2), then the value of a is:
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: 5^1x5^1/2x5^3+5^-3/2 = 5^(a+2)
5^3/2x5^3+5^-3/2
5^9/2+5^-3/2
5^6/2
5^3 = 5^(a+2)
now, 3 = a+2
a=1
ANSWER:B
Answer: (B) 1
Question: The diagonals of a rhombus are 10 cm and 12 cm. Find its area?
(A) 158
(B) 60
(C) 150
(D) 123
(E) 117
Rationale: 1/2 * 10 * 12 = 60
Answer:B
Answer: (B) 60
Question: A and B start a business with investments of Rs.5000 and Rs.4500 respectively.After 4 months,A takes out half of his capital.After two more months,B takes out one-third of his capital while C joins them with a capital of Rs.7000.At the end of a year,they earn a profit of Rs.5080.Find the share of each member in the profit.
(A) A - Rs.1400,B - Rs.1900,C - Rs.1780
(B) A - Rs.1600,B - Rs.1800,C - Rs.1680
(C) A - Rs.1800,B - Rs.1500,C - Rs.1780
(D) A - Rs.1680,B - Rs.1600,C - Rs.1800
(E) None of these
Rationale: Solution
A : B : C =(5000x4+2500x8) : (4500x6+3000x6): (7000x6)
= 40000 : 42000 : 45000 = 4 : 42 : 45.
A’s share = Rs. (5080x40/127) = Rs. 1600.
B’s share = Rs. (5080x45/127) = Rs. 1800.
C’s share = Rs. (5080x42/127) = Rs. 1680. Answer B
Answer: (B) A - Rs.1600,B - Rs.1800,C - Rs.1680
Question: What is the least number should be added to 1100, so the sum of the number is completely divisible by 23?
(A) 1
(B) 2
(C) 5
(D) 4
(E) 8
Rationale: (1100 / 23) gives remainder 19
19 + 4 = 23, So we need to add 4
Answer : D
Answer: (D) 4
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) 22
(B) 50
(C) 99
(D) 288
(E) 12
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: If d<0, which of the following represents a positive number?
(A) d|d|
(B) |d|d
(C) |d|/d
(D) -d|d|
(E) d/ |d|
Rationale: Answer : D
Answer: (D) -d|d|
Question: A circular mat with diameter 18 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
(A) 5/12
(B) 3/5
(C) 1/2
(D) 3/8
(E) 5/6
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(9)(9)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(81/24)
I hope this is easy to follow, so with some simplification i get (1/8)(3) = (3/8) Answer is D
Answer: (D) 3/8
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 7/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
(A) 9/80
(B) 3/10
(C) 387/800
(D) 35/80
(E) 497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 21/80 = 59/80
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (59/80)(7/10) = 1 - 413/800 = 387/800
C
Answer: (C) 387/800
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 24 days, then C alone can do it in?
(A) 1
(B) 7
(C) 8
(D) 9
(E) 6
Rationale: C = 1/4 - 1/12 – 1/24 = 1/8 => 8 days'
Answer: C
Answer: (C) 8
Question: If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
(A) 16 2/3%
(B) 16 2/6%
(C) 16 8/3%
(D) 17 2/3%
(E) 16 2/1%
Rationale: Let the price of the article be Rs. 100.
20% of 100 = 20.
New price = 100 + 20 = Rs. 120
Required percentage = (120 - 100)/120 * 100
= 20/120 * 100 = 50/3 = 16 2/3%.
Answer:A
Answer: (A) 16 2/3%
Question: Both Robert and Alice leave from the same location at 6:00 a.m. driving in the same direction, but in separate cars. Robert drives 30 miles per hour while Alice drives 40 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?
(A) 2 p.m.
(B) 3 p.m.
(C) 4 p.m.
(D) 8 p.m.
(E) 9 p.m.
Rationale: 6:00 am so 6 hours later is 12:00 pm
In six hours, Robert will have driven 6*30 = 180 miles
In six hours, Alive will have driven 6*40 = 240 miles
So Robert needs 240-180 = 60 miles do catch Alice up.
So at 30 mph, he will need 2 hours
12:00 pm + 2 hours = 2:00 pm
ANS : A
Answer: (A) 2 p.m.
