RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: John and Rose play the following game with n sticks on a table. Each must remove 1,2,3,4, or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If John goes first, which of the following is a value of n such that Rose can always win no matter how John plays?
A.7
B.10
C.11
D.12
Answer: D.12
Explanation: If the number of sticks on a table is a multiple of 6, then the second player will win in any case (well if the player is smart enough).
Consider n=6, no matter how many sticks will be removed by the first player (1, 2, 3 ,4 or 5), the rest (5, 4, 3, 2, or 1) can be removed by the second one.
The same for n=12: no matter how many sticks will be removed by the first player 1, 2, 3 ,4 or 5, the second one can remove 5, 4, 3, 2, or 1 so that to leave 6 sticks on the table and we are back to the case we discussed above.
Answer: D.
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.1 km long?
A.2 mins 14 sec
B.2 mins 34 sec
C.156 sec
D.134 sec
Answer: C.156 sec
Explanation: D = 25 * 60 + 1100 = 2600 m
T = 2600/60 * 18/5 = 156 sec
ANSWER:C
Question: 5: 3 = 4/3: x. The value of x is?
A.1
B.2
C.3
D.4/5
Answer: D.4/5
Explanation: x * 5 = 3 * 4/3
x *5= 4
x=4/5
ANSWER:D
Question: In what ratio mental A at Rs.68 per kg be mixed with another metal at Rs.96 per kg so that cost of alloy (mixture) is Rs.72 per kg?
A.6:1
B.4:7
C.3:7
D.9:5
Answer: A.6:1
Explanation: (96-72)/(72-68)=24/4=6/1
ANSWER:A
Question: A certain sum of money doubles itself in 20 years in how much many years will it trible itself at the same rate?
A.20 years
B.76 years
C.88 years
D.40 years
Answer: D.40 years
Explanation: 100 ---- 100 --- 20
100 --- 20
--------------------
300 ---- 40 years
Answer: D
Question: In how many ways can live 2boys and 4 girls sit in a row such that all boys sit together?
A.240
B.120
C.150
D.720
Answer: A.240
Explanation: Treat all boys as one unit. Now there are four students and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 2! ways.
Required number of arrangements
= 5! * 2! = 240
Answer: A
Question: A, B and C enter into a partnership. They invest Rs. 80,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
A.6 : 4 : 8
B.6 : 4 : 7
C.6 : 4 : 2
D.6 : 4 : 1
Answer: B.6 : 4 : 7
Explanation: A : B : C = (80000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 288 : 192 : 336
= 6 : 4 : 7.
Answer: B
Question: Two trains are running at 40 km/h and 20 km/h respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?
A.23 m
B.23 2⁄9 m
C.27 m
D.27 7⁄9 m
Answer: D.27 7⁄9 m
Explanation: Relative speed = (40 – 20) km/h
= (20 × 5⁄18) m/sec = (50⁄9) m/sec
Length of faster train
= (50⁄9 × 5) m = 250⁄9m = 277⁄9 m
Answer D
Question: 131,95,70,54, ?
A.42
B.45
C.44
D.40
Answer: B.45
Explanation: 131 - 95 = 36 = 6^2
95 - 70 = 25 = 5^2
70 - 54 = 16 = 4^2
so we can write
54 - x = 09 = 3^2 , where x is the next number
x = 54 - 9 = 45
so the next number will be 45
ANSWER:B
Question: Ram buys a plot of 5200 sq. ft. The cost of the Plot is Rs.48 per sq. ft.He has to pay 17% of the total cost as the booking cost for the plot.How much he has to pay as booking cost?
A.Rs.42432
B.Rs.42436
C.Rs. 42518
D.Rs. 42560
Answer: A.Rs.42432
Explanation: 5200*48*17/100=42432
ANSWER:A
Question: A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
A.$234,000
B.$227,000
C.$148,000
D.$479,000
Answer: C.$148,000
Explanation: 6% x = 8,880 : x = selling price of house.
x = $148,000 : solve for x
correct answer C.
