mathewhe/aqua_rat huggingface dataset:
Question: Deby normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Deby averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
(A) 135
(B) 105
(C) 95
(D) 75
(E) 45
Rationale: Deby normally drives to work in 45 minutes at an average speed of 40 miles per hour.Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Answer: (D) 75
Question: In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ?
(A) 5.56 km/hr.
(B) 5.06 km/hr.
(C) 5.76 km/hr.
(D) 6.76 km/hr.
(E) 5.72 km/hr.
Rationale: Time taken by A to cover 100 m =(60 X 60 / 8000)	x 100 sec = 45 sec.
B covers (100 - 4) m = 96 m in (45 + 15) sec = 60 sec.
B's speed = (96 x 60 x 60)/(60 x 1000)km/hr = 5.76 km/hr.
Answer is C
Answer: (C) 5.76 km/hr.
Question: A boat running up stram takes 4 hours to cover a certain distance, while it takes 8 hours to cover the same distance running down stream. what is the ratio between the speed of the boat and the speed of water current respectively?
(A) 2 : 3
(B) 5 : 6
(C) 4 : 5
(D) 3 : 1
(E) 8 : 1
Rationale: Explanation:
Let speed of boat is x km/h and speed stream is y km/hr
4(x+y) = 8(x-y)
4x+4y = 8x-8y
12y = 4x
3y = x
x/y = 3/1
3 : 1
Answer: Option D
Answer: (D) 3 : 1
Question: Jane received an assorted bouquet of 25 flowers which included 8 white flowers,7 lavender flowers and 9 purple flowers.
She closed her eyes a pulled one flower from the bouquet. She opened her eyes, noticed that it was white and placed it aside. She closed her eyes and pulled a 2nd flower from the bouquet. What is the probability that the 2nd flower will also be white?
(A) 8/25
(B) 7/24
(C) 7/25
(D) 8/25
(E) 9/15
Rationale: Solution: Initially, there are 25 flowers total. After the first white flower is removed, 7 white flowers remain and a total of 24 flowers overall are left in the bouquet.
Probability = Favorable outcomes / Total out comes
Therefore, probability = 7/24
Answer Option: B
Answer: (B) 7/24
Question: A man travelled from the village to the post-office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village
(A) 20
(B) 87
(C) 276
(D) 198
(E) 171
Rationale: Explanation:
Average speed = (2 ×a × b)/(a + b) here a = 25 b = 4
Average speed = 2 × 25 × 4/(25 + 4) = 200/29 kmph.
Distance covered in 5 hours 48 minutes = Speed × time
Distance = (200/29) × (29/5) = 40 kms
Distance covered in 5 hours 48 minutes = 40 kms
Distance of the post office from the village = (40/2) =20 km.
Answer: A
Answer: (A) 20
Question: The mean of 50 observations is 200. But later he found that there is decrements of 15 from each observations. what is the the updated mean is ?
(A) 165
(B) 185
(C) 198
(D) 221
(E) 240
Rationale: 185
Answer is B
Answer: (B) 185
Question: Let R1 and R2 respectively denote the maximum and minimum possible remainders when (276)n is divided by 91 for any natural number n,n>= 144. Find R1+R2.
(A) 89
(B) 90
(C) 91
(D) 92
(E) 93
Rationale: But the least value for n can be= 144 (as given in question, n>=144)
So, 3n/91= 3*144/91= 68
now, the highest remainder can be when it reaches 68+3+3+3+3+3+3+3= 89
(as each time we increment n by 1 the remainder increases by 3,
3*145/91= 71- remiander
3*146/91= 74
3*147/91=77
... so on and so far upto 89 after which it becomes 89+3= 92 which means it crosses 91)
Hence least remainder would be 92 -91=1
and highest remainder = 89
R1+ R2= 89+1 = 90
ANSWER:B
Answer: (B) 90
Question: Set A contains all the even numbers between 12 and 60 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 850
(B) 1250
(C) 1650
(D) 2050
(E) 2450
Rationale: Each term in set B is 50 more than the corresponding term in set A.