Question: a merchant sold an article at a loss of 12%,. if the selling price had been increased by $50 the merchant would have made a profit of 8%. what is the cost price of the article?
(A) $550
(B) $500
(C) $510
(D) $565
(E) $520
Rationale: Let C.P. be $x
Then 108% of x - 88% of x = 100
20% of x = 100
x/5 = 100
x = 500
Answer is B
Answer: (B) $500
Question: Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year 12 members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 0 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
(A) 52
(B) 67
(C) 71
(D) 66
(E) 79
Rationale: n(E or F or I) = n(E) + n(F) + n(I) - n(E and F) - n(F and I) - n(I and E) +n(E and F and I)
n(E or F or I) = 26 + 26 + 32 - 12 - 0 - 6 + 0
Why is the number of people who traveled to E and F and I 0? Because no one traveled to both England and France. So obviously, no one would have traveled to England, France and Italy.
n(E or F or I) = 66
Answer (D)
Answer: (D) 66
Question: A glass was filled with 25 ounces of water, and 0.04 ounce of the water evaporated each day during a 10-day period. What percent of the original amount of water evaporated during this period?
(A) 0.004%
(B) 0.04%
(C) 0.4%
(D) 1.6%
(E) 20%
Rationale: In 10 days 10*0.04=0.4 ounces of water evaporated, which is 0.4/25âˆ—100=1.6 of the original amount of water.
Answer: D.
Answer: (D) 1.6%
Question: How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length?
(A) 12.9 sec
(B) 12.1 sec
(C) 24.2 sec
(D) 16.8 sec
(E) 14.9 sec
Rationale: Speed = 36 * 5/18 = 10 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/10 = 24.2 sec.
Answer: C
Answer: (C) 24.2 sec
Question: The wheel of a motorcycle 70cm in diameter makes 40 revolutions in every 10sec.What is the speed of motorcycle n km/hr?
(A) 31.65
(B) 31.68
(C) 31.62
(D) 31.61
(E) 31.67
Rationale: Explanation:
In this type of question, we will first calculate the distance covered in given time.
Distance covered will be : Number of revolutions x Circumference
So we will be having distance and time, from which we can calculate the speed.
Radius of wheel = 70 / 2 = 35 cm
Distance covered in 40 revolutions will be = 88 m
Distance covered in 1 sec =
Answer: B) 31.68kmph
Answer: (B) 31.68
Question: On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. Find the divisor.
(A) 179
(B) 189
(C) 199
(D) 169
(E) None of them
Rationale: Divisor = Dividend - Remainder / Quotient
= 15968-37 / 89
= 179.
Answer is A.
Answer: (A) 179
Question: A garrison of 500 persons had provisions for 27 days. After 3 days a reinforcement of 300 persons arrived. For how many more days will the remaining food last now?
(A) 12 days
(B) 16 days
(C) 14 days
(D) 15 days
(E) None of these
Rationale: Explanation :
Given that fort had provision for 500 persons for 27 days
Hence, after 3 days, the remaining food is sufficient for 500 persons for 24 days
Remaining persons after 3 days = 500 + 300 = 800
Assume that after 10 days,the remaining food is sufficient for 800 persons for x days
More men, Less days (Indirect Proportion)
⇒Men500:800}::x:24
⇒500 × 24 = 800x
⇒ 5 × 24 = 8x
⇒ x = 5 × 3 = 15. Answer : Option D
Answer: (D) 15 days
Question: A business executive and his client are charging their dinner tab on the executive's expense account.The company will only allow them to spend a total of 75$ for the meal.Assuming that they will pay 7% in sales tax for the meal and leave a 15% tip,what is the most their food can cost?
(A) 69.55$
(B) 50.63$
(C) 60.95$
(D) 52.15$
(E) 53.15$
Rationale: let x is the cost of the food
1.07x is the gross bill after including sales tax
1.15* 1.07x=75
x=60.95
Hence, the correct option is C
Answer: (C) 60.95$
Question: A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 2 gallons of paint cover an area of 3P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
(A) 440P/mx
(B) 880mx/P
(C) 880mx/3P
(D) 1760mx/3P
(E) 1760P/3mx
Rationale: 1 square foot needs 2/3P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For two stripes, the total area is 880mx square feet.