Question: If w = (x – 5)^2 + (x + 1)^2 – 6, then y is least when x =
A.-2
B.-1
C.0
D.2
Answer: D.2
Explanation: Let us transform the formula:
w = (x – 5)² + (x +1)² – 6 =
x² – 10x + 25 + x² + 2x + 1 – 6 =
2x² – 8x + 20 = 2 × (x² – 4x + 10) =
2 × ((x² – 4x + 4) + 6) =
2 × ((x – 2)² + 6)
Any square is greater or equal 0. Therefore the formula possess the least value when (x – 2)² = 0.
x – 2 = 0
x = 2
The correct answer is choice (D).
Question: What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?
A.Rs.325
B.Rs.545
C.Rs.560
D.Rs.550
Answer: A.Rs.325
Explanation: Let each instalment be Rs.x .
1st year = [x + (x * 12 * 2)/100]
2nd year = [ x + (x *12 * 1)/100]
3rd year = x
Then, [x + (x * 12 * 2)/100] + [ x + (x *12 * 1)/100] + x =1092
3x + ( 24x/100 ) + ( 12x/100 ) = 1092
336x =109200
x = 325
Each instalment = Rs. 325 Answer: A
Question: If a real number x is chosen at random in the interval [0,4] and a real number y is chosen at random in the interval [0,5], what is the probability that x < y?
A.3/5
B.2/5
C.7/10
D.3/4
Answer: A.3/5
Explanation: Since x is in [0,4] and y is in [0,5] we can draw a rectangle in the coordinate plane with vertices (0, 0), (4, 0), (0, 5), and (4, 5).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 8.
The whole rectangle has an area of 20.
P(x < y) = (20-8)/20 = 12/20 = 3/5
The answer is A.
Question: How many Books each of Volume 250 meter cube can be packed into a crate of volume 4500 meter cube
A.25
B.cannot be determined
C.10
D.15
Answer: B.cannot be determined
Explanation: Gud question with a simple concept.
In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.
In above with volume given , we can come up with different shapes, so we cant know the answer
For ex :4500 m3 can be 450*10 or 45*100 or just 4500*1 we don't know , so we cant calculate
Answer : B
Question: A company has 15 managers and 75 associates. The 15 managers have an average salary of $60,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?
A.$35,000
B.$45,000
C.$55,000
D.$65,000
Answer: A.$35,000
Explanation: Another method is to get ratios
Say 30000=a and
We know the # of people are in 1:5 ratio
Average=(2a*1+a*5)/6= 7a/6=35000
Answer is A. $35,000
Question: If p=n-8 , m=n+10; then in terms of p,m is ?
A.m= p+8
B.m= p+18
C.m= p-18
D.m= p-8
Answer: B.m= p+18
Explanation: p = n-8
That is,n = p+8.
Therefore,
m = n+10
m= p+8+10
m= p+18
ANSWER:B
Question: When asked what the time is,a person answered that the amount of time left is 2/6 of the time already completed.what is the time.
A.2 PM
B.9 PM
C.3 PM
D.6 PM
Answer: D.6 PM
Explanation: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=2/6x⇒x=18
Time is 6 PM
Answer:D
Question: Linda spent 2/4 of her savings on furniture and the rest on a TV. If the TV cost her $300, what were her original savings?
A.$900
B.$300
C.$600
D.$700
Answer: C.$600
Explanation: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 2 / 4 = 1 / 2 on a TV
But the TV cost her $300. So 1 / 2 of her savings is $300. So her original savings are 2 times $300 = $600
correct answer C
Question: 617 + 6.017 + 0.617 + 6.0017 = ?
A.62.96357
B.62963.57
C.62.96357
D.629.6357
Answer: D.629.6357
Explanation: Option D
Question: All the stocks on the over-the-counter market are designated by either a 2 letter or 3 letter codes that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
A.2(26^5)
B.26(26^4)
C.27(26^2)
D.26(26^5)
Answer: C.27(26^2)
Explanation: with 2 letters: 26^2
with 3 letters: 26^3
26^2 + 26^3 = 27*(26^2)
C
Question: The simple interest on Rs.13000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for two years at the same rate of interest.
A.3052.82
B.3039.89
C.3052.85
D.3039.51
Answer: D.3039.51
Explanation: R = 100 I / PT
=> R = (100 * 7200)/ (13000 * 5) = 11.07%
CI = P{ [1 + R /100]n - 1}
= 13000 { [ 1 + 11.07 / 100]^2 - 1} = Rs.3039.51
Answer:D
Question: If x^2 + 1/x^2 = 3,what is the value of x^4 + 1/x^4 ?
