divelab/Sys2Bench huggingface dataset:
Question: A man can hit a target once in 8 shots. If he fires 4 shots in succession, how many ways that he will hit his target?
Options:
A)71/23
B)81/13
C)81/29
D)17/29
E)91/32
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 - 1/8= 7/8
Therefore, the probability that he will not hit the target in any of the four shots = 7/8 ^4 = 17/29
D
Answer: D
Question: How many zeroes are there at the end of the number N, if N = 150! + 300! ?
Options:
A)28
B)31
C)34
D)37
E)40
Rationale: The number of zeroes at the end of 150! will be less than the number of zeroes at the end of 300!
Hence it is sufficient to calculate the number of zeroes at the end of 150!
The number of zeroes = [150/5] + [150/25] + [150/125] = 30 + 6 + 1 = 37
The answer is D.
Answer: D
Question: The average of 10 numbers is calculated as 14. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)A)16
B)B)15
C)C)19
D)D)22
E)E)24
Rationale: Explanation:
10 * 14 + 36 – 26 = 150=>150/10 = 15
B)
Answer: B
Question: 9 children can complete a piece of work in 360 days; 18 men can complete the same piece of work in 72 days and 12 women can complete it in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work?
Options:
A)68 days
B)81 days
C)96 days
D)124 days
E)126 days
Rationale: Explanation:
1 child’s 1 day’s work = 1/360 ×9 = 1/3240
10 children’s 1 day’s work = 1/324
1 man’s 1 day’s work = 1/72 × 18 = 1/1296
4 men’s 1 day’s work = 1 ×4/1296 = 1/324
12 women’s 1 day’s work = 1/162 given
Then, (4 men + 12 women + 10 children)’s 1 day’s work = 1/324 + 1/162 + 1/324
= 1/324 + 2/324 + 1/324 = 4/324 = 1/81
Therefore, the required No. of days = 81 days.
Answer: Option B
Answer: B
Question: Praveen starts business with Rs.3360 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
Options:
A)s.7500
B)s.8640
C)s.8500
D)s.9000
E)s.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3360 * 12/7x = 2/3
=> 14x = 120960
=> x = 8640.
ANSWER:B
Answer: B
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number R?
Options:
A)60
B)80
C)40
D)120
E)160
Rationale: (1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=R
Answer: B
Answer: B
Question: The banker's discount on Rs.1350 due a certain time hence is Rs.135. Find the true discount and the banker's gain.
Options:
A)12
B)15
C)18
D)21
E)None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1350 / 135
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.135,
T.D	= Rs.(10 / 11 x 135)
= Rs.123.
And, B.G	= Rs(135 - 123)
= Rs.12.
Answer A
Answer: A
Question: An athlete runs 360 metres race in 24 seconds. What is his speed?
Options:
A)23
B)64.8
C)37
D)30
E)28
Rationale: Speed=Distance/Time = 360/20 = 18 m/s = 18 * 18/5 = 64.8 km/hr
Answer :B
Answer: B
Question: Excluding stoppages, the speed of a bus is 80 kmph and including stoppages, it is 60 kmph. For how many minutes does the bus stop per hour?
Options:
A)12 min
B)20 min
C)25 min
D)30 min
E)15 min
Rationale: Due to stoppages, it covers 20 km less.
Time taken to cover 20 km = (20/80 x 60) min = 15 min
Answer : E
Answer: E
Question: Find a sum for first 7 prime no's from number series?
Options:
A)24
B)56
C)30
D)34
E)36
Rationale: Required sum = (2 + 3 + 5 + 7 + 11+13+17) = 56
Note: 1 is not a prime number
Option B
Answer: B
Question: A number when divided by 342 gives a remainder 47. When the same number ift divided by 19, what would be the remainder ?
Options:
A)8
B)5
C)9
D)6
E)16
Rationale: On dividing the given number by 342, let k be the quotient and 47 as remainder.
Then, number – 342k + 47 = (19 x 18k + 19 x 2 + 9) = 19 (18k + 2) + 9.
