divelab/Sys2Bench huggingface dataset:
Question: Machine–A produces 40% of the total output and Machine-B produces 60% of the total output. An average of nine units out of a thousand goods manufactured by Machine-A and one unit of 150 units produced by Machine-B prove to be defective. What is the probability that a unit chosen at random from the total daily output of the factory is defective?
Options:
A)0.76
B)0.076
C)0.0076
D)0.00076
E)7.6e-05
Rationale: Let total Production be 10000 units....
A produces 4000 units and 36 units are defective
B produces 6000 units and 40 units are defective
So, Out of total 10,000 units 76 units are defective...
So the required probability = 76/10000 => 0.0076
Answer will be (C)
Answer: C
Question: The sum of three integers is 23. The largest integer is 3 times the middle integer, and the smallest integer is 12 less than the largest integer. What is the product of the three integers?
Options:
A)125
B)150
C)175
D)225
E)275
Rationale: Let x be the middle integer. Then the largest is 3x and the smallest is 3x - 12.
3x - 12 + x + 3x = 23
x = 5
The three integers are 3, 5, and 15.
The product is 3*5*15 = 225
The answer is D.
Answer: D
Question: What is the unit digit in 7^105?
Options:
A)2
B)3
C)1
D)5
E)7
Rationale: Unit digit in 7^105 = unit digit in [(7^4)^26 ]* 7
But unit digit in 7^4=1
unit digit 7^105 = 1*7 = 7
Answer is E
Answer: E
Question: Andy has 20 pairs of matched gloves. If he loses 13 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
Options:
A)9
B)11
C)13
D)14
E)15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair
Case1: If 13 gloves are gone the maximum probability of losing maximum gloves is 13 pairs of gloves out of 20. This means i m having 7 pairs of gloves. [Minimum number of gloves i can have is 7 pairs]
Case2: If 13 gloves are gone the maximum probability of losing minimum gloves is 13/2 = 6.5 means i can lose 7 glove. in this scenario i will be having 13 gloves.
Hence10 < Available Glove Pair < 14
any given time I cant possess 14 glove pair for the above mentioned scenario. And thats the answer. D.
Answer: D
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 445, the last number of the doorplates is 705. How many houses are there?
Options:
A)141
B)111
C)121
D)131
E)101
Rationale: So it starts from 445 and goes like 447, 449,...... 705. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([705-445][/2]+1 = 131
Ans D
Answer: D
Question: The sum q of prime numbers that are greater than 60 but less than 70 is
Options:
A) 67
B) 128
C) 191
D) 197
E) 260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum q of 61 and 67 is 128.
Answer B.
Answer: B
Question: What is the ratio E of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Options:
A)1/4
B)3/8
C)1/2
D)3/5
E)2
Rationale: One side surface area of a cube = x*x = x^2
Total 6 sides = 6x^2
As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.
L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2
W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2
Total 6 sides = 8x^2 + 2x^2 = 10x^2
Ratio of cube area to rectangular area E= 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (D)
Answer: D
Question: Given a + b = 1, find the value of 2a + 2b. Two solutions are presented below. Only
one is correct, even though both yield the correct answer.
Options:
A)3
B)5
C)4
D)2
E)1
Rationale: Because a + b = 1,
2a + 2b = 2(a + b) = 2 × 1 = 2.
correct answer D
Answer: D
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
Options:
A)271
B)180
C)188
D)127
E)211
Rationale: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Answer: B
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 90 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)70,20 kmph
B)78,10 kmph
C)70,70 kmph
D)78,10 kmph
E)70,12 kmph
Rationale: Speed of the boat in still water
= (50+90)/2
= 70 kmph. Speed of the stream
= (90-50)/2
= 20 kmph.
Answer:A
Answer: A
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 17th, and 18th terms in the sequence?
Options:
A)2^18
B)3(2^16)
C)7(2^16)
D)3(2^16)
E)7(2^15)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
17th term 2^16
18th term 2^17
adding all three
we get
(2^16)+(2^16)*2
so answer is 2^16(1+2)=>3(2^16)
answer B
Answer: B
Question: If x is an odd integer and y and z are even integers, which of the following CANNOT be an integer?
