divelab/Sys2Bench huggingface dataset:
Question: A retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 70 percent greater than the wholesale price. If the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent?
Options:
A)26
B)37.5
C)42
D)19
E)50
Rationale: Answer: D= 19.
Assume Rs. 100 to be the price at which the retailer buys from wholesaler.
70% increase makes Retail price = 170.
Now 30% decrease -> (1-30/100) * 170 = 119.
Now compared to the wholesale price of 100, 19% increase is what will have the same effect as increasing the wholesale price.
Answer: D
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 555. What is the sum of the last 5 integers in the sequence?
Options:
A) 585
B) 580
C) 575
D) 570
E) 565
Rationale: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+555=580
B
Answer: B
Question: Given that 268x74= 19532, find the value of 2.68x.74.
Options:
A)1.9532
B)1.0025
C)1.5693
D)1.0266
E)None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9532
Answer A
Answer: A
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and VIOLET. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
Options:
A)12
B)14
C)18
D)19
E)20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, VIOLET) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: D
Question: How many seconds will it take for a car that is traveling at a constant rate of 77 miles per hour to travel a distance of 21 yards?	(1 mile = 1,160 yards)
Options:
A).1
B)0.3
C)0.6
D)2
E)1.6
Rationale: speed = 77 miles/hr = 37.64 yard/s
distance = 21 yards
time = distance/speed
=21/37.64
=0.6 sec
ans - C
Answer: C
Question: One pipe can fill a pool twice as faster as the second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?
Options:
A)10
B)15
C)15.5
D)12.5
E)18
Rationale: Say the rate of the slower pipe is R pool/hour, then the rate of the faster pipe would be 2R. Since when both pipes are opened, they fill the pool in five hours, then their combined rate is 1/5 pool/hour.
Thus we have that R + 2R = 1/5 --> R = 1/15 pool/hour --> time is reciprocal of rate thus it's 15/1 =15 hours.
Answer: B.
Answer: B
Question: A tin of oil was 4/5full.when 6 bottles of oil were taken out and four bottles of oil were poured into it, it was ¾ full. how many bottles of oil can the tin contain?
Options:
A)40
B)30
C)20
D)21
E)34
Rationale: Suppose x bottles can fill the tin completely
Then4/5x-3/4x=6-4
X/20=2
X=40
Therefore required no of bottles =40
Option :A
Answer: A
Question: The average age 9 men of a gang are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new men than the old number?
Options:
A)10
B)12
C)18
D)22
E)24
Rationale: 9 * 2 = 18 years
C
Answer: C
Question: A company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
Options:
A)25
B)66
C)18
D)19
E)01
Rationale: Explanation:
Dividend on 1 share = (12.5 * 50)/100 = Rs.6.25
Rs.25 is income on an investment of Rs.100
Rs.6.25 is income on an investment of Rs. (6.25 * 100)/25 = Rs.25
ANSWER: A
Answer: A
Question: If x and y are non-zero integers, and 49x^4 – 4y^4 = 7x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
Options:
A)2y^2
B)2y^2+1/7
C)2y^4
D)2y^2-1/7
E)2y^2+1/8
Rationale: 49x^4 – 4y^4 = 7x^2 + 2y^2
(7x^2 + 2y^2) (7x^2 - 2y^2) = 7x^2 + 2y^2
7x^2 - 2y^2 = 1
7x^2 = 2y^2+1
x^2 = 2y^2+1/7
Answer : B
Answer: B
Question: Find the simple interest on Rs. 71,000 at 16 2/3% per year for 9 months.
Options:
A)7500
B)6500
C)8875
D)9500
E)None of them
Rationale: P = Rs.71000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(71,000*(50/3)*(3/4)*(1/100))= Rs.8875
Answer is C.
Answer: C
Question: Company Z has 58 employees. If the number of employees having birthdays on Wednesday is more than the number of employees having birthdays on any other day of the week, each of which have same number of birth-days, what is the minimum number of employees having birthdays on Wednesday.