The given number when divided by 19, gives (18k + 2) as quotient and 9 as remainder
Answer C
Answer: C
Question: Which of the following must be true =>
A) The Average of N Consecutive integers is an integer for N being Even
B) The Average of N Consecutive integers is an integer for N being Odd
C) The product N(N+1)(N+2) for integer N must be divisible by both 3 and 6
D) 2N+1 is always Odd irrespective of N.
Options:
A)B,C,D
B)A,C,D
C)B,C
D)Only D
E)All of them
Rationale: A) The Average of N Consecutive integers is an integer for N being Even. False. For consecutive integers when number of integers is even, average= middle two terms/2= O+E/2 (can not be an integer)
B) The Average of N Consecutive integers is an integer for N being Odd. The middle term will be the average, and this term is odd integer.
C) The product N(N+1)(N+2) for integer N must be divisible by both 3 and 6. Either the product will be 0 or will have multiple of both 2 and 3 and 6. True.
D) 2N+1 is always Odd irrespective of N. What if =1/2, then 2N+1= 2
only B and C are true.
ANSWER:C
Answer: C
Question: area of square = sum of areas of rect1(41*27) and rect2(41*14). find square side
Options:
A)93
B)40
C)41
D)42
E)58
Rationale: area of square=1107+574
area of square=1681
side of the square=sqrt(1681)=41
ANSWER:C
Answer: C
Question: If $x is invested at a constant annually compound interest rate of k percent, what is the ratio of the total amount including interest after 5n years to that after 3n years?
Options:
A)(1+k/100)^2n
B)(1+k)^n
C)(1+kn/100)
D)(1+n/100)^k
E)(1+kn)
Rationale: Amount after 3n years will be = x ( 1 + k/100)^5n
Amount after 3n years will be = x ( 1 + k/100)^3n
So, required ratio will be -
{ x ( 1 + k/100)^5n } / {x ( 1 + k/100)^3n } = (1+k/100)^n
Hence answer will be a. (1+k/100)^2n
A
Answer: A
Question: Last year Elaine spent 10% of her annual earnings on rent. This year she earned 15% more than last year and she spent 30% of her annual earnings on rent. The amount she spent on rent this year is what percent of the amount spent on rent last year?
Options:
A) 252.5
B) 364.5
C) 367.5
D) 375
E) 345
Rationale: For this it is easiest to use simple numbers. Let's assume that Elaine's annual earnings last year were $100.
She would've spent $10 of this on rent.
This year she earned 15% more, or $115.
She would've spent 30% of this on rent, or $34.5
Do $34.5/$10
This will give you 345%
E is the correct answer.
Answer: E
Question: x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 14. Which of the following is NOT a possible value for y + b?
Options:
A)24
B)21
C)20
D)17
E)15
Rationale: Important note: remainder is ALWAYS less than divisor, thus y>6 and b>14 --> y+b>20.
Answer: C.
Answer: C
Question: Machine A can make 350 widgets in 1 hour, and machine B can make 250 widgets in 1 hour. If both machines work together, how much time will it take them to make a total of 2000 widgets?
Options:
A)3 hour and 20 minutes
B)3 hour and 24 minutes
C)3 hour and 30 minutes
D)3 hour and 36 minutes
E)3 hour and 40 minutes
Rationale: (350+250)t=2000
600t=2000
t=10/3
t=3 hour and 20 minutes
Answer: A
Answer: A
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is :
Options:
A)700
B)690
C)650
D)698
E)728
Rationale: Explanation :
Simple Interest (SI) for 1 year = 854-815 = 39
Simple Interest (SI) for 3 years = 39 × 3 = 117
Principal = 815 - 117 = Rs.698
Answer : Option D
Answer: D
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)32
B)20
C)287
D)277
E)291
Rationale: 900 ---- 180
100 ---- ? => 20
Answer: B
Answer: B
Question: Find the value of 1/(3+1/(3+1/(3-1/3)))?