Options:
A)y/z
B)x/y
C)z/x
D)yx/z
E)zx/y
Rationale: x = Odd
y = Even
z = Even
Checking Options:
A. y/z Even/Even may be an Integer e.g. 4/2=2 Hence Incorrect Option
B. x/y Odd/Even CAN NEVER be an Integer Hence Correct Option
Answer : B
Answer: B
Question: Train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds. The length of train P is three-fourths the length of train Q. What is the ratio of the speed of train P to that of train Q?
Options:
A)15:8
B)15:5
C)15:9
D)15:2
E)15:3
Rationale: Given that train P crosses a pole in 30 seconds and train Q crosses the same pole in one minute and 15 seconds.
Let the length of train P be LP and that of train Q be LQ
given that LP = 3/4 LQ
As the train P and Q crosses the pole in 30 seconds and 75 seconds respectively,
=> Speed of train P = VP = LP/30
Speed of train Q = VQ = LQ/75
LP = 3/4 LQ
=> VP = 3/4 LQ/(30) = LQ/40
Ratio of their speeds = VP : VQ
= LQ/40 : LQ/75 => 1/40 : 1/75 = 15:8
Answer:A
Answer: A
Question: Find the greatest number which leaves the same remainder when it divides 20, 40 and 90.
Options:
A)18
B)8
C)12
D)10
E)None of these
Rationale: 90 - 40 = 50
40 - 20 = 20
90 - 20 = 70
The H.C.F of 20, 50 and 70 is 10.
ANSWER:D
Answer: D
Question: It takes one machine 5 hours to complete a production order and another machine 3 hours to complete the same order. How many hours would it take both amhcines working simultaneously at their respective rates to complete the order?
Options:
A)a) 7/12
B)b) 1 1/2
C)c) 2 2/9
D)d) 3 1/2
E)e) 7
Rationale: RT = W
Given:
R = 1/5 + 1/4 = 9/20
T = ?
W = 1
T = 1 / (9/20) = 20/9 = 2 2/9
Answer: C
Answer: C
Question: What is the least number to be subtracted from 990 to make it a perfect square?
Options:
A)100
B)90
C)30
D)71
E)80
Rationale: The numbers less than 990 and are squares of certain number is 900.
The least number that should be subtracted from 990 to make it perfect square = 990 - 900 = 90.
ANSWER:B
Answer: B
Question: The area of a triangle is with base 4m and height 5m?
Options:
A)20 m2
B)10 m2
C)82 m2
D)54 m2
E)28 m2
Rationale: 1/2 * 4 * 5
= 10 m2
Answer:B
Answer: B
Question: When a random experiment is conducted, the probability that event A occurs is 1/3. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?
Options:
A)8/27
B)10/31
C)12/37
D)14/41
E)16/49
Rationale: One case is: 1/3*1/3*2/3*2/3=4/81
The total number of possible cases is 4C2 = 6
P(event A occurs exactly twice) = 6*(4/81) = 8/27
The answer is A.
Answer: A
Question: After spending 40 percent machinery, 25 percent in building , 15 percent in raw material and 5 percent on furniture . John had a balance of Rs.1305. Total money with him was?
Options:
A)7800
B)8700
C)9000
D)9200
E)9300
Rationale: [100 - (40+25+5+15)] % of x = 1305
\inline \Rightarrow 15% of x =1305
\inline \Rightarrow \frac{15}{100}\times x=1305
\inline \therefore x=\frac{1305\times 100}{15}=8700
B
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)10
B)99
C)88
D)77
E)52
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: A
Question: The H.C.F. of two numbers is 20 and the other two factors of their L.C.M. are 21 and 23. The larger of the two numbers is
Options:
A)276
B)299
C)312
D)460
E)None
Rationale: Solution
Clearly, the numbers are (20 x 21) and (20 x 23).
Larger number = (20 x 23)	= 460.
Answer D
Answer: D
Question: A 12 by 16 rectangle is inscribed in circle. What is the circumference of the circle?