Options:
A)6
B)10
C)8
D)9
E)12
Rationale: Say the number of people having birthdays on Wednesday is x and the number of people having birthdays on each of the other 6 days is y. then x + 6y = 54.
Now, plug options for x. Only B and E give an integer value for y. But only for B x > y as needed.
Answer: B.
Answer: B
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1234
B)1456
C)1500
D)1600
E)1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: E
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)17
B)10
C)23
D)27
E)72
Rationale: 4/12 + x/15
= 1
x = 10
Answer: B
Answer: B
Question: The three sides of an acute angled triangle (all in cms) are 12, 19 and b. How many integer values can b take?
Options:
A)23
B)22
C)15
D)8
E)7
Rationale: In acute angle triangles all angles in the triangle should be less than 90.
The maximum length of b can be when it is the hypotenuse of the triangle.
So, b= sqrt(12^2 + 19^2) = 22.5 (approx)
The maximum length of b can be when side of length 12 is the hypotenuse of the triangle.
So, b = sqrt (19^2 - 12^2) = 14.7 (approx)
So, b>14.7 and b<22.5.
Hence, possible values for b can be 15,16,17,18,19,20,21 and 22. Total 8 values.
Answer D.
Answer: D
Question: An electric pump can fill a tank in 4 hours. Because of a leak in the tank, it took 8hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
Options:
A)10hours
B)12hours
C)8hours
D)5hours
E)15hours
Rationale: Work done by the leak in 1 hour = 1/4 - 1/8 = 1/8
The leak will empty the tank in 8hours
Answer is C
Answer: C
Question: which of the following will not give a prime number on taking square root?
Options:
A)576
B)144
C)529
D)64
E)256
Rationale: A prime number is a number greater than 1, whose only two whole-number factors are 1 and itself.
here square root of 529 is 23 which is having only two factor, one and its self.
23 is a prime number
answer is C
Answer: C
Question: According to a recent student poll, 4/5 out of 20 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?
Options:
A)62/95
B)52/95
C)92/95
D)42/95
E)32/95
Rationale: 16 students are interested, 4 are not interested
Prob = 1 - 4C2/20C2 = 1 - (4*3/(20*19))=1 - 3/95 = 92/95
Answer : C
Answer: C
Question: A sum of money at simple interest amounts to Rs. 815 in 2 years and to Rs. 854 in 3 years. The sum is:
Options:
A)500
B)698
C)780
D)737
E)None
Rationale: Sol.
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 2 years = Rs. (39 * 2) = Rs. 78.
âˆ´ Principal = Rs. (815 - 78) = Rs. 737.
Answer D
Answer: D
Question: Mrs. Smith is 8 years more than twice the age of his son. The ages of son is 12.Find the age of mother and find the difference between their ages.
Options:
A)20yrs
B)22yrs
C)24yrs
D)26yrs
E)28yrs
Rationale: Age of Smith = 32yrs; Difference between their ages = 20
Let, age of son x=12
Smith is 8 years more than twice the age of his son, y = 8+2(x)
=8+2(12)
=8+24
=32yrs
Difference = 32 - 12
=20yrs
ANSWER:A
Answer: A
Question: If A(k)=(k+1)^-k, and k=0, what is the value of A(A(A(k)))?
Options:
A)0
B)(2/3)^(1/2)
C)1
D)(3/2)^(1/2)
E)(2/3)^-2
Rationale: A(A(A(0)))=A(A(1))=A(1/2)=(1/2+1)^-1/2=(2/3)^(1/2)
Thus, the answer is B.
Answer: B
Question: If a and b are prime numbers, which of the following CANNOT be the sum of a and b?
Options:
A)19
B)25
C)33
D)46
E)53
Rationale: If we subtract 2 from each of the first three options, we see that it gives a prime number.
19-2 = 17
25-2 = 23
33-2 = 31
Now 46-3 = 43.
Thus the only number left is 53.
ANSWER:E
Answer: E
Question: A train passes a station platform in 50 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)615 m
B)240 m
C)168 m
D)300 m
E)691 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/50 = 15 => x
= 300 m
Answer: D
Answer: D
Question: Set S consists of integers {6, 8, 10, 12, 14}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 30%. What is the value of integer n?