A.7
B.12
C.14
D.16
Answer: A.7
Explanation: IMPORTANT: I notice that if we SQUARE x², we get x⁴, and if we SQUARE 1/x², we get 1/x⁴, so let's see what happens if we take the equation x² + 1/x² = 3 andSQUAREboth sides:
(x² + 1/x²)²= 9
So, (x² + 1/x²)(x² + 1/x²) = 9
Expand to get: x⁴ + 1 + 1 + 1/x⁴ = 9
Simplify: x⁴ + 1/x⁴ = 7
Answer: A
Question: The value of x + x(xx) when x = 2
A. 10
B. 16
C. 18
D. 36
Answer: A. 10
Explanation: x + x(xx)
Put the value of x = 2 in the above expression we get,
2 + 2(22)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10 The answer is (A)
Question: A software programmer does 20% of the work in 60% of the time, and 80% of the work in the remaining 20% of the time. If the code he writes is X lines long and he was given one month (30 days) to accomplish the task, then, assuming that the programmer works at a constant rate in each of the two stages, How many lines of code were written in the last two weeks, in terms of X?
A.13x /15
B.15x/15
C.7x/15
D.2x/30
Answer: D.2x/30
Explanation: Take X=30 lines
80% of 30 = 24 lines
20% of 30 = 6 lines
W - R - T
6 lines - r1 - 24 (first 80% of the 30 days)
24 lines - r2 - 6 ( last 20% of the 20 days)
r1 = 1/4r2 = 4
Now Work in last 14 days = 6 days programmer worked at r2 + 8days programmer worked at r1
=> 6 * 4 + 8 * 1/4 = 24 + 2 = 26
Insert, X=30 in all options => D is the answer.
Question: Find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm.
A.370 cm2
B.365 cm2
C.380 cm2
D.384 cm2
Answer: D.384 cm2
Explanation: Explanation: Let other diagonal = 2x cm.
Since diagonals of a rhombus bisect each other at right angles, we have:
(20)2 = (12)2 + (x)2 =>x =√(20)2 – (12)2= √256= 16 cm. _I
So, other diagonal = 32 cm.
Area of rhombus = (1/2) x (Product of diagonals) =(1/2× 24 x 32) cm2 = 384 cm2
Answer: Option D
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
A.3
B.7
C.4
D.9
Answer: A.3
Explanation: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Question: The value of x + x(xx) when x = 7 is:
A.8
B.10
C.350
D.14
Answer: C.350
Explanation: x + x(xx)
Put the value of x = 7 in the above expression we get,
7 + 7(7*7)
= 350
ANSWER : (C
Question: A 4-letter code word consists of letters A, B. If the code includes all the three letters, how many such codes are possible?
A.72
B.12
C.36
D.24
Answer: B.12
Explanation: Note that the correct answer to this question is 36, not 72.
AB-AB can be arranged in 4!/2!=12 ways;;
Total: 12.
Answer: B.
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
A.25 days
B.14 days
C.24 days
D.145 days
Answer: C.24 days
Explanation: 2c =1/4 + 1/6 – 1/3 = 1/12
c = 1/24 => 24 days
Answer: C
Question: If a 2 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?
A.50%
B.100%
C.150%
D.200%
Answer: B.100%
Explanation: The area A of the large cube is 2*2*6 = 24 square cm.
The area of the 8 small cubes is 8*6 = 48 = 2A, an increase of 100%.
The answer is B.
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
A.700
B.726
C.800
D.278
Answer: C.800
Explanation: n:
25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer:C
Question: The ratio of pens to pencils is 5 to 6. There are 7 more pencils than pens. How many pencils are there?
A.36
B.42
C.48
D.55
Answer: B.42
Explanation: Let the number of pens be 5x and the number of pencils be 6x.
6x - 5x = 7
x = 7
The number of pencils is 42.
The answer is B.
Question: In a sports club with 30 members, 17 play badminton and 17 play tennis and 2 do not play either. How many members play both badminton and tennis?
A.7
B.6
C.9
D.10
Answer: B.6
Explanation: Let x play both badminton and tennis so 17-x play only badminton and 17-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(17-x)+x+2=30
36-2x+x=30
36-x=30
x=6
So 6 members play both badminton and tennis.