Options:
A)5π
B)10π
C)15π
D)20π
E)30π
Rationale: The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: D
Answer: D
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 20 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week?
Options:
A)4
B)3
C)2
D)5
E)6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 20 T-C=10 -> T= 15. C=5.
Mo drinks 3 cups of tea a day then number of days that are not rainy = 15/3 = 5
So number of rainy days = 7-5 = 2
C is the answer.
Answer: C
Question: A company, Chauncy Co., has an annual travel budget of $55,000. The accounting department estimates that transportation expenses will increase 5 percent in the coming year, and nontransportation travel expenses will increase by 15 percent in the coming year. Last year, Chauncy Co. spent $19,500 on transportation-related expenses, and $35,000 on non transportation travel expenses. If the annual travel budget does not increase this year, and if the accounting department’s estimates are correct, how far over the annual travel budget will expenses be this year?
Options:
A)Expenses will not go over the budget.
B)$500
C)$4,225
D)$5,725
E)$60,725
Rationale: Annual travel budget of $55,000
Let, Transportation expenses = T = 19500
and Non-Transportation expenses = N=35000
i.e. Increased Transportation expenses = 1.05T = 20475
and Increased Non-Transportation expenses = 1.15N = 40250
Total Expense = 20475+40250 = 60725
Expense over Budget = Budget - expense = 55000-60725 = 5725
Answer: Option D
Answer: D
Question: A train moves with a speed of 108 kmph. Its speed in metres per second is
Options:
A)10.8
B)18
C)30
D)38.8
E)None
Rationale: Solution
Speed	= 108 Kmph
= (108 x 5/18)m/sec
= 30 m/sec.
Answer C
Answer: C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire?
Options:
A)2 meters
B)4 meters
C)5 meters
D)3 meters
E)7 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 96,000 m : C is the circumference
C = 4 meters
correct answer B
Answer: B
Question: In how many years, Rs. 150 will produce the same interest at 6% as Rs. 500 produce in 2 years at 4½% ?
Options:
A)4 years
B)5 years
C)8 years
D)9 years
E)12 years
Rationale: Explanation :
Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.500 at 4½ % for 2 years
150×6×n/100=500×9/2×2/100
150×6×n=500×9/2×2
150×6×n=500×9
n=5 years
Answer : Option B
Answer: B
Question: On Monday, a certain animal shelter housed 58 cats and dogs. By Friday, 1/6 of the cats and 1/5 of the dogs had been adopted; no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: To maximize the number of pets adopted, we should maximize the number of dogs adopted since 1/5 > 1/6.
The greatest multiple of 5 less than 58 is 40 (such that the remaining number is divisible by 6), so let's assume there were 40 dogs and 18 cats.
Then the maximum number of adopted pets is 1/5*(40) + 1/6*(18) = 8 + 3 = 11.
The answer is E.
Answer: E
Question: Along a yard 414 metres long, 24 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
Options:
A)18
B)19
C)10
D)11
E)12
Rationale: Explanation:
24 trees have 23 gaps between them,
Required distance (414/23) = 18
Option A
Answer: A
Question: If 7 and 11 are prime numbers, which of the following CANNOT be the sum of a and b?
Options:
A)18
B)36
C)19
D)54
E)72
Rationale: ANS = C
Answer: C
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 240 m in length?
Options:
A)18.9 sec
B)88.9 sec
C)22.9 sec
D)21.00 sec
E)72.0 sec
Rationale: D = 110 + 240 = 350 m
S = 60 * 5/18 = 50/3
T = 350 * 3/50 = 21.00 sec
Answer: D
Answer: D
Question: An investor deposited $5,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
Options:
A)$5050
B)$5101
C)$5202
D)$5303
E)$5404
Rationale: The amount in the account after 6 months is 1.02*1.02($5,000) = $5202
The answer is C.
Answer: C
Question: The number of years of service of the eight employees in a production department are 15, 10, 9, 17, 6, 8, 14 and 16. What is the range in the number of years of service of the eight employees?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: = 17-6
= 11
Answer B
Answer: B
Question: How many litres of pure acid are there in 8 litres of a 20% solution
Options:
A)1.5
B)1.6
C)1.7
D)1.8
E)1.9
Rationale: Explanation:
Question of this type looks a bit typical, but it is too simple, as below...