Options:
A)10
B)12
C)16
D)22
E)28
Rationale: The average of the numbers in set S is 10.
If we increase the mean by 30%, the new mean is 13.
Thus, on average, 5 numbers increase by 3.
Therefore n = 13+15 = 28
The answer is E.
Answer: E
Question: A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?
Options:
A)7 km/hr
B)7.2 km/hr
C)8 km/hr
D)8.4 km/hr
E)8.9 km/hr
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: B
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
Options:
A)180
B)277
C)129
D)187
E)987
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer: A
Answer: A
Question: When the positive integer A is divided by 9 and 8, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 8, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
Options:
A)48
B)49
C)56
D)65
E)72
Rationale: A = 9k+3 = 8j+4
B = 9m+3 = 8n+4
A-B = 9(k-m) = 8(j-n)
Thus A-B is a multiple of 9 and 8, so it is multiple of 72.
The answer is E.
Answer: E
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 8000 in a long term bond that pays 8 percent interest, compounded annually, what will be the approximate total amount of investment 18 years later, when Pat is ready for college?
Options:
A)$20000
B)$15000
C)$32000
D)$10000
E)$9000
Rationale: Since investment doubles in 70/r years then for r=8 it'll double in 70/8=~9 years (we are not asked about the exact amount so such an approximation will do). Thus in 18 years investment will double twice and become ($8,000*2)*2=$32,000 (after 9 years investment will become $8,000*2=$16,000 and in another 9 years it'll become $16,000*2=$32,000).
Answer: C.
Answer: C
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 59?
Options:
A)s.3944
B)s.4012
C)s.3942
D)s.3965
E)s.3929
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 59
= Rs.4012.
Answer: B
Answer: B
Question: A third of Arunâ€™s marks in mathematics exceed a half of his marks in English by 15.If he got 170 marks in two subjects together how many marks did he got in English?
Options:
A)120,50
B)180,60
C)180,90
D)120,40
E)None of them
Rationale: Let Arunâ€™s marks in Mathematics and English be x and y
Then (1/3)x-(1/2)y=15
2x-3y=90â€¦â€¦>(1)
x+y=170â€¦â€¦.>(2)
solving (1) and (2)
x=120
and y=50
Answer is A.
Answer: A
Question: The product of all the prime numbers less than 17 is closest to which of the following powers of 10?
Options:
A)10^9
B)10^8
C)10^7
D)10^6
E)10^5
Rationale: OA: E
Answer: E
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
Options:
A)15 mins
B)20 mins
C)10 mins
D)25 mins
E)30 mins
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distance/speed=9/54 hour=1/6 hour = 60/6 min=10 min
Answer is C.
Answer: C
Question: The L.C.M. of 2 numbers is 66. The numbers are in the ratio 2:3. Find their sum?
Options:
A)36
B)40
C)48
D)32
E)55
Rationale: Let the numbers be 2x and 3x
L.C.M. = 6x
6x = 66
x = 11
The numbers are = 22 and 33
Required sum = 22+33 = 55
Answer is E
Answer: E
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)Rs.92
B)Rs.70
C)Rs.90
D)Rs.28
E)Rs.20
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15
= Rs.90.
Answer:C
Answer: C
Question: For a certain exam,a score of 86 was 5 standard deviations above mean and a score of 67 was 2.5 standard deviations above mean.What was the mean score for the exam?
Options:
A)50
B)55
C)48
D)42
E)49
Rationale: Mean+5SD=86
Mean+2.5SD=67
By solving above equations we get,
SD (absolute value)=7.6
Mean=48
ANS. C
Answer: C
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
Options:
A)240
B)227
C)267
D)287
E)267
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 281
Answer: A
Answer: A
Question: A bag consists of 50 marbles, of which 5 are blue, 9 are red, and the remainder are white. If Lisa is to select a marble from the bag at random, what is the probability that the marble will be red or white?