The difference of the sums = 25 * 50 = 1250.
The answer is B.
Answer: (B) 1250
Question: The average (arithmetic mean) of four different positive integers is 10. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 0
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 10
=> 5x + 2 + a = 40
=> 5x + a = 40
=> a = 40 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=8
This gives us a= 40 - 40 = 0
Therefore the minimum value that the fourth integer can have is 0. Option E.
Answer: (E) 0
Question: 38, 85, 22,75, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
(A) a- 56
(B) b- 68
(C) c- 69
(D) d- 71
(E) e- 78.5
Rationale: Important:- Arrange the numbers in ascending order first.
13, 22, 31, 38, 47, 75, 82, 85
3/4th of the number list represents- 75 (6th number)
remaining 1/4th list represents 82 (7 th number)
78.5 fits in between above 2
Answer:- E
Answer: (E) e- 78.5
Question: Here is a simple arithmetical puzzle in his own flowery, poetical language.
If one-fifth of a hive of bees flew to the badamba flower, one-third flew to the slandbara, three times the difference of these two numbers flew to an arbour, and one bee continued to fly about, attracted on each side by the fragrant Ketaki and Malati, what was the total number of bees?
(A) 11
(B) 15
(C) 18
(D) 17
(E) 19
Rationale: B
15
The number of bees was 15
Answer: (B) 15
Question: Machine A and machine R are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine R. Machine R produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: [Reveal]Spoiler:
TimeR: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6
Answer: (A) 6
Question: How many positive even integers less than 100 contain digits 3 or 9?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 10
Rationale: Two digit numbers:
3 at tens place: 30,32,34,36,38
9 at tens place: 90,92,94,96,98
If 3 and 7 is at units place, the number cant be even
Total:5+5= 10
Answer E
Answer: (E) 10
Question: For any a and b that satisfy |a – b| = b – a and a > 0, then |a + 2| + |-b| + |b – a| + |ab| =
(A) -ab + 3
(B) ab + 2b + 2
(C) ab + 2b – 2a – 3
(D) -ab + 2b + 3
(E) ab + 3
Rationale: Observation-1: |a – b| = b – a
which is possible only when signs of a and b are Same
Since Given a > 0
so we figure out that a and b are both positive
Observation-2: |a – b| must be Non-Negative and so should be the value of b-a which is possible only when absolute value of b is greater than or equal to absolute value of a
Now you may choose the values of a and b based on above observations
e.g. b = 2 and a=1 and check the value of given functions and options
|a + 2| + |-b| + |b – a| + |ab| = |1 + 2| + |-2| + |2 – 1| + |1*2| = 8
-ab + 3 = -1*2+3=1
ab + 2b + 2= 1*2+4+2=8
ab + 2b – 2a – 3=1*2+2*2-2*1-3=1
-ab + 2b + 3=5
ab + 3=5
Answer : B
Answer: (B) ab + 2b + 2
Question: Rathi took a loan for 6 years at the rate of 5% per annum on Simple Interest, If the total interest paid was Rs. 1230, Find the principal amount?
(A) 4000
(B) 3500
(C) 3100
(D) 4100
(E) 5000
Rationale: P = SI * 100/R*T
P = 1230*100/6*5==>4100
ANSWER D
Answer: (D) 4100
Question: Winson will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
(A) 5
(B) 6
(C) 9
(D) 24
(E) 26
Rationale: Winson will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: (A) 5
Question: Two employees A and B are paid a total of Rs. 550 per week by their employer. If A is paid 150 percent of the sum paid to B, how much is B paid per week?
(A) 130
(B) 140
(C) 150
(D) 220
(E) 280
Rationale: Let the amount paid to A per week = x
and the amount paid to B per week = y
Then x + y = 550
But x = 150% of y = 150y/100 = 15y/10
∴15y/10 + y = 550
⇒ y[15/10 + 1] = 550
⇒ 25y/10 = 550
⇒ 25y = 5500
⇒ y = 5500/25 =Rs.220
D)
Answer: (D) 220
Question: A military garrison in a wild frontier has 600 men who have provisions to last 22 weeks. At the end of 6 weeks they are joined by another 300 men. How long will the provisions last?
