divelab/Sys2Bench huggingface dataset:
Question: If √x = x, then which of the following must be true?
Options:
A)x is positive
B)x=1
C)x^2>x
D)x is non-negative
E)None of the above
Rationale: Square both the sides we get
x = x^2
x^2 - x= 0
x(x-1)=0
either x=0 or x=1
So, answer will be D
Answer: D
Question: Andrew started saving at the beginning of the year and had saved $240 by the end of the year. He continued to save and by the end of 2 years had saved a total of $600. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
Options:
A)11%
B)25%
C)44%
D)50%
E)125%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 600
Saving in 2nd year + 240 = 600
Saving in 2nd year = 600 - 240 = 360
Change in Value = 360 - 240 = 120
Original Value = 240
Percentage Increase = (120 / 240 ) * 100
= (1/2 ) * 100 = 50 % ..... Answer D......
Answer: D
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Explanation:
Given that A+B = 12 + B + C
=> A – C = 12 + B – B = 12
=> C is younger than A by 12 years
Answer: Option B
Answer: B
Question: In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes” takes up 54° of the chart, how much of the Roberts’s $20,000 annual budget is dedicated to clothes and shoes?
Options:
A)$1,500
B)$3,000
C)$4,500
D)$5,000
E)$5,400
Rationale: Given for clothes and shoes” takes up 54° of the circular chart.
Then clothes and shoes = 54/360 * 20000.
=> 3000.
Answer:option B is correct answer...
Answer: B
Question: In an automobile market of spare parts dealers and workshops, average earning of a spare parts dealer per day is $520 and the average earning of a workshop is $700. Considering there are 40 shops in market and number of spare parts dealer shops exceeds the workshops by 4. What is the average earning of this market consisting of only spare parts dealers and workshops.
Options:
A)535
B)562
C)594
D)601
E)648
Rationale: Let the number of workshops be x
number of s.p.d=x+4
x+x+4=40 = 2x=36 = x=18
workshops are 18 in number and spd are 22 in number
Average earning of the market= ((520x22)+(700x18))/40
=(11440+12600)/40
=24040/40
=601
Answer: D
Answer: D
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
Options:
A)51.25
B)51.29
C)51.22
D)51.38
E)51.12
Rationale: Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500)
= Rs.51.25.
Answer: a
Answer: A
Question: Each cell of a certain kind of bacteria produces two more cells. The life span of each cell is 10 minutes and each cell multiples only once in its life time, when it is exactly one minute old. If a new cell is placed in an empty box at time t = 0, then how many live cells will be there in the box just after t = 20 minutes?
Options:
A)2048 × 1023
B)1024 × 1023 cells
C)(1024)²
D)1023 × 1025
E)1023 × 1026
Rationale: see total cells created after
1min be 2^1
2min be 2^2
3 min be 2^3.......
thus after 20 min 2^20 will be created
now after 10 min 1 cell will die (2^0)
after 11 min 2 cells die (2^1)
similarly after 20 min 2^10 cells die
thus total cells remained=(2^20)-(1024)
or (1024)^2-1024
or1024*(1024-1)
i.e, 1024*1023
ANSWER:B
Answer: B
Question: A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 60 vehicles that are not Speedsters, how many Speedster convertibles are there?
Options:
A)36
B)96
C)100
D)76
E)72
Rationale: Total Vehicle = 2/3 of speedster + 1/3 of others.
Speedster convertibles = 2/3 total vehicle * 4 /5
Given : 1/3 constitutes 60 Vehicles. hence 2/3 constitutes 120
Speedster convertibls = 120 * 4/5 = 96
B
Answer: B
Question: The difference between the place values of two sevens in the numeral 69758472 is
Options:
A)0
B)100
C)6993
D)699930
E)None of these
Rationale: Required difference = (700000 - 70) = 699930
Answer: Option D
Answer: D
Question: Average expenditure of a person for the first 3 days of a week is Rs. 310 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
Options:
A)350
B)370
C)390
D)430
E)None
Rationale: Explanation:
Assumed mean = Rs. 310
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 310 + Rs. 40 = Rs. 350
Correct Option: A
Answer: A
Question: Tom planted vegetables in a rectangular garden that was 25 feet long and 15 feet wide. He used
1/3 of the area for corn and 1/5 of it for peas. How many square feet are left for other vegetables?
Options:
A)175 sq. ft.