It will be 8 * 20/100 = 1.6
Answer: Option B
Answer: B
Question: There are 300 seniors at Morse High School, and 50% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 20% of all the students at Morse have cars, how many students are in the three lower grades?
Options:
A)600
B)900
C)1200
D)1350
E)1500
Rationale: Let x be the number of students in the lower three grades.
0.1x + 150 = 0.2(x+300)
0.1x = 900
x = 900
The answer is B.
Answer: B
Question: A garrison of 2000 men has provisions for 60 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement?
Options:
A)1500
B)1893
C)1979
D)1900
E)1278
Rationale: 2000 ---- 60
2000 ---- 45
x ----- 20
x*20 = 2000*45
x = 4500
2000
-------
1500
Answer: A
Answer: A
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent Q of her bushes have only yellow roses?
Options:
A)20
B)30
C)50
D)70
E)80
Rationale: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, 0.8T+x=T
x=0.2T
so,Q= 1.5x=0.3T
30% flowers are yellow flowers
OA B
Answer: B
Question: The sum of three numbers is 245. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
Options:
A)20
B)30
C)38
D)48
E)75
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 245
or 49x = 245 or x = 5
⇒ Second number = 15x = 15 × 5 = 75
Answer E
Answer: E
Question: During the months May through October, Teddy the bear septuples his weight, and during the months November through April, Teddy loses 100 pounds. If at the beginning of November 1973, Teddy's weight was m pounds, what was Teddy's weight in pounds by the end of April 1976?
Options:
A)49m - 1300
B)49m - 1200
C)7m - 1300
D)7m - 1200
E)7m
Rationale: Nov ' 73 = m
April ' 74 = m - 100
Oct ' 74 = 7m - 300
April' 75 = 7m - 400
Oct' 75 = 49m - 1200
April'76 = 49m - 1300
Hence answer will be (A) 49m - 1300
Answer: A
Question: The area of a square is equal to four times the area of a rectangle of dimensions 25 cm * 16 cm. What is the perimeter of the square?
Options:
A)80 cm
B)100 cm
C)120 cm
D)140 cm
E)160 cm
Rationale: Area of the square = s * s = 4(25 * 16)
=> s * s= 2 * 2 * 5 * 5 * 4 * 4
=> s =2 * 5 * 4 = 40 cm
Perimeter of the square = 4 * 40 = 160 cm.
Answer: E
Answer: E
Question: There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)288
B)277
C)786
D)791
E)380
Rationale: The total number of stations = 20
From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 20P2 ways.
20P2 = 20 * 19 = 380.
Answer: E
Answer: E
Question: A library branch originally contained 18360 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/2 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
Options:
A)2.5%
B)20%
C)28.3%
D)45.2%
E)73.6%
Rationale: Fiction Novels = 5,508
Transferred to another location = 6,120
Transferred fiction novels = 3,060
Non Transferred Fiction Novels = 2,448
Percent of the remaining collection was fiction novels = 2,448/(18360 - 6120 ) * 100 => 20%
Hence answer will be (B)
Answer: B
Question: Each week a restaurant serving Mexican food uses the same volume of chili paste, which comes in either 35-ounce cans or 25-ounce cans of chili paste. If the restaurant must order 20 more of the smaller cans than the larger cans to fulfill its weekly needs, then how manysmallercans are required to fulfill its weekly needs?
Options:
A)60
B)70
C)80
D)100
E)120
Rationale: let x be the number of 35 ounce cans. Therefore (x+20) is the number of 25 ounce cans.
Total volume is same, therefore
35x=25(x+20)
10x=500
x=50
Therefore, number of 15 ounce cans=50+20=70
Ans - B
Answer: B
Question: Evaluate 30!/28!