The number of gallons needed is (880mx)*(2/3P) = 1760mx/3P gallons.
The answer is D.
Answer: (D) 1760mx/3P
Question: A train 330 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) 6
(C) 7
(D) 18
(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 = [330 * 3/55] sec
= 18 sec
Answer: D
Answer: (D) 18
Question: What sum of money will produce Rs.70 as simple interest in 4 years at 3 1/2 percent?
(A) 288
(B) 500
(C) 299
(D) 2766
(E) 2912
Rationale: 70 = (P*4*7/2)/100
P = 500.Answer: B
Answer: (B) 500
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/487
(C) 1/429
(D) 1/876
(E) 1/429
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue
= 3C3/15C3
= (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer:A
Answer: (A) 1/455
Question: r=4^(n+2), then in terms of r, 9^n=
(A) r^2/81
(B) r^2/9
(C) r^2/256
(D) r/3
(E) r
Rationale: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 4^2 = 16
and you need the value of 16^n which is 16^0 = 1
So when you put r = 16 in the options, you should get 1. Only option (A) satisfies.
Answer (C)
Answer: (C) r^2/256
Question: How many positive integers Q between 200 and 300 (both inclusive) are not divisible by 2, 3 or 5?
(A) 3
(B) 16
(C) 75
(D) 24
(E) 26
Rationale: 1) I figured there are 101 integers (300 - 200 + 1 = 101). Since the set begins with an even and ends with an even, there are 51 evens.
2) Question says integers are not divisible by 2, leaving all of the odds (101 - 51 = 50 integers).
3) Question says integers are not divisible by 5, removing all the integers ending in 5 (already took out those ending in 0). Take out 10 integers (2?5, ? = 0 to 9), leaving us with 40 integers.
4) Now the painstaking part. We have to remove the remaining numbers that are multiples of 3. Those are 201, 207, 213, 219, 231, 237, 243, 249, 261, 267, 273, 279, 291, and 297...a total of 14 numbers. 26 numbers left!
6) Answer choice E.
Answer: (E) 26
Question: Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
(A) 30%
(B) 100/3%
(C) 35%
(D) 44%
(E) None of these
Rationale: Explanation :
C.P. of 6 articles = Rs. 5
=> C.P. of 1 article = Rs. 5/6
S.P. of 5 articles = Rs. 6
=> S.P. of 1 article = Rs. 6/5
Profit earned per article = 6/5 - 5/6 = 11/30
% Profit = 11/30∗6/5∗100% = 44%
Answer : D
Answer: (D) 44%
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 1
Rationale: flight ==> x hrs
600/x - 600/x+1/2 = 200
x(2x+1) = 3
2x2+x-3=0
x=1
ANSWER E
Answer: (E) 1
Question: Three coins are tossed. What is the probability of getting at most two tails?
(A) 2
(B) 6/7
(C) 7/8
(D) 25
(E) 5/1
Rationale: Explanation :
Total number of outcomes possible when a coin is tossed = 2
Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 × 2 × 2 = 8
E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}
Hence, p(E)=n(E)/n(S)=7/8
C
Answer: (C) 7/8
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 38 years. What is the age of Deepak at present?
(A) 77 years
(B) 15 years
(C) 66 years
(D) 24 years
(E) 55 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 38 => x = 8
Deepak's age = 3x = 24 years.
Answer: D
Answer: (D) 24 years
Question: A can do a piece of work in 20 days and B can do it in 30 days and C can do it 10 days. They started the work together and A leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost?
(A) 13
(B) 16
(C) 25
(D) 14
(E) 15
Rationale: 2/20 + x/30 + 4/10 = 1
x = 300/20= 15
Answer: E
Answer: (E) 15
Question: Two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds. The ratio of their speeds is:
(A) 1 : 1
(B) 3 : 2
(C) 3 : 8
(D) 3 : 25
(E) 3 : 4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 20 x meters, and length of the second train = 18 y meters. (20 x + 15 y) / (x + y) = 19
==> 20 x + 18 y = 19 x + 19 y ==> x = y ==> x/y = 1/1
Answer: Option A
Answer: (A) 1 : 1
Question: Find the value of 72519 x 9999 = m?