B)176 sq. ft.
C)177 sq. ft.
D)178 sq. ft.
E)179 sq. ft.
Rationale: area of garden is 25 x 15 = 375 sq. ft.
1/3 x 375 = 125 sq. ft. for corn
1/5 x 375 = 75 sq. ft. for peas
125 + 75 = 200 sq. ft. used
375 - 200 = 175 sq. ft. left over
correct answer A
Answer: A
Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land heads up on the first flip but not on the last 4 flips?
Options:
A)1/4
B)1/8
C)1/16
D)1/32
E)1/64
Rationale: P(HTTTT) = 1/2*1/2*1/2*1/2*1/2 = 1/32
The answer is D.
Answer: D
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 :19
B)12 : 15 :29
C)12 : 15 :11
D)12 : 15 :16
E)12 : 15 :13
Rationale: Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24)
= 12 : 15 : 16.
Answer: D
Answer: D
Question: Bank account A contains exactly x dollars, an amount that will decrease by 10% each month for the next two months. Bank account B contains exactly y dollars, an amount that will increase by 20% each month for the next two months. If A and B contain the same amount at the end of two months, what is the ratio of x√x to y√y?
Options:
A)4 : 3
B)3 : 2
C)16 : 9
D)2 : 1
E)9 : 4
Rationale: Explanation:
Account A has amount after 2 months = 0.9*0.9*x = 0.81*x
Account B has amount after 2 months = 1.2*1.2*y = 1.44*y
0.81*x=1.44*y --> √(x/y)=√(1.44/0.81) = 12/9 = 4/3.
Ans A
Answer: A
Question: |x+3| – |4-x| = |5+x| How many solutions will this equation have?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: You have |x+3| - |4-x| = |8+x|
First, look at the three values independently of their absolute value sign, in other words:
|x+3| - |4-x| = |8+x|
(x+3) - (4-x) = (8+x)
Now, you're looking at x < - 8, so x is a number less than -8. Let's pretend x = -10 here to make things a bit easier to understand.
when x=-10
I.) (x+3)
(-10+3)
(-7)
II.) (4-x)
(4-[-10]) (double negative, so it becomes positive)
(4+10)
(14)
III.) (8+x)
(8+-10)
(-2)
In other words, when x < -8, (x+3) and (8+x) are NEGATIVE. To solve problems like this, we need to check for the sign change.
Here is how I do it step by step.
I.) |x+3| - |4-x| = |8+x|
II.) IGNORE absolute value signs (for now) and find the values of x which make (x+3), (4-x) and (8+x) = to zero as follows:
(x+3)
x=-3
(-3+3) = 0
(4-x)
x=4
(4-4) = 0
(8+x)
x=-8
(8+-8) = 4
E
Answer: E
Question: At a certain school 25% of the students join a band, 25% play a sport and 20% both join the band and play a sport. if a randomly selected student is a member of the band, what is the probablility that the student also plays a sport?
Options:
A)1) 3/4
B)2)1/5
C)3)2/5
D)4)1/2
E)5)4/5
Rationale: This is the way to approach the question:
25% of the students join a band => 25% of the students either only join a band or both join a band and play sports
25% of the students play sports => 25% of the students either only play sports or both play sports and join a band
If a randomly selected student is a member of the band, then probability that the student also plays a sport = percentage of cases in which the student can do both/percentage of cases in which the student can just play sports or do both
=20%/25% = 4/5
The answer is therefore (E)
Answer: E
Question: What is the units digit of 18! + 1 ?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.
The units digit of 18! + 1 is 1.
The answer is A.
Answer: A
Question: A 14 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
Options:
A)5/14
B)3/14
C)8/21
D)6/7
E)2/5
Rationale: A square with an area of 4 has a perimeter of 8.
For the area to be >4, the longer piece must be >8.
The wire must be cut within 6 meters from either end.
The probability of this is 12/14 = 6/7.
The answer is D.
Answer: D
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.50 km and 1.25 km respectively. The time taken by the slower train to cross the faster train in seconds is?
Options:
A)12
B)77
C)66
D)99
E)11
Rationale: Relative speed = 60 + 90 = 150 km/hr.
= 150 * 5/18 = 125/3 m/sec.
Distance covered = 1.50 + 1.25 = 2.75 km = 2750 m.
Required time = 2750 * 3/125 = 66 sec.