Options:
A)13/89
B)15/87
C)27/89
D)27/87
E)89/27
Rationale: 1/[3 + (1/(3+1/(3 - 1/3)))]
=> 1/[3 + 1/(3 + 1/(8/3))]
=> 1/[3 + 1/(3 + 3/8)]
=> 1/[3 + 8/27]
=> 1/(89/27)
=> 27/89
C)
Answer: C
Question: If the average (arithmetic mean) of 5 positive temperatures is p degrees Fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be:
Options:
A)6p
B)4p
C)5p/3
D)3p/2
E)3p/5
Rationale: The sum of three greatest should be more than sum of two lowest.
The total sum is; 5p
A. 6p; 6p is more than 5p. Not possible.
B. 4p; 5p-4p=p(Possible)
C. 5p/3; 10p/3; 10p/3 > 5p/3. Not possible
D. 3p/2; 7p/2; 7p/2 > 3p/2. Not possible
E. 3p/5; 22p/5; 22p/5 > 3p/5. Not possible.
Ans:B
Answer: B
Question: Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
Options:
A)20
B)92
C)300
D)372
E)476
Rationale: # of letters = 8, # of ways to choose 3 letters out of 8 when order matters is P38=8!/(8−3)!=336 which means that there can be 336 different sequences. As 36 sequences were not assigned then 336-36=300 sequences were assigned, so there are 300 participants.
ANSWER:C
Answer: C
Question: A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first year, 13.5 % the next year, 12% the third year, and so on, what will be its value at the end of 10 years, all percentages applying to the original cost?
Options:
A)Rs2,00,000
B)Rs1,05,000
C)Rs4,05,000
D)Rs 6,50,000
E)None
Rationale: Explanatory Answer
Let the cost of an equipment is Rs. 100.
Now the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 15 and d = - 1.5.
Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5
Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.
The total cost being Rs. 6,00,000/100 * 17.5 = Rs. 1,05,000.
Answer B
Answer: B
Question: A persons salary iis decreased by steps of 20%, 15% and 10%. What will be the percentage decrease, if the salary is decreased in a single shot?
Options:
A)34.8%
B)36.8%
C)38.8%
D)39.8%
E)32.8%
Rationale: Let x is his initial salary.
After 1st decrease, x1 = x- (x*20/100) = x - x/5 = 4x/5
After 2nd decrease, x2 = 4x/5 - ((4x/5)*15/100) = 4x/5 - 3x/25 = 17x/25
After 3rd decrease, x3 = 17x/25 -((17x/25)*10/100) = 17x/25 - 17x/250 = 153x/250
So if its decreased in single shot, x - y(decreased) = 153x/250
=> y = x - 153x/250 => y = 97x/250 => y = 0.388x => y = 38.8%
ANSWER:C
Answer: C
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
Options:
A)2:3:9
B)24:25:36
C)7:6:10
D)12 : 15 : 16
E)None of these
Rationale: Explanation:
Aman : Rakhi : Sagar =(70000Ã—36)=(70000Ã—36) :(105000Ã—30):(105000Ã—30) :(140000Ã—24):(140000Ã—24)
=12:15:16=12:15:16.
ANSWER IS D
Answer: D
Question: 35 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
Options:
A)87
B)18
C)42
D)16
E)10
Rationale: Binders Books Days
35 1400 21
x 1600 20
x/35 = (1600/1400) * (21/20) => x = 42
Answer:C
Answer: C
Question: Which of the following numbers has the greatest number of distinct prime factors?
Options:
A)165
B)192
C)228
D)330
E)332
Rationale: 165=3*5*11
192=2^6 *3
228=2^2 *3*19
330=2*3*5*11
332=2^2 * 83
330 has 4 distinct prime factors
Answer D
Answer: D
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)766 sq.cm
B)165 sq.cm
C)186 sq.cm
D)168 sq.cm
E)600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer:E:
Answer: E
Question: An bus covers a certain distance at a speed of 300 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
Options:
A)1520 km/hr
B)1640 km/hr
C)1656 km/hr
D)1500 km/hr
E)1520 km/hr
Rationale: Distance = (300 x 5) = 1500 km.
Required speed = 1500 km/hr.