Options:
A)3/4
B)2/4
C)1/4
D)1/8
E)9/10
Rationale: bag consists of 50 marbles, of which 5 are blue, 9 are red
remainder are white. So, white = 50 - 5 - 9 = 36.
probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white
probability that the marble will be red or white = 9/50+36/50 = 45/50 = 9/10
Hence, answer will be E.
Answer: E
Question: Car A runs at the speed of 50km/hr & reaches its destination in 6hr. Car B runs at the speed of 100 km/h & reaches its destination in 1h. What is the respective ratio of distances covered by Car A & Car B?
Options:
A)11 : 5
B)3 :1
C)13 : 7
D)15 : 7
E)16 : 9
Rationale: Sol. Distance travelled by Car A = 50 × 6 = 300 km
Distance travelled by Car B = 100 × 1 = 100 km
Ratio = 300/100 = 3 :1
Answer : B
Answer: B
Question: Find the least number of candidates in an examination so that the percentage of successful candidates should be 76.8%:
Options:
A)95
B)105
C)125
D)135
E)145
Rationale: suppose no. of total candidates are 'y' and successful are 'x'.
(x/y)*(100)=76.8 or x/y=0.768
or y=x/0.768
here we need minimum value of y, which is obtained by minimum value of x.
if put x=768 then y=1000
now we will try decrease value of x than we will find less value of y. so factorized 768 by 2 further.
if put x=384 then y=500
if put x=192 then y=250
if put x=96 then y=125(answer)
if put x=48 then y=62.5(not integer)
so ans is 125
ANSWER:D
Answer: D
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 600 per sq.metre.
Options:
A)Rs. 15,000
B)Rs. 15,500
C)Rs. 12,375
D)Rs. 16,500
E)None
Rationale: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (600 x 20.625)
= Rs.12,375.
Answer C
Answer: C
Question: P can do a certain work in 20 days. Q is 60% more efficient than P. How many days does Q alone take to do the same job?
Options:
A)18.5
B)16.5
C)12.5
D)10.5
E)8.5
Rationale: Each day, P can do 1/20 of the work.
Each day, Q can do 1.6/20 of the work = 16/200 of the work
The time taken by B alone to complete the total work is 200/16 = 12.5 days.
The answer is C.
Answer: C
Question: Among the employees of a certain company, 52 percent of the employees are male and 48 percent are female. In this company 70 percent of the male employees are married and 60 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
Options:
A) 0.3
B) 0.4
C) 0.45
D) 0.6
E) 0.7
Rationale: Much faster: draw 4 quadrants
______________Male (52%)_____Female (48%)
Married :__________70%____________50%
Not Married:_______30%____________60%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,52 x 0,30 + 0,50 x 0,60 = 0,15 + 0,3 (approx.)
Solution: approx. 0,45 (answer C)
Answer: C
Question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
Options:
A)7
B)8
C)9
D)6
E)4
Rationale: Explanation:
39 + 20 = 59/13 = 7 (Remainder)
Answer: A
Answer: A
Question: How many integers k greater than 100 and less than 700 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Not sure if this is the shortest.. But this is how I did this
There are 5 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. ...
5. 506 | 607
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 5 sets with 10 such number in each set will give 5 x 10 = 50 integers.
A
Answer: A
Question: A man can row 3.9 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
Options:
A)1.9
B)1.7
C)1.3
D)1.5
E)1.1
Rationale: Speed of boat in still water (b) = 3.9 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.3 km/hr.
Answer: C
Answer: C
Question: In the x- y plane, there are 4 points (0,0), (0,4), (5,4), and (5,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
Options:
A)2/3
B)2/5
C)3/4
D)3/7
E)5/8
Rationale: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 20.
P(x+y<4) = 8/20 = 2/5
The answer is B.
Answer: B
Question: In the rectangle below, the line MN cuts the rectangle into two regions. Find x the length of segment NB so that the area of the quadrilateral MNBC is 40% of the total area of the rectangle.