(A) 13 1/3
(B) 12 1/3
(C) 10 2/3
(D) 12 1/2
(E) 12 3/4
Rationale: Total provisions=600*22*7=92400
Provisions used for in 6 weeks=6*7*600=25200
remaining provisions=67200
remaining provisions need to be split between 900(600+300) people.
Number of provisions per person= 67200/900
we need to find the answer in terms of weeks=(67200/900)/7=10 2/3
Answer:C
Answer: (C) 10 2/3
Question: I sold a book at a profit of 10%. Had I sold it for $110 more, 15% would have been gained. Find the cost price?
(A) $2000
(B) $2200
(C) $3000
(D) $3120
(E) $1540
Rationale: 115% of cost - 110% of cost = $110
5% of cost = $110
cost = 110*100/5 = $2200
Answer is B
Answer: (B) $2200
Question: eleven books,consisting of 5 engineering books , 4 maths books,2 physics books are arranged in a shelf at random .what is the probability that books of each kind are all together?
(A) 0.001443
(B) 0.002443
(C) 0.003443
(D) 0.004443
(E) 0.005443
Rationale: 3 lots can be arranged in 5!x3!x4!x2!
total arrangements possible= 11!
hence probability of the same=(5!x3!x4!x2!)/11!=0.001443
ANSWER:A
Answer: (A) 0.001443
Question: If x > 6 and y < -6, then which of the following must be true ?
(A) x/y > 1
(B) x/y < -1
(C) x/y < 0
(D) x + y > 0
(E) xy > 0
Rationale: Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
D should be the answer.
Answer: (D) x + y > 0
Question: If the probability of rain on any given day in City X is 50%, what is probability that it rains on exactly 3 days in a 4 day period?
(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16
(E) 3/16
Rationale: One possible way is rain-rain-rain-no rain.
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
The number of possible ways is 4C3 = 4, so we multiply this by 4.
P(rain on exactly 3 days) = 4*1/16 = 4/16 = 1/4
The answer is B.
Answer: (B) 1/4
Question: An escalator moves towards the top level at the rate of 11 ft.sec and its length is 140 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.
(A) 14 sec
(B) 10 sec
(C) 12 sec
(D) 8 sec
(E) 9 sec
Rationale: Time taken to cover the entire length = tot.dist/resultant speed
= 140/ (11+3)
= 10sec
ANSWER:B
Answer: (B) 10 sec
Question: A seller has 1000 kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is?
(A) 350 kg
(B) 360 kg
(C) 400 kg
(D) 600 kg
(E) 700 kg
Rationale: By rule of alligation,
Profit% by selling 1st part Profit% by selling 2nd part
8 18
Net % profit
14
18-14=4 14-8=6
=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3
Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit)
=1000×35
= 600 kg
D
Answer: (D) 600 kg
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 24 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
(A) 240 m
(B) 180 m
(C) 260 m
(D) 224 m
(E) 239 m
Rationale: A
180 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 24)m = 360 m.
Let the length of the platform be x metres.
Then, (x + 360)/36 = 15
--> x + 360 = 540
x = 180m. B
Answer: (B) 180 m
Question: A and B tanks are there. 1/8th of the tank B is filled in 22Hrs. What is time to fill the full tank
(A) 175
(B) 176
(C) 177
(D) 178
(E) 179
Rationale: 1/8th = 22 hrs
therefore entire tank is 8 x 22.
176hrs
Full tank ll be filled in 176 hrs
ANSWER:B
Answer: (B) 176
Question: Jerry is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 mint , and the remainder an even mixture of salt, pepper and sugar. If Jerry accidentally doubles the mint and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
(A) 15/29
(B) 5/8
(C) 5/16
(D) 1/2
(E) 13/27
Rationale: Olive oil = 5/8 = 15/24 --> 15 parts out of 24;
mint = 1/4 = 6/24 --> 6 parts out of 24;
Salt + pepper + sugar = 1-(15/24+6/24)= 3/24, so each = 1/24 --> 1 part out of 24 each;
If mint = 12 (instead of 6) and sugar = 0 (instead of 1) then total = 15+12+1+1+0 = 29 parts out of which 15 parts are olive oil --> proportion = 15/29.