B
Question: Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in
A.9
B.8
C.4
D.3
Answer: D.3
Explanation: Explanation:
Let x men can do the in 12 days and the required number of days be z
More men, Less days [Indirect Proportion]
Less work, Less days [Direct Proportion ]
Answer: D) 3 days
Question: What is the units digit of (147^21)^48 ?
A.1
B.3
C.5
D.7
Answer: A.1
Explanation: The units digit of the exponents of 7 repeat in a cycle of four, which is {7,9,3,1}. The number 21 has the form 4n+1 so the units digit is 7 inside the bracket. The number 48 has the form 4n, so the units digit is 1. The answer is A.
Question: There are 10 person among whom two are brother. The total number of ways in which these persons can be seated around a round table so that exactly one person sit between the brothers , is equal to:
A.2!*7!
B.2!*8!
C.3!*7!
D.3!*8!
Answer: A.2!*7!
Explanation: Solution: Total number of ways = 7!*2!.
Answer: Option A
Question: Express a speed of 414 kmph in meters per second?
A.201 mps
B.114 mps
C.118 mps
D.115mps
Answer: D.115mps
Explanation: 414* 5/18 = 115 mps
Answer: D
Question: Ramesh purchased a refrigerator for Rs. 13500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
A.34778
B.26888
C.2899
D.18975
Answer: D.18975
Explanation: Price at which the TV set is bought = Rs. 13,500
Discount offered = 20%
Marked Price = 13500 * 100/80 = Rs. 16875
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 17250 * 110/100
= Rs. 18975
Answer: D
Question: Of the four-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A.6048
B.3648
C.7248
D.1448
Answer: A.6048
Explanation: Of the four-digit positive integers that have no digits equal to zero, how many have two digits that are equal to each other and the remaining digit different from the other two?
A. 24
B. 36
C. 72
D. 144
E. 216
Choosing the digit for p - 9 ways;
Choosing the digit for q - 8 ways;
Choosing the digit for r - 7ways;
# of permutations of 3 digits in ppqr - 4!/2!
Total: 9*8*7*4!/2!=6048.
Answer: A.
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
A.1 : 96
B.1 : 97
C.1 : 98
D.1 : 99
Answer: A.1 : 96
Explanation: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x = 1: 96.
Answer: Option A
Question: Gao earns $25.00 for each house she cleans. She refuses to work weekends. Monday she cleaned 2 houses 1 on Tuesday and only 3 more for the rest of the week. How much money did Gao earn this week?
A.$160
B.$140
C.$170
D.$165
Answer: A.$160
Explanation: Adding all the houses together is 2+1+3=6. If she gets $25 for each house then you must multiply 25 and 6. 25 x 6 =160. She got $160 this week.
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
A.65 Kmph
B.70 Kmph
C.72 Kmph
D.75 Kmph
Answer: C.72 Kmph
Explanation: Explanation:
Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER IS C
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements Q.
A.a) Q=48
B.b) Q=144
C.c) Q=240
D.d) 288
Answer: C.c) Q=240
Explanation: One specificboy is seated to either of end seat, lets call him b1
One specificgirl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Question: The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
A.4
B.8
C.16
D.12
Answer: B.8
Explanation: Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Let ten's and unit's digits be 2x and x respectively.
Then, (10 x 2x + x) - (10x + 2x) = 36
9x = 36
x = 4.
Required difference = (2x + x) - (2x - x) = 2x = 8.
answer :B
Question: If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocal of the numbers is equal to:
A.55/601
B.601/55
C.11/120
D.120/11
Answer: C.11/120
Explanation: Let the numbers be a and b.
Then, a + b = 55 and ab = 5 * 120 = 600.
Required sum = 1/a + 1/b = (a + b)/ab = 55/600 = 11/120.
ANSWER:C
Question: In what time will a railway train 90 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.8 sec
B.1 sec
C.9 sec
D.6 sec
Answer: C.9 sec
Explanation: T = 90/36 * 18/5
= 9 sec
Answer:C
Question: Dawson professes to sell his goods at the cost price but he made use of 600 grams instead of a kg, what is the gain percent?