Options:
A)720
B)600
C)870
D)910
E)650
Rationale: we have 30!/28! = 30*29*28!/28! = 30*29 = 870
Answer is C
Answer: C
Question: Last year the price per share of Stock Y increased by s percent and the earnings per share of Stock Y increased by t percent, where s is greater than t. By what percent did the ratio of price per share to earnings per share increase, in terms of s and t?
Options:
A)[100(s – t)] / (100 + s + t) %
B)[100(s – t)] / (100 + s) %
C)100*(s-t)/(100+t) %
D)(s – t) %
E)t/s %
Rationale: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+s/100) and the new earning is: E*(1 + t/100)
The new P/E is: (1+s/100)P/(1+t/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+s/100)/(1+t/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(s-t)/(100+t) % Answer : C
Answer: C
Question: The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?
Options:
A)0.2
B)0.25
C)0.3
D)0.35
E)0.5
Rationale: Blood group -	frequency
A - 50
B - 65
O - 70
AB - 15
Let P(E) be the event of getting O blood group
P(E) = Frequency for O blood group / Total frequencies in the above table
= 70 / (65+50+70+15)
= 70 / 200
= 0.35
My answer is (D)
Answer: D
Question: How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
A. 3.5 years
Options:
A)7 years
B)4 years
C)5 years
D)3 years
E)1 years
Rationale: Time = (100 * 81) / (450 * 4.5) = 4 years.Answer:B
Answer: B
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE.
Options:
A)110
B)112
C)114
D)116
E)119
Rationale: Total no' of arrangements 5P5 = 5! = 120
no' of arrangements start with AE = 1 × 6 = 6
no' of arrangements which do not start with AE = 120 - 6 = 114.
C
Answer: C
Question: What is the present worth of Rs. 198 due in 2 years at 5% simple interest per annum?
Options:
A)128
B)277
C)180
D)888
E)171
Rationale: Let the present worth be Rs. x. Then,
S.I. = (198 - x)
(x * 5 * 2) / 100 = (198 - x)
10x = 19800 - 100x
110x = 19800 => x = 180.
Answer: C
Answer: C
Question: At the store, Sam bought a shirt and a toaster. There was a 6% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?
Options:
A)0.94(K – T)
B)0.94K – T
C)0.94(K – 1.06T)
D)(K – T)/1.06
E)(K/1.06) – T
Rationale: 1.06S + 1.06T = K
1.06S = K - 1.06T
S = (K/1.06) - T
The answer is E.
Answer: E
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 20 Gallons of water and 40 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
Options:
A)300
B)75
C)100
D)150
E)175
Rationale: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 40 gallons salt is added and 20 gallons of water is added.
So salt now becomes -> (0.2x + 40) and water --> (0.6x+20)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+40) = (0.6x+20)/2 => 0.4x+80 =0.6x+20 =>0.2x =60
Solving, x = 300
Answer : A
Answer: A
Question: Two partners (Pella and Leon) invested Rs.7000 and Rs.18000, respectively in a business. Pella runs the business while Leon is a sleeping partner in the business. Pella receives 6% of the profit for managing the business the rest is divided in proportion of their capitals. Out of a total profit of Rs.8500, how much did Pella receive?
Options:
A)3004.84
B)3019.84
C)2747.2
D)3059.84
E)3029.84
Rationale: ratio of their investments Rs.7000:18000=7:18
6% of the profit for managing the business =6/100*8500=510
remaining profit=8500-510=7990
share profit in ratio of investment 7990/25 =319.6
Pella's ratio share=7*319.6=2237.2
total money Ben collects=2237.2+510=2747.2
Answer: C
Answer: C
Question: X is an even number and Y is a positive odd number. Which of the following expressions cannot be even?
Options:
A)(XY)^Y
B)X^3Y^3
C)X^3
D)XY
E)Y^2
Rationale: If x is even, let x = 0 and see what happens.
A. [(0)(Y)]^Y = 0 (EVEN - ELIMINATE)
B. 0³Y³ = 0 (EVEN - ELIMINATE)
C. 0³ = 0 (EVEN - ELIMINATE)
D. (0)Y = 0 (EVEN - ELIMINATE)
E. Y²
Answer:E
Answer: E