Answer: A.
Answer: (A) 15/29
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9 ?
(A) 0.15
(B) 0.2
(C) 0.25
(D) 0.3
(E) 0.33
Rationale: The total number of pairs possible is 4*5=20. Out of these 20 pairs only 4 sum up to 9: (2, 7); (3, 6), (4, 5) and (5, 4). The probability thus is 4/20=0.2.
Answer: B.
Answer: (B) 0.2
Question: If CRY is coded as MRYC then how will GET be coded?
(A) MTEG
(B) MGET
(C) MEGT
(D) METG
(E) None of these
Rationale: The letters of word (1)(2)(3) is written by prefixing M and ordering letters
(2)(3)(1)
So GET= METG
ANSWER:D
Answer: (D) METG
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 77 cm2
(B) 66 cm2
(C) 54 cm2
(D) 44 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer: E
Answer: (E) 35 cm2
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 22
(B) 17
(C) 25
(D) 27
(E) 12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75) = 25 points to C.Answer: C
Answer: (C) 25
Question: A motorist knows five different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
(A) 4
(B) 8
(C) 12
(D) 24
(E) 30
Rationale: Explanation:
Total number of routes from Bristol to Carlisle = (5 x 3 x 2) = 30.
Answer: E
Answer: (E) 30
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
(A) 65 liters
(B) 88 liters
(C) 10 liters
(D) 45 liters
(E) 8 liters
Rationale: Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters. Answer: C
Answer: (C) 10 liters
Question: A number whose one-fourth part is increased by 5 is equal to the third part diminished by 5.
(A) 100
(B) 80
(C) 120
(D) 60
(E) 50
Rationale: Explanation:
Let the number be x. Then,
x/4 + 5 = x/3 - 5 => x/4 - x/3 = -10
=> 3x - 4x = -120
=> x = 120
Answer: Option C
Answer: (C) 120
Question: When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 5. If 1 < m < 300, what is the greatest possible value of m?
(A) 160
(B) 180
(C) 200
(D) 220
(E) 240
Rationale: 13*9 = 117
Let's start with 5, and keep adding 13 until we find a number with the form 9k+2.
5, 18, 31, 44, 57, 70, 83 = 9*9+2
The next possible number is 83 + 117 = 200
The next possible number would be greater than 300.
The answer is C.
Answer: (C) 200
Question: What should come in place of the question mark(?) in each of the following questions ?
6% of 350+ (?)% of 200 = 75% of 40
(A) 5
(B) 4.5
(C) 5.5
(D) 7
(E) 8
Rationale: Explanation :
let x% of 220 = 75% of 40 - 60% of 350 = 9 or x=9x100/220 = 45/11 = 4.09
Answer : Option B
Answer: (B) 4.5
Question: If a is an odd integer and b is an even integer which of the following must be an integer :
(A) a/b
(B) ab
(C) 2a+b
(D) 2(a+b)
(E) option B C and D
Rationale: a= odd = e.g 3
b=even = e.g 6
A. odd/even for example 3/6 = 0.5 no even no odd
B. odd * even = 3 * 6 = 18 even
C. 2*odd + even = even + even even
D. 2(even + odd) = 2(odd) even
Hence E it is.
Answer: (E) option B C and D
Question: In Jessica's opinion, her weight is greater than 65 kg but less than 72 kg. Her brother doest not agree with Jessica and he thinks that Jessica's weight is greater than 60 kg but less than 70 kg. Her mother's view is that her weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Jessica?
(A) 67 kg.
(B) 68 kg.
(C) 69 kg.
(D) Data inadequate
(E) None of these
Rationale: Explanation: Let Jessica's weight by X kg.
According to Jessica, 65 < X < 72
According to Jessica's brother, 60 < X < 70.