Answer: C
Answer: C
Question: What is the speed required for a bike to cover a distance of 720 km in 12 hours?
Options:
A)50 kmh
B)40 kmh
C)100 kmh
D)60 kmh
E)80 kmh
Rationale: Speed= Distance / Time
Speed = 720 / 12 = 60
Answer: D
Answer: D
Question: If a positive integer n is divisible by both 2 and 5, then n must also be divisible by which of the following?
I. 10
II. 7
III. 40
Options:
A)None
B)I only
C)II only
D)I and II
E)II and III
Rationale: A multiple of 2 and 5 is also a multiple of 10, but not necessarily a multiple of 7 or 40.
The answer is B.
Answer: B
Question: The list price of an article is Rs.70. A customer pays Rs.61.11 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)7%
C)10%
D)3%
E)4%
Rationale: Explanation:
70*(90/100)*((100-x)/100) = 61.11
x = 3%
D
Answer: D
Question: In a party attended by 9 persons, each clinch their glass with every other. How many glass clinches?
Options:
A)51
B)52
C)34
D)35
E)36
Rationale: Total no. of person = 11
Total no. of glass clinches = n(n-1)/2
=9*8/2
= 36
ANSWER:E
Answer: E
Question: Which of the following triples of numbers have the same standard deviation as the numbers p, q, and r?
I. p-2, q-2, r-2
II. 0, p-q, r-q
III. p-4, q+5, r-1
Options:
A)I only
B)II only
C)I and III only
D)II and I only
E)I, II, and III
Rationale: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {p-2, q-2, r-2} is obtained by subtracting 2 from each term of {p, q, r}
Set {0, p-q, r-q} is obtained by subtracting s from each term of {p, q, r}
Set {p-4, q+5, r-1} is totally different from {p, q, r}.
Thus the answer is I and II only.
Answer:D.
Answer: D
Question: 5.40 can be expressed in terms of percentage as
Options:
A)5.04%
B)50.4%
C)209%
D)540%
E)None of these
Rationale: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
5.40 * 100 = 540
Answer: Option D
Answer: D
Question: If XY denotes X is raised to the power Y, Find the last two digits of 19413843+ 19614181
Options:
A)67
B)97
C)55
D)32
E)62
Rationale: 1721^3856
unit digit= 1^2=1
10th digit=5*6=30=0 means last two digit =1
and 1982^4181
unit digit=1
10th digit=8*2=16 mean last two digit= 61
hence,
61+1= 62
Answer: E
Question: What is the rate percent when the simple interest on Rs.780 amount to Rs.130 in 4 Years?
Options:
A)4.16
B)5.16
C)6.16
D)7.16
E)8.16
Rationale: 130 = (780*4*R)/100
R = 4.16%
Answer: A
Answer: A
Question: Find the fourth proportion to 2,3,6
Options:
A)18
B)12
C)9
D)3
E)4
Rationale: Explanation:
2:3 :: 6:x
=> 2/3 = 6/x
=> x = 18/2
=> x = 9
Option C
Answer: C
Question: Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.2,10,000 earned at the end of 3 years from the start of the business in 1999?
Options:
A)Rs.45,000
B)Rs.50,000
C)Rs.70,000
D)Rs.75,000
E)none
Rationale: Solution
Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)
= 1260000 : 840000 : 420000
= 3 : 2 : 1.
Rajeev's share	=Rs.(210000×2/6)
= Rs.70000.
Answer C
Answer: C
Question: If 15 machine can finish a job in 36 days, then how many more machines would be needed to finish the job in one -fourth less time?
Options:
A)a. 5
B)b. 8
C)c. 10
D)d. 12
E)e. 16
Rationale: You might think of this in a management context - we can use the principle of 'person-hours' to solve any problem where we have identical workers. So, using simpler numbers, suppose you know that 6 identical employees, working simultaneously, would finish a job in 5 hours. Then that job requires 6*5 = 30 total hours of person-work. If instead you wanted the job done in 3 hours, you'd assign 30/3 = 10 employees to do the job, because you want to get a total of 30 hours of work from the employees.
We can solve this problem identically. If 15 machines (identical ones, I assume) work simultaneously for 36 days, they will do a total of 15*36 machine-days of work. So the job requires 15*36 days of machine work in total. We instead want the job done in 1/4 less time, so in 27 days. So we'll need 15*36/27 = 20 machines, or 5 additional machines.