(A) 34545481
(B) 45461743
(C) 24117456
(D) 725117481
(E) 45541177
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20 % premium . If the company declares 5% dividend at the end of the year , then how much does he get ?
(A) 500
(B) 600
(C) 650
(D) 700
(E) 750
Rationale: No of shares = 14400/120 = 120
Face value = 100*120 = 12000
Annual income = 5/100*12000 = 600
ANSWER B
Answer: (B) 600
Question: A trader sells 75 meters of cloth for Rs. 4950 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) 51
(B) 88
(C) 90
(D) 42
(E) 22
Rationale: SP of 1m of cloth = 4950/75 = Rs. 66
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 66 - Rs. 15 = Rs. 51
Answer:A
Answer: (A) 51
Question: Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 2, she will stop rolling the cube. What is the probability that Molly will roll the die less than 2 times before stopping?
(A) 11/180
(B) 1/6
(C) 25/216
(D) 91/216
(E) 27/128
Rationale: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:
The probability that Molly will roll the die once: P=1/6 (she gets 2 on the first roll);
P = 1/6
Answer: B
Answer: (B) 1/6
Question: There are 11 boys and 10 girls in a class. If three students are selected at random, in how many ways that 3 girl & 2 boys are selected ?
(A) 6600
(B) 1300
(C) 6780
(D) 1976
(E) 2448
Rationale: E = event that 3 girl and 2 boys are selected
n(E) = we have to select 2 boys from 11 and 3 girl from 10
= 11C2 * 10C3
= 6600
Ans - A
Answer: (A) 6600
Question: What is the sum of the different positive prime factors of 380?
(A) 5
(B) 10
(C) 15
(D) 17
(E) 26
Rationale: Prime factorization of 380
=38 * 10
=2*19 * 10
=2*19 * 2*5
=2^2 * 5 * 19
Sum of the different positive prime factors of 380 = 2+5+19
=26
Answer E
Answer: (E) 26
Question: If the population of a certain country increases at the rate of 1 person every 60 seconds, by how many persons does the population increase in 2 Hours?
(A) 120
(B) 80
(C) 100
(D) 150
(E) 140
Rationale: Answer = 1 * 120(2 hour = 120 minutes)= 120
Answer = A
Answer: (A) 120
Question: Reena and Shaloo are partners in a business, Reena invests Rs, 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months, out of a profit of Rs. 31,570, Reena's share is ?
(A) 12628
(B) 12228
(C) 22812
(D) 12727
(E) 11922
Rationale: Ratio of their shares = (35000 * 8) : (42000 * 10) = 2 : 3.
Reena's share Rs. 31570 * (2 / 5) = Rs. 12628
Answer: A
Answer: (A) 12628
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 535 m
(B) 178 m
(C) 186 m
(D) 168 m
(E) 150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 9
= 150 m
Answer:E
Answer: (E) 150 m
Question: A four-character password consists of one letter of the alphabet and three different digits between 1 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 5,040
(B) 18,720
(C) 26,208
(D) 37,440
(E) 52,000
Rationale: 4 character password: DLDD
First digit can be chosen in 9 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 8 ways.
Next digit can be chosen in 7 ways.
This gives us 9*26*8*7ways
Now, the letter can also be DDLD so there will be another 9*26*8*7 ways
Total = 9*26*8*7*2 = 26,208 ways C
Answer: (C) 26,208
Question: Factor | Percent of Respondents |
User-friendly | 56% |
Fast response time | 48% |
Bargain prices | 42% |
The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,100 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”
(A) 286
(B) 336
(C) 360
(D) 384
(E) 420
Rationale: The way I looked at is is as follows:
UserFriendly(UF) + FastResponse (FR) = 30%
UF leftover = 56 - 30 = 26%
FR leftover = 48 - 30 = 18%
Sum these = 74% (ie. 74% were either UF+FR, UF, FR)
26% leftover is the maximum number for Bargain Price
26/100 * 1100 = 26 * 11 = 286 (A).
Answer: (A) 286
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 25 gallons of gasoline?
(A) 190
(B) 284.6
(C) 300
(D) 305
(E) 312
Rationale: To maximize the distance that SUV could be driven on 25 gallons of gasoline , we need consider only highway driving .
Max distance = 25 * 12.2 = 305
Answer D
Answer: (D) 305