D
Answer: D
Question: Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)10
B)11.3
C)13
D)14
E)15
Rationale: Speed of the first train = 120/9 = 13.3 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 13.3 + 8 = 21.3 m/sec.
Required time = (120 + 120)/21.3 = 11.3 sec.
Answer: Option B
Answer: B
Question: The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
Options:
A)6
B)4
C)2
D)5
E)1
Rationale: Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
ANSWER B
Answer: B
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 45 sec. The length of each train is?
Options:
A)50
B)26
C)27
D)62.5
E)21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/45 = 25/9 => x = 65.5.
Answer: D
Answer: D
Question: A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 126 km downstream.
Options:
A)4 hours
B)5 hours
C)6 hours
D)7 hours
E)8 hours
Rationale: Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph
Time = distance/speed = 126/21 = 6 hours
Option C
Answer: C
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
Options:
A)Rs. 520
B)Rs. 480
C)Rs. 420
D)Rs. 200
E)Rs. 600
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 21
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(21 – 20) / 20] * 100
= 5 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 5% p.a.
SI = (PRT/100)
20 = (X*5*2) / 100
X = Rs. 200
ANSWER: D
Answer: D
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
Options:
A)3:9
B)3:0
C)ratio 3:5
D)3:2
E)3:1
Rationale: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5
Answer: C
Answer: C
Question: If the sum of a number and its square is 210, what is the number?
Options:
A)14
B)26
C)28
D)91
E)none of these
Rationale: Let the number be x. Then,
x + x2 = 210
(x + 15)(x - 14) = 0
x = 14
ANSWER:A
Answer: A
Question: The edges of a cuboid are 4 cm, 4 cm and 6 cm. Find the volume of the cuboid?
Options:
A)90
B)60
C)96
D)80
E)72
Rationale: 4*4*6
= 96
Answer: C
Answer: C
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 210 inclusive?
Options:
A)90
B)95
C)100
D)120
E)110
Rationale: 10 and 190 inclusive would mean there are 21 terms.
No need to add up all the terms and further divide by 21 since the terms are evenly spaced in ascending order from 10, 20, 30........210
The middle term is the average which is the tenth term = 120
D is the answer.
Answer: D
Question: Working together, Jose and Jane can complete an assigned task in 5 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 15 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
Options:
A)26 days
B)15 days
C)60 days
D)65 days
E)36 days
Rationale: Assume:
Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day
Together, they does (x+y)/xy job in a day. This is equals to 1/20. So
(x+y)/xy = 1/5
5(x+y) = xy
Next, we're told 1 job takes 15 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.
x/2 + y/2 = 15
x+y = 30
So
xy = 150
The answer choices are:
26 days
15 days
60 days
65 days
36 days
From the answer choices, So I'll go for 15 days for Jose and 10 days for Jane.
Answer : B
Answer: B
Question: Which four figure number contains four different digits and meets the following criteria? The first digit is twice the value of the fourth digit and two more than the second digit. The third digit is one more than the first digit and four more than the fourth digit.
Options:
A)5367
B)6473
C)3573
D)3262
E)7364
Rationale: B
6473
Answer: B
Question: k = 2^n + 9, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
Options:
A)2^n - 8
B)2^n - 2
C)2^n+5
D)2^n + 4
E)2^n
Rationale: Given: k, M and N are integers
If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)
We're told that 9 is a divisor of 2^n + 9
We also know that 9 is a divisor of9.
So, applying the aboverule, 9 is a divisor of 2^n + 9 +9, and 9 is a divisor of 2^n +9 -9 =2^n
E
Answer: E
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
Options:
A)12, 9
B)10, 5
C)12, 7
D)11, 6
E)13, 8
Rationale: Explanation:
x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER IS C
Answer: C
Question: Lakshmi took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If she paid Rs. 960 as interest at the end of the loan period, what was the rate of interest?
Options:
A)8
B)7
C)6
D)5
E)4
Rationale: Let rate = R% and time = R years.