According to Jessica's mohter, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required average= (66+67+68 /3) = (201 /3) = 67kg
Answer: Option A
Answer: (A) 67 kg.
Question: List D consists of 12 consecutive integers. If -4 is the least integer in list D, what is the range of positive integers in list D?
(A) 5
(B) 6
(C) 7
(D) 11
(E) 12
Rationale: Since -4 is the least integer in list D, then 7 is the largest integer in that list. Thus the range of the positive integers in the list is 7-1=6.
Answer: B.
Answer: (B) 6
Question: If n and k are integers whose product is 4900, which of the following statements must be true?
(A) n+k>0
(B) n does not equal k
(C) Either n or k is a multiple of 10
(D) If n is even, then k is odd
(E) If n is odd, then k is even
Rationale: If n is odd and k is odd, then the product is odd.
The answer is E.
Answer: (E) If n is odd, then k is even
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) 140
(B) 130
(C) 120
(D) 150
(E) 145
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
Answer is E.
Answer: (E) 145
Question: Find the best average of the first 10 multiples of 7....
(A) 30.5
(B) 38.5
(C) 40
(D) 43.5
(E) 55.5
Rationale: the exp is - 7(1+2+3+4+5+6+7+8+9+10)/10 =>
7(10(10+1)/10*2 =>
7(110)/10*2 = 38.5
ANSWER B
Answer: (B) 38.5
Question: What is 35% of 4/13 of 845?
(A) 58
(B) 69
(C) 80
(D) 91
(E) 102
Rationale: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 845, or 1/9 of 845. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 845 is a bit more than 810, so (1/9)*845 will be a bit more than 90.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 91, so this is the answer to choose.
The answer is C.
Answer: (C) 80
Question: Which of these expressions has the greatest value?
(A) 1856721/1856725
(B) 1288542/1288743
(C) 1354321/1314325
(D) 1608521/1608526
(E) 1532156/1532159
Rationale: Using elimination method on options
1354321/1314325 = 1.03043082951...
ANSWER:C
Answer: (C) 1354321/1314325
Question: For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 2/7, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
(A) 5/27
(B) 2/9
(C) 1/2
(D) 4/9
(E) 2/3
Rationale: P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)
P(of burning out in 1st 6 mnth)= 2/7
--->P( of not burning out in 1st 6 mnth)=1-2/7=5/7
---->P(of not burning out in a six mnth period)=1/2 *5/7=1/3
--->P(of burning out in a six mnth period)=1-1/3=2/3
now
P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)
=5/7 * 2/3=1/2
Ans C
Answer: (C) 1/2
Question: What day of the week does May 28 2006 fall on
(A) Saturday
(B) Monday
(C) Sunday
(D) Thursday
(E) Tuesday
Rationale: Explanation :
28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday
Answer : Option C
Answer: (C) Sunday
Question: If $2000 was invested at an annual interest rate of 5.6% compounded annually, which of the following represents the amount the investment was worth after 3 years?
(A) 2000 (1.056)(3)
(B) 2000 (1.056)^3
(C) 2000 (1+3(0.056))
(D) 2000 (1+(0.056)^3)
(E) 2000 (3+1.056)
Rationale: the formula is CI=P(1+r/100)^t
in this case i think B is the ans
Answer: (B) 2000 (1.056)^3
Question: The heights of three individuals are in the ratio 4 : 5 : 6. If the sum of the heights of the heaviest and the lightest boy is 150cm more than the height of the third boy, what is the weight of the lightest boy?
(A) 120cm
(B) 150cm
(C) 160cm
(D) 190cm
(E) of these
Rationale: Let the heights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 150
=> 5k = 150=> k = 30
Therefore the height of the lightest boy
= 4k = 4(30) = 120 cm.
ANSWER:A
Answer: (A) 120cm
Question: The sum of number of boys and girls in a school is 400. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
(A) 50
(B) 40
(C) 60
(D) 80
(E) 70
Rationale: We have x+x% of 400 = 400
x + x/100 * 400 = 400
5 * x = 400
x = 80
Answer is D
Answer: (D) 80