Options:
A)1 meter
B)2 meter
C)3 meter
D)4 meter
E)5 meter
Rationale: Solution
We first note that
MC = 20 - 5 = 15
The quadrilateral MNBC is a trapezoid and its area A is given by
A = (1/2) × 10 × (x + MC) = 5 (x + 15)
40% of the area of the rectangle is equal to
40% × (20 × 10) = (40 / 100) × 200 = 80
Since the area of MNBC is equal to 40% the area of the rectangle, we can write
5(x + 15) = 80
5x + 75 = 80
5x = 5
x = 1 meter
ANSWER IS A
Answer: A
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If t of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
Options:
A) y/R
B) y/(R-x)
C) xy/(R-x)
D) ty/(R(R-t))
E) y/(R(R-x))
Rationale: y/(R-t)- y/R
if we simplify this we get choice D, which is the correct answer.
Answer: D
Question: The ratio of number of boys to that of girls in a school is 3:2.if 20% of boys and 25 % of girls are scholarship holders,find the percentage of those who are not scholarship holders.
Options:
A)75
B)76
C)77
D)78
E)79
Rationale: since ratio be 3:2 let there is 100 students so there are 60 boys and 40 girls.so 60/40=3:2.now we find 80% of boys who are not scholarship holder so 80% of 60 is 48.now we find out 75% of girls who are not scholarship holder so 75% of 40 is 30.
so total number who are not scholarship holder is 48+30=78
ANSWER:D
Answer: D
Question: Two brands of detergent are to be combined. Detergent X contains 20 percent bleach and 80 percent soap, while Detergent Y contains 45 percent bleach and 55 percent soap. If the combined mixture is to be 35 percent bleach, what percent of the final mixture should be Detergent X?
Options:
A)10%
B)32 1/2 %
C)35%
D)40%
E)60%
Rationale: Let we mix x units of detergent X and y units of detergent Y
Bleach Soap Total
Detergent X 0.20x 0.80x x
Detergent Y 0.45y 0.55y y
Combined 0.20x+0.45y 0.80x+0.55y x+y
Percentage of bleach in combined mixture = (0.20x+0.45y)/(x+y) = 35/100
20x + 45y = 35x + 35y
10y = 15x
x/y = 2/3
So, percentage of detergent x = x*100/(x+y) = (x/y)*100/ ((x/y)+1)
= (2/3)*100/((2/3)+1)
= 200/5 = 40%
So, Answer will be D
Answer: D
Question: If a fair coin is flipped eight times in a row, what is the probability that there will be at least one head and one tail?
Options:
A)3/4
B)11/12
C)31/32
D)127/128
E)255/256
Rationale: The number of possible outcomes is 2^8 = 256
There is one way to get no heads and one way to get no tails.
Thus there are 254 outcomes with at least one head and one tail.
P(at least one head and one tail) = 254/256 = 127/128
The answer is D.
Answer: D
Question: A trader marks his goods at such a price that he can deduct 15% for cash and yet make 20% profit. Find the marked price of an item which costs him 90 :
Options:
A)135 11⁄13
B)105 3⁄21
C)127 1⁄17
D)95 1⁄21
E)None of these
Rationale: SP = 90 × 1.2 = 108
Marked price = 108⁄0.85 = 127.05
Answer C
Answer: C
Question: A man has 3 blue shirts, 3 green shirts and 1 red shirt. Everyday of the week we wears a different shirt, how many ways can he choose his shirts to wear them along the week? Consider that he never wears a shirt more than one time a week and he ways wears all his shirts on the week.
Options:
A)6!/3!(2)
B)7!/3!(2)
C)6!/3!1!
D)7!/2!(3)
E)7!/2!(2)
Rationale: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The man has 7 shirts which there are 3 blue shirts, 3 green shirts and 1 red.
Number of arrangements = 7!/3!(2)
Answer: B
Answer: B
Question: The average of first 9 prime numbers is?
Options:
A)10.11
B)11.11
C)12.11
D)13.11
E)14.11
Rationale: Sum of 10 prime no. = 100
Average = 100/9 = 11.11
ANSWER:B
Answer: B