A
Answer: A
Question: If k is a multiple of 3 and k=(m2)nk=(m2)n, where m and n are prime numbers, which of the following must be a multiple of 9?
Options:
A)m^2
B)n^2
C)mn
D)mn^2
E)(mn)^2
Rationale: must be a multiple of 9
m and n are prime...lets have 2 and 3
now either of then can be a 3...
a) m can be 2 and n = 3...out
b) n can be 2 and m = 3...out
c) m = 2 and n=3 ...out
d) n can be 2 and m = 3...out
e) m = 2/3 or n = 3/2 both satisfies .......must be a multiple of 9
ANSWER:E
Answer: E
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 200 kilometers?
Options:
A)4.5
B)5
C)6.5
D)7.5
E)8.5
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 180 kilometers?
200 ÷ 40 = 5 × 1 gallon = 5 gallons
correct answer B
Answer: B
Question: A series of number is given: 5, 6, 12, 5, 7, 13, 5,__14, 5, 9, 15.. What number fills the blank?
Options:
A)6
B)5
C)9
D)8
E)11
Rationale: Looking at the series we can see 1 is added to 6, then to 7, then to 8 and so on...
The answer is option D (8)
Answer: D
Question: A, B and C start a business each investing 2,000. After 6 months A withdrew 1000, B withdrew 1000 and C invests 1000 more. At the end of the year, a total profit of 6600 was recorded. Find the share of B.
Options:
A)20,000
B)21,200
C)1,800
D)20,500
E)None of these
Rationale: Ratio of the capitals of A, B and C
= 2000 Ã— 6 + 1000 Ã— 6 : 2000 Ã— 6 + 1000 Ã— 6 : 2000 Ã— 6 + 3000 Ã— 6
= 18000 : 18000 : 30000 = 18 : 18 : 30
Bâ€™s share = (6600 Ã— 18â„66) = 1800
Answer C
Answer: C
Question: A worker is paid x rupees for painting every 5 metres of a wall and y rupees for painting every extra metre. During one week, he painted 5 metres on Monday, 6 metres on Tuesday, 7 metres on Wednesday, 8 metres on Thursday and 9 metres on Friday. What is his average daily earning rupees for the five day week?
Options:
A)x + 2y
B)(5x + 9y)/5
C)10x + (8/5)y
D)None of these
E)Cannot be determined
Rationale: Explanation :
On Monday, the payment = Rs x
On Tuesday, the payment = Rs (x + y)
On Wednesday, the payment = Rs (x + 2y)
On Thursday, the payment = Rs (x + 3y)
On Friday, the payment = Rs (x + 4y)
Average daily earning during the five-day week = (5x + 10y)/5
= x + 2y
Answer : A
Answer: A
Question: If x is a positive, single-digit integer such that 2/3*x, 2x, x, and x + 2, and 3x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: The big hints are thatx is a 1-digit integerAND (2/3)x, 2x, x, and x + 2, and 3x – 2 are ALLintegers
For (2/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers
When x =3, we get the following terms: (2/3)(3), 2(3),3,3+ 2, and 3(3) – 2.
When we evaluate these terms we get: 4, 6, 3, 5 and 7
Rearrange to get: 2, 4, 5, 6, 7. So, when x = 3, we getconsecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)
Answer:
C
Answer: C
Question: The average age of father and his two sons is 38 Years. Five years ago, the average age of the two sons was 16 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
Options:
A)45
B)46
C)72
D)48
E)49
Rationale: The total present age of father and two sons is 3x38 = 114 yrs
The total present age of sons is (16+5) X 2 = 42Years
so, present age of father is 114 â€“ 42 = 72 yrs
Answer C
Answer: C
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
Options:
A)18
B)77
C)66
D)55
E)41
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer:A
Answer: A
Question: Three persons A, B and C divide a certain amount of money such that A's share is Rs.4 less than half of the total amount. B's share is Rs.8 more than half of what is left and finally C takes the which is Rs.14. Find the total amount they initially had with them?
Options:
A)Rs.68
B)Rs.85
C)Rs.80
D)Rs.56
E)Rs.29
Rationale: Let the total amount be Rs.P
Let shares of A and B be Rs.X and Rs.Y respectively.
Given, C's share was Rs.14.