A.13 2/3%
B.14 2/3%
C.15 2/3%
D.16 2/3%
Answer: D.16 2/3%
Explanation: Answer:	600 --- 100
100 --- ? => 16 2/3%
Answer:D
Question: Three friends (Fred, James and Kelly) are employees of a company. Their respective salaries are in the ratio of 4 : 6 : 7. James and Kelly's salaries together is Rs. 8840. By what percent is Kelly's salary than that of Sarah?
A.40%
B.60%
C.90%
D.70%
Answer: D.70%
Explanation: Explanation:
Let the salaries be 4x, 6x and 7x respectively.
Then,6x + 7x = 8840 => x = 680.
Fred's salary = Rs. 2800, James's salary = Rs. 4080, and Kelly's salary Rs. 4760.
Excess of Kelly's salary over Fred's=[ (1960 /2800) x 100] = 70%.
Answer: D
Question: In order to complete a reading assignment on time, Terry planned to read 100 pages per day. However, she read only 50 pages per day at first, leaving 800 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
A.12
B.14
C.16
D.10
Answer: D.10
Explanation: D=100*X - according to the plan, assignment to be completed on time reading 100 pages per day for next X days. But, Terry's plans changed so she read as follow:
50 pages for first Y days and 800 pages for last 6 days, we get these equations:
50*Y+800=100*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 60 pages per day and 6 leftover days used to complete a lump 780 pages
From above we find that X=Y+6 and 50Y+800=100Y+600 or 50Y=200 --->>>>> Y=4, hence X=10
Answer : D
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A.8/15
B.7/15
C.6/15
D.5/15
Answer: A.8/15
Explanation: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
Answer is A.
Question: Given that x = 2^b – (8^32 + 16^5), which of the following values for b yields the lowest value for |x|?
A.94
B.95
C.96
D.97
Answer: C.96
Explanation: 8^32 + 16^5 = 2^96 + 2^20
Compared to 2^96, the value of 2^20 is negligible.
2^96 - (2^96 +2^20) will minimize the value of |x|.
The answer is C.
Question: In how many ways can the letters of the word "COMPUTER" be arranged?
A.36480
B.40320
C.44290
D.48360
Answer: B.40320
Explanation: The total ways of arranging the letters = 8! = 40320
The answer is B.
Question: Alex deposited x dollars into a new account that earned 4 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
A.w/(1+1.08)
B.w/(1.08+1.16)
C.w/(1.16+1.24)
D.w/(1.04+1.04^2)
Answer: D.w/(1.04+1.04^2)
Explanation: Account at the end of the first year would be 1.04x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.04x+x) dollars. Account at the end of the second year would be (1.04x+x)*1.04=w --> x(1.04^2+1.04)=w --> x=w/(1.04+1.04^2).
Answer: D.
Question: A certain bacteria colony doubles in size every day for 22 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?
A.6.33
B.7.5
C.21
D.15
Answer: C.21
Explanation: Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be
Day 1 – B
Day 2 – 2B
Day 3 – 4B
Day 4 – 8B
.
.
.
Day 22 – 2^19 B
It can be implied that the capacity of the habitat is 2^19 B.
Case 2: There are 2 bacteria which keep doubling every day. So, the count would be
Day 1 – 2B
Day 2 – 4B
Day 3 – 8B
.
.
.
Day 18 – 2^18 B
Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.
Hence, 21 is the answer
C
Question: A toy store sells small, medium, and large toy trucks in each of the colors red, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
A.1/4
B.1/3
C.5/9
D.7/12
Answer: C.5/9
Explanation: Probability of NOT selecting medium out of 3 sizes = 2/3
Probability of NOT selecting red out of 3 colours = 2/3
Total probability of NOT selecting red and medium = (2/3)*(2/3) = 4/9
Required probability = 1 - 4/9 (this will select at least one of red and medium)
= 5/9
The answer is C.
Question: A sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?
A.$3,000
B.$3,150
C.$4,000
D.$2,500
Answer: D.$2,500
Explanation: We're told that a sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $600.
Since the salesperson receives a $100 salary, the remaining $500 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.
Let's TEST Answer C: $4,000
Since 20% of $1,000 = $200
20% of $4,000 = 4($200) = $800
This is TOO HIGH (it's supposed to be $500), so we need a LOWER total sales figure.
Let's TEST Answer D: $2,500
Since 20% of $1,000 = $200
20% of $2,500 = 2.5($200) = $500
This is an exact MATCH for what we were told, so this MUST be the answer.
Final Answer:
D