Then, (1500 * R * R) / 100 = 960
15R2 = 960
R2 = 64 => R = 8
Answer:A
Answer: A
Question: If Danny scored 86, 75, 52, 87, 85 and 82 marks (out of 100) in English, Social Studies, Art, Music, Biology and French. What are his average marks ?
Options:
A)77.8
B)75.8
C)67.8
D)87.8
E)97.8
Rationale: Explanation:, 75, 52, 87 and 82
Average = (86+ 75 + 52 + 87 + 85 + 82 )/ 6 = 77.8.
Answer: A)77.8
Answer: A
Question: Let the polynomials be:
P1(x)=3x2−7x+3,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
Options:
A)2x2 + 11x - 7
B)-2x2 - 11x + 5
C)-2x2 - 11x + 6
D)2x2 - 9x + 7
E)None of these
Rationale: Solution:
P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=
3x2−7x+3−5x2−4x+2=3x2−7x+3−5x2−4x+2=
−2x2−11x+5
Answer B
Answer: B
Question: A salesperson gets a 15% commission on each sale he makes. How many sales of $270 each must he make in order to reach a salary of at least $1000?
Options:
A)15
B)24
C)25
D)26
E)52
Rationale: Soln:-
10% of 270 = 27.
5% of 270 = 13.5.
so,
15 % of 270 = 40.5
total salary required 1000
earning from single sale 40.5
# of sale = 1000/40.5 = 24.62
Approx 25 sale
ANSWER:C
Answer: C
Question: Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
Options:
A)12 : 15 28
B)12 : 15 :29
C)12 : 15 :99
D)12 : 15 :16
E)12 : 15 :11
Rationale: Explanation:
Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16.
Answer: D) 12 : 15 :16
Answer: D
Question: A factory has 15 machines of equal efficiency in its factory. The annual manufacturing costs are Rs.42,000 & establishment charges are Rs.12,000. The annual output of the company is Rs.70,000. The annual output and manufacturing costs are directly proportional to the number of machines. The shareholders get 12.512.5 profit, which is directly proportional to the annual output of the company. If 7.147.14 machines remain closed throughout the year, then the % decrease in the amountof profit of the shareholders would be?
Options:
A)12.5%
B)13.5%
C)14%
D)15%
E)16%
Rationale: Option(B) is correct
Original profit
= 70,000−42,000−12,000=16,00070,000−42,000−12,000=16,000
If 7.14%7.14% of 14 i.e. one of the machines closed throughout the year, then change in profit will be:
=1314×[70,000−42,000]=1314×[70,000−42,000]
=14,000=14,000
Thus, decrease in the profit %%
=200016000×100=200016000×100
=12.5%
A
Answer: A
Question: Sue planted 4 times as many apple seeds as she planted orange seeds. 15 percent of the apple seeds grew into trees, and 10 percent of the orange seeds grew into trees. If a total of 420 apple trees and orange trees grew from the seeds, how many orange seeds did Sue plant?
Options:
A)540
B)600
C)660
D)720
E)760
Rationale: Sue planted 4 times as many apple seeds as she planted orange seeds.
Yes, apple:orange be 4:1 but this translates to Apple = 4*Orange and not 4*Apple = Orange
Let Orange be x
Apple = 4*Orange = 4x
0.15Apple + 0.10Orange = 420
=> 0.15*4x + 0.10*x = 420
=> 0.7x = 420
=> x = 600
So, answer will be B
Answer: B
Question: The proportion of water to alcohol in Solution A is 5:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
Options:
A)36.7%
B)37.6%
C)38.3%
D)39.8%
E)40.5%
Rationale: Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(1/6)(V/2)+(3/5)(V/2)=V/12+3V/10=23V/60.
The concentration of alcohol is 23/60=38.3%
The answer is C.
Answer: C
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.
Options:
A)40
B)60
C)120
D)90
E)100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 60 kmph, speed of B must be 80*(3/2) = 90 kmph
D
Answer: D
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates C apply to what fraction of a week?
Options:
A) 1/2
B) 5/8
C) 9/14
D) 16/21
E) 9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates C/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: C