X + Y + 14 = P --- (1)
From the given data, X = P/2 - 4 --- (2)
Remaining amount = P - (P/2 - 4) = P/2 + 4
Y = 1/2(P/2 + 4) + 8
=> P/4 + 10 --- (3)
From (1), (2) and (3)
P/2 - 4 + P/4 + 10 + 14 = P
=> 3P/4 + 20 = P
=> P - 3P/4 = 20
=> P/4 = 20 => P = Rs.80
Answer: C
Answer: C
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
Options:
A)150
B)388
C)278
D)277
E)268
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer: A
Answer: A
Question: In what ratio must rice of Rs.32per kg be mixed with rice of Rs.42 per kg so that cost of mixture is Rs.20 per kg?
Options:
A)13:6
B)13:5
C)11:6
D)11:5
E)12:5
Rationale: (20-42)/(32-20)=22/12=11:6
ANSWER:C
Answer: C
Question: The average weight of a class is x pounds. When a new student weighing 60 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?
Options:
A)85
B)86
C)88
D)90
E)92
Rationale: When the student weighs 80 pounds the average weight is x - 1 pounds;
When the student weighs 110 pounds the average weight is x + 4 pounds.
So, the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 30/5 = 6 students (including the new one). So, initially there were 5 student.
Total weight = 5x + 80 = 6(x-1) --> x = 88 pounds.
Answer: C.
Answer: C
Question: A man's age is 125% of what it was 10 years ago, but 83 1/3%
of what it will be after 10 years. What is his present age?
Options:
A)70
B)60
C)50
D)40
E)35
Rationale: Age before 10 years =x
125x/100=x+10
125x=100x+1000
x=1000/25=40
Present age =x+10=40+10=50
answer :C
Answer: C
Question: If the speed of X inch per second is equivalent to the speed of Y meter per hour, what is Y in terms of X? (1 meter=39.3701 inch)
Options:
A)21.44X
B)33.35X
C)67.77X
D)91.44X
E)111.3X
Rationale: X inch per second -->
--> 3,600X per hour(as there are 3,600 seconds in one hour);
--> 3,600X/39.3701=91.44X meter per hour (as there are 39.3701 inch in one meter).
Answer: D.
Answer: D
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 3500. The difference between the profit shares of A and C is?
Options:
A)621
B)1400
C)236
D)600
E)211
Rationale: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 3500
=> 5 parts out of 15 parts is Rs. 3500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (3500) = Rs. 1400
Answer:B
Answer: B
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 9 digits of the integer x will all be zero?
Options:
A)26
B)32
C)37
D)44
E)49
Rationale: 2*5 will give one 0 at the end. We need 2^9*5^9 to get 9 zeroes at the end.
There are many 2's, so we need to find the first 9 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35, 40...which gives us 9.
To have at least 9 zeroes at the end, a => 40.
The answer is D.
Answer: D
Question: 36 men can complete a piece of work in 18 days. In how many days will 54 men complete the same work ?
Options:
A)24
B)77
C)88
D)29
E)12
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
54 : 36 :: 18 : x
x = 12
Answer: E) 12 days
Answer: E
Question: The function f(Z) represents the number of ways that prime numbers can be uniquely summed to form a certain number Z such that Z = a + b + c + d… where those summed variables are each prime and a ≤ b ≤ c ≤ d ... For instance f(8) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5. What is f(12)?
Options:
A)4
B)5
C)6
D)9
E)7
Rationale: Its better to start with 2 and check whether sum of two primes is primes is even.
1) 2(6 times)
2) 2(3 times) + 3(2 times)
3) 2(2 times) + 3 + 5
4) 2 + 3 + 7
5) 2 + 5 + 5
6) 3(4 times)
7) 5 + 7
Answer: E
Answer: E
Question: Machine A can finish a job in 4 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The combined rate is 1/4+1/12+1/6 = 1/2 of the job per hour.
The time to complete the job is 2/1 = 2 hours.
The answer is B.
Answer: B
Question: A certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle. By what percent is the time between maintenance checks increased by using the additive?
Options:
A)25%
B)33 1/3%
C)50%
D)66 2/3%
E)75%
Rationale: General formula for percent increase or decrease, (percent change):
percent=Change/Original∗100
So, the time between maintenance checks increased by 25−20/20∗100=25
Answer: A.
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 30, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Rs 15
B)Rs 12.10
C)Rs 24.70
D)Rs 36.80
E)None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 30 - 5 - 0.30
=24.70
Answer : C